Scaled density functional theory correlation functionals.
Ghouri, Mohammed M; Singh, Saurabh; Ramachandran, B
2007-10-18
We show that a simple one-parameter scaling of the dynamical correlation energy estimated by the density functional theory (DFT) correlation functionals helps increase the overall accuracy for several local and nonlocal functionals. The approach taken here has been described as the "scaled dynamical correlation" (SDC) method [Ramachandran, J. Phys. Chem. A 2006, 110, 396], and its justification is the same as that of the scaled external correlation (SEC) method of Brown and Truhlar. We examine five local and five nonlocal (hybrid) DFT functionals, the latter group including three functionals developed specifically for kinetics by the Truhlar group. The optimum scale factors are obtained by use of a set of 98 data values consisting of molecules, ions, and transition states. The optimum scale factors, found with a linear regression relationship, are found to differ from unity with a high degree of correlation in nearly every case, indicating that the deviation of calculated results from the experimental values are systematic and proportional to the dynamic correlation energy. As a consequence, the SDC scaling of dynamical correlation decreases the mean errors (signed and unsigned) by significant amounts in an overwhelming majority of cases. These results indicate that there are gains to be realized from further parametrization of several popular exchange-correlation functionals.
Locality of correlation in density functional theory.
Burke, Kieron; Cancio, Antonio; Gould, Tim; Pittalis, Stefano
2016-08-07
The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that EC → -AC ZlnZ + BCZ as Z → ∞, where Z is the atomic number, AC is known, and we estimate BC to be about 37 mhartree. The local density approximation yields AC exactly, but a very incorrect value for BC, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with BC a functional of the TF density for the system. The implications for the construction of approximate density functionals are discussed.
Joubert, Daniel P.
2012-03-01
It is shown that the density-functional-theory exchange and correlation functionals satisfy 0=γEhx[ρN]+2Ecγ[ρN]-γEhx[ρN-1γ]-2Ecγ[ρN-1γ]+2∫d3r'[ρN-10(r)-ρN-1γ(r)]v0([ρN];r)+∫d3r'[ρN-10(r)-ρN-1γ(r)]r·∇v0([ρN];r)+∫d3r'ρN(r)r·∇vcγ([ρN];r)-∫d3r'ρN-1γ(r)r·∇vcγ([ρN-1γ];r)-∫d3r'fγ(r)r·∇vhxcγ([ρN];r)-2∫d3r'fγ(r)vhxcγ([ρN];r). In the derivation of this equation the adiabatic connection formulation is used, where the ground-state density of an N-electron system ρN is kept constant independent of the electron-electron coupling strength γ. Here Ehx[ρ] is the Hartree plus exchange energy, Ecγ[ρ] is the correlation energy, vhxcγ[ρ] is the Hartree plus exchange-correlation potential, vc[ρ] is the correlation potential, and v0[ρ]is the Kohn-Sham potential. The charge densities ρN and ρN-1γ are the N- and (N-1)-electron ground-state densities of the same Hamiltonian at electron-electron coupling strength γ. fγ(r)=ρN(r)-ρN-1γ(r) is the Fukui function. This equation can be useful in testing the internal self-consistency of approximations to the exchange and correlation functionals. As an example the identity is tested on the analytical Hooke's atom charge density for some frequently used approximate functionals.
Equilibrium time correlation functions in the low density limit
Beijeren, H. van; Lanford, O.E.; Lebowitz, J.L.; Spohn, H.
1980-01-01
We consider a system of hard spheres in thermal equilibrium. Using Lanford's result about the convergence of the solutions of the BBGKY hierarchy to the solutions of the Boltzmann hierarchy, we show that in the low-density limit (Boltzmann-Grad limit): (i) the total time correlation function is
Density-functional formula for strongly correlated systems
Institute of Scientific and Technical Information of China (English)
WANG Huaiyu; HAN Rushan; CHEN Nanxian
2005-01-01
Density functional method is applied for strongly correlated systems. Based on the assumption that the systems are composed of electrons in singly-occupied orbitals and those in doubly-occupied orbitals, a set of self-consistent equations are obtained by standard variation procedure. The equations consist of two parts. One part is to solve the wave functions of the electrons in singly-occupied orbitals and the other is to solve the wave functions of the electrons in doubly-occupied orbitals. The physical meanings of the terms appearing in the equations are discussed.
Brorsen, Kurt R; Yang, Yang; Pak, Michael V; Hammes-Schiffer, Sharon
2017-05-04
The development of approximate exchange-correlation functionals is critical for modern density functional theory. A recent analysis of atomic systems suggested that some modern functionals are straying from the path toward the exact functional because electron densities are becoming less accurate while energies are becoming more accurate since the year 2000. To investigate this trend for more chemically relevant systems, the electron densities in the bonding regions and the atomization energies are analyzed for a series of diatomic molecules with 90 different functionals. For hybrid generalized gradient approximation functionals developed since the year 2000, the errors in densities and atomization energies are decoupled; the accuracy of the energies remains relatively consistent while the accuracy of the densities varies significantly. Such decoupling is not observed for generalized gradient and meta-generalized gradient approximation functionals. Analysis of electron densities in bonding regions is found to be important for the evaluation of functionals for chemical systems.
Vyboishchikov, Sergei F
2017-09-03
We propose a simple method of calculating the electron correlation energy density e_c(r) and the correlation potential V_c(r) from second-order Møller-Plesset amplitudes and its generalization for the case of a Configuration Interaction wavefunction, based on Nesbet's theorem. The correlation energy density obtained by this method for free and spherically confined Be and He atoms was employed to fit a local analytical density functional based on Wigner's functional. The functional is capable to reproduce a strong increase of the correlation energy with decreasing the confined radius for the Be atom. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Transport through correlated systems with density functional theory
Kurth, S.; Stefanucci, G.
2017-10-01
We present recent advances in density functional theory (DFT) for applications in the field of quantum transport, with particular emphasis on transport through strongly correlated systems. We review the foundations of the popular Landauer–Büttiker(LB) + DFT approach. This formalism, when using approximations to the exchange-correlation (xc) potential with steps at integer occupation, correctly captures the Kondo plateau in the zero bias conductance at zero temperature but completely fails to capture the transition to the Coulomb blockade (CB) regime as the temperature increases. To overcome the limitations of LB + DFT, the quantum transport problem is treated from a time-dependent (TD) perspective using TDDFT, an exact framework to deal with nonequilibrium situations. The steady-state limit of TDDFT shows that in addition to an xc potential in the junction, there also exists an xc correction to the applied bias. Open shell molecules in the CB regime provide the most striking examples of the importance of the xc bias correction. Using the Anderson model as guidance we estimate these corrections in the limit of zero bias. For the general case we put forward a steady-state DFT which is based on one-to-one correspondence between the pair of basic variables, steady density on and steady current across the junction and the pair local potential on and bias across the junction. Like TDDFT, this framework also leads to both an xc potential in the junction and an xc correction to the bias. Unlike TDDFT, these potentials are independent of history. We highlight the universal features of both xc potential and xc bias corrections for junctions in the CB regime and provide an accurate parametrization for the Anderson model at arbitrary temperatures and interaction strengths, thus providing a unified DFT description for both Kondo and CB regimes and the transition between them.
Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy
Perdew, John P.; Constantin, Lucian A.
2007-04-01
We construct a Laplacian-level meta-generalized-gradient-approximation (meta-GGA) for the noninteracting (Kohn-Sham orbital) positive kinetic energy density τ of an electronic ground state of density n . This meta-GGA is designed to recover the fourth-order gradient expansion τGE4 in the appropriate slowly varying limit and the von Weizsäcker expression τW=∣∇n∣2/(8n) in the rapidly varying limit. It is constrained to satisfy the rigorous lower bound τW(r)⩽τ(r) . Our meta-GGA is typically a strong improvement over the gradient expansion of τ for atoms, spherical jellium clusters, jellium surfaces, the Airy gas, Hooke’s atom, one-electron Gaussian density, quasi-two-dimensional electron gas, and nonuniformly scaled hydrogen atom. We also construct a Laplacian-level meta-GGA for exchange and correlation by employing our approximate τ in the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA density functional. The Laplacian-level TPSS gives almost the same exchange-correlation enhancement factors and energies as the full TPSS, suggesting that τ and ∇2n carry about the same information beyond that carried by n and ∇n . Our kinetic energy density integrates to an orbital-free kinetic energy functional that is about as accurate as the fourth-order gradient expansion for many real densities (with noticeable improvement in molecular atomization energies), but considerably more accurate for rapidly varying ones.
Patching the Exchange-Correlation Potential in Density Functional Theory.
Huang, Chen
2016-05-10
A method for directly patching exchange-correlation (XC) potentials in materials is derived. The electron density of a system is partitioned into subsystem densities by dividing its Kohn-Sham (KS) potential among the subsystems. Inside each subsystem, its projected KS potential is required to become the total system's KS potential. This requirement, together with the nearsightedness principle of electronic matters, ensures that the electronic structures inside subsystems can be good approximations to the total system's electronic structure. The nearsightedness principle also ensures that subsystem densities could be well localized in their regions, making it possible to use high-level methods to invert the XC potentials for subsystem densities. Two XC patching methods are developed. In the local XC patching method, the total system's XC potential is improved in the cluster region. We show that the coupling between a cluster and its environment is important for achieving a fast convergence of the electronic structure in the cluster region. In the global XC patching method, we discuss how to patch the subsystem XC potentials to construct the XC potential in the total system, aiming to scale up high-level quantum mechanics simulations of materials. Proof-of-principle examples are given.
Yang, Yang; Brorsen, Kurt R.; Culpitt, Tanner; Pak, Michael V.; Hammes-Schiffer, Sharon
2017-09-01
Multicomponent density functional theory (DFT) enables the consistent quantum mechanical treatment of both electrons and protons. A major challenge has been the design of electron-proton correlation (epc) functionals that produce even qualitatively accurate proton densities. Herein an electron-proton correlation functional, epc17, is derived analogously to the Colle-Salvetti formalism for electron correlation and is implemented within the nuclear-electronic orbital (NEO) framework. The NEO-DFT/epc17 method produces accurate proton densities efficiently and is promising for diverse applications.
Mattsson, Ann E.; Wills, John M.
2013-03-01
The inability to computationally describe the physics governing the properties of actinides and their alloys is the poster child of failure of existing Density Functional Theory exchange-correlation functionals. The intricate competition between localization and delocalization of the electrons, present in these materials, exposes the limitations of functionals only designed to properly describe one or the other situation. We will discuss the manifestation of this competition in real materials and propositions on how to construct a functional able to accurately describe properties of these materials. I addition we will discuss both the importance of using the Dirac equation to describe the relativistic effects in these materials, and the connection to the physics of transition metal oxides. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Towards efficient orbital-dependent density functionals for weak and strong correlation
Zhang, Igor Ying; Perdew, John P; Scheffler, Matthias
2016-01-01
We present a new paradigm for the design of exchange-correlation functionals in density-functional theory. Electron pairs are correlated explicitly by means of the recently developed second order Bethe-Goldstone equation (BGE2) approach. Here we propose a screened BGE2 (sBGE2) variant that efficiently regulates the coupling of a given electron pair. sBGE2 correctly dissociates H$_2$ and H$_2^+$, a problem that has been regarded as a great challenge in density-functional theory for a long time. The sBGE2 functional is then taken as a building block for an orbital-dependent functional, termed ZRPS, which is a natural extension of the PBE0 hybrid functional. While worsening the good performance of sBGE2 in H$_2$ and H$_2^{+}$, ZRPS yields a remarkable and consistent improvement over other density functionals across various chemical environments from weak to strong correlation.
The correlation function for density perturbations in an expanding universe. II - Nonlinear theory
Mcclelland, J.; Silk, J.
1977-01-01
A formalism is developed to find the two-point and higher-order correlation functions for a given distribution of sizes and shapes of perturbations which are randomly placed in three-dimensional space. The perturbations are described by two parameters such as central density and size, and the two-point correlation function is explicitly related to the luminosity function of groups and clusters of galaxies
Energy Technology Data Exchange (ETDEWEB)
Tao, Jianmin [Los Alamos National Laboratory; Perdew, John P [TULANE UNIV; Staroverov, Viktor N [UNIV OF WESTERN ONTARIO; Scuseria, Gustavo E [RICE UNIV
2008-01-01
We construct a nonlocal density functional approximation with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating between different approximations suitable for two extreme regions of the electron density. In a 'normal' region, the exact exchange-correlation hole density around an electron is semilocal because its spatial range is reduced by correlation and because it integrates over a narrow range to -1. These regions are well described by popular semilocal approximations (many of which have been constructed nonempirically), because of proper accuracy for a slowly-varying density or because of error cancellation between exchange and correlation. 'Abnormal' regions, where non locality is unveiled, include those in which exchange can dominate correlation (one-electron, nonuniform high-density, and rapidly-varying limits), and those open subsystems of fluctuating electron number over which the exact exchange-correlation hole integrates to a value greater than -1. Regions between these extremes are described by a hybrid functional mixing exact and semi local exchange energy densities locally (i.e., with a mixing fraction that is a function of position r and a functional of the density). Because our mixing fraction tends to 1 in the high-density limit, we employ full exact exchange according to the rigorous definition of the exchange component of any exchange-correlation energy functional. Use of full exact exchange permits the satisfaction of many exact constraints, but the nonlocality of exchange also requires balanced nonlocality of correlation. We find that this nonlocality can demand at least five empirical parameters (corresponding roughly to the four kinds of abnormal regions). Our local hybrid functional is perhaps the first accurate size-consistent density functional with full exact exchange. It satisfies other known
Description of correlated densities for few-electron atoms by simple functional forms
Energy Technology Data Exchange (ETDEWEB)
Porras, I.; Arias de Saavedra, F. [Univ. de Granada (Spain). Dept. de Fisica Moderna
1999-02-20
Simple analytical functional forms for the electron density of two- and three-electron atoms which reproduce fairly the correlated (exact) values are presented. The procedure is based on the fitting of an auxiliary f(r) function which has adequate properties for this purpose and can be extended to more complex atoms.
Directory of Open Access Journals (Sweden)
Serge B. Provost
2015-07-01
Full Text Available This paper provides a simplified representation of the exact density function of R, the sample correlation coefficient. The odd and even moments of R are also obtained in closed forms. Being expressed in terms of generalized hypergeometric functions, the resulting representations are readily computable. Some numerical examples corroborate the validity of the results derived herein.
The role of exchange and correlation in time-dependent density-functional theory for photoionization
Stener, M.; Decleva, P.; Görling, A.
2001-05-01
Atomic photoionization cross sections are calculated by time-dependent density-functional (TDDF) methods using different exchange-correlation potentials including the exact one. The exchange-correlation kernel is treated in the adiabatic local density approximation (ALDA). Results for the exact full and the exact exchange-only Kohn-Sham (KS) potential are very similar, the calculated photo cross section agree very well with experimental data. Thus the exact correlation potential seems to have no influence on photoionization and the ALDA for the exchange-correlation kernel seems to be sufficient for most features of the cross sections. The TDDF method employing the exact exchange-only KS potential in combination with the ALDA exchange-correlation kernel therefore is a promising approach to describe photoionization. Deviations from experiment are observed for the widths and shape of the autoionization resonances and have to be attributed to deficiencies of the ALDA exchange-correlation kernel. The calculation of widths and shapes of autoionization resonances therefore may serve as a severe test for new approximate exchange-correlation density-functionals. The asymptotically exact exchange-correlation potential of van Leeuwen and Baerends also leads to quite good photo cross section, which, however, shows deficiencies close to the ionization threshold and in the energetic position of the autoionization resonances. Supplementation of the exact exchange potential with the LDA correlation potential leads to a worsening of the photo cross section because the LDA correlation potential is too attractive.
DEFF Research Database (Denmark)
Lacevic, N.; Starr, F. W.; Schrøder, Thomas
2003-01-01
two-point time-dependent density correlation functions, while providing information about the transient "caging" of particles on cooling, are unable to provide sufficiently detailed information about correlated motion and dynamical heterogeneity. Here, we study a four-point, time-dependent density...... simulations of a binary Lennard-Jones mixture approaching the mode coupling temperature from above. We find that the correlations between particles measured by g4(r,t) and S4(q,t) become increasingly pronounced on cooling. The corresponding dynamical correlation length xi4(t) extracted from the small......-q behavior of S4(q,t) provides an estimate of the range of correlated particle motion. We find that xi4(t) has a maximum as a function of time t, and that the value of the maximum of xi4(t) increases steadily from less than one particle diameter to a value exceeding nine particle diameters in the temperature...
Mo, Yuxiang; Tao, Jianmin
2016-01-01
Recently, Tao and Mo proposed an accurate meta-generalized gradient approximation for the exchange-correlation energy. The exchange part is derived from the density matrix expansion, while the correlation part is obtained by improving the TPSS correlation in the low-density limit. To better understand this exchange functional, in this work, we combine the TM exchange with the original TPSS correlation, which we call TMTPSS, and make a systematic assessment on molecular properties. The test sets include the 223 G3/99 enthalpies of formation, 58 electron affinities, 8 proton affinities, 96 bond lengths, 82 harmonic frequencies, and 10 hydrogen-bonded molecular complexes. Our calculations show that the TMTPSS functional is competitive with or even more accurate than TM functional for some properties. In particular, it is the most accurate nonempirical semilocal DFT for the enthalpies of formation and harmonic vibrational frequencies, suggesting the robustness of TM exchange.
DEFF Research Database (Denmark)
Wellendorff, Jess; Lundgård, Keld Troen; Møgelhøj, Andreas
2012-01-01
A methodology for semiempirical density functional optimization, using regularization and cross-validation methods from machine learning, is developed. We demonstrate that such methods enable well-behaved exchange-correlation approximations in very flexible model spaces, thus avoiding the overfit...
Fiebig, H R
2002-01-01
We study various aspects of extracting spectral information from time correlation functions of lattice QCD by means of Bayesian inference with an entropic prior, the maximum entropy method (MEM). Correlator functions of a heavy-light meson-meson system serve as a repository for lattice data with diverse statistical quality. Attention is given to spectral mass density functions, inferred from the data, and their dependence on the parameters of the MEM. We propose to employ simulated annealing, or cooling, to solve the Bayesian inference problem, and discuss practical issues of the approach.
DEFF Research Database (Denmark)
Cornaton, Y.; Stoyanova, A.; Jensen, Hans Jørgen Aagaard;
2013-01-01
An alternative separation of short-range exchange and correlation energies is used in the framework of second-order range-separated density-functional perturbation theory. This alternative separation was initially proposed by Toulouse and relies on a long-range-interacting wave function instead...... expression when expanded in perturbation theory. In contrast to the usual RSDH functionals, RSDHf describes the coupling between long- and short-range correlations as an orbital-dependent contribution. Calculations on the first four noble-gas dimers show that this coupling has a significant effect...
Klatt, Michael A.; Torquato, Salvatore
2016-08-01
In the first paper of this series, we introduced Voronoi correlation functions to characterize the structure of maximally random jammed (MRJ) sphere packings across length scales. In the present paper, we determine a variety of different correlation functions that arise in rigorous expressions for the effective physical properties of MRJ sphere packings and compare them to the corresponding statistical descriptors for overlapping spheres and equilibrium hard-sphere systems. Such structural descriptors arise in rigorous bounds and formulas for effective transport properties, diffusion and reactions constants, elastic moduli, and electromagnetic characteristics. First, we calculate the two-point, surface-void, and surface-surface correlation functions, for which we derive explicit analytical formulas for finite hard-sphere packings. We show analytically how the contact Dirac delta function contribution to the pair correlation function g2(r ) for MRJ packings translates into distinct functional behaviors of these two-point correlation functions that do not arise in the other two models examined here. Then we show how the spectral density distinguishes the MRJ packings from the other disordered systems in that the spectral density vanishes in the limit of infinite wavelengths; i.e., these packings are hyperuniform, which means that density fluctuations on large length scales are anomalously suppressed. Moreover, for all model systems, we study and compute exclusion probabilities and pore size distributions, as well as local density fluctuations. We conjecture that for general disordered hard-sphere packings, a central limit theorem holds for the number of points within an spherical observation window. Our analysis links problems of interest in material science, chemistry, physics, and mathematics. In the third paper of this series, we will evaluate bounds and estimates of a host of different physical properties of the MRJ sphere packings that are based on the
Nafziger, Jonathan; Wasserman, Adam
2015-12-21
One of the most important open challenges in modern Kohn-Sham (KS) density-functional theory (DFT) is the correct treatment of systems involving fractional electron charges and spins. Approximate exchange-correlation functionals struggle with such systems, leading to pervasive delocalization and static correlation errors. We demonstrate how these errors, which plague density-functional calculations of bond-stretching processes, can be avoided by employing the alternative framework of partition density-functional theory (PDFT) even using the local density approximation for the fragments. Our method is illustrated with explicit calculations on simple systems exhibiting delocalization and static-correlation errors, stretched H2 (+), H2, He2 (+), Li2 (+), and Li2. In all these cases, our method leads to greatly improved dissociation-energy curves. The effective KS potential corresponding to our self-consistent solutions displays key features around the bond midpoint; these are known to be present in the exact KS potential, but are absent from most approximate KS potentials and are essential for the correct description of electron dynamics.
Current Density Functional Theory Using Meta-Generalized Gradient Exchange-Correlation Functionals.
Furness, James W; Verbeke, Joachim; Tellgren, Erik I; Stopkowicz, Stella; Ekström, Ulf; Helgaker, Trygve; Teale, Andrew M
2015-09-08
We present the self-consistent implementation of current-dependent (hybrid) meta-generalized gradient approximation (mGGA) density functionals using London atomic orbitals. A previously proposed generalized kinetic energy density is utilized to implement mGGAs in the framework of Kohn-Sham current density functional theory (KS-CDFT). A unique feature of the nonperturbative implementation of these functionals is the ability to seamlessly explore a wide range of magnetic fields up to 1 au (∼235 kT) in strength. CDFT functionals based on the TPSS and B98 forms are investigated, and their performance is assessed by comparison with accurate coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) data. In the weak field regime, magnetic properties such as magnetizabilities and nuclear magnetic resonance shielding constants show modest but systematic improvements over generalized gradient approximations (GGA). However, in the strong field regime, the mGGA-based forms lead to a significantly improved description of the recently proposed perpendicular paramagnetic bonding mechanism, comparing well with CCSD(T) data. In contrast to functionals based on the vorticity, these forms are found to be numerically stable, and their accuracy at high field suggests that the extension of mGGAs to CDFT via the generalized kinetic energy density should provide a useful starting point for further development of CDFT approximations.
Katriel, Jacob; Bauer, Michael; Springborg, Michael; McCarthy, Shane P; Thakkar, Ajit J
2007-07-14
Reparametrization of Wigner's correlation energy density functional yields a very close fit to the correlation energies of the helium isoelectronic sequence. However, a quite different reparametrization is required to obtain an equally close fit to the isoelectronic sequence of Hooke's atom. In an attempt to avoid having to reparametrize the functional for different choices of the one-body potential, we propose a parametrization that depends on global characteristics of the ground-state electron density as quantified by scale-invariant combinations of expectation values of local one-body operators. This should be viewed as an alternative to the density-gradient paradigm, allowing one to introduce the nonlocal dependence of the density functional on the density in a possibly more effective way. Encouraging results are obtained for two-electron systems with one-body potentials of the form r(zeta) with zeta=-12,+12,1, which span the range between the Coulomb potential (zeta=-1) and the Hooke potential (zeta=2).
Filatov, M; Cremer, D
2005-01-01
It is demonstrated that the LYP correlation functional is not suited to be used for the calculation of electron spin resonance hyperfine structure (HFS) constants, nuclear magnetic resonance spin-spin coupling constants, magnetic, shieldings and other properties that require a balanced account of
Current Density-Functional Theory using meta-Generalized Gradient Exchange--Correlation Functionals
Furness, James W; Tellgren, Erik I; Stopkowicz, Stella; Ekström, Ulf; Helgaker, Trygve; Teale, Andrew M
2015-01-01
We present the self-consistent implementation of current-dependent (hybrid) meta generalized gradient approximation (mGGA) density functionals using London atomic orbitals. A previously proposed generalized kinetic energy density is utilized to implement mGGAs in the framework of Kohn--Sham current density-functional theory (KS-CDFT). A unique feature of the non-perturbative implementation of these functionals is the ability to seamlessly explore a wide range of magnetic fields up to 1 a.u. ($\\sim 235000$T) in strength. CDFT functionals based on the TPSS and B98 forms are investigated and their performance is assessed by comparison with accurate CCSD(T) data. In the weak field regime magnetic properties such as magnetizabilities and NMR shielding constants show modest but systematic improvements over GGA functionals. However, in strong field regime the mGGA based forms lead to a significantly improved description of the recently proposed perpendicular paramagnetic bonding mechanism, comparing well with CCSD(T...
Multiconfiguration Pair-Density Functional Theory: A New Way To Treat Strongly Correlated Systems.
Gagliardi, Laura; Truhlar, Donald G; Li Manni, Giovanni; Carlson, Rebecca K; Hoyer, Chad E; Bao, Junwei Lucas
2017-01-17
The electronic energy of a system provides the Born-Oppenheimer potential energy for internuclear motion and thus determines molecular structure and spectra, bond energies, conformational energies, reaction barrier heights, and vibrational frequencies. The development of more efficient and more accurate ways to calculate the electronic energy of systems with inherently multiconfigurational electronic structure is essential for many applications, including transition metal and actinide chemistry, systems with partially broken bonds, many transition states, and most electronically excited states. Inherently multiconfigurational systems are called strongly correlated systems or multireference systems, where the latter name refers to the need for using more than one ("multiple") configuration state function to provide a good zero-order reference wave function. This Account describes multiconfiguration pair-density functional theory (MC-PDFT), which was developed as a way to combine the advantages of wave function theory (WFT) and density functional theory (DFT) to provide a better treatment of strongly correlated systems. First we review background material: the widely used Kohn-Sham DFT (which uses only a single Slater determinant as reference wave function), multiconfiguration WFT methods that treat inherently multiconfigurational systems based on an active space, and previous attempts to combine multiconfiguration WFT with DFT. Then we review the formulation of MC-PDFT. It is a generalization of Kohn-Sham DFT in that the electron kinetic energy and classical electrostatic energy are calculated from a reference wave function, while the rest of the energy is obtained from a density functional. However, there are two main differences with respent to Kohn-Sham DFT: (i) The reference wave function is multiconfigurational rather than being a single Slater determinant. (ii) The density functional is a function of the total density and the on-top pair density rather than
Density-functional theory of strongly correlated Fermi gases in elongated harmonic traps
Xianlong, Gao; Polini, Marco; Asgari, Reza; Tosi, M. P.
2006-03-01
Two-component Fermi gases with tunable repulsive or attractive interactions inside quasi-one-dimensional (Q1D) harmonic wells may soon become the cleanest laboratory realizations of strongly correlated Luttiger and Luther-Emery liquids under confinement. We present a microscopic Kohn-Sham density-functional theory of these systems, with specific attention to a gas on the approach to a confinement-induced Feshbach resonance. The theory employs the one-dimensional Gaudin-Yang model as the reference system and transfers the appropriate Q1D ground-state correlations to the confined inhomogeneous gas via a suitable local-density approximation to the exchange and correlation energy functional. Quantitative understanding of the role of the interactions in the bulk shell structure of the axial density profile is thereby achieved. While repulsive intercomponent interactions depress the amplitude of the shell structure of the noninteracting gas, attractive interactions stabilize atomic-density waves through spin pairing. These should be clearly observable in atomic clouds containing of the order of up to 100 atoms.
Cornaton, Yann; Stoyanova, Alexandrina; Jensen, Hans Jørgen Aa.; Fromager, Emmanuel
2013-01-01
An alternative separation of short-range exchange and correlation energies is used in the framework of second-order range-separated density-functional perturbation theory. This alternative separation was initially proposed by Toulouse et al. [Theor. Chem. Acc. 114, 305 (2005)] and relies on a long-range interacting wavefunction instead of the non-interacting Kohn-Sham one. When second-order corrections to the density are neglected, the energy expression reduces to a range-separated double-hyb...
Ritschel, Gerhard; Eisfeld, Alexander
2014-09-01
We present a scheme to express a bath correlation function (BCF) corresponding to a given spectral density (SD) as a sum of damped harmonic oscillations. Such a representation is needed, for example, in many open quantum system approaches. To this end we introduce a class of fit functions that enables us to model ohmic as well as superohmic behavior. We show that these functions allow for an analytic calculation of the BCF using pole expansions of the temperature dependent hyperbolic cotangent. We demonstrate how to use these functions to fit spectral densities exemplarily for cases encountered in the description of photosynthetic light harvesting complexes. Finally, we compare absorption spectra obtained for different fits with exact spectra and show that it is crucial to take properly into account the behavior at small frequencies when fitting a given SD.
Sun, Jianwei; Perdew, John P.; Yang, Zenghui; Peng, Haowei
2016-05-01
The uniform electron gas and the hydrogen atom play fundamental roles in condensed matter physics and quantum chemistry. The former has an infinite number of electrons uniformly distributed over the neutralizing positively charged background, and the latter only one electron bound to the proton. The uniform electron gas was used to derive the local spin density approximation to the exchange-correlation functional that undergirds the development of the Kohn-Sham density functional theory. We show here that the ground-state exchange-correlation energies of the hydrogen atom and many other 1- and 2-electron systems are modeled surprisingly well by a different local spin density approximation (LSDA0). LSDA0 is constructed to satisfy exact constraints but agrees surprisingly well with the exact results for a uniform two-electron density in a finite, curved three-dimensional space. We also apply LSDA0 to excited or noded 1-electron densities, where it works less well. Furthermore, we show that the localization of the exact exchange hole for a 1- or 2-electron ground state can be measured by the ratio of the exact exchange energy to its optimal lower bound.
Energy Technology Data Exchange (ETDEWEB)
Mentel, Ł. M.; Meer, R. van; Gritsenko, O. V. [Section Theoretical Chemistry, VU University, Amsterdam (Netherlands); Pohang University of Science and Technology, Pohang (Korea, Republic of); Baerends, E. J. [Section Theoretical Chemistry, VU University, Amsterdam (Netherlands); Pohang University of Science and Technology, Pohang (Korea, Republic of); Chemistry Department, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia)
2014-06-07
For chemistry an accurate description of bond weakening and breaking is vital. The great advantage of density matrix functionals, as opposed to density functionals, is their ability to describe such processes since they naturally cover both nondynamical and dynamical correlation. This is obvious in the Löwdin-Shull functional, the exact natural orbital functional for two-electron systems. We present in this paper extensions of this functional for the breaking of a single electron pair bond in N-electron molecules, using LiH, BeH{sup +}, and Li{sub 2} molecules as prototypes. Attention is given to the proper formulation of the functional in terms of not just J and K integrals but also the two-electron L integrals (K integrals with a different distribution of the complex conjugation of the orbitals), which is crucial for the calculation of response functions. Accurate energy curves are obtained with extended Löwdin-Shull functionals along the complete dissociation coordinate using full CI calculations as benchmark.
Pure density functional for strong correlation and the thermodynamic limit from machine learning
Li, Li; Baker, Thomas E.; White, Steven R.; Burke, Kieron
2016-12-01
We use the density-matrix renormalization group, applied to a one-dimensional model of continuum Hamiltonians, to accurately solve chains of hydrogen atoms of various separations and numbers of atoms. We train and test a machine-learned approximation to F [n ] , the universal part of the electronic density functional, to within quantum chemical accuracy. We also develop a data-driven, atom-centered basis set for densities which greatly reduces the computational cost and accurately represents the physical information in the machine-learning calculation. Our calculation (a) bypasses the standard Kohn-Sham approach, avoiding the need to find orbitals, (b) includes the strong correlation of highly stretched bonds without any specific difficulty (unlike all standard DFT approximations), and (c) is so accurate that it can be used to find the energy in the thermodynamic limit to quantum chemical accuracy.
Rohr, Daniel R; Pernal, Katarzyna; Gritsenko, Oleg V; Baerends, Evert Jan
2008-10-28
A recently proposed series of corrections to the earliest JK-only functionals has considerably improved the prospects of density matrix functional theory (DMFT). Still, the most advanced of these functionals (correction C3) requires a preselection of the terms in the pair density Gamma(r(1),r(2)) involving the bonding and antibonding natural orbitals (NOs) belonging to an electron pair bond. Ideally, a DMFT functional should only depend on the NOs and their occupation numbers, and we propose a functional with an occupation number driven weighing of terms in the pair density. These are formulated as "damping" for certain ranges of occupation numbers of the two-electron cumulant that arises in the expansion of the two-particle density matrix of the paradigmatic two-electron system. This automatic version of C3, which we denote AC3, provides the correct dissociation limit for electron pair bonds and it excellently reproduces the potential energy curves of the multireference configuration interaction (MRCI) method for the dissociation of the electron pair bond in the series of the ten-electron hydrides CH(4), NH(3), H(2)O, and HF. AC3 reproduces closely the experimental equilibrium distances and at R(e) it yields correlation energies of the ten-electron systems with an average error in the absolute values of only 3.3% compared to the MRCI values. We stress the importance of treatment of strong correlation cases (NO occupation numbers differing significantly from 2.0 and 0.0) by appropriate terms in the cumulant.
Exchange-Correlation Effects for Noncovalent Interactions in Density Functional Theory.
Otero-de-la-Roza, A; DiLabio, Gino A; Johnson, Erin R
2016-07-12
In this article, we develop an understanding of how errors from exchange-correlation functionals affect the modeling of noncovalent interactions in dispersion-corrected density-functional theory. Computed CCSD(T) reference binding energies for a collection of small-molecule clusters are decomposed via a molecular many-body expansion and are used to benchmark density-functional approximations, including the effect of semilocal approximation, exact-exchange admixture, and range separation. Three sources of error are identified. Repulsion error arises from the choice of semilocal functional approximation. This error affects intermolecular repulsions and is present in all n-body exchange-repulsion energies with a sign that alternates with the order n of the interaction. Delocalization error is independent of the choice of semilocal functional but does depend on the exact exchange fraction. Delocalization error misrepresents the induction energies, leading to overbinding in all induction n-body terms, and underestimates the electrostatic contribution to the 2-body energies. Deformation error affects only monomer relaxation (deformation) energies and behaves similarly to bond-dissociation energy errors. Delocalization and deformation errors affect systems with significant intermolecular orbital interactions (e.g., hydrogen- and halogen-bonded systems), whereas repulsion error is ubiquitous. Many-body errors from the underlying exchange-correlation functional greatly exceed in general the magnitude of the many-body dispersion energy term. A functional built to accurately model noncovalent interactions must contain a dispersion correction, semilocal exchange, and correlation components that minimize the repulsion error independently and must also incorporate exact exchange in such a way that delocalization error is absent.
Current Issues in Finite-T Density-Functional Theory and Warm-Correlated Matter †
Directory of Open Access Journals (Sweden)
M. W. C. Dharma-wardana
2016-03-01
Full Text Available Finite-temperature density functional theory (DFT has become of topical interest, partly due to the increasing ability to create novel states of warm-correlated matter (WCM.Warm-dense matter (WDM, ultra-fast matter (UFM, and high-energy density matter (HEDM may all be regarded as subclasses of WCM. Strong electron-electron, ion-ion and electron-ion correlation effects and partial degeneracies are found in these systems where the electron temperature Te is comparable to the electron Fermi energy EF. Thus, many electrons are in continuum states which are partially occupied. The ion subsystem may be solid, liquid or plasma, with many states of ionization with ionic charge Zj. Quasi-equilibria with the ion temperature Ti ≠ Te are common. The ion subsystem in WCM can no longer be treated as a passive “external potential”, as is customary in T = 0 DFT dominated by solid-state theory or quantum chemistry. Many basic questions arise in trying to implement DFT for WCM. Hohenberg-Kohn-Mermin theory can be adapted for treating these systems if suitable finite-T exchange-correlation (XC functionals can be constructed. They are functionals of both the one-body electron density ne and the one-body ion densities ρj. Here, j counts many species of nuclei or charge states. A method of approximately but accurately mapping the quantum electrons to a classical Coulomb gas enables one to treat electron-ion systems entirely classically at any temperature and arbitrary spin polarization, using exchange-correlation effects calculated in situ, directly from the pair-distribution functions. This eliminates the need for any XC-functionals. This classical map has been used to calculate the equation of state of WDM systems, and construct a finite-T XC functional that is found to be in close agreement with recent quantum path-integral simulation data. In this review, current developments and concerns in finite-T DFT, especially in the context of non-relativistic warm
The correlation function for density perturbations in an expanding universe. I - Linear theory
Mcclelland, J.; Silk, J.
1977-01-01
The evolution of the two-point correlation function for adiabatic density perturbations in the early universe is studied. Analytical solutions are obtained for the evolution of linearized spherically symmetric adiabatic density perturbations and the two-point correlation function for these perturbations in the radiation-dominated portion of the early universe. The results are then extended to the regime after decoupling. It is found that: (1) adiabatic spherically symmetric perturbations comparable in scale with the maximum Jeans length would survive the radiation-dominated regime; (2) irregular fluctuations are smoothed out up to the scale of the maximum Jeans length in the radiation era, but regular fluctuations might survive on smaller scales; (3) in general, the only surviving structures for irregularly shaped adiabatic density perturbations of arbitrary but finite scale in the radiation regime are the size of or larger than the maximum Jeans length in that regime; (4) infinite plane waves with a wavelength smaller than the maximum Jeans length but larger than the critical dissipative damping scale could survive the radiation regime; and (5) black holes would also survive the radiation regime and might accrete sufficient mass after decoupling to nucleate the formation of galaxies.
Multiflavor Correlation Functions in non-Abelian Gauge Theories at Finite Density in two dimensions
Christiansen, H R; Christiansen, Hugo R.; Schaposnik, Fidel A.
1996-01-01
We compute vacuum expectation values of products of fermion bilinears for two-dimensional Quantum Chromodynamics at finite flavored fermion densities. We introduce the chemical potential as an external charge distribution within the path-integral approach and carefully analyse the contribution of different topological sectors to fermion correlators. We show the existence of chiral condensates exhibiting an oscillatory inhomogeneous behavior as a function of a chemical potential matrix. This result is exact and goes in the same direction as the behavior found in QCD$_4$ within the large $N$ approximation.
Pure density functional for strong correlations and the thermodynamic limit from machine learning
Li, Li; White, Steven R; Burke, Kieron
2016-01-01
We use density-matrix renormalization group, applied to a one-dimensional model of continuum Hamiltonians, to accurately solve chains of hydrogen atoms of various separations and numbers of atoms. We train and test a machine-learned approximation to $F[n]$, the universal part of the electronic density functional, to within quantum chemical accuracy. Our calculation (a) bypasses the standard Kohn-Sham approach, avoiding the need to find orbitals, (b) includes the strong correlation of highly-stretched bonds without any specific difficulty (unlike all standard DFT approximations) and (c) is so accurate that it can be used to find the energy in the thermodynamic limit to quantum chemical accuracy.
Aldegunde, Manuel; Kermode, James R.; Zabaras, Nicholas
2016-04-01
This paper presents the development of a new exchange-correlation functional from the point of view of machine learning. Using atomization energies of solids and small molecules, we train a linear model for the exchange enhancement factor using a Bayesian approach which allows for the quantification of uncertainties in the predictions. A relevance vector machine is used to automatically select the most relevant terms of the model. We then test this model on atomization energies and also on bulk properties. The average model provides a mean absolute error of only 0.116 eV for the test points of the G2/97 set but a larger 0.314 eV for the test solids. In terms of bulk properties, the prediction for transition metals and monovalent semiconductors has a very low test error. However, as expected, predictions for types of materials not represented in the training set such as ionic solids show much larger errors.
Correlated electron dynamics and memory in time-dependent density functional theory
Energy Technology Data Exchange (ETDEWEB)
Thiele, Mark
2009-07-28
Time-dependent density functional theory (TDDFT) is an exact reformulation of the time-dependent many-electron Schroedinger equation, where the problem of many interacting electrons is mapped onto the Kohn-Sham system of noninteracting particles which reproduces the exact electronic density. In the Kohn-Sham system all non-classical many-body effects are incorporated in the exchange-correlation potential which is in general unknown and needs to be approximated. It is the goal of this thesis to investigate the connection between memory effects and correlated electron dynamics in strong and weak fields. To this end one-dimensional two-electron singlet systems are studied. At the same time these systems include the onedimensional helium atom model, which is an established system to investigate the crucial effects of correlated electron dynamics in external fields. The studies presented in this thesis show that memory effects are negligible for typical strong field processes. Here the approximation of the spatial nonlocality is of primary importance. For the photoabsorption spectra on the other hand the neglect of memory effects leads to qualitative and quantitative errors, which are shown to be connected to transitions of double excitation character. To develop a better understanding of the conditions under which memory effects become important quantum fluid dynamics has been found to be especially suitable. It represents a further exact reformulation of the quantum mechanic many-body problem which is based on hydrodynamic quantities such as density and velocity. Memory effects are shown to be important whenever the velocity field develops strong gradients and dissipative effects contribute. (orig.)
Yan, Zidan; Perdew, John P.; Kurth, Stefan
2000-03-01
Within a density functional context, the random phase approximation (RPA) for the correlation emergy makes a short-range error which is well-suited for correction by a local spin density or generalized gradient approximation (GGA). Here we construct a GGA for the short-range correction, following the same reliable procedure used earlier to construct the GGA for the whole exchange-correlation energy: real-space cutoff of the spurious long-range contribution to the gradient expansion of the hole around an electron. The resulting density functional is nearly local, and predicts a substantial correction to the RPA correlation energy of an atom but \\underlinevery small corrections to the RPA atomization energy of a molecule, which may by itself come close to "chemical accuracy", and to the RPA surface energy of a metal. A by-product of this work is a density functional for the system-averaged correlation hole within RPA.
Energy Technology Data Exchange (ETDEWEB)
Backes, Steffen
2017-04-15
The study of the electronic properties of correlated systems is a very diverse field and has lead to valuable insight into the physics of real materials. In these systems, the decisive factor that governs the physical properties is the ratio between the electronic kinetic energy, which promotes delocalization over the lattice, and the Coulomb interaction, which instead favours localized electronic states. Due to this competition, correlated electronic systems can show unique and interesting properties like the Metal-Insulator transition, diverse phase diagrams, strong temperature dependence and in general a high sensitivity to the environmental conditions. A theoretical description of these systems is not an easy task, since perturbative approaches that do not preserve the competition between the kinetic and interaction terms can only be applied in special limiting cases. One of the most famous approaches to obtain the electronic properties of a real material is the ab initio density functional theory (DFT) method. It allows one to obtain the ground state density of the system under investigation by mapping onto an effective non-interacting system that has to be found self-consistently. While being an exact theory, in practical implementations certain approximations have to be made to the exchange-correlation potential. The local density approximation (LDA), which approximates the exchange-correlation contribution to the total energy by that of a homogeneous electron gas with the corresponding density, has proven quite successful in many cases. Though, this approximation in general leads to an underestimation of electronic correlations and is not able to describe a metal-insulator transition due to electronic localization in the presence of strong Coulomb interaction. A different approach to the interacting electronic problem is the dynamical mean-field theory (DMFT), which is non-perturbative in the kinetic and interaction term but neglects all non
Andrade, Xavier
2011-01-01
We propose a new approach to approximate the exchange and correlation (XC) functional in density functional theory. The XC potential is considered as an electrostatic potential, generated by a fictitious XC density, which is in turn a functional of the electronic density. We apply the approach to develop a correction scheme that fixes the asymptotic behavior of any approximated XC potential for finite systems. Additionally, the correction procedure gives the value of the derivative discontinuity; therefore it can directly predict the fundamental gap as a ground-state property.
Magneto-structural correlations in trinuclear Cu(II) complexes: a density functional study
Rodríguez-Forteá, A; Alvarez, S; Centre-De Recera-En-Quimica-Teorica; Alemany, P A; Centre-De Recera-En-Quimica-Teorica
2003-01-01
Density functional theoretical methods have been used to study magneto-structural correlations for linear trinuclear hydroxo-bridged copper(II) complexes. The nearest-neighbor exchange coupling constant shows very similar trends to those found earlier for dinuclear compounds for which the Cu-O-Cu angle and the out of plane displacement of the hydrogen atoms at the bridge are the two key structural factors that determine the nature of their magnetic behavior. Changes in these two parameters can induce variations of over 1000 cm sup - sup 1 in the value of the nearest-neighbor coupling constant. On the contrary, coupling between next-nearest neighbors is found to be practically independent of structural changes with a value for the coupling constant of about -60 cm sup - sup 1. The magnitude calculated for this coupling constant indicates that considering its value to be negligible, as usually done in experimental studies, can lead to considerable errors, especially for compounds in which the nearest-neighbor c...
Deur, Killian; Mazouin, Laurent; Fromager, Emmanuel
2017-01-01
Ensemble density functional theory (eDFT) is an exact time-independent alternative to time-dependent DFT (TD-DFT) for the calculation of excitation energies. Despite its formal simplicity and advantages in contrast to TD-DFT (multiple excitations, for example, can be easily taken into account in an ensemble), eDFT is not standard, which is essentially due to the lack of reliable approximate exchange-correlation (x c ) functionals for ensembles. Following Smith et al. [Phys. Rev. B 93, 245131 (2016), 10.1103/PhysRevB.93.245131], we propose in this work to construct an exact eDFT for the nontrivial asymmetric Hubbard dimer, thus providing more insight into the weight dependence of the ensemble x c energy in various correlation regimes. For that purpose, an exact analytical expression for the weight-dependent ensemble exchange energy has been derived. The complementary exact ensemble correlation energy has been computed by means of Legendre-Fenchel transforms. Interesting features like discontinuities in the ensemble x c potential in the strongly correlated limit have been rationalized by means of a generalized adiabatic connection formalism. Finally, functional-driven errors induced by ground-state density-functional approximations have been studied. In the strictly symmetric case or in the weakly correlated regime, combining ensemble exact exchange with ground-state correlation functionals gives better ensemble energies than when calculated with the ground-state exchange-correlation functional. However, when approaching the asymmetric equiensemble in the strongly correlated regime, the former approximation leads to highly curved ensemble energies with negative slope which is unphysical. Using both ground-state exchange and correlation functionals gives much better results in that case. In fact, exact ensemble energies are almost recovered in some density domains. The analysis of density-driven errors is left for future work.
Energy Technology Data Exchange (ETDEWEB)
Betzinger, Markus
2011-12-14
In this thesis, we extended the applicability of the full-potential linearized augmented-plane-wave (FLAPW) method, one of the most precise, versatile and generally applicable electronic structure methods for solids working within the framework of density-functional theory (DFT), to orbital-dependent functionals for the exchange-correlation (xc) energy. Two different schemes that deal with orbital-dependent functionals, the Kohn-Sham (KS) and the generalized Kohn-Sham (gKS) formalism, have been realized. Hybrid functionals, combining some amount of the orbital-dependent exact exchange energy with local or semi-local functionals of the density, are implemented within the gKS scheme. We work in particular with the PBE0 hybrid of Perdew, Burke, and Ernzerhof. Our implementation relies on a representation of the non-local exact exchange potential - its calculation constitutes the most time consuming step in a practical calculation - by an auxiliary mixed product basis (MPB). In this way, the matrix elements of the Hamiltonian corresponding to the non-local potential become a Brillouin-zone (BZ) sum over vector-matrix-vector products. Several techniques are developed and explored to further accelerate our numerical scheme. We show PBE0 results for a variety of semiconductors and insulators. In comparison with experiment, the PBE0 functional leads to improved band gaps and an improved description of localized states. Even for the ferromagnetic semiconductor EuO with localized 4f electrons, the electronic and magnetic properties are correctly described by the PBE0 functional. Subsequently, we discuss the construction of the local, multiplicative exact exchange (EXX) potential from the non-local, orbital-dependent exact exchange energy. For this purpose we employ the optimized effective potential (OEP) method. Central ingredients of the OEP equation are the KS wave-function response and the single-particle density response function. We show that a balance between the LAPW
Gritsenko, O. V.; Rubio, A.; Balbás, L. C.; Alonso, J. A.
1993-03-01
The model Coulomb pair-correlation functions proposed several years ago by Gritsenko, Bagaturyants, Kazansky, and Zhidomirov are incorporated into the self-consistent local-density approximation (LDA) scheme for electronic systems. Different correlation functions satisfying well-established local boundary conditions and integral conditions have been tested by performing LDA calculations for closed-shell atoms. Those correlation functions contain a single parameter which can be optimized by fitting the atomic correlation energies to empirical data. In this way, a single (universal) value of the parameter is found to give a very good fit for all the atoms studied. The results provide a substantial improvement of calculated correlation energies as compared to the usual LDA functionals and the scheme should be useful for molecular and cluster calculations.
Holland, Jason P; Green, Jennifer C
2010-04-15
The electronic absorption spectra of a range of copper and zinc complexes have been simulated by using time-dependent density functional theory (TD-DFT) calculations implemented in Gaussian03. In total, 41 exchange-correlation (XC) functionals including first-, second-, and third-generation (meta-generalized gradient approximation) DFT methods were compared in their ability to predict the experimental electronic absorption spectra. Both pure and hybrid DFT methods were tested and differences between restricted and unrestricted calculations were also investigated by comparison of analogous neutral zinc(II) and copper(II) complexes. TD-DFT calculated spectra were optimized with respect to the experimental electronic absorption spectra by use of a Matlab script. Direct comparison of the performance of each XC functional was achieved both qualitatively and quantitatively by comparison of optimized half-band widths, root-mean-squared errors (RMSE), energy scaling factors (epsilon(SF)), and overall quality-of-fit (Q(F)) parameters. Hybrid DFT methods were found to outperform all pure DFT functionals with B1LYP, B97-2, B97-1, X3LYP, and B98 functionals providing the highest quantitative and qualitative accuracy in both restricted and unrestricted systems. Of the functionals tested, B1LYP gave the most accurate results with both average RMSE and overall Q(F) unity (>0.990) for the copper complexes. The XC functional performance in spin-restricted TD-DFT calculations on the zinc complexes was found to be slightly worse. PBE1PBE, mPW1PW91 and B1LYP gave the most accurate results with typical RMSE and Q(F) values between 5.3 and 7.3%, and epsilon(SF) around 0.930. These studies illustrate the power of modern TD-DFT calculations for exploring excited state transitions of metal complexes.
Borgoo, Alex; Teale, Andrew M; Tozer, David J
2012-01-21
Correlated electron densities, experimental ionisation potentials, and experimental electron affinities are used to investigate the homogeneity of the exchange-correlation and non-interacting kinetic energy functionals of Kohn-Sham density functional theory under density scaling. Results are presented for atoms and small molecules, paying attention to the influence of the integer discontinuity and the choice of the electron affinity. For the exchange-correlation functional, effective homogeneities are highly system-dependent on either side of the integer discontinuity. By contrast, the average homogeneity-associated with the potential that averages over the discontinuity-is generally close to 4/3 when the discontinuity is computed using positive affinities for systems that do bind an excess electron and negative affinities for those that do not. The proximity to 4/3 becomes increasingly pronounced with increasing atomic number. Evaluating the discontinuity using a zero affinity in systems that do not bind an excess electron instead leads to effective homogeneities on the electron abundant side that are close to 4/3. For the non-interacting kinetic energy functional, the effective homogeneities are less system-dependent and the effect of the integer discontinuity is less pronounced. Average values are uniformly below 5/3. The study provides information that may aid the development of improved exchange-correlation and non-interacting kinetic energy functionals. © 2012 American Institute of Physics
Quantal density functional theory
Sahni, Viraht
2016-01-01
This book deals with quantal density functional theory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The treated time-independent QDFT constitutes a special case. In the 2nd edition, the theory is extended to include the presence of external magnetostatic fields. The theory is a description of matter based on the ‘quantal Newtonian’ first and second laws which is in terms of “classical” fields that pervade all space, and their quantal sources. The fields, which are explicitly defined, are separately representative of electron correlations due to the Pauli exclusion principle, Coulomb repulsion, correlation-kinetic, correlation-current-density, and correlation-magnetic effects. The book further describes Schrödinger theory from the new physical perspective of fields and quantal sources. It also describes traditional Hohenberg-Kohn-Sham DFT, and explains via QDFT the physics underlying the various energy functionals and functional derivatives o...
Luo, Xiaochun; Schramm, David N.
1993-01-01
One of the crucial aspects of density perturbations that are produced by the standard inflation scenario is that they are Gaussian where seeds produced by topological defects tend to be non-Gaussian. The three-point correlation function of the temperature anisotropy of the cosmic microwave background radiation (CBR) provides a sensitive test of this aspect of the primordial density field. In this paper, this function is calculated in the general context of various allowed non-Gaussian models. It is shown that the Cosmic Background Explorer and the forthcoming South Pole and balloon CBR anisotropy data may be able to provide a crucial test of the Gaussian nature of the perturbations.
Smith, J. C.; Pribram-Jones, A.; Burke, K.
2016-06-01
Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. We extract various exact free-energy correlation components and the exact adiabatic connection formula.
Filatov, Michael; Liu, Fang; Kim, Kwang S.; Martínez, Todd J.
2016-12-01
The spin-restricted ensemble-referenced Kohn-Sham (REKS) method is based on an ensemble representation of the density and is capable of correctly describing the non-dynamic electron correlation stemming from (near-)degeneracy of several electronic configurations. The existing REKS methodology describes systems with two electrons in two fractionally occupied orbitals. In this work, the REKS methodology is extended to treat systems with four fractionally occupied orbitals accommodating four electrons and self-consistent implementation of the REKS(4,4) method with simultaneous optimization of the orbitals and their fractional occupation numbers is reported. The new method is applied to a number of molecular systems where simultaneous dissociation of several chemical bonds takes place, as well as to the singlet ground states of organic tetraradicals 2,4-didehydrometaxylylene and 1,4,6,9-spiro[4.4]nonatetrayl.
Energy Technology Data Exchange (ETDEWEB)
Brics, Martins; Kapoor, Varun; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)
2013-07-01
Time-dependent density functional theory (TDDFT) with known and practicable exchange-correlation potentials does not capture highly correlated electron dynamics such as single-photon double ionization, autoionization, or nonsequential ionization. Time-dependent reduced density matrix functional theory (TDRDMFT) may remedy these problems. The key ingredients in TDRDMFT are the natural orbitals (NOs), i.e., the eigenfunctions of the one-body reduced density matrix (1-RDM), and the occupation numbers (OCs), i.e., the respective eigenvalues. The two-body reduced density matrix (2-RDM) is then expanded in NOs, and equations of motion for the NOs can be derived. If the expansion coefficients of the 2-RDM were known exactly, the problem at hand would be solved. In practice, approximations have to be made. We study the prospects of TDRDMFT following a top-down approach. We solve the exact two-electron time-dependent Schroedinger equation for a model Helium atom in intense laser fields in order to study highly correlated phenomena such as the population of autoionizing states or single-photon double ionization. From the exact wave function we calculate the exact NOs, OCs, the exact expansion coefficients of the 2-RDM, and the exact potentials in the equations of motion. In that way we can identify how many NOs and which level of approximations are necessary to capture such phenomena.
Ghosh, Soumen; Cramer, Christopher J; Truhlar, Donald G; Gagliardi, Laura
2017-04-01
Predicting ground- and excited-state properties of open-shell organic molecules by electronic structure theory can be challenging because an accurate treatment has to correctly describe both static and dynamic electron correlation. Strongly correlated systems, i.e., systems with near-degeneracy correlation effects, are particularly troublesome. Multiconfigurational wave function methods based on an active space are adequate in principle, but it is impractical to capture most of the dynamic correlation in these methods for systems characterized by many active electrons. We recently developed a new method called multiconfiguration pair-density functional theory (MC-PDFT), that combines the advantages of wave function theory and density functional theory to provide a more practical treatment of strongly correlated systems. Here we present calculations of the singlet-triplet gaps in oligoacenes ranging from naphthalene to dodecacene. Calculations were performed for unprecedently large orbitally optimized active spaces of 50 electrons in 50 orbitals, and we test a range of active spaces and active space partitions, including four kinds of frontier orbital partitions. We show that MC-PDFT can predict the singlet-triplet splittings for oligoacenes consistent with the best available and much more expensive methods, and indeed MC-PDFT may constitute the benchmark against which those other models should be compared, given the absence of experimental data.
Gould, Tim; Dobson, John F.
2013-01-01
By exploiting freedoms in the definitions of "correlation," "exchange," and "Hartree" physics in ensemble systems, we better generalise the notion of "exact exchange" (EXX) to systems with fractional occupations of the frontier orbitals, arising in the dissociation limit of some molecules. We introduce the linear EXX ("LEXX") theory whose pair distribution and energy are explicitly piecewise linear in the occupations f^{σ }i. We provide explicit expressions for these functions for frontier s and p shells. Used in an optimised effective potential (OEP) approach the LEXX yields energies bounded by the piecewise linear "ensemble EXX" (EEXX) energy and standard fractional optimised EXX energy: EEEXX ⩽ ELEXX ⩽ EEXX. Analysis of the LEXX explains the success of standard OEP methods for diatoms at large spacing, and why they can fail when both spins are allowed to be non-integer so that "ghost" Hartree interactions appear between opposite spin electrons in the usual formula. The energy ELEXX contains a cancellation term for the spin ghost case. It is evaluated for H, Li, and Na fractional ions with clear derivative discontinuities for all cases. The p-shell form reproduces accurate correlation-free energies of B-F and Al-Cl. We further test LEXX plus correlation energy calculations on fractional ions of C and F and again we find both derivative discontinuities and good agreement with exact results.
Gould, Tim; Dobson, John F
2013-01-07
By exploiting freedoms in the definitions of "correlation," "exchange," and "Hartree" physics in ensemble systems, we better generalise the notion of "exact exchange" (EXX) to systems with fractional occupations of the frontier orbitals, arising in the dissociation limit of some molecules. We introduce the linear EXX ("LEXX") theory whose pair distribution and energy are explicitly piecewise linear in the occupations f(i)(σ). We provide explicit expressions for these functions for frontier s and p shells. Used in an optimised effective potential (OEP) approach the LEXX yields energies bounded by the piecewise linear "ensemble EXX" (EEXX) energy and standard fractional optimised EXX energy: E(EEXX) ≤ E(LEXX) ≤ E(EXX). Analysis of the LEXX explains the success of standard OEP methods for diatoms at large spacing, and why they can fail when both spins are allowed to be non-integer so that "ghost" Hartree interactions appear between opposite spin electrons in the usual formula. The energy E(LEXX) contains a cancellation term for the spin ghost case. It is evaluated for H, Li, and Na fractional ions with clear derivative discontinuities for all cases. The p-shell form reproduces accurate correlation-free energies of B-F and Al-Cl. We further test LEXX plus correlation energy calculations on fractional ions of C and F and again we find both derivative discontinuities and good agreement with exact results.
Holas, A; March, N H; Rubio, Angel
2005-11-15
Holas and March [Phys. Rev. A. 51, 2040 (1995)] gave a formally exact theory for the exchange-correlation (xc) force F(xc)(r)= -inverted Deltaupsilon(xc)(r) associated with the xc potential upsilon(xc)(r) of the density-functional theory in terms of low-order density matrices. This is shown in the present study to lead, rather directly, to the determination of a sum rule nF(xc)=0 relating the xc force with the ground-state density n(r). Some connection is also made with an earlier result relating to the external potential by Levy and Perdew [Phys. Rev. A. 32, 2010 (1985)] and with the quite recent study of Joubert [J. Chem. Phys. 119, 1916 (2003)] relating to the separation of the exchange and correlation contributions.
Pande, Vikram
2016-01-01
Graphite is the most widely used and among the most widely-studied anode materials for lithium-ion batteries. Lithium intercalation into graphite has been extensively studied theoretically using density functional theory (DFT) calculations, complemented by experimental studies through X-ray diffraction, spectroscopy, optical imaging and other techniques. However, previous theoretical studies have not directly included van der Waals (vdW) interactions in their density functional theory calculations and vdW interactions play a crucial role in determining the stable phases. In this work, we present a first principles based model using DFT calculations, employing Bayesian Error Estimation Functional with van der Waals (BEEF-vdW) as the exchange correlation functional, and statistical thermodynamics to determine the phase transformations and subsequently, the thermodynamic intercalation potential diagram. We explore the entire configurational phase space by determining the important interactions and applying clust...
Zou, Peng; Dalfovo, Franco; Sharma, Rishi; Liu, Xia-Ji; Hu, Hui
2016-11-01
We theoretically investigate the dynamic structure factor of a strongly interacting Fermi gas at the crossover from Bardeen-Cooper-Schrieffer superfluids to Bose-Einstein condensates, by developing an improved random phase approximation within the framework of a density functional theory (DFT)—the so-called superfluid local density approximation. Compared with the previous random-phase-approximation studies based on the standard Bogoliubov-de Gennes equations, the use of the DFT greatly improves the accuracy of the equation of state at the crossover, and leads to a better description of both collective Bogoliubov-Anderson-Goldstone phonon mode and single-particle fermionic excitations at small transferred momentum. Near unitarity, where the s-wave scattering length diverges, we show that the single-particle excitations start to significantly contribute to the spectrum of dynamic structure factor once the frequency is above a threshold of the energy gap at 2{{Δ }}. The sharp rise in the spectrum at this threshold can be utilized to measure the pairing gap Δ. Together with the sound velocity determined from the phonon branch, the dynamic structure factor provides us some key information of the crossover Fermi superfluid. Our predictions could be examined in experiments with 6Li or 40K atoms using Bragg spectroscopy.
Kinetic theory of correlated fluids: from dynamic density functional to Lattice Boltzmann methods.
Marconi, Umberto Marini Bettolo; Melchionna, Simone
2009-07-07
Using methods of kinetic theory and liquid state theory we propose a description of the nonequilibrium behavior of molecular fluids, which takes into account their microscopic structure and thermodynamic properties. The present work represents an alternative to the recent dynamic density functional theory, which can only deal with colloidal fluids and is not apt to describe the hydrodynamic behavior of a molecular fluid. The method is based on a suitable modification of the Boltzmann transport equation for the phase space distribution and provides a detailed description of the local structure of the fluid and its transport coefficients. Finally, we propose a practical scheme to solve numerically and efficiently the resulting kinetic equation by employing a discretization procedure analogous to the one used in the Lattice Boltzmann method.
Energy Technology Data Exchange (ETDEWEB)
Guarini, E. [Istituto Nazionale per la Fisica della Materia, Unita di Ricerca di Firenze, Polo Scientifico Universita di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino (Italy); Barocchi, F. [Istituto Nazionale per la Fisica della Materia, Unita di Ricerca di Firenze, Polo Scientifico Universita di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino (Italy); Dipartimento di Fisica, Polo Scientifico Universita di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino (Italy); Celli, M.; Zoppi, M. [Istituto Nazionale per la Fisica della Materia, Unita di Ricerca di Firenze, Polo Scientifico Universita di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino (Italy); Istituto di Fisica Applicata ' ' Nello Carrara' ' , Consiglio Nazionale delle Ricerche, via Panciatichi 56/30, 50127 Firenze (Italy); Fischer, H.E. [Institut Laue-Langevin, BP 156, 38042 Grenoble Cedex 9 (France); Magli, R. [Istituto Nazionale per la Fisica della Materia, Unita di Ricerca di Firenze, Polo Scientifico Universita di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino (Italy); Dipartimento di Chimica e Biochimica Medica, Universita di Milano, LITA, via F. lli Cervi 93, 20090 Segrate Milano (Italy)
2002-07-01
An extensive neutron diffraction investigation on low-density (n<4.35 nm{sup -3}) states of helium gas along the 6-K isotherm has been performed by means of both wide- and small-angle experiments, allowing for the extraction of the zero- and first-order density coefficients of c(k), the Fourier transform of the direct correlation function, in a very wide wavevector region extending from k=1 nm{sup -1} to k=160 nm{sup -1}. The two independent measurements provide quantitatively consistent results, and the experimental quantities show a good agreement with the thermodynamic (i.e. k=0) data. The comparison of the experimental pure two-body correlation with the corresponding result of a classical calculation clearly indicates the need of a quantum-mechanical approach. (orig.)
Fontana, Raffaella; Magli, Renato
1993-08-01
Recent accurate measurements performed on liquid Kr have been used to test some of the models proposed in the literature for the triplet correlation function g 3( r, s). It turns out that neither the superposition approximation suggested by Kirkwood (J.P. Hansen and I.R. McDonald, Theory of simple liquids, Academic Press, London, 1986), nor a modification of it which partially takes into account linear density effects (H. Fredrikze, Ph.D. Thesis, Delft, 1985) are able to satisfactorily reproduce the experimental isothermal derivatives of the structure factor. Also the uniform fluid model (P.A. Egelstaff, D.I. Page and C.R.T. Heard, J. Phys. C, 4 (1971) 1453), gives a poor representation especially at lower densities. It is concluded that, in order to correctly describe triplet correlation effects, a full account of the irreducible contributions to g 3( r, s) is necessary.
Nawa, Kenji; Kitaoka, Yukie; Nakamura, Kohji; Imamura, Hiroshi; Akiyama, Toru; Ito, Tomonori; Weinert, M.
2016-07-01
The ground-state electronic configurations of the correlated organometallic metallocenes, M Cp2,M =V , Cr, Mn, Fe, Co, and Ni, are investigated using constraint density functional theory combined with nonempirical Ueff parameters determined from linear-response theory. The relative stability of the various d -orbital electronic configurations of these organometallic molecules is found to be sensitive to the amount of correlation. Using nonempirical values of Ueff, the calculated electronic configurations are in agreement with the experiments: 4A2 g ,3E2 g ,6A1 g ,1A1 g ,2E1 g , and 3A2 g for the VCp2,CrCp2,MnCp2,FeCp2,CoCp2 , and NiCp2, respectively.
Description of Pairing correlation in Many-Body finite systems with density functional theory
Hupin, Guillaume
2010-01-01
Different steps leading to the new functional for pairing based on natural orbitals and occupancies proposed in ref. [D. Lacroix and G. Hupin, arXiv:1003.2860] are carefully analyzed. Properties of quasi-particle states projected onto good particle number are first reviewed. These properties are used (i) to prove the existence of such a functional (ii) to provide an explicit functional through a 1/N expansion starting from the BCS approach (iii) to give a compact form of the functional summing up all orders in the expansion. The functional is benchmarked in the case of the picked fence pairing Hamiltonian where even and odd systems, using blocking technique are studied, at various particle number and coupling strength, with uniform and random single-particle level spacing. In all cases, a very good agreement is found with a deviation inferior to 1% compared to the exact energy.
Gould, Tim
2013-01-01
By considering the physics of non-interacting ensembles we better generalise the notion of `exact exchange' (EXX) to systems with fractional occupations in the frontier orbitals (called LEXX), in part by exploiting ambiguities in the definitions of `correlation', `exchange' and `Hartree' physics in ensemble systems. The LEXX is employed in an optimised effective potential (OEP) approach (OLEXX) to approximate groundstate energies, where it is bounded by the `ensemble EXX' (EEXX) energy and standard fractional OEXX energy via $E^{\\EEXX}\\leq E^{\\OLEXX} \\leq E^{\\OEXX}$. Analysis of the OLEXX explains the success of standard OEP methods for diatoms at large spacing, and why they can fail when both spins are allowed to be non-integer. The OLEXX is demonstrated on H, Li and Na with fractional electron number with improvements over OEXX for all cases.
Partition density functional theory
Nafziger, Jonathan
Partition density functional theory (PDFT) is a method for dividing a molecular electronic structure calculation into fragment calculations. The molecular density and energy corresponding to Kohn Sham density-functional theory (KS-DFT) may be exactly recovered from these fragments. Each fragment acts as an isolated system except for the influence of a global one-body 'partition' potential which deforms the fragment densities. In this work, the developments of PDFT are put into the context of other fragment-based density functional methods. We developed three numerical implementations of PDFT: One within the NWChem computational chemistry package using basis sets, and the other two developed from scratch using real-space grids. It is shown that all three of these programs can exactly reproduce a KS-DFT calculation via fragment calculations. The first of our in-house codes handles non-interacting electrons in arbitrary one-dimensional potentials with any number of fragments. This code is used to explore how the exact partition potential changes for different partitionings of the same system and also to study features which determine which systems yield non-integer PDFT occupations and which systems are locked into integer PDFT occupations. The second in-house code, CADMium, performs real-space calculations of diatomic molecules. Features of the exact partition potential are studied for a variety of cases and an analytical formula determining singularities in the partition potential is derived. We introduce an approximation for the non-additive kinetic energy and show how this quantity can be computed exactly. Finally a PDFT functional is developed to address the issues of static correlation and delocalization errors in approximations within DFT. The functional is applied to the dissociation of H2 + and H2.
Parry, A. O.; Rascón, C.; Willis, G.; Evans, R.
2014-09-01
We study the density-density correlation function G(r, r‧) in the interfacial region of a fluid (or Ising-like magnet) with short-ranged interactions using square gradient density functional theory. Adopting a simple double parabola approximation for the bulk free-energy density, we first show that the parallel Fourier transform G(z, z‧ q) and local structure factor S(z q) separate into bulk and excess contributions. We attempt to account for both contributions by deriving an interfacial Hamiltonian, characterised by a wavevector dependent surface tension σ(q), and then reconstructing density correlations from correlations in the interface position. We show that the standard crossing criterion identification of the interface, as a surface of fixed density (or magnetization), does not explain the separation of G(z, z‧ q) and the form of the excess contribution. We propose an alternative definition of the interface position based on the properties of correlations between points that ‘float’ with the surface and show that this describes the full q and z dependence of the excess contributions to both G and S. However, neither the ‘crossing-criterion’ nor the new ‘floating interface’ definition of σ(q) are quantities directly measurable from the total structure factor Stot(q) which contains additional q dependence arising from the non-local relation between fluctuations in the interfacial position and local density. Since it is the total structure factor that is measured experimentally or in simulations, our results have repercussions for earlier attempts to extract and interpret σ(q).
Energy Technology Data Exchange (ETDEWEB)
Torres, M.B. [Dpto. de Matematicas y Computacion, Universidad de Burgos, Burgos (Spain); Balbas, L.C. [Dpto. de Fisica Teorica, Universidad de Valladolid, Valladolid (Spain)
2002-06-17
The atomic exchange-correlation (xc) potential with the correct -1/r asymptotic behaviour constructed by Parr and Ghosh (Parr R G and Ghosh S K 1995 Phys. Rev. A 51 3564) is adapted here to study, within time density functional theory, the linear response to external fields of (i) neutral and charged sodium clusters, and (ii) doped clusters of the type Na{sub n}Pb (n=4, 6, 16). The resulting photoabsorption cross sections are compared to experimental results, when available, and to results from previous calculations using local and non-local xc functionals. The calculated static polarizabilities and plasmon frequencies are closer to the experimental values than previous results. (author)
Deur, Killian; Fromager, Emmanuel
2016-01-01
Ensemble density functional theory (eDFT) is an exact time-independent alternative to time-dependent DFT (TD-DFT) for the calculation of excitation energies. Despite its formal simplicity and advantages in contrast to TD-DFT (multiple excitations, for example, can be easily taken into account in an ensemble), eDFT is not standard which is essentially due to the lack of reliable approximate exchange-correlation (xc) functionals for ensembles. Following Burke and coworkers [Phys. Rev. B 93, 245131 (2016)], we propose in this work to construct an exact eDFT for the nontrivial asymmetric Hubbard dimer, thus providing more insight into the weight dependence of the ensemble xc energy in various correlation regimes. For that purpose, an exact analytical expression for the weight-dependent ensemble exchange energy has been derived. The complementary exact ensemble correlation energy has been computed by means of Legendre-Fenchel transforms. Interesting features like discontinuities in the ensemble xc potential in the...
Energy Technology Data Exchange (ETDEWEB)
Soderlind, P; Wolfer, W
2007-07-27
Spin and orbital and electron correlations are known to be important when treating the high-temperature {delta} phase of plutonium within the framework of density-functional theory (DFT). One of the more successful attempts to model {delta}-Pu within this approach has included condensed-matter generalizations of Hund's three rules for atoms, i.e., spin polarization, orbital polarization, and spin-orbit coupling. Here they perform a quantitative analysis of these interactions relative rank for the bonding and electronic structure in {delta}-Pu within the DFT model. The result is somewhat surprising in that spin-orbit coupling and orbital polarization are far more important than spin polarization for a realistic description of {delta}-Pu. They show that these orbital correlations on their own, without any formation of magnetic spin moments, can account for the low atomic density of the {delta} phase with a reasonable equation-of-state. In addition, this unambiguously non-magnetic (NM) treatment produces a one-electron spectra with resonances close to the Fermi level consistent with experimental valence band photoemission spectra.
Choi, Jinwoo; Chang, Eonho; Anstine, Dylan M.; Chakraborty, Himadri
2016-05-01
We study the ground state properties of C60 and C240 molecules in a spherical frame of local density approximation (LDA). Within this mean-field theory, two different approximations to the exchange-correlation (xc) functional are used: (i) The Gunnerson-Lundqvist parametrization augmented by a treatment to correct for the electron self-interaction and (ii) the van Leeuwen and Baerends (LB94) model potential that inclusively restores electron's asymptotic properties. Results show differences in the ground-state potential, level energies and electron densities between the two xc choices. We then use the ground structure to find the excited and ionized states of the systems and calculate dipole single-photoionization cross sections in a time-dependent LDA method that incorporates linear-response dynamical correlations. Comparative effects of the choices of xc on collective plasmon and single-excitation Auger resonances as well as on geometry driven cavity oscillations are found significant. The work is supported by the NSF, USA.
Choi, Jinwoo; Chang, EonHo; Anstine, Dylan M.; Madjet, Mohamed El-Amine; Chakraborty, Himadri S.
2017-02-01
We study the photoionization properties of the C60 versus C240 molecule in a spherical jellium frame of the density-functional method. Two prototypical approximations of the exchange-correlation (xc) functional are used: (i) the Gunnarsson-Lundqvist parametrization [Gunnarsson and Lundqvist, Phys. Rev. B 13, 4274 (1976), 10.1103/PhysRevB.13.4274] with a correction for the electron self-interaction (SIC) introduced artificially from the outset and (ii) a gradient-dependent augmentation of approximation (i) using the van Leeuwen and Baerends model potential [van Leeuwen and Baerends, Phys. Rev. A 49, 2421 (1994), 10.1103/PhysRevA.49.2421], in lieu of SIC, that restores electrons' asymptotic properties intrinsically within the formalism. Ground-state results from the two schemes for both molecules show differences in the shapes of mean-field potentials and bound-level properties. The choice of an xc scheme also significantly alters the dipole single-photoionization cross sections obtained by an ab initio method that incorporates linear-response dynamical correlations. Differences in the structures and ionization responses between C60 and C240 uncover the effect of molecular size on the underlying physics. Analysis indicates that the collective plasmon resonances with the gradient-based xc option produce results noticeably closer to the experimental data available for C60.
Choi, Jinwoo; Anstine, Dylan M; Madjet, Mohamed El-Amine; Chakraborty, Himadri S
2016-01-01
We study the photoionization properties of the C_60 versus C_240 molecule in a spherical jellium frame of density functional method. Two different approximations to the exchange-correlation (xc) functional are used: (i) The Gunnerson-Lundqvist parametrization [Phys. Rev. B 13, 4274 (1976)] with an explicit correction for the electron self-interaction (SIC) and (ii) a gradient-dependent augmentation of (i) by using the van Leeuwen and Baerends model potential [Phys. Rev. A 49, 2421 (1994)], in lieu of SIC, to implicitly restore electrons' asymptotic properties. Ground state results from the two schemes for both molecules show differences in the shapes of mean-field potentials and bound-level properties. The choice of a xc scheme also significantly alters the dipole single-photoionization cross sections obtained by an abinitio method that incorporates linear-response dynamical correlations. Differences in the structures and ionization responses between C_60 and C_240 uncover the effect of molecular size on the ...
Laboratory Density Functionals
Giraud, B. G.
2007-01-01
We compare several definitions of the density of a self-bound system, such as a nucleus, in relation with its center-of-mass zero-point motion. A trivial deconvolution relates the internal density to the density defined in the laboratory frame. This result is useful for the practical definition of density functionals.
Laboratory Density Functionals
Giraud, B G
2007-01-01
We compare several definitions of the density of a self-bound system, such as a nucleus, in relation with its center-of-mass zero-point motion. A trivial deconvolution relates the internal density to the density defined in the laboratory frame. This result is useful for the practical definition of density functionals.
Energy Technology Data Exchange (ETDEWEB)
Lembarki, A.
1994-12-01
In this work, we have developed some gradient-corrected exchange-correlation functionals. This study is in keeping with the density functional theory (DFT) formalism. In the first part of this memory, a description of Hartree-Fock (HF), post-HF and density functional theories is given. The second part is devoted the study the different approximations of DFT exchange-correlation functionals which have been proposed in the last years. In particular, we have underlined the approximations used for the construction of these functionals. The third part of this memory consists in the development of new gradient-corrected functionals. In this study, we have established a new relation between exchange energy, correlation energy and kinetic energy. We have deduced two new possible forms of exchange or correlation functionals, respectively. In the fourth part, we have studied the exchange potential, for which the actual formulation does not satisfy some theoretical conditions, such as the asymptotic behavior -1/r. Our contribution lies in the development of an exchange potential with a correct asymptotic -1/r behavior for large values of r. In this chapter, we have proposed a model which permits the obtention of the exchange energy from the exchange potential, using the virial theorem. The fifth part of this memory is devoted the application of these different functionals to simple systems (H{sub 2}O, CO, N{sub 2}O, H{sub 3}{sup +} and H{sub 5}{sup +}) in order to characterize the performance of DFT calculations in regards to those obtained with post-HF methods. (author). 215 refs., 8 figs., 28 tabs.
Energy Technology Data Exchange (ETDEWEB)
Kim, Song Soo [Department of Radiology, Chungnam National University Hospital, Chungnam National University School of Medicine (Korea, Republic of); Seo, Joon Beom, E-mail: seojb@amc.seoul.kr [Department of Radiology, University of Ulsan College of Medicine, Asan Medical Center (Korea, Republic of); Kim, Namkug; Chae, Eun Jin [Department of Radiology, University of Ulsan College of Medicine, Asan Medical Center (Korea, Republic of); Lee, Young Kyung [Department of Radiology, Kyung Hee University Hospital at Gangdong (Korea, Republic of); Oh, Yeon Mok; Lee, Sang Do [Division of Pulmonology, Department of Internal Medicine, University of Ulsan College of Medicine, Asan Medical Center (Korea, Republic of)
2014-01-15
Objectives: To determine the improvement of emphysema quantification with density correction and to determine the optimal site to use for air density correction on volumetric computed tomography (CT). Methods: Seventy-eight CT scans of COPD patients (GOLD II–IV, smoking history 39.2 ± 25.3 pack-years) were obtained from several single-vendor 16-MDCT scanners. After density measurement of aorta, tracheal- and external air, volumetric CT density correction was conducted (two reference values: air, −1000 HU/blood, +50 HU). Using in-house software, emphysema index (EI) and mean lung density (MLD) were calculated. Differences in air densities, MLD and EI prior to and after density correction were evaluated (paired t-test). Correlation between those parameters and FEV{sub 1} and FEV{sub 1}/FVC were compared (age- and sex adjusted partial correlation analysis). Results: Measured densities (HU) of tracheal- and external air differed significantly (−990 ± 14, −1016 ± 9, P < 0.001). MLD and EI on original CT data, after density correction using tracheal- and external air also differed significantly (MLD: −874.9 ± 27.6 vs. −882.3 ± 24.9 vs. −860.5 ± 26.6; EI: 16.8 ± 13.4 vs. 21.1 ± 14.5 vs. 9.7 ± 10.5, respectively, P < 0.001). The correlation coefficients between CT quantification indices and FEV{sub 1}, and FEV{sub 1}/FVC increased after density correction. The tracheal air correction showed better results than the external air correction. Conclusion: Density correction of volumetric CT data can improve correlations of emphysema quantification and PFT.
Goodpaster, Jason D; Barnes, Taylor A; Manby, Frederick R; Miller, Thomas F
2012-12-14
Density functional theory (DFT) embedding provides a formally exact framework for interfacing correlated wave-function theory (WFT) methods with lower-level descriptions of electronic structure. Here, we report techniques to improve the accuracy and stability of WFT-in-DFT embedding calculations. In particular, we develop spin-dependent embedding potentials in both restricted and unrestricted orbital formulations to enable WFT-in-DFT embedding for open-shell systems, and develop an orbital-occupation-freezing technique to improve the convergence of optimized effective potential calculations that arise in the evaluation of the embedding potential. The new techniques are demonstrated in applications to the van-der-Waals-bound ethylene-propylene dimer and to the hexa-aquairon(II) transition-metal cation. Calculation of the dissociation curve for the ethylene-propylene dimer reveals that WFT-in-DFT embedding reproduces full CCSD(T) energies to within 0.1 kcal/mol at all distances, eliminating errors in the dispersion interactions due to conventional exchange-correlation (XC) functionals while simultaneously avoiding errors due to subsystem partitioning across covalent bonds. Application of WFT-in-DFT embedding to the calculation of the low-spin/high-spin splitting energy in the hexaaquairon(II) cation reveals that the majority of the dependence on the DFT XC functional can be eliminated by treating only the single transition-metal atom at the WFT level; furthermore, these calculations demonstrate the substantial effects of open-shell contributions to the embedding potential, and they suggest that restricted open-shell WFT-in-DFT embedding provides better accuracy than unrestricted open-shell WFT-in-DFT embedding due to the removal of spin contamination.
Yu, Haoyu S; He, Xiao; Truhlar, Donald G
2016-03-08
Kohn-Sham density functional theory is widely used for applications of electronic structure theory in chemistry, materials science, and condensed-matter physics, but the accuracy depends on the quality of the exchange-correlation functional. Here, we present a new local exchange-correlation functional called MN15-L that predicts accurate results for a broad range of molecular and solid-state properties including main-group bond energies, transition metal bond energies, reaction barrier heights, noncovalent interactions, atomic excitation energies, ionization potentials, electron affinities, total atomic energies, hydrocarbon thermochemistry, and lattice constants of solids. The MN15-L functional has the same mathematical form as a previous meta-nonseparable gradient approximation exchange-correlation functional, MN12-L, but it is improved because we optimized it against a larger database, designated 2015A, and included smoothness restraints; the optimization has a much better representation of transition metals. The mean unsigned error on 422 chemical energies is 2.32 kcal/mol, which is the best among all tested functionals, with or without nonlocal exchange. The MN15-L functional also provides good results for test sets that are outside the training set. A key issue is that the functional is local (no nonlocal exchange or nonlocal correlation), which makes it relatively economical for treating large and complex systems and solids. Another key advantage is that medium-range correlation energy is built in so that one does not need to add damped dispersion by molecular mechanics in order to predict accurate noncovalent binding energies. We believe that the MN15-L functional should be useful for a wide variety of applications in chemistry, physics, materials science, and molecular biology.
Energy Technology Data Exchange (ETDEWEB)
Lee, Sang Uck [Univ. of Ulsan, Ulsan (Korea, Republic of)
2013-08-15
The accurate prediction of vertical excitation energies is very important for the development of new materials in the dye and pigment industry. A time-dependent density functional theory (TD-DFT) approach coupled with 22 different exchange-correlation functionals was used for the prediction of vertical excitation energies in the halogenated copper phthalocyanine molecules in order to find the most appropriate functional and to determine the accuracy of the prediction of the absorption wavelength and observed spectral shifts. Among the tested functional, B3LYP functional provides much more accurate vertical excitation energies and UV-vis spectra. Our results clearly provide a benchmark calibration of the TD-DFT method for phthalocyanine based dyes and pigments used in industry.
Tekarli, Sammer M; Drummond, Michael L; Williams, T Gavin; Cundari, Thomas R; Wilson, Angela K
2009-07-30
The performance of 44 density functionals used in conjunction with the correlation consistent basis sets (cc-pVnZ where n = T and Q) has been assessed for the gas-phase enthalpies of formation at 298.15 K of 3d transition metal (TM) containing systems. Nineteen molecules were examined: ScS, VO, VO(2), Cr(CO)(6), MnS, MnCl(2), Mn(CO)(5)Cl, FeCl(3), Fe(CO)(5), CoH(CO)(4), NiCl(2), Ni(CO)(4), CuH, CuF, CuCl, ZnH, ZnO, ZnCl, and Zn(CH(3))(2). Of the functionals examined, the functionals that resulted in the smallest mean absolute deviation (MAD, in parentheses, kcal mol(-1)) from experiment were B97-1 (6.9), PBE1KCIS (8.1), TPSS1KCIS (9.6), B97-2 (9.7), and B98 (10.7). All five of these functionals include some degree of Hartree-Fock (HF) exchange. The impact of increasing the basis set from cc-pVTZ to cc-pVQZ was found to be slight for the generalized gradient approximation (GGA) and meta-GGA (MGGA) functionals studied, indicating basis set saturation at the triple-zeta level. By contrast, for most of the generalized gradient exchange (GGE), hybrid GGA (HGGA), and hybrid meta-GGA (HMGGA) functionals considered, improvements in the average MAD of 2-3 kcal mol(-1) were seen upon progressing to a quadruple-zeta level basis set. Overall, it was found that the functionals that include Hartree-Fock exchange performed best overall, but those with greater than 40% HF exchange exhibit significantly poor performance for the prediction of enthalpies of formation for 3d TM complexes. Carbonyl-containing complexes, a mainstay in organometallic TM chemistry, are demonstrated to be exceedingly difficult to describe accurately with all but 2 of the 44 functionals considered. The most accurate functional, for both CO-containing and CO-free compounds, is B97-1/cc-pVQZ, which is shown to be capable of yielding results within 1 kcal mol(-1) of high-level ab initio composite methodologies.
Goodpaster, Jason D; Manby, Frederick R; Miller, Thomas F
2012-01-01
Density functional theory (DFT) embedding provides a formally exact framework for interfacing correlated wave-function theory (WFT) methods with lower-level descriptions of electronic structure. Here, we report techniques to improve the accuracy and stability of WFT-in-DFT embedding calculations. In particular, we develop spin-dependent embedding potentials in both restricted and unrestricted orbital formulations to enable WFT-in-DFT embedding for open-shell systems, and we develop an orbital-occupation-freezing technique to improve the convergence of optimized effective potential (OEP) calculations that arise in the evaluation of the embedding potential. The new techniques are demonstrated in applications to the van-der-Waals-bound ethylene-propylene dimer and to the hexaaquairon(II) transition-metal cation. Calculation of the dissociation curve for the ethylene-propylene dimer reveals that WFT-in-DFT embedding reproduces full CCSD(T) energies to within 0.1 kcal/mol at all distances, eliminating errors in th...
Letterman, Roger G; DeYonker, Nathan J; Burkey, Theodore J; Webster, Charles Edwin
2016-12-22
Acquisition of highly accurate energetic data for chromium-containing molecules and various chromium carbonyl complexes is a major step toward calibrating bond energies and thermal isomerization energies from mechanisms for Cr-centered photochromic materials being developed in our laboratories. The performance of six density functionals in conjunction with seven basis sets, utilizing Gaussian-type orbitals, has been evaluated for the calculation of gas-phase enthalpies of formation and enthalpies of reaction at 298.15 K on various chromium-containing systems. Nineteen molecules were examined: Cr(CO)6, Cr(CO)5, Cr(CO)5(C2H4), Cr(CO)5(C2ClH3), Cr(CO)5(cis-(C2Cl2H2)), Cr(CO)5(gem-(C2Cl2H2)), Cr(CO)5(trans-(C2Cl2H2)), Cr(CO)5(C2Cl3H), Cr(CO)5(C2Cl4), CrO2, CrF2, CrCl2, CrCl4, CrBr2, CrBr4, CrOCl2, CrO2Cl2, CrOF2, and CrO2F2. The performance of 69 density functionals in conjunction with a single basis set utilizing Slater-type orbitals (STO) and a zeroth-order relativistic approximation was also evaluated for the same test set. Values derived from density functional theory were compared to experimental values where available, or values derived from the correlation consistent composite approach (ccCA). When all reactions were considered, the functionals that exhibited the smallest mean absolute deviations (MADs, in kcal mol(-1)) from ccCA-derived values were B97-1 (6.9), VS98 (9.0), and KCIS (9.4) in conjunction with quadruple-ζ STO basis sets and B97-1 (9.3) in conjunction with cc-pVTZ basis sets. When considering only the set of gas-phase reaction enthalpies (ΔrH°gas), the functional that exhibited the smallest MADs from ccCA-derived values were B97-1 in conjunction with cc-pVTZ basis sets (9.1) and PBEPBE in conjunction with polarized valence triple-ζ basis set/effective core potential combination for Cr and augmented and multiple polarized triple-ζ Pople style basis sets (9.5). Also of interest, certainly because of known cancellation of errors, PBEPBE with the
Lu, K Q; Li, Z P; Yao, J M; Meng, J
2015-01-01
We report the first global study of dynamic correlation energies (DCEs) associated with rotational motion and quadrupole shape vibrational motion in a covariant energy density functional (CEDF) for 575 even-even nuclei with proton numbers ranging from $Z=8$ to $Z=108$ by solving a five-dimensional collective Hamiltonian, the collective parameters of which are determined from triaxial relativistic mean-field plus BCS calculation using the PC-PK1 force. After taking into account these beyond mean-field DCEs, the root-mean-square (rms) deviation with respect to nuclear masses is reduced significantly down to 1.14 MeV, which is smaller than those of other successful CEDFs: NL3* (2.96 MeV), DD-ME2 (2.39 MeV), DD-ME$\\delta$ (2.29 MeV) and DD-PC1 (2.01 MeV). Moreover, the rms deviation for two-nucleon separation energies is reduced by $\\sim34\\%$ in comparison with cranking prescription.
Engel, J
2006-01-01
The Hohenberg-Kohn theorem and Kohn-Sham procedure are extended to functionals of the localized intrinsic density of a self-bound system such as a nucleus. After defining the intrinsic-density functional, we modify the usual Kohn-Sham procedure slightly to evaluate the mean-field approximation to the functional, and carefully describe the construction of the leading corrections for a system of fermions in one dimension with a spin-degeneracy equal to the number of particles N. Despite the fact that the corrections are complicated and nonlocal, we are able to construct a local Skyrme-like intrinsic-density functional that, while different from the exact functional, shares with it a minimum value equal to the exact ground-state energy at the exact ground-state intrinsic density, to next-to-leading order in 1/N. We briefly discuss implications for real Skyrme functionals.
Cao, X. G.; Cai, X. Z.; Ma, Y. G.; Fang, D. Q.; Zhang, G. Q.; Guo, W.; Chen, J. G.; Wang, J. S.
2012-10-01
Proton-neutron, neutron-neutron, and proton-proton momentum-correlation functions (Cpn,Cnn, and Cpp) are systematically investigated for 15C and other C-isotope-induced collisions at different entrance channel conditions within the framework of the isospin-dependent quantum-molecular-dynamics model complemented by the correlation after burner (crab) computation code. 15C is a prime exotic nucleus candidate due to the weakly bound valence neutron coupling with closed-neutron-shell nucleus 14C. To study density dependence of the correlation function by removing the isospin effect, the initialized 15C projectiles are sampled from two kinds of density distribution from the relativistic mean-field (RMF) model in which the valence neutron of 15C is populated in both 1d5/2 and 2s1/2 states, respectively. The results show that the density distributions of the valence neutron significantly influence the nucleon-nucleon momentum-correlation function at large impact parameters and high incident energies. The extended density distribution of the valence neutron largely weakens the strength of the correlation function. The size of the emission source is extracted by fitting the correlation function by using the Gaussian source method. The emission source size as well as the size of the final-state phase space are larger for projectile samplings from more extended density distributions of the valence neutron, which corresponds to the 2s1/2 state in the RMF model. Therefore, the nucleon-nucleon momentum-correlation function can be considered as a potentially valuable tool to diagnose exotic nuclear structures, such as the skin and halo.
Quantal Density Functional Theory II
Sahni, Viraht
2009-01-01
Discusses approximation methods and applications of Quantal Density Functional Theory (QDFT), a local effective-potential-energy theory of electronic structure. This book describes approximations methods based on the incorporation of different electron correlations, as well as a many-body perturbation theory within the context of QDFT
Electron correlation by polarization of interacting densities
Whitten, Jerry L
2016-01-01
Coulomb interactions that occur in electronic structure calculations are correlated by allowing basis function components of the interacting densities to polarize, thereby reducing the magnitude of the interaction. Exchange integrals of molecular orbitals are not correlated. The modified Coulomb interactions are used in single-determinant or configuration interaction calculations. The objective is to account for dynamical correlation effects without explicitly introducing higher spherical harmonic functions into the molecular orbital basis. Molecular orbital densities are decomposed into a distribution of spherical components that conserve the charge and each of the interacting components is considered as a two-electron wavefunction embedded in the system acted on by an average field Hamiltonian plus . A method of avoiding redundancy is described. Applications to atoms, negative ions and molecules representing different types of bonding and spin states are discussed.
Dogu, Beril; Kuran, Banu; Yilmaz, Figen; Usen, Ahmet; Sirzai, Hulya
2013-08-01
The objective of this study is to assess the role of hand bone mineral density (BMD) as a prospective marker for hand function and the correlation of hand BMD with X-ray findings and hand functioning in patients with established rheumatoid arthritis (RA). Eighty-three female patients diagnosed with RA were enrolled. All BMD measurements were performed on both hands. The radiological evaluation was conducted according to the van der Heijde modification of the Sharp method (Sharp/van der Heijde). Duruöz Hand Index (DHI) was used to establish the disability in the hands. Furthermore, handgrip strength (HGS), pinch strength (PS), lateral pinch (LP), tip-to-tip pinch (TTP) and three-fingered pinch (TFP) on both the dominant and the non-dominant hands was measured. A significant positive correlation between hand BMD and HGS as well as all PSs with p DHI (p > 0.05). The hand BMD and the Sharp/van der Heijde scores were significantly in reverse correlation (p DHI-related variants, HGS and PS and the total DHI scores were reversely correlated, while there was a positive significant association with radiological scores (p DHI, HGS, LP, TTP, TFP and radiographic total scores. Our study demonstrated that a one-off hand BMD measurement failed to adequately indicate a loss in hand function as measured by DHI. Ultimately, HGS and TTP were shown to be the most effective indicators for measuring hand functions.
Density Functionals of Chemical Bonding
Directory of Open Access Journals (Sweden)
Mihai V. Putz
2008-06-01
Full Text Available The behavior of electrons in general many-electronic systems throughout the density functionals of energy is reviewed. The basic physico-chemical concepts of density functional theory are employed to highlight the energy role in chemical structure while its extended influence in electronic localization function helps in chemical bonding understanding. In this context the energy functionals accompanied by electronic localization functions may provide a comprehensive description of the global-local levels electronic structures in general and of chemical bonds in special. Becke-Edgecombe and authorÃ¢Â€Â™s Markovian electronic localization functions are discussed at atomic, molecular and solid state levels. Then, the analytical survey of the main workable kinetic, exchange, and correlation density functionals within local and gradient density approximations is undertaken. The hierarchy of various energy functionals is formulated by employing both the parabolic and statistical correlation degree of them with the electronegativity and chemical hardness indices by means of quantitative structure-property relationship (QSPR analysis for basic atomic and molecular systems.
Bulat, Felipe A; Toro-Labbé, Alejandro; Champagne, Benoît; Kirtman, Bernard; Yang, Weitao
2005-07-01
The performance of the optimized effective potential procedure for exact exchange in calculating static electric-field response properties of push-pull pi-conjugated systems has been studied, with an emphasis on NO2-(CH=CH)n-NH2 chains. Good agreement with Hartree-Fock dipole moments and (hyper)polarizabilities is obtained; particularly noteworthy is the chain length dependence for beta/n. Thus, the problem that conventional density-functional theory functionals dramatically overestimate these properties is largely solved, although there remains a significant correlation contribution that cannot be accounted for with current correlation functionals.
Directory of Open Access Journals (Sweden)
Orzan Marius
2016-06-01
Full Text Available Background: Assessment of the hemodynamic significance of a coronary artery stenosis is a challenging task, being extremely important for the establishment of indication for revascularization in atherosclerotic coronary artery stenosis. The aim of this study was to evaluate the role of a new marker reflecting the functional significance of a coronary artery stenosis, represented by the attenuation degree of contrast density along the stenosis by Coronary CT.
Santra, Biswajit; Klimeš, Jiří; Tkatchenko, Alexandre; Alfè, Dario; Slater, Ben; Michaelides, Angelos; Car, Roberto; Scheffler, Matthias
2013-10-01
Density-functional theory (DFT) has been widely used to study water and ice for at least 20 years. However, the reliability of different DFT exchange-correlation (xc) functionals for water remains a matter of considerable debate. This is particularly true in light of the recent development of DFT based methods that account for van der Waals (vdW) dispersion forces. Here, we report a detailed study with several xc functionals (semi-local, hybrid, and vdW inclusive approaches) on ice Ih and six proton ordered phases of ice. Consistent with our previous study [B. Santra, J. Klimeš, D. Alfè, A. Tkatchenko, B. Slater, A. Michaelides, R. Car, and M. Scheffler, Phys. Rev. Lett. 107, 185701 (2011)] which showed that vdW forces become increasingly important at high pressures, we find here that all vdW inclusive methods considered improve the relative energies and transition pressures of the high-pressure ice phases compared to those obtained with semi-local or hybrid xc functionals. However, we also find that significant discrepancies between experiment and the vdW inclusive approaches remain in the cohesive properties of the various phases, causing certain phases to be absent from the phase diagram. Therefore, room for improvement in the description of water at ambient and high pressures remains and we suggest that because of the stern test the high pressure ice phases pose they should be used in future benchmark studies of simulation methods for water.
Weck, Philippe F; Kim, Eunja
2016-09-29
The structure-property relationships of bulk CeO2 and Ce2O3 have been investigated using AM05 and PBEsol exchange-correlation functionals within the frameworks of Hubbard-corrected density functional theory (DFT+U) and density functional perturbation theory (DFPT+U). Compared with conventional PBE+U, RPBE+U, PW91+U and LDA+U functionals, AM05+U and PBEsol+U describe experimental crystalline parameters and properties of CeO2 and Ce2O3 with superior accuracy, especially when +U is chosen close to its value derived by the linear-response approach. The present findings call for a reexamination of some of the problematic oxide materials featuring strong f- and d-electron correlation using AM05+U and PBEsol+U.
DEFF Research Database (Denmark)
Bysted, Tommy Kristensen; Hamila, R.; Gabbouj, M.
1998-01-01
A new correlation function called the Teager correlation function is introduced in this paper. The connection between this function, the Teager energy operator and the conventional correlation function is established. Two applications are presented. The first is the minimization of the Teager error...... norm and the second one is the use of the instantaneous Teager correlation function for simultaneous estimation of TDOA and FDOA (Time and Frequency Difference of Arrivals)....
Vyboishchikov, Sergei F
2016-12-05
We report correlation energies, electron densities, and exchange-correlation potentials obtained from configuration interaction and density functional calculations on spherically confined He, Be, Be(2+) , and Ne atoms. The variation of the correlation energy with the confinement radius Rc is relatively small for the He, Be(2+) , and Ne systems. Curiously, the Lee-Yang-Parr (LYP) functional works well for weak confinements but fails completely for small Rc . However, in the neutral beryllium atom the CI correlation energy increases markedly with decreasing Rc . This effect is less pronounced at the density-functional theory level. The LYP functional performs very well for the unconfined Be atom, but fails badly for small Rc . The standard exchange-correlation potentials exhibit significant deviation from the "exact" potential obtained by inversion of Kohn-Sham equation. The LYP correlation potential behaves erratically at strong confinements. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
Rebolini, Elisa
2015-01-01
We present a range-separated linear-response time-dependent density-functional theory (TDDFT) which combines a density-functional approximation for the short-range response kernel and a frequency-dependent second-order Bethe-Salpeter approximation for the long-range response kernel. This approach goes beyond the adiabatic approximation usually used in linear-response TDDFT and aims at improving the accuracy of calculations of electronic excitation energies of molecular systems. A detailed derivation of the frequency-dependent second-order Bethe-Salpeter correlation kernel is given using many-body Green-function theory. Preliminary tests of this range-separated TDDFT method are presented for the calculation of excitation energies of four small molecules: N2, CO2, H2CO, and C2H4. The results suggest that the addition of the long-range second-order Bethe-Salpeter correlation kernel overall slightly improves the excitation energies.
Smith, Andrew M.; Davis, Robert Ben; LaVerde, Bruce T.; Jones, Douglas C.; Band, Jonathon L.
2012-01-01
Using the patch method to represent the continuous spatial correlation function of a phased pressure field over a structural surface is an approximation. The approximation approaches the continuous function as patches become smaller. Plotting comparisons of the approximation vs the continuous function may provide insight revealing: (1) For what patch size/density should the approximation be very good? (2) What the approximation looks like when it begins to break down? (3) What the approximation looks like when the patch size is grossly too large. Following these observations with a convergence study using one FEM may allow us to see the importance of patch density. We may develop insights that help us to predict sufficient patch density to provide adequate convergence for the intended purpose frequency range of interest
Cao, X G; Ma, Y G; Fang, D Q; Zhang, G Q; Guo, W; Chen, J G; Wang, J S; 10.1103/PhysRevC.86.044620
2012-01-01
Proton-neutron, neutron-neutron and proton-proton momentum correlation functions ($C_{pn}$, $C_{nn}$, $C_{pp}$) are systematically investigated for $^{15}$C and other C isotopes induced collisions at different entrance channel conditions within the framework of the isospin-dependent quantum molecular dynamics (IDQMD) model complemented by the CRAB (correlation after burner) computation code. $^{15}$C is a prime exotic nucleus candidate due to the weakly bound valence neutron coupling with closed-neutron shell nucleus $^{14}$C. In order to study density dependence of correlation function by removing the isospin effect, the initialized $^{15}$C projectiles are sampled from two kinds of density distribution from RMF model, in which the valence neutron of $^{15}$C is populated on both 1$d$5/2 and 2$s$1/2 states, respectively. The results show that the density distributions of valence neutron significantly influence nucleon-nucleon momentum correlation function at large impact parameter and high incident energy. T...
Energy Technology Data Exchange (ETDEWEB)
Duguet, T. [IRFU/Service de Physique Nucleaire, CEA, Centre de Saclay, Gif-sur-Yvette (France); Instituut voor Kern- en Stralingsfysica, KU Leuven, Leuven (Belgium); Michigan State University, National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, East Lansing, MI (United States); Bender, M. [Centre d' Etudes Nucleaires de Bordeaux Gradignan, Universite Bordeaux, UMR5797, Gradignan (France); Centre d' Etudes Nucleaires de Bordeaux Gradignan, CNRS/IN2P3, UMR5797, Gradignan (France); Ebran, J.P. [CEA, DAM, DIF, Arpajon (France); Lesinski, T.; Soma, V. [IRFU/Service de Physique Nucleaire, CEA, Centre de Saclay, Gif-sur-Yvette (France)
2015-12-15
This programmatic paper lays down the possibility to reconcile the necessity to resum many-body correlations into the energy kernel with the fact that safe multi-reference energy density functional (EDF) calculations cannot be achieved whenever the Pauli principle is not enforced, as is for example the case when many-body correlations are parametrized under the form of empirical density dependencies. Our proposal is to exploit a newly developed ab initio many-body formalism to guide the construction of safe, explicitly correlated and systematically improvable parametrizations of the off-diagonal energy and norm kernels that lie at the heart of the nuclear EDF method. The many-body formalism of interest relies on the concepts of symmetry breaking and restoration that have made the fortune of the nuclear EDF method and is, as such, amenable to this guidance. After elaborating on our proposal, we briefly outline the project we plan to execute in the years to come. (orig.)
Carter, Ellison M; Katz, Lynn E; Speitel, Gerald E; Ramirez, David
2011-08-01
Formaldehyde (HCHO) adsorption isotherms were developed for the first time on three activated carbons representing one activated carbon fiber (ACF) cloth, one all-purpose granular activated carbon (GAC), and one GAC commercially promoted for gas-phase HCHO removal. The three activated carbons were evaluated for HCHO removal in the low-ppm(v) range and for water vapor adsorption from relative pressures of 0.1-0.9 at 26 °C where, according to the IUPAC isotherm classification system, the adsorption isotherms observed exhibited Type V behavior. A Type V adsorption isotherm model recently proposed by Qi and LeVan (Q-L) was selected to model the observed adsorption behavior because it reduces to a finite, nonzero limit at low partial pressures and it describes the entire range of adsorption considered in this study. The Q-L model was applied to a polar organic adsorbate to fit HCHO adsorption isotherms for the three activated carbons. The physical and chemical characteristics of the activated carbon surfaces were characterized using nitrogen adsorption isotherms, X-ray photoelectron spectroscopy (XPS), and Boehm titrations. At low concentrations, HCHO adsorption capacity was most strongly related to the density of basic surface functional groups (SFGs), while water vapor adsorption was most strongly influenced by the density of acidic SFGs.
Energy Technology Data Exchange (ETDEWEB)
Vivas-Reyes, R.; Aria, A. [Universidad de Cartagena, Cartagena (Colombia). Facultad de Ciencias Naturales y Exactas. Grupo de Quimica Cuantica y Computacional]. E-mail: rvivasr@unicartagena.edu.co
2008-07-01
Quantum Chemical calculations for group 14 elements of Periodic Table (C, Si, Ge, Sn, Pb) and their functional groups have been carried out using Density Functional Theory (DFT) based reactivity descriptors such as group electronegativities, hardness and softness. DFT calculations were performed for a large series of tetra coordinated Sn compounds of the CH{sub 3}SnRR'X type, where X is a halogen and R and R' are alkyl, halogenated alkyl, alkoxy, or alkyl thio groups. The results were interpreted in terms of calculated electronegativity and hardness of the SnRR'X groups, applying a methodology previously developed by Geerlings and coworkers (J. Phys. Chem. 1993, 97, 1826). These calculations allowed to see the regularities concerning the influence of the nature of organic groups RR' and inorganic group X on electronegativities and hardness of the SnRR'X groups; in this case, it was found a very good correlation between the electronegativity of the fragment and experimental {sup 119}Sn chemical shifts, a property that sensitively reflects the change in the valence electronic structure of molecules. This work was complemented with the study of some compounds of the EX and ER types, where E= C, Si, Ge, Sn and R= CH{sub 3}, H, which was performed to study the influence that the central atom has on the electronegativity and hardness of molecules, or whether these properties are mainly affected for the type of ligand bound to the central atom. All these calculations were performed using the B3PW91 functional together with the 6-3 1 1 + + G basis set level for H, C, Si, Ge, F, Cl and Br atoms and the 3-21G for Sn and I atoms. (author)
Mardirossian, Narbe; Head-Gordon, Martin
2016-06-01
A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation is presented. The final 12-parameter functional form is selected from approximately 10 × 109 candidate fits that are trained on a training set of 870 data points and tested on a primary test set of 2964 data points. The resulting density functional, ωB97M-V, is further tested for transferability on a secondary test set of 1152 data points. For comparison, ωB97M-V is benchmarked against 11 leading density functionals including M06-2X, ωB97X-D, M08-HX, M11, ωM05-D, ωB97X-V, and MN15. Encouragingly, the overall performance of ωB97M-V on nearly 5000 data points clearly surpasses that of all of the tested density functionals. In order to facilitate the use of ωB97M-V, its basis set dependence and integration grid sensitivity are thoroughly assessed, and recommendations that take into account both efficiency and accuracy are provided.
Multicomponent density functional theory embedding formulation.
Culpitt, Tanner; Brorsen, Kurt R; Pak, Michael V; Hammes-Schiffer, Sharon
2016-07-28
Multicomponent density functional theory (DFT) methods have been developed to treat two types of particles, such as electrons and nuclei, quantum mechanically at the same level. In the nuclear-electronic orbital (NEO) approach, all electrons and select nuclei, typically key protons, are treated quantum mechanically. For multicomponent DFT methods developed within the NEO framework, electron-proton correlation functionals based on explicitly correlated wavefunctions have been designed and used in conjunction with well-established electronic exchange-correlation functionals. Herein a general theory for multicomponent embedded DFT is developed to enable the accurate treatment of larger systems. In the general theory, the total electronic density is separated into two subsystem densities, denoted as regular and special, and different electron-proton correlation functionals are used for these two electronic densities. In the specific implementation, the special electron density is defined in terms of spatially localized Kohn-Sham electronic orbitals, and electron-proton correlation is included only for the special electron density. The electron-proton correlation functional depends on only the special electron density and the proton density, whereas the electronic exchange-correlation functional depends on the total electronic density. This scheme includes the essential electron-proton correlation, which is a relatively local effect, as well as the electronic exchange-correlation for the entire system. This multicomponent DFT-in-DFT embedding theory is applied to the HCN and FHF(-) molecules in conjunction with two different electron-proton correlation functionals and three different electronic exchange-correlation functionals. The results illustrate that this approach provides qualitatively accurate nuclear densities in a computationally tractable manner. The general theory is also easily extended to other types of partitioning schemes for multicomponent systems.
Multicomponent density functional theory embedding formulation
Culpitt, Tanner; Brorsen, Kurt R.; Pak, Michael V.; Hammes-Schiffer, Sharon
2016-07-01
Multicomponent density functional theory (DFT) methods have been developed to treat two types of particles, such as electrons and nuclei, quantum mechanically at the same level. In the nuclear-electronic orbital (NEO) approach, all electrons and select nuclei, typically key protons, are treated quantum mechanically. For multicomponent DFT methods developed within the NEO framework, electron-proton correlation functionals based on explicitly correlated wavefunctions have been designed and used in conjunction with well-established electronic exchange-correlation functionals. Herein a general theory for multicomponent embedded DFT is developed to enable the accurate treatment of larger systems. In the general theory, the total electronic density is separated into two subsystem densities, denoted as regular and special, and different electron-proton correlation functionals are used for these two electronic densities. In the specific implementation, the special electron density is defined in terms of spatially localized Kohn-Sham electronic orbitals, and electron-proton correlation is included only for the special electron density. The electron-proton correlation functional depends on only the special electron density and the proton density, whereas the electronic exchange-correlation functional depends on the total electronic density. This scheme includes the essential electron-proton correlation, which is a relatively local effect, as well as the electronic exchange-correlation for the entire system. This multicomponent DFT-in-DFT embedding theory is applied to the HCN and FHF- molecules in conjunction with two different electron-proton correlation functionals and three different electronic exchange-correlation functionals. The results illustrate that this approach provides qualitatively accurate nuclear densities in a computationally tractable manner. The general theory is also easily extended to other types of partitioning schemes for multicomponent systems.
Density functional theory in quantum chemistry
Tsuneda, Takao
2014-01-01
This book examines density functional theory based on the foundation of quantum chemistry. Unconventional in approach, it reviews basic concepts, then describes the physical meanings of state-of-the-art exchange-correlation functionals and their corrections.
Wang, Nick X; Wilson, Angela K
2005-08-18
The HSO and HOS isomers have been revisited using the DFT functionals, B3LYP, B3PW91, and PBE, in combination with tight d-augmented correlation consistent basis sets, cc-pV(x+d)Z and aug-cc-pV(x+d)Z for second-row atoms. Structures, vibrationally averaged structures, relative energies, harmonic and anharmonic frequencies, enthalpies of formation of HSO and HOS, and the barrier for the HSO/HOS isomerization have been determined. These results were compared with results from previous DFT and ab initio studies in which the standard correlation consistent basis sets were used. The relative energies of the two isomers converge more rapidly and smoothly with respect to increasing basis set size for the tight d-augmented sets than for the standard basis sets. Our best calculations, B3PW91/aug-cc-pV(5+d)Z, for the relative energy of the isomers are in excellent agreement with previous CCSD(T) results given by Wilson and Dunning.
Bell Inequalities and Pseudo-functional densities
Geurdes, J F
2001-01-01
A local hidden variable model with pseudo-functional density function restricted to a binary probability event space is demonstrated to be able to reproduce the quantum correlation in an Einstein Podolsky Rosen Bohm and Aharonov type of experiment. In the density function use is made of Hadamard's finite part which disables the possibility to derive Bell's inequality from models with such a type of density function.
Härtel, Andreas; Kohl, Matthias; Schmiedeberg, Michael
2015-10-01
The fundamental measure approach to classical density functional theory has been shown to be a powerful tool to predict various thermodynamic properties of hard-sphere systems. We employ this approach to determine not only one-particle densities but also two-particle correlations in binary and six-component mixtures of hard spheres in the vicinity of a hard wall. The broken isotropy enables us to carefully test a large variety of theoretically predicted two-particle features by quantitatively comparing them to the results of Brownian dynamics simulations. Specifically, we determine and compare the one-particle density, the total correlation functions, their contact values, and the force distributions acting on a particle. For this purpose, we follow the compressibility route and theoretically calculate the direct correlation functions by taking functional derivatives. We usually observe an excellent agreement between theory and simulations, except for small deviations in cases where local crystal-like order sets in. Our results set the course for further investigations on the consistency of functionals as well as for structural analysis on, e.g., the primitive model. In addition, we demonstrate that due to the suppression of local crystallization, the predictions of six-component mixtures are better than those in bidisperse or monodisperse systems. Finally, we are confident that our results of the structural modulations induced by the wall lead to a deeper understanding of ordering in anisotropic systems in general, the onset of heterogeneous crystallization, caging effects, and glassy dynamics close to a wall, as well as structural properties in systems with confinement.
Lunedei, Enrico; Albarello, Dario
2016-03-01
Synthetic dispersion curves are here computed in the frame of an ambient-vibration full-wavefield model, which relies on the description of both ambient-vibration ground displacement and its sources as stochastic fields defined on the Earth's surface, stationary in time and homogeneous in space. In this model, previously developed for computing synthetic Horizontal-to-Vertical Spectral Ratio curves, the power spectral density function and the spatial autocorrelation of the displacement are naturally described as functions of the power spectral density function of the generating forces and of the subsoil properties (via the relevant Green's function), by also accounting for spatial correlation of these forces. Dispersion curves are computed from the displacement power spectral density function and from the spatial autocorrelation according with the well-known f-k and SPAC techniques, respectively. Two examples illustrate the way this new ambient-vibration model works, showing its possible use in better understanding the role of the surface waves in forming the dispersion curves, as well as its capability to capture some remarkable experimental findings.
Correlation Functions and Spin
Tyc, T
2000-01-01
The k-electron correlation function of a free chaotic electron beam is derived with the spin degree of freedom taken into account. It is shown that it can be expressed with the help of correlation functions for a polarized electron beam of all orders up to k and the degree of spin polarization. The form of the correlation function suggests that if the electron beam is not highly polarized, observing multi-particle correlations should be difficult. The result can be applied also to chaotic photon beams, the degree of spin polarization being replaced by the degree of polarization.
Multiconfiguration Pair-Density Functional Theory.
Li Manni, Giovanni; Carlson, Rebecca K; Luo, Sijie; Ma, Dongxia; Olsen, Jeppe; Truhlar, Donald G; Gagliardi, Laura
2014-09-09
We present a new theoretical framework, called Multiconfiguration Pair-Density Functional Theory (MC-PDFT), which combines multiconfigurational wave functions with a generalization of density functional theory (DFT). A multiconfigurational self-consistent-field (MCSCF) wave function with correct spin and space symmetry is used to compute the total electronic density, its gradient, the on-top pair density, and the kinetic and Coulomb contributions to the total electronic energy. We then use a functional of the total density, its gradient, and the on-top pair density to calculate the remaining part of the energy, which we call the on-top-density-functional energy in contrast to the exchange-correlation energy of Kohn-Sham DFT. Because the on-top pair density is an element of the two-particle density matrix, this goes beyond the Hohenberg-Kohn theorem that refers only to the one-particle density. To illustrate the theory, we obtain first approximations to the required new type of density functionals by translating conventional density functionals of the spin densities using a simple prescription, and we perform post-SCF density functional calculations using the total density, density gradient, and on-top pair density from the MCSCF calculations. Double counting of dynamic correlation or exchange does not occur because the MCSCF energy is not used. The theory is illustrated by applications to the bond energies and potential energy curves of H2, N2, F2, CaO, Cr2, and NiCl and the electronic excitation energies of Be, C, N, N(+), O, O(+), Sc(+), Mn, Co, Mo, Ru, N2, HCHO, C4H6, c-C5H6, and pyrazine. The method presented has a computational cost and scaling similar to MCSCF, but a quantitative accuracy, even with the present first approximations to the new types of density functionals, that is comparable to much more expensive multireference perturbation theory methods.
Kornobis, Karina; Wong, Bryan M; Lodowski, Piotr; Jaworska, Maria; Andruniów, Tadeusz; Rudd, Kenneth; Kozlowski, Pawel M; 10.1021/jp110914y
2011-01-01
Time-dependent density functional theory (TD-DFT) and correlated ab initio methods have been applied to the electronically excited states of vitamin B12 (cyanocobalamin or CNCbl). Different experimental techniques have been used to probe the excited states of CNCbl, revealing many issues that remain poorly understood from an electronic structure point of view. Due to its efficient scaling with size, TD-DFT emerges as one of the most practical tools that can be used to predict the electronic properties of these fairly complex molecules. However, the description of excited states is strongly dependent on the type of functional used in the calculations. In the present contribution, the choice of a proper functional for vitamin B12 was evaluated in terms of its agreement with both experimental results and correlated ab initio calculations. Three different functionals, i.e. B3LYP, BP86, and LC-BLYP, were tested. In addition, the effect of relative contributions of DFT and HF to the exchange-correlation functional ...
Semiclassics in Density Functional Theory
Lee, Donghyung; Cangi, Attila; Elliott, Peter; Burke, Kieron
2009-03-01
Recently, we published an article [1] about the semiclassical origin of density functional theory. We showed that the density and the kinetic energy density of one dimensional finite systems with hard walls can be expressed in terms of the external potential using the semiclassical Green's function method. Here, we show a uniformization scheme for the semiclassical density and the kinetic energy density for turning-point problems.[1] P. Elliott, D. Lee, A. Cangi, and K. Burke, Phys. Rev. Lett. 100, 256406 (2008).
Energy Technology Data Exchange (ETDEWEB)
Sokolov, Alexander Yu., E-mail: asokolov@uga.edu; Schaefer, Henry F. [Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602 (United States); Kutzelnigg, Werner [Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum (Germany)
2014-08-21
A new approach to density cumulant functional theory is developed that derives density cumulant N-representability conditions from an approximate Fock space unitary transformation. We present explicit equations for the third- and fourth-order two-particle cumulant N-representability, as well as the second-order contributions that depend on the connected three-particle density cumulant. These conditions are used to formulate the ODC-13 method and the non-iterative (λ{sub 3}) correction that employ an incomplete description of the fourth-order two-particle cumulant N-representability and the second-order three-particle correlation effects, respectively. We perform an analysis of the ODC-13 N-representability description for the dissociation of H{sub 2} and apply the ODC-13 method and the (λ{sub 3}) correction to diatomic molecules with multiple bond character and the symmetry-breaking tetraoxygen cation (O{sub 4}{sup +}). For the O{sub 4}{sup +} molecule, the vibrational frequencies of the ODC-13(λ{sub 3}) method do not exhibit spatial symmetry breaking and are in a good agreement with the recent infrared photodissociation experiment. We report the O{sub 4}{sup +} equilibrium structure, harmonic frequencies, and dissociation energy computed using ODC-13(λ{sub 3}) with a diffuse, core-correlated aug-cc-pCVTZ basis set.
Garza, Alejandro J; Alencar, Ana G Sousa; Sun, Jianwei; Perdew, John P; Scuseria, Gustavo E
2015-01-01
Contrary to standard coupled cluster doubles (CCD) and Brueckner doubles (BD), singlet-paired analogues of CCD and BD (denoted here as CCD0 and BD0) do not break down when static correlation is present, but neglect substantial amounts of dynamic correlation. In fact, CCD0 and BD0 do not account for any contributions from multielectron excitations involving only same-spin electrons at all. We exploit this feature to add---without introducing double counting, self-interaction, or increase in cost---the missing correlation to these methods via meta-GGA density functionals (TPSS and SCAN). Furthermore, we improve upon these CCD0+DFT blends by invoking range separation: the short- and long-range correlations absent in CCD0/BD0 are evaluated with DFT and the direct random phase approximation (dRPA), respectively. This corrects the description of long-range van der Waals forces. Comprehensive benchmarking shows that the combinations presented here are very accurate for weakly correlated systems, while also providing...
Duguet, T; Ebran, J -P; Lesinski, T; Somà, V
2015-01-01
This programmatic paper lays down the possibility to reconcile the necessity to resum many-body correlations into the energy kernel with the fact that safe multi-reference energy density functional (EDF) calculations cannot be achieved whenever the Pauli principle is not strictly enforced, as is for example the case when many-body correlations are parametrized under the form of empirical density dependencies. Our proposal is to exploit a newly developed ab initio many-body formalism to guide the construction of safe, explicitly correlated and systematically improvable parametrizations of the {\\it off-diagonal} energy and norm kernels that lie at the heart of the nuclear EDF method. The many-body formalism of interest relies on the concepts of symmetry breaking {\\it and} restoration that have made the fortune of the nuclear EDF method and is, as such, amenable to this guidance. After elaborating on our proposal, we briefly outline the project we plan to execute in the years to come.
Kraisler, Eli; Kelson, Itzhak
2010-01-01
The total energies and the spin states for atoms and their first ions with Z = 1-86 are calculated within the the local spin-density approximation (LSDA) and the generalized-gradient approximation (GGA) to the exchange-correlation (xc) energy in density-functional theory. Atoms and ions for which the ground-state density is not pure-state v-representable, are treated as ensemble v- representable with fractional occupations of the Kohn-Sham system. A newly developed algorithm which searches over ensemble v-representable densities [E. Kraisler et al., Phys. Rev. A 80, 032115 (2009)] is employed in calculations. It is found that for many atoms the ionization energies obtained with the GGA are only modestly improved with respect to experimental data, as compared to the LSDA. However, even in those groups of atoms where the improvement is systematic, there remains a non-negligible difference with respect to the experiment. The ab-initio electronic configuration in the Kohn-Sham reference system does not always equ...
Labat, Frédéric; Baranek, Philippe; Domain, Christophe; Minot, Christian; Adamo, Carlo
2007-04-21
The two polymorphs of TiO2, rutile and anatase, have been investigated at the ab initio level using different Hamiltonians with all-electron Gaussian and projector augmented plane wave basis sets. Their equilibrium lattice parameters, relative stabilities, binding energies, and band structures have been evaluated. The calculations have been performed at the Hartree-Fock, density functional theory (DFT), and hybrid (B3LYP and PBE0) levels. As regards DFT, the local density and generalized gradient (PBE) approximations have been used. Our results show an excellent agreement with the experimental band structures and binding energies for the B3LYP and PBE0 functionals, while the best structural descriptions are obtained at the PBE0 level. However, no matter which Hamiltonian and method are used, anatase is found more stable than rutile, in contrast with recent experimental reports, although the relative stabilities of the two phases are very close to each other. Nevertheless, based on the overall results, the hybrid PBE0 functional appears as a good compromise to obtain an accurate description of both structural and electronic properties of solids.
Pair Correlation Function Integrals
DEFF Research Database (Denmark)
Wedberg, Nils Hejle Rasmus Ingemar; O'Connell, John P.; Peters, Günther H.J.;
2011-01-01
numerical tests complementing previous results. Pure molecular fluids are here studied in the isothermal-isobaric ensemble with isothermal compressibilities evaluated from the total correlation function integrals and compared with values derived from volume fluctuations. For systems where the radial......We describe a method for extending radial distribution functions obtained from molecular simulations of pure and mixed molecular fluids to arbitrary distances. The method allows total correlation function integrals to be reliably calculated from simulations of relatively small systems. The long......, and J. Abildskov, Mol. Simul. 36, 1243 (2010); Fluid Phase Equilib. 302, 32 (2011)], but describe here its theoretical basis more thoroughly and derive long-distance approximations for the direct correlation functions. We describe the numerical implementation of the method in detail, and report...
Shukla, Manoj K.; Leszczynski, Jerzy
2010-11-01
A comprehensive analysis of the performance of the TD-DFT method using different density functionals including recently developed medium and long-range correlation corrected density functionals have been carried out for lower-lying electronic singlet valence transitions of nucleic acid bases and the Watson-Crick base pairs in the gas phase and in the water solution. The standard 6-311++G(d,p) basis set was used. Ground state geometries of bases and base pairs were optimized at the M05-2X/6-311++G(d,p) level. The nature of potential energy surfaces (PES) was ascertained through the harmonic vibrational frequency analysis; all geometries were found to be minima at the respective PES. Electronic singlet vertical transition energies were also computed at the CC2/def2-TZVP level in the gas phase. The effect of state-specific water solvation on TD-DFT computed transition energies was considered using the PCM model. For the isolated bases the performance of the B3LYP functional was generally found to be superior among all functionals, but it measurably fails for charge-transfer states in the base pairs. The CC2/def2-TZVP computed transition energies were also revealed to be inferior compared with B3LYP results for the isolated bases. The performance of the ωB97XD, CAM-B3LYP and BMK functionals were found to be similar and comparable with the CC2 results for the isolated bases. However, for the Watson-Crick adenine-thymine and guanine-cytosine base pairs the performance of the ωB97XD functional was found to be the best among all the studied functionals in the present work in predicting the locally excited transitions as well as charge transfer states.
Caruso, Fabio; Hellgren, Maria; Ren, Xinguo; Rinke, Patrick; Rubio, Angel; Scheffler, Matthias
2012-01-01
For the paradigmatic case of H2-dissociation we compare state-of-the-art many-body perturbation theory (MBPT) in the GW approximation and density-functional theory (DFT) in the exact-exchange plus random-phase approximation for the correlation energy (EX+cRPA). For an unbiased comparison and to prevent spurious starting point effects both approaches are iterated to full self-consistency (i.e. sc-RPA and sc-GW). The exchange-correlation diagrams in both approaches are topologically identical, but in sc-RPA they are evaluated with non-interacting and in sc-GW with interacting Green functions. This has a profound consequence for the dissociation region, where sc-RPA is superior to sc-GW. We argue that for a given diagrammatic expansion, the DFT framework outperforms the many-body framework when it comes to bond-breaking. We attribute this to the difference in the correlation energy rather than the treatment of the kinetic energy.
Density fluctuations and correlations of confined fluids
Varea, C.; Robledo, A.
The density fluctuations about the equilibrium structure of fluids confined by parallel planar walls are analyzed for the cases of identical and symmetrically opposed fields at the walls. We determine the stability matrix (of the second derivatives of the free energy functional with respect to the density) for conditions both above and below the wetting transition temperature Tw of the semi-infinite system and corroborate in all cases that the equilibrium configurations are stable. We identify the fluctuations close to the walls and in the middle of the slab and discuss their effect when the wall separation L diverges. For competing walls above Tw the localized fluctuation with lowest eigenvalue describes the displacements of the incipient wetting films that become unimpeded interfacial translations for L→∞. Below Tw the fluctuations with lowest eigenvalue correspond to stiffer deformations extended across the slab. For identical walls above Tw coexisting states display incipient prewetting films and the lowest eigenvalue describes the nature of their growth as L increases. We also calculate the pair correlation function for the inhomogeneous states and, for symmetrically opposed walls, we obtain standard Ornstein-Zernike (OZ) behavior at the walls, but find significant deviations from this law at the interface-like region in the middle of the slab. To model fluids with short-ranged forces we use a ferromagnetic Ising-type Hamiltonian in mean-field approximation.
Density functional theory: Foundations reviewed
Energy Technology Data Exchange (ETDEWEB)
Kryachko, Eugene S., E-mail: eugene.kryachko@ulg.ac.be [Bogolyubov Institute for Theoretical Physics, Kiev, 03680 (Ukraine); Ludeña, Eduardo V., E-mail: popluabe@yahoo.es [Centro de Química, Instituto Venezolano de Investigaciones Científicas, IVIC, Apartado 21827, Caracas 1020-A (Venezuela, Bolivarian Republic of); Prometheus Program, Senescyt (Ecuador); Grupo Ecuatoriano para el Estudio Experimental y Teórico de Nanosistemas, GETNano, USFQ, N104-E, Quito (Ecuador); Escuela Politécnica Superior del Litoral, ESPOL, Guayaquil (Ecuador)
2014-11-10
-geared functionals. These problems are discussed by making reference to ab initio DFT as well as to the local-scaling-transformation version of DFT, LS-DFT. In addition, we examine the question of the accuracy of approximate exchange–correlation functionals in the light of their non-observance of the variational principle. Why do approximate functionals yield reasonable (and accurate) descriptions of many molecular and condensed matter properties? Are the conditions imposed on exchange and correlation functionals sufficiently adequate to produce accurate semi-empirical functionals? In this respect, we consider the question of whether the results reflect a true approach to chemical accuracy or are just the outcome of a virtuoso-like performance which cannot be systematically improved. We discuss the issue of the accuracy of the contemporary DFT results by contrasting them to those obtained by the alternative RDMT and NOFT. We discuss the possibility of improving DFT functionals by applying in a systematic way the N-representability conditions on the 2-RDM. In this respect, we emphasize the possibility of constructing 2-matrices in the context of the local scaling transformation version of DFT to which the N-representability condition of RDM theory may be applied. We end up our revision of HKS-DFT by considering some of the problems related to spin symmetry and discuss some current issues dealing with a proper treatment of open-shell systems. We are particularly concerned, as in the rest of this paper, mostly with foundational issues arising in the construction of functionals. We dedicate the whole Section 4 to the local-scaling transformation version of density functional theory, LS-DFT. The reason is that in this theory some of the fundamental problems that appear in HKS-DFT, have been solved. For example, in LS-DFT the functionals are, in principle, designed to fulfill v- and N-representability conditions from the outset. This is possible because LS-DFT is based on density
Rizzo, Antonio; Cappelli, Chiara; Jansík, Branislav; Jonsson, Dan; Sałek, Paweł; Coriani, Sonia; Agren, Hans
2004-11-08
We present the results of an extended study of five birefringences--Kerr, Cotton-Mouton, Buckingham, Jones, and Magnetoelectric--on benzene in the gas phase. The relevant molecular quantities--first-order properties, linear, quadratic, and cubic response functions--are computed employing the density-functional theory (DFT) response theory, with a choice of functionals. In some cases, different functionals are employed for the wave-function computational step and for the subsequent analytical response calculation to determine the combination yielding at the same time the optimal energy and energy derivative results. Augmented correlation consistent basis sets of double and triple zeta quality are used. The DFT results are compared to those obtained at the Hartree-Fock level and in some cases within a coupled cluster singles and doubles electronic structure model. The study tries to assess the ability of the DFT response theory to describe a wide range of properties in a system of rather large size and high complexity. The relative strength of the five birefringences for plausible experimental conditions is determined and, when possible, comparison is made with the results of the measurements.
Gedanken Densities and Exact Constraints in Density Functional Theory
Perdew, John P; Sun, Jianwei; Burke, Kieron
2014-01-01
Approximations to the exact density functional for the exchange-correlation energy of a many-electron ground state can be constructed by satisfying constraints that are universal, i.e., valid for all electron densities. Gedanken densities are designed for the purpose of this construction, but need not be realistic. The uniform electron gas is an old gedanken density. Here, we propose a spherical two-electron gedanken density in which the dimensionless density gradient can be an arbitrary positive constant wherever the density is non-zero. The Lieb-Oxford lower bound on the exchange energy can be satisfied within a generalized gradient approximation (GGA) by bounding its enhancement factor or simplest GGA exchange-energy density. This enhancement-factor bound is well known to be sufficient, but our gedanken density shows that it is also necessary. The conventional exact exchange-energy density satisfies no such local bound, but energy densities are not unique, and the simplest GGA exchange-energy density is no...
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A temperature-constrained cascade correlation network(TCCCN), a back-propagation neural network(BP), and multiple linear regression(MLR) models were applied to quantitative structure-activity relationship(QSAR) modeling, on the basis of a set of 35 nitrobenzene derivatives and their acute toxicities. These structural quantum-chemical descriptors were obtained from the density functional theory(DFT). Stepwise multiple regression analysis was performed and the model was obtained. The value of the calibration correlation coefficient R is 0.925, and the value of cross-validation correlation coefficient R is 0.87. The standard error S=0.308 and the cross-validated(leave-one-out) standard error Scv=0.381. Principal component analysis(PCA) was carried out for parameter selection. RMS errors for training set via TCCCN and BP are 0.067 and 0.095, respectively, and RMS errors for testing set via TCCCN and BP are 0.090 and 0.111, respectively. The results show that TCCCN performs better than BP and MLR.
A multiconfigurational hybrid density-functional theory
Sharkas, Kamal; Jensen, Hans Jørgen Aa; Toulouse, Julien; 10.1063/1.4733672
2012-01-01
We propose a multiconfigurational hybrid density-functional theory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the electron-electron interaction. This gives a straightforward extension of the usual hybrid approximations by essentially adding a fraction \\lambda of exact static correlation in addition to the fraction \\lambda of exact exchange. Test calculations on the cycloaddition reactions of ozone with ethylene or acetylene and the dissociation of diatomic molecules with the Perdew-Burke-Ernzerhof (PBE) and Becke-Lee-Yang-Parr (BLYP) density functionals show that a good value of \\lambda is 0.25, as in the usual hybrid approximations. The results suggest that the proposed multiconfigurational hybrid approximations can improve over usual density-functional calculations for situations with strong static correlation effects.
Development of New Density Functional Approximations
Su, Neil Qiang; Xu, Xin
2017-05-01
Kohn-Sham density functional theory has become the leading electronic structure method for atoms, molecules, and extended systems. It is in principle exact, but any practical application must rely on density functional approximations (DFAs) for the exchange-correlation energy. Here we emphasize four aspects of the subject: (a) philosophies and strategies for developing DFAs; (b) classification of DFAs; (c) major sources of error in existing DFAs; and (d) some recent developments and future directions.
Casida, Mark E.; Salahub, Dennis R.
2000-11-01
The time-dependent density functional theory (TD-DFT) calculation of excitation spectra places certain demands on the DFT exchange-correlation potential, vxc, that are not met by the functionals normally used in molecular calculations. In particular, for high-lying excitations, it is crucial that the asymptotic behavior of vxc be correct. In a previous paper, we introduced a novel asymptotic-correction approach which we used with the local density approximation (LDA) to yield an asymptotically corrected LDA (AC-LDA) potential [Casida, Casida, and Salahub, Int. J. Quantum Chem. 70, 933 (1998)]. The present paper details the theory underlying this asymptotic correction approach, which involves a constant shift to incorporate the effect of the derivative discontinuity (DD) in the bulk region of finite systems, and a spliced asymptotic correction in the large r region. This is done without introducing any adjustable parameters. We emphasize that correcting the asymptotic behavior of vxc is not by itself sufficient to improve the overall form of the potential unless the effect of the derivative discontinuity is taken into account. The approach could be used to correct vxc from any of the commonly used gradient-corrected functionals. It is here applied to the LDA, using the asymptotically correct potential of van Leeuwen and Baerends (LB94) in the large r region. The performance of our AC-LDA vxc is assessed for the calculation of TD-DFT excitation energies for a large number of excitations, including both valence and Rydberg states, for each of four small molecules: N2, CO, CH2O, and C2H4. The results show a significant improvement over those from either the LB94 or the LDA functionals. This confirms that the DD is indeed an important element in the design of functionals. The quality of TDLDA/LB94 and TDLDA/AC-LDA oscillator strengths were also assessed in what we believe to be the first rigorous assessment of TD-DFT molecular oscillator strengths in comparison with
LOCAL-DENSITY FUNCTIONAL AND ON-SITE CORRELATIONS - THE ELECTRONIC-STRUCTURE OF LA2CUO4 AND LACUO3
CZYZYK, MT; SAWATZKY, GA
1994-01-01
State-of-the-art electronic-structure calculations based on the local-density approximation (LDA) to the density functional fail to reproduce the insulating antiferromagnetic ground state in the parent compounds of the high-temperature oxide superconductors. Similar problems have been observed earli
Hexagonalization of Correlation Functions
Fleury, Thiago
2016-01-01
We propose a nonperturbative framework to study general correlation functions of single-trace operators in $\\mathcal{N}=4$ supersymmetric Yang-Mills theory at large $N$. The basic strategy is to decompose them into fundamental building blocks called the hexagon form factors, which were introduced earlier to study structure constants using integrability. The decomposition is akin to a triangulation of a Riemann surface, and we thus call it hexagonalization. We propose a set of rules to glue the hexagons together based on symmetry, which naturally incorporate the dependence on the conformal and the R-symmetry cross ratios. Our method is conceptually different from the conventional operator product expansion and automatically takes into account multi-trace operators exchanged in OPE channels. To illustrate the idea in simple set-ups, we compute four-point functions of BPS operators of arbitrary lengths and correlation functions of one Konishi operator and three short BPS operators, all at one loop. In all cases,...
Connection formula for thermal density functional theory
Pribram-Jones, Aurora
2015-01-01
The adiabatic connection formula of ground-state density functional theory relates the correlation energy to a coupling-constant integral over a purely potential contribution, and is widely used to understand and improve approximations. The corresponding formula for thermal density functional theory is cast as an integral over temperatures instead, ranging upwards from the system's physical temperature to infinite temperatures. Several formulas yield one component of the thermal correlation free energy in terms of another, many of which can be expressed either in terms of temperature- or coupling-constant integration. We illustrate with the uniform electron gas.
Density functionals from deep learning
McMahon, Jeffrey M
2016-01-01
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep learning is developed to approximate this functional. Deep learning allows computational models that are capable of naturally discovering intricate structure in large and/or high-dimensional data sets, with multiple levels of abstraction. As no assumptions are made as to the form of this structure, this approach is much more powerful and flexible than traditional approaches. As an example application, the model is shown to perform well on approximating the kinetic-energy density functional for noninteracting electrons. The model is analyzed in detail, and its advantages over conventional machine learning are discussed.
Integer Discontinuity of Density Functional Theory
Mosquera, Martin A
2014-01-01
Density functional approximations to the exchange-correlation energy of Kohn-Sham theory, such as the local density approximation and generalized gradient approximations, lack the well-known integer discontinuity, a feature that is critical to describe molecular dissociation correctly. Moreover, standard approximations to the exchange-correlation energy also fail to yield the correct linear dependence of the ground-state energy on the number of electrons when this is a non-integer number obtained from the grand canonical ensemble statistics. We present a formal framework to restore the integer discontinuity of any density functional approximation. Our formalism derives from a formula for the exact energy functional and a new constrained search functional that recovers the linear dependence of the energy on the number of electrons.
Gritsenko, Oleg; Baerends, Evert Jan
2004-07-08
Time-dependent density functional theory (TDDFT) calculations of charge-transfer excitation energies omegaCT are significantly in error when the adiabatic local density approximation (ALDA) is employed for the exchange-correlation kernel fxc. We relate the error to the physical meaning of the orbital energy of the Kohn-Sham lowest unoccupied molecular orbital (LUMO). The LUMO orbital energy in Kohn-Sham DFT--in contrast to the Hartree-Fock model--approximates an excited electron, which is correct for excitations in compact molecules. In CT transitions the energy of the LUMO of the acceptor molecule should instead describe an added electron, i.e., approximate the electron affinity. To obtain a contribution that compensates for the difference, a specific divergence of fxc is required in rigorous TDDFT, and a suitable asymptotically correct form of the kernel fxc(asymp) is proposed. The importance of the asymptotic correction of fxc is demonstrated with the calculation of omegaCT(R) for the prototype diatomic system HeBe at various separations R(He-Be). The TDDFT-ALDA curve omegaCT(R) roughly resembles the benchmark ab initio curve omegaCT CISD(R) of a configuration interaction calculation with single and double excitations in the region R=1-1.5 A, where a sizable He-Be interaction exists, but exhibits the wrong behavior omegaCT(R)
Ramaniah, Lavanya M.; Kamal, C.; Kshirsagar, Rohidas J.; Chakrabarti, Aparna; Banerjee, Arup
2013-10-01
Hydrogen bonding is one of the most important and ubiquitous interactions present in Nature. Several studies have attempted to characterise and understand the nature of this very basic interaction. These include both experimental and theoretical investigations of different types of chemical compounds, as well as systems subjected to high pressure. The O-H..O bond is of course the best studied hydrogen bond, and most studies have concentrated on intermolecular hydrogen bonding in solids and liquids. In this paper, we analyse and characterise normal hydrogen bonding of the general type, D-H...A, in intramolecular hydrogen bonding interactions. Using a first-principles density functional theory approach, we investigate low energy conformers of the twenty α-amino acids. Within these conformers, several different types of intramolecular hydrogen bonds are identified. The hydrogen bond within a given conformer occurs between two molecular groups, either both within the backbone itself, or one in the backbone and one in the side chain. In a few conformers, more than one (type of) hydrogen bond is seen to occur. Interestingly, the strength of the hydrogen bonds in the amino acids spans quite a large range, from weak to strong. The signature of hydrogen bonding in these molecules, as reflected in their theoretical vibrational spectra, is analysed. With the new first-principles data from 51 hydrogen bonds, various parameters relating to the hydrogen bond, such as hydrogen bond length, hydrogen bond angle, bond length and vibrational frequencies are studied. Interestingly, the correlation between these parameters in these bonds is found to be in consonance with those obtained in earlier experimental studies of normal hydrogen bonds on vastly different systems. Our study provides some of the most detailed first-principles support, and the first involving vibrational frequencies, for the universality of hydrogen bond correlations in materials.
Hwang, Jungseek
2016-03-31
We introduce an approximate method which can be used to simulate the optical conductivity data of correlated multiband systems for normal and superconducting cases by taking advantage of a reversed process in comparison to a usual optical data analysis, which has been used to extract the electron-boson spectral density function from measured optical spectra of single-band systems, like cuprates. We applied this method to optical conductivity data of two multiband pnictide systems (Ba0.6K0.4Fe2As2 and LiFeAs) and obtained the electron-boson spectral density functions. The obtained electron-boson spectral density consists of a sharp mode and a broad background. The obtained spectral density functions of the multiband systems show similar properties as those of cuprates in several aspects. We expect that our method helps to reveal the nature of strong correlations in the multiband pnictide superconductors.
Roper, Ian P E; Besley, Nicholas A
2016-03-21
The simulation of X-ray emission spectra of transition metal complexes with time-dependent density functional theory (TDDFT) is investigated. X-ray emission spectra can be computed within TDDFT in conjunction with the Tamm-Dancoff approximation by using a reference determinant with a vacancy in the relevant core orbital, and these calculations can be performed using the frozen orbital approximation or with the relaxation of the orbitals of the intermediate core-ionised state included. Both standard exchange-correlation functionals and functionals specifically designed for X-ray emission spectroscopy are studied, and it is shown that the computed spectral band profiles are sensitive to the exchange-correlation functional used. The computed intensities of the spectral bands can be rationalised by considering the metal p orbital character of the valence molecular orbitals. To compute X-ray emission spectra with the correct energy scale allowing a direct comparison with experiment requires the relaxation of the core-ionised state to be included and the use of specifically designed functionals with increased amounts of Hartree-Fock exchange in conjunction with high quality basis sets. A range-corrected functional with increased Hartree-Fock exchange in the short range provides transition energies close to experiment and spectral band profiles that have a similar accuracy to those from standard functionals.
Pressure Correction in Density Functional Theory Calculations
Lee, S H
2008-01-01
First-principles calculations based on density functional theory have been widely used in studies of the structural, thermoelastic, rheological, and electronic properties of earth-forming materials. The exchange-correlation term, however, is implemented based on various approximations, and this is believed to be the main reason for discrepancies between experiments and theoretical predictions. In this work, by using periclase MgO as a prototype system we examine the discrepancies in pressure and Kohn-Sham energy that are due to the choice of the exchange-correlation functional. For instance, we choose local density approximation and generalized gradient approximation. We perform extensive first-principles calculations at various temperatures and volumes and find that the exchange-correlation-based discrepancies in Kohn-Sham energy and pressure should be independent of temperature. This implies that the physical quantities, such as the equation of states, heat capacity, and the Gr\\"{u}neisen parameter, estimat...
Density functional calculations of nanoscale conductance
Energy Technology Data Exchange (ETDEWEB)
Koentopp, Max; Chang, Connie [Department of Chemistry and Chemical Biology, Rutgers University, 610 Taylor Road, Piscataway, NJ 08854 (United States); Burke, Kieron [Department of Chemistry, UC Irvine, 1102 Natural Sciences 2, Irvine, CA 92697 (United States); Car, Roberto [Department of Chemistry and Princeton Institute for the Science and Technology of Materials (PRISM), Princeton University, Princeton, NJ 08544 (United States)
2008-02-27
Density functional calculations for the electronic conductance of single molecules are now common. We examine the methodology from a rigorous point of view, discussing where it can be expected to work, and where it should fail. When molecules are weakly coupled to leads, local and gradient-corrected approximations fail, as the Kohn-Sham levels are misaligned. In the weak bias regime, exchange-correlation corrections to the current are missed by the standard methodology. For finite bias, a new methodology for performing calculations can be rigorously derived using an extension of time-dependent current density functional theory from the Schroedinger equation to a master equation. (topical review)
Extended screened exchange functional derived from transcorrelated density functional theory
Umezawa, Naoto
2017-09-01
We propose a new formulation of the correlation energy functional derived from the transcorrelated method in use in density functional theory (TC-DFT). An effective Hamiltonian, HTC, is introduced by a similarity transformation of a many-body Hamiltonian, H , with respect to a complex function F: HTC=1/F H F . It is proved that an expectation value of HTC for a normalized single Slater determinant, Dn, corresponds to the total energy: E [n ] = ⟨Ψn|H |Ψn ⟩ /⟨Ψn|Ψn ⟩ = ⟨Dn|HTC|Dn ⟩ under the two assumptions: (1) The electron density n (r ) associated with a trial wave function Ψn = DnF is v -representable and (2) Ψn and Dn give rise to the same electron density n (r ). This formulation, therefore, provides an alternative expression of the total energy that is useful for the development of novel correlation energy functionals. By substituting a specific function for F, we successfully derived a model correlation energy functional, which resembles the functional form of the screened exchange method. The proposed functional, named the extended screened exchange (ESX) functional, is described within two-body integrals and is parametrized for a numerically exact correlation energy of the homogeneous electron gas. The ESX functional does not contain any ingredients of (semi-)local functionals and thus is totally free from self-interactions. The computational cost for solving the self-consistent-field equation is comparable to that of the Hartree-Fock method. We apply the ESX functional to electronic structure calculations for a solid silicon, H- ion, and small atoms. The results demonstrate that the TC-DFT formulation is promising for the systematic improvement of the correlation energy functional.
Density Functionals with Broad Applicability in Chemistry
Energy Technology Data Exchange (ETDEWEB)
Zhao, Yan; Truhlar, Donald G.
2008-02-01
The research described in this product was performed in part in the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the Department of Energy's Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. Although density functional theory is widely used in the computational chemistry community, the most popular density functional, B3LYP, has some serious shortcomings: (i) it is better for main-group chemistry than for transition metals; (ii) it systematically underestimates reaction barrier heights; (iii) it is inaccurate for interactions dominated by mediumrange correlation energy, such as van der Waals attraction, aromatic-aromatic stacking, and alkane isomerization energies. We have developed a variety of databases for testing and designing new density functionals. We used these data to design new density functionals, called M06-class (and, earlier, M05-class) functionals, for which we enforced some fundamental exact constraints such as the uniform-electron-gas limit and the absence of self-correlation energy. Our M06-class functionals depend on spin-up and spin-down electron densities (i.e., spin densities), spin density gradients, spin kinetic energy densities, and, for nonlocal (also called hybrid) functionals, Hartree-Fock exchange. We have developed four new functionals that overcome the above-mentioned difficulties: (a) M06, a hybrid meta functional, is a functional with good accuracy “across-theboard” for transition metals, main group thermochemistry, medium-range correlation energy, and barrier heights; (b) M06- 2X, another hybrid meta functional, is not good for transition metals but has excellent performance for main group chemistry, predicts accurate valence and Rydberg electronic excitation energies, and is an excellent functional for aromatic-aromatic stacking interactions; (c) M06-L is not as accurate as M06 for barrier heights but is the most accurate
The benchmark of gutzwiller density functional theory in hydrogen systems
Energy Technology Data Exchange (ETDEWEB)
Yao, Y.; Wang, Cai-Zhuang; Ho, Kai-Ming
2012-02-23
We propose an approximate form of the exchange-correlation energy functional for the Gutzwiller density functional theory. It satisfies certain physical constraints in both weak and strong electron correlation limits. We benchmark the Gutzwiller density functional approximation in the hydrogen systems, where the static correlation error is shown to be negligible. The good transferability is demonstrated by applications to the hydrogen molecule and some crystal structures.
The Benchmark of Gutzwiller Density Functional Theory in Hydrogen Systems
Energy Technology Data Exchange (ETDEWEB)
Yao, Yongxin; Wang, Cai-Zhuang; Ho, Kai-Ming
2011-01-13
We propose an approximate form of the exchange-correlation energy functional for the Gutzwiller density functional theory. It satisfies certain physical constraints in both weak and strong electron correlation limits. We benchmark the Gutzwiller density functional approximation in the hydrogen systems, where the static correlation error is shown to be negligible. The good transferability is demonstrated by applications to the hydrogen molecule and some crystal structures. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012
Kim, Do Yun; Hänni, Simon; Schüttauf, Jan-Willem; van Swaaij, René A C M M; Zeman, Miro
2016-08-17
Optical and electrical properties of hydrogenated nanocrystalline silicon (nc-Si:H) solar cells are strongly influenced by the morphology of underlying substrates. By texturing the substrates, the photogenerated current of nc-Si:H solar cells can increase due to enhanced light scattering. These textured substrates are, however, often incompatible with defect-less nc-Si:H growth resulting in lower Voc and FF. In this study we investigate the correlation between the substrate morphology, the nc-Si:H solar-cell performance, and the defect density in the intrinsic layer of the solar cells (i-nc-Si:H). Statistical surface parameters representing the substrate morphology do not show a strong correlation with the solar-cell parameters. Thus, we first quantify the line density of potentially defective valleys of randomly textured ZnO substrates where the opening angle is smaller than 130° (ρSi:H (ρdefect), which is obtained by fitting external photovoltaic parameters from experimental results and simulations. We confirm that when ρ<130 increases the Voc and FF significantly drops. It is also observed that ρdefect increases following a power law dependence of ρ<130. This result is attributed to more frequently formed defective regions for substrates having higher ρ<130.
Energy Technology Data Exchange (ETDEWEB)
Arantes, J. T.; Lima, M. P.; Fazzio, A.; Xiang, H.; Wei, S. H.; Dalpian, G. M.
2009-04-01
The structural and electronic properties of perylene diimide liquid crystal PPEEB are studied using ab initio methods based on the density functional theory (DFT). Using available experimental crystallographic data as a guide, we propose a detailed structural model for the packing of solid PPEEB. We find that due to the localized nature of the band edge wave function, theoretical approaches beyond the standard method, such as hybrid functional (PBE0), are required to correctly characterize the band structure of this material. Moreover, unlike previous assumptions, we observe the formation of hydrogen bonds between the side chains of different molecules, which leads to a dispersion of the energy levels. This result indicates that the side chains of the molecular crystal not only are responsible for its structural conformation but also can be used for tuning the electronic and optical properties of these materials.
Interpretation of van der Waal density functionals
Hyldgaard, Per; Schröder, Elsebeth
2014-01-01
The nonlocal correlation energy in the van der Waals density functional (vdW-DF) method [Phys. Rev. Lett. 92, 246401 (2004); Phys. Rev. B 76, 125112 (2007); Phys. Rev. B 89, 035412 (2014)] can be interpreted in terms of a coupling of zero-point energies of characteristic modes of semilocal exchange-correlation (xc) holes. These xc holes reflect the internal functional in the framework of the vdW-DF method [Phys. Rev. B 82, 081101(2010)]. We explore the internal xc hole components, showing that they share properties with those of the generalized-gradient approximation. We use these results to illustrate the nonlocality in the vdW-DF description and analyze the vdW-DF formulation of nonlocal correlation.
Spin in Density-Functional Theory
Jacob, Christoph R; 10.1002/qua.24309
2012-01-01
The accurate description of open-shell molecules, in particular of transition metal complexes and clusters, is still an important challenge for quantum chemistry. While density-functional theory (DFT) is widely applied in this area, the sometimes severe limitations of its currently available approximate realizations often preclude its application as a predictive theory. Here, we review the foundations of DFT applied to open-shell systems, both within the nonrelativistic and the relativistic framework. In particular, we provide an in-depth discussion of the exact theory, with a focus on the role of the spin density and possibilities for targeting specific spin states. It turns out that different options exist for setting up Kohn-Sham DFT schemes for open-shell systems, which imply different definitions of the exchange-correlation energy functional and lead to different exact conditions on this functional. Finally, we suggest some possible directions for future developments.
Energy Technology Data Exchange (ETDEWEB)
Mattsson, Ann Elisabet; Modine, Normand Arthur; Desjarlais, Michael Paul; Muller, Richard Partain; Sears, Mark P.; Wright, Alan Francis
2006-11-01
A finite temperature version of 'exact-exchange' density functional theory (EXX) has been implemented in Sandia's Socorro code. The method uses the optimized effective potential (OEP) formalism and an efficient gradient-based iterative minimization of the energy. The derivation of the gradient is based on the density matrix, simplifying the extension to finite temperatures. A stand-alone all-electron exact-exchange capability has been developed for testing exact exchange and compatible correlation functionals on small systems. Calculations of eigenvalues for the helium atom, beryllium atom, and the hydrogen molecule are reported, showing excellent agreement with highly converged quantumMonte Carlo calculations. Several approaches to the generation of pseudopotentials for use in EXX calculations have been examined and are discussed. The difficult problem of finding a correlation functional compatible with EXX has been studied and some initial findings are reported.
Reduced density-matrix functionals from many-particle theory
Schade, Robert; Kamil, Ebad; Blöchl, Peter
2017-07-01
In materials with strong electron correlation the proper treatment of local atomic physics described by orbital occupations is crucial. Reduced density-matrix functional theory is a natural extension of density functional theory for systems that are dominated by orbital physics. We review the current state of reduced density-matrix functional theory (RDMFT). For atomic structure relaxations or ab-initio molecular dynamics the combination of density functional theory (DFT) and dynamical mean-field theory (DMFT) possesses a number of disadvantages, like the cumbersome evaluation of forces. We therefore describe a method, DFT+RDMFT, that combines many-particle effects based on reduced density-matrix functional theory with a density functional-like framework. A recent development is the construction of density-matrix functionals directly from many-particle theory such as methods from quantum chemistry or many-particle Green's functions. We present the underlying exact theorems and describe current progress towards quantitative functionals.
Correlation Functions and Power Spectra
DEFF Research Database (Denmark)
Larsen, Jan
2006-01-01
The present lecture note is a supplement to the textbook Digital Signal Processing by J. Proakis and D.G. Manolakis used in the IMM/DTU course 02451 Digital Signal Processing and provides an extended discussion of correlation functions and power spectra. The definitions of correlation functions...... and spectra for discrete-time and continuous-time (analog) signals are pretty similar. Consequently, we confine the discussion mainly to real discrete-time signals. The Appendix contains detailed definitions and properties of correlation functions and spectra for analog as well as discrete-time signals....... It is possible to define correlation functions and associated spectra for aperiodic, periodic and random signals although the interpretation is different. Moreover, we will discuss correlation functions when mixing these basic signal types. In addition, the note include several examples for the purpose...
Billiards correlation functions
Pedro, G; Pedro, Garrido; Giovanni, Gallavotti
1993-01-01
Abstract: We discuss various experiments on the time decay of velocity autocorrelation functions in billiards. We perform new experiments and find results which are compatible with an exponential mixing hypothesis, first put forward by [FM]: they do not seem compatible with the stretched exponentials believed, in spite of [FM], to describe the mixing. The analysis led us to several byproducts: we obtain information about the normal diffusive nature of the motion and we consider the probability distribution of the number of collisions in time $t_m$ (as $t_m\\to\\io$) finding a strong dependence on some geometric characteristics of the locus of the billiards obstacles.
Billiards correlation functions
Energy Technology Data Exchange (ETDEWEB)
Garrido, P.L. [Universidad de Granada (Spain); Gallavotti, G. [Universita di Roma (Italy)
1994-07-01
We discuss various experiments on the time decay of velocity autocorrelation functions in billiards. We perform new experiments and find results which are compatible with an exponential mixing hypothesis first put forward by Friedman and Martin (GM): they do not seem compatible with the stretched exponentials believed, in spite of FM and more recently of Chernov, to describe the mixing. The analysis leads to several byproducts: we obtain information about the normal diffusive nature of the motion and we consider the probability distribution of the number of collisions in time t{sub m} (as t{sub m} {yields} {infinity}), finding a strong dependence on some geometric characteristics of the locus of the billiard obstacles.
Quantal density functional theory. 2. ed.
Energy Technology Data Exchange (ETDEWEB)
Sahni, Viraht
2016-07-01
This book is on quantal density functional theory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The time-independent QDFT constitutes a special case. The 2{sup nd} edition describes the further development of the theory, and extends it to include the presence of an external magnetostatic field. The theory is based on the 'quantal Newtonian' second and first laws for the individual electron. These laws are in terms of 'classical' fields that pervade all space, and their quantal sources. The fields are separately representative of the electron correlations that must be accounted for in local potential theory. Recent developments show that irrespective of the type of external field the electrons are subject to, the only correlations beyond those due to the Pauli exclusion principle and Coulomb repulsion that need be considered are solely of the correlation-kinetic effects. Foundational to QDFT, the book describes Schroedinger theory from the new perspective of the single electron in terms of the 'quantal Newtonian' laws. Hohenberg-Kohn density functional theory (DFT), new understandings of the theory and its extension to the presence of an external uniform magnetostatic field are described. The physical interpretation via QDFT, in terms of electron correlations, of Kohn-Sham DFT, approximations to it and Slater theory are provided.
Superfluid LDA (SLDA): Local Density Approximation for Systems with Superfluid Correlations
Bulgac, A; Bulgac, Aurel; Yu, Yongle
2004-01-01
We present a concise account of our development of the first genuine Local Density Approximation (LDA) to the Energy Density Functional (EDF) for fermionic systems with superfluid correlations, with a particular emphasis to nuclear systems.
Density Functional Approach Based on Numerically Obtained Bridge Functional
Institute of Scientific and Technical Information of China (English)
ZHOUShi－Qi
2002-01-01
The ornstein-zenike equation is solved with the Rogers-Young approximation for bulk hard sphere fluid and Lennard-Jones fluid for several state points.Then the resulted bulk fluid radial distribution function combined with the test particle method is employed to determine numerically the function relationship of bridge functional as a function of indirect correlation function.It is found that all of the calculated points from different phase space state points for a same type of fluid collapse onto a same smooth curve.Then the numerically obtained curve is used to substitute the analytic expression of the bridge functional as a function of indirect correlation function required in the methodology [J.Chem.Phys,112(2000)8079] to determine the density distribution of non-uniform hard sphere fluid and Lennard-Jones fluid.The good agreement of theoretical predictions with the computer simulation data is obtained.The present numerical procedure incroporates the knowledge of bulk fluid radial distribution function into the constructing of the density functional approximation and makes the original methodology more accurate and more filexible for various interaction potential fluid.
Density Functional Approach Based on Numerically Obtained Bridge Functional
Institute of Scientific and Technical Information of China (English)
ZHOU Shi-Qi
2002-01-01
The Ornstein Zernike equation is solved with the Rogers Young approximation for bulk hard sphere fluidand Lennard-Jones fluid for several state points. Then the resulted bulk fluid radial distribution function combinedwith the test particle method is employed to determine numerically the function relationship of bridge functional as afunction of indirect correlation function. It is found that all of the calculated points from different phase space statepoints for a same type of fluid collapse onto a same smooth curve. Then the numerically obtained curve is used tosubstitute the analytic expression of the bridge functional as a function of indirect correlation function required in themethodology [J. Chem. Phys. 112 (2000) 8079] to deterrnine the density distribution of non-uniform hard spherefluid and Lennard Jones fluid. The good agreement of theoretical predictions with the computer simulation data isobtained. The present numerical procedure incorporates the knowledge of bulk fluid radial distribution function intothe constructing of the density functional approximation and makes the original methodology more accurate and moreflexible for various interaction potential fluid.
Optimally focused cold atom systems obtained using density-density correlations.
Putra, Andika; Campbell, Daniel L; Price, Ryan M; De, Subhadeep; Spielman, I B
2014-01-01
Resonant absorption imaging is a common technique for detecting the two-dimensional column density of ultracold atom systems. In many cases, the system's thickness along the imaging direction greatly exceeds the imaging system's depth of field, making the identification of the optimally focused configuration difficult. Here we describe a systematic technique for bringing Bose-Einstein condensates (BEC) and other cold-atom systems into an optimal focus even when the ratio of the thickness to the depth of field is large: a factor of 8 in this demonstration with a BEC. This technique relies on defocus-induced artifacts in the Fourier-transformed density-density correlation function (the power spectral density, PSD). The spatial frequency at which these artifacts first appear in the PSD is maximized on focus; the focusing process therefore both identifies and maximizes the range of spatial frequencies over which the PSD is uncontaminated by finite-thickness effects.
Density functional theory on phase space
Blanchard, Philippe; Várilly, Joseph C
2010-01-01
Forty-five years after the point de d\\'epart [1] of density functional theory, its applications in chemistry and the study of electronic structures keep steadily growing. However, the precise form of the "divine" energy functional in terms of the electron density [2] still eludes us --and possibly will do so forever [3]. In what follows we examine a formulation in the same spirit with phase-space variables. The validity of Hohenberg-Kohn-Levy-type theorems on phase space is recalled. We study the representability problem for reduced Wigner functions, and proceed to analyze properties of the new functional. Along the way, new results on states in the phase-space formalism of quantum mechanics are established. Natural Wigner orbital theory is developed in depth, with the final aim of constructing accurate correlation-exchange functionals on phase space. A new proof of the overbinding property of the Mueller functional is given. This exact theory supplies its home at long last to that illustrious ancestor, the T...
Insight and progress in density functional theory
Yang, Weitao; Mori-Sanchez, Paula; Cohen, Aron J.
2012-12-01
Density functional theory of electronic structure is widely and successfully applied in simulations throughout engineering and sciences. However, there are spectacular failures for many predicted properties. The errors include underestimation of the barriers of chemical reactions, the band gaps of materials, the energies of dissociating molecular ions and charge transfer excitation energies. Typical DFT calculations also fail to describe degenerate or near degenerate systems, as arise in the breaking of chemical bonds, and strongly correlated materials. These errors can all be characterized and understood through the perspective of fractional charges and fractional spins introduced recently.
Energy density functional for nuclei and neutron stars
Erler, J; Nazarewicz, W; Rafalski, M; Reinhard, P -G
2012-01-01
We aim to develop a nuclear energy density functional that can be simultaneously applied to finite nuclei and neutron stars. We use the self-consistent nuclear density functional theory (DFT) with Skyrme energy density functionals and covariance analysis to assess correlations between observables for finite nuclei and neutron stars. In a first step two energy functionals -- a high density energy functional giving reasonable neutron properties, and a low density functional fitted to nuclear properties -- are matched. In a second step, we optimize a new functional using exactly the same protocol as in earlier studies pertaining to nuclei but now including neutron star data. This allows direct comparisons of performance of the new functional relative to the standard one. The new functional TOV-min yields results for nuclear bulk properties (energy, r.m.s. radius, diffraction radius, surface thickness) that are of the same quality as those obtained with the established Skyrme functionals, including SV-min. When c...
Correlation functions on conical defects
Smolkin, Michael
2015-01-01
We explore the new technique developed recently in \\cite{Rosenhaus:2014woa} and suggest a correspondence between the $N$-point correlation functions on spacetime with conical defects and the $(N+1)$-point correlation functions in regular Minkowski spacetime. This correspondence suggests a new systematic way to evaluate the correlation functions on spacetimes with conical defects. We check the correspondence for the expectation value of a scalar operator and of the energy momentum tensor in a conformal field theory and obtain the exact agreement with the earlier derivations for cosmic string spacetime. We then use this correspondence and do the computations for a generic scalar operator and a conserved vector current. For generic unitary field theory we compute the expectation value of the energy momentum tensor using the known spectral representation of the $2$-point correlators of stress-energy tensor in Minkowski spacetime.
Denis, Pablo A
2005-09-01
We have investigated the SX (X = first- or second-row atom), SO2, and SO3 molecules employing the correlation-consistent (cc), the recently developed polarization-consistent (pc), and three Pople-type basis sets, in conjunction with the B3LYP functional. The results confirmed that the aug-pc basis sets represent a great contribution in terms of cost-benefits. In the case of the B3LYP functional, when employing the aug-pc-3 and aug-pc-4 basis sets, it is possible to obtain results that are of aug-cc-pV(5+d)Z and aug-cc-pV(6+d)Z quality, respectively, at a much lower cost. The estimations obtained employing smaller members of the family are of nearly double-ζ quality and do not provide reliable results. There is no basis set of quadruple-ζ quality among the polarized-consistent basis sets, although in terms of composition, the aug-pc-3 basis set is a QZ basis set. A precise estimation of the Kohn-Sham complete basis set (CBS) limit with the aug-pc-X basis sets is too difficult for the B3LYP functional because the ∞(aug-pc-4, aug-pc-3, aug-pc-2) extrapolation gives the same results as those of the aug-pc-4 basis set. This is in contrast with the results observed for ab initio methodologies for which the largest basis sets provided the best estimation of the CBS limit. In our opinion, the closest results to the B3LYP/CBS limit are expected to be those obtained with a two-point extrapolation employing the aug-cc-pV(X+d)Z (X = 5, 6) basis sets. The results obtained with this extrapolation are very close to those predicted by the ∞(aug-pc-3, aug-pc-2, aug-pc-1) extrapolation, and that provides a cheaper but more inaccurate alternative to estimate the CBS limit. Minor problems were found for the aug-pc-X basis sets and the B3LYP functional for molecules in which sulfur is bound to a very electronegative element, such as SO, SF, SO2, and SO3. For these molecules, the cc basis sets were demonstrated to be more useful. The importance of tight d functions was observed
Chachiyo, Teepanis
2016-07-01
A simple correlation energy functional for the uniform electron gas is derived based on the second-order Moller-Plesset perturbation theory. It can reproduce the known correlation functional in the high-density limit, while in the mid-density range maintaining a good agreement with the near-exact correlation energy of the uniform electron gas to within 2 × 10-3 hartree. The correlation energy is a function of a density parameter rs and is of the form a * ln ( 1 + /b r s + /b rs 2 ) . The constants "a" and "b" are derived from the known correlation functional in the high-density limit. Comparisons to the Ceperley-Alder's near-exact Quantum Monte Carlo results and the Vosko-Wilk-Nusair correlation functional are also reported.
Density functionals and dimensional renormalization for an exactly solvable model
Kais, S.; Herschbach, D. R.; Handy, N. C.; Murray, C. W.; Laming, G. J.
1993-07-01
We treat an analytically solvable version of the ``Hooke's Law'' model for a two-electron atom, in which the electron-electron repulsion is Coulombic but the electron-nucleus attraction is replaced by a harmonic oscillator potential. Exact expressions are obtained for the ground-state wave function and electron density, the Hartree-Fock solution, the correlation energy, the Kohn-Sham orbital, and, by inversion, the exchange and correlation functionals. These functionals pertain to the ``intermediate'' density regime (rs≥1.4) for an electron gas. As a test of customary approximations employed in density functional theory, we compare our exact density, exchange, and correlation potentials and energies with results from two approximations. These use Becke's exchange functional and either the Lee-Yang-Parr or the Perdew correlation functional. Both approximations yield rather good results for the density and the exchange and correlation energies, but both deviate markedly from the exact exchange and correlation potentials. We also compare properties of the Hooke's Law model with those of two-electron atoms, including the large dimension limit. A renormalization procedure applied to this very simple limit yields correlation energies as good as those obtained from the approximate functionals, for both the model and actual atoms.
Some Correlations for Saturated-Liquid Density of Refrigerant Mixtures
Maezawa, Yukishige; Sato, Haruki; Watanabe, Koichi
Three methods to correlate and estimate the saturated-1iquid density of refrigerant mixtures are compared and evaluated on the basis of the measurements for five bibary and one ternary mixtures performed by the present authors. The first of them is a method using Peng-Robinson equation (PR-method) proposed originally by Peneloux et al. Since this method dose not require any measurements of the saturated-liquid density of mixture, it is useful for the estimation. However, the applicability of this method to various substances may be restricted. The second is the modified Rackett equation proposed by Spencer and Dannar (mR-method). The temperature functional form of this equation is quite simple, so it is useful to use it as a functional form of the fitting. Unfortunately this method can not be used for strongly non-ideal mixtures. The last one is the Hankinson-Brobst-Thomson equation (HBT-method). This method can provide the most accurate density values among the three methods with two kinds of binary parameters where these binary parameters are introduced by the present authors. In the case that many experimental saturated liquid densities of mixtures are available in the wide range of temperatures, the HBT-method is recommended for the practical use.
Correlation Degree and Correlation Coefficient of Multi- Output Functions
Institute of Scientific and Technical Information of China (English)
JU Gui-zhi; ZHAO Ya-qun
2005-01-01
We present definitions of the correlation degree and correlation coefficient of multi-output functions. Two relationships about the correlation degree of multi-output functions are proved. One is between the correlation degree and independency,the other is between the correlation degree and balance. Especially the paper discusses the correlation degree of affine multioutput functions. We demonstrate properties of the correlation coefficient of multi-output functions. One is the value range of the correlation coefficient, one is the relationship between the correlation coefficient and independency, and another is the sufficient and necessary condition that two multi-output functions are equivalent to each other.
Aimé, Carole; Plet, Benoit; Manet, Sabine; Schmitter, Jean-Marie; Huc, Ivan; Oda, Reiko; Sauers, Ronald R; Romsted, Laurence S
2008-11-20
Understanding ion specific effects on the solution properties of association colloids is a major unsolved problem, and we are studying the chemistry of gemini surfactants in the gas-phase by mass spectrometry and density functional theory (DFT) to probe ion specific effects in the absence of water. Products from gas-phase fragmentation chemistry of dication-monoanion pairs, M2+X(-), of C16H33(CH3)2N+-(CH2)(n-) +N(CH3)2C16H33.2X(-) gemini surfactants were determined by using sequential collision induced dissociation mass spectrometry. The spacer length "n" was systematically varied (n = 2, 3, 4, and 6) for each counterion investigated (X(-) = F(-), Br(-), Cl(-), I(-), NO3(-), CF3CO2(-), and PF6(-)). The M2+X(-) pairs fragment into monocationic products from competing E2 and S N2 pathways that are readily quantified by tandem MS. The dominant reaction pathway depends on dication and anion structure because it switches from E2 to S N2 with decreasing anion basicity and increasing spacer length. For spacer lengths n = 4 and 6, the major S N2 product shifts from attack at methylene to methyl on the quaternary ammonium group. DFT calculations of gemini headgroup model bolaform salts, CH3(CH3)2N+-(CH2)(n-)+N(CH3)2CH3.2X(-) (X(-) = F(-), Cl(-), Br(-), and I(-), n = 2-4), primarily of activation enthalpies, DeltaH, but also of free energies and entropies for the dication-monoanion pairs, M2+X(-), provide qualitative explanations for the MS structure-reactivity patterns. DeltaH values for S N2 reactions are independent of X(-) type and spacer length, while E2 reactions show a significant increase in DeltaH with decreasing anion basicity and a modest increase with spacer length. Comparisons with the DeltaH values of model CH3CH2(CH3)3N+X(-) halides show that the second charge on the dicationic ion pairs does not significantly affect DeltaH and that the change in distance between the nucleophile and leaving group in the ground and transition states structures in S N2 reactions
A Density Functional Theory Study
Lim, XiaoZhi
2011-12-11
Complexes with pincer ligand moieties have garnered much attention in the past few decades. They have been shown to be highly active catalysts in several known transition metal-catalyzed organic reactions as well as some unprecedented organic transformations. At the same time, the use of computational organometallic chemistry to aid in the understanding of the mechanisms in organometallic catalysis for the development of improved catalysts is on the rise. While it was common in earlier studies to reduce computational cost by truncating donor group substituents on complexes such as tertbutyl or isopropyl groups to hydrogen or methyl groups, recent advancements in the processing capabilities of computer clusters and codes have streamlined the time required for calculations. As the full modeling of complexes become increasingly popular, a commonly overlooked aspect, especially in the case of complexes bearing isopropyl substituents, is the conformational analysis of complexes. Isopropyl groups generate a different conformer with each 120 ° rotation (rotamer), and it has been found that each rotamer typically resides in its own potential energy well in density functional theory studies. As a result, it can be challenging to select the most appropriate structure for a theoretical study, as the adjustment of isopropyl substituents from a higher-energy rotamer to the lowest-energy rotamer usually does not occur during structure optimization. In this report, the influence of the arrangement of isopropyl substituents in pincer complexes on calculated complex structure energies as well as a case study on the mechanism of the isomerization of an iPrPCP-Fe complex is covered. It was found that as many as 324 rotamers can be generated for a single complex, as in the case of an iPrPCP-Ni formato complex, with the energy difference between the global minimum and the highest local minimum being as large as 16.5 kcalmol-1. In the isomerization of a iPrPCP-Fe complex, it was found
Exact conditions on the temperature dependence of density functionals
Burke, Kieron; Grabowski, Paul E; Pribram-Jones, Aurora
2015-01-01
Universal exact conditions guided the construction of most ground-state density functional approximations in use today. We derive the relation between the entropy and Mermin free energy density functionals for thermal density functional theory. Both the entropy and sum of kinetic and electron-electron repulsion functionals are shown to be monotonically increasing with temperature, while the Mermin functional is concave downwards. Analogous relations are found for both exchange and correlation. The importance of these conditions is illustrated in two extremes: the Hubbard dimer and the uniform gas.
Exact conditions on the temperature dependence of density functionals
Burke, K.; Smith, J. C.; Grabowski, P. E.; Pribram-Jones, A.
2016-05-01
Universal exact conditions guided the construction of most ground-state density functional approximations in use today. We derive the relation between the entropy and Mermin free energy density functionals for thermal density functional theory. Both the entropy and sum of kinetic and electron-electron repulsion functionals are shown to be monotonically increasing with temperature, while the Mermin functional is concave downwards. Analogous relations are found for both exchange and correlation. The importance of these conditions is illustrated in two extremes: the Hubbard dimer and the uniform gas.
Van Hove correlation functions for identical fermions
Macke, Wilhelm; Miesenböck, Helga M.; Hingerl, Kurt; Bachlechner, Martina E.
1989-02-01
For a quantum system of identical fermions a partition of the density-density correlation function in its ``self'' and ``distinct'' part is presented. These quantities show different properties than their classical counterparts, e.g., they violate the ``detailed balance'' and are not necessarily real. Nevertheless it can be expected that they will provide a good tool for a better description of the self-motion in many-particle systems and are therefore investigated in second-order perturbation theory of the interparticle potential.
Energy Technology Data Exchange (ETDEWEB)
Kapoor, Varun; Brics, Martins; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)
2013-07-01
Autoionizing states are inaccessible to time-dependent density functional theory (TDDFT) using known, adiabatic Kohn-Sham (KS) potentials. We determine the exact KS potential for a numerically exactly solvable model Helium atom interacting with a laser field that is populating an autoionizing state. The exact single-particle density of the population in the autoionizing state corresponds to that of the energetically lowest quasi-stationary state in the exact KS potential. We describe how this exact potential controls the decay by a barrier whose height and width allows for the density to tunnel out and decay with the same rate as in the ab initio time-dependent Schroedinger calculation. However, devising a useful exchange-correlation potential that is capable of governing such a scenario in general and in more complex systems is hopeless. As an improvement over TDDFT, time-dependent reduced density matrix functional theory has been proposed. We are able to obtain for the above described autoionization process the exact time-dependent natural orbitals (i.e., the eigenfunctions of the exact, time-dependent one-body reduced density matrix) and study the potentials that appear in the equations of motion for the natural orbitals and the structure of the two-body density matrix expanded in them.
Exact Maps in Density Functional Theory for Lattice Models
Dimitrov, Tanja; Fuks, Johanna I; Rubio, Angel
2015-01-01
In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and for the first time the exact density-to-wavefunction map that underly the Hohenberg-Kohn theorem in density functional theory. Having the explicit wavefunction-to- density map at hand, we are able to construct arbitrary observables as functionals of the ground-state density. We analyze the density-to-potential map as the distance between the fragments of a system increases and the correlation in the system grows. We observe a feature that gradually develops in the density-to-potential map as well as in the density-to-wavefunction map. This feature is inherited by arbitrary expectation values as functional of the ground-state density. We explicitly show the excited-state energies, the excited-state densities, and the correlation entropy as functionals of the ground-state density. All of them show this exact feature that sharpens as the coupling of the fragmen...
Linear-response thermal time-dependent density functional theory
Pribram-Jones, Aurora; Burke, Kieron
2015-01-01
The van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. This produces a natural method for generating new thermal exchange-correlation (XC) approximations.
Zhang, Wei-Bing; Li, Jie; Tang, Bi-Yu
2013-06-28
The structural, electronic, magnetic, and elastic properties of hexagonal nickel sulfide (NiS) have been investigated comparatively by Density Functional theory (DFT) and DFT plus correction for on-site Coulomb interaction (DFT+U), in which two different exchange correlation functionals local density approximations (LDA) and general gradient approximations (GGA) in the form of Perdew-Burke-Ernzerhof (PBE) are used. Our results indicate LDA and PBE methods predict hexagonal NiS to be a paramagnetic metal whereas LDA(PBE)+U calculations with reasonable on-site Coulomb interaction energy give the antiferromagnetic insulating state of low temperature hexagonal NiS successfully. Meanwhile, compared with LDA(PBE) results, LDA(PBE)+U methods give larger lattice parameters, crystal volume, and shear constant c44, consistent with the experimental picture during high-low temperature phase transition of hexagonal NiS, in which an increase of the shear constant c44 and lattice parameters were found in the low-temperature antiferromagnetic phase. The present DFT and DFT+U calculations provide a reasonable description for the properties of high temperature and low temperature hexagonal NiS respectively, which indicates that electronic correlation is responsible for this high-low temperature phase transition.
Spatial correlation between weed species densities and soil properties
DEFF Research Database (Denmark)
Walter, Mette; Christensen, Svend; Simmelsgaard, Svend Erik
2002-01-01
-correlated with the phosphorus content in the soil in all years. The density of Veronica spp. and Poa annua L. was negatively cross-correlated with pH in all three years. Other spatial cross-correlations that were found in this study were inconsistent over time or field site. The densities of some of the weed species were......The spatial cross-correlation between weed species densities and six soil properties within fields was analysed using cross-semivariograms. The survey was carried out in three successive years in two fields. The most consistent relationship between weed species density (numbers m−2) and soil...... spatially cross-correlated with more than one soil property. The results showed that the range of spatial dependence varied not only between fields, but also between weed species and soil properties, as well as between years. This study indicates that the weed pattern is field-specific and that the spatial...
Orbital functionals in density-matrix- and current-density-functional theory
Energy Technology Data Exchange (ETDEWEB)
Helbig, N.
2006-05-15
Density-Functional Theory (DFT), although widely used and very successful in the calculation of several observables, fails to correctly describe strongly correlated materials. In the first part of this work we, therefore, introduce reduced-densitymatrix- functional theory (RDMFT) which is one possible way to treat electron correlation beyond DFT. Within this theory the one-body reduced density matrix (1- RDM) is used as the basic variable. Our main interest is the calculation of the fundamental gap which proves very problematic within DFT. In order to calculate the fundamental gap we generalize RDMFT to fractional particle numbers M by describing the system as an ensemble of an N and an N+1 particle system (with N{<=}M{<=}N+1). For each fixed particle number, M, the total energy is minimized with respect to the natural orbitals and their occupation numbers. This leads to the total energy as a function of M. The derivative of this function with respect to the particle number has a discontinuity at integer particle number which is identical to the gap. In addition, we investigate the necessary and sufficient conditions for the 1- RDM of a system with fractional particle number to be N-representable. Numerical results are presented for alkali atoms, small molecules, and periodic systems. Another problem within DFT is the description of non-relativistic many-electron systems in the presence of magnetic fields. It requires the paramagnetic current density and the spin magnetization to be used as basic variables besides the electron density. However, electron-gas-based functionals of current-spin-density-functional Theory (CSDFT) exhibit derivative discontinuities as a function of the magnetic field whenever a new Landau level is occupied, which makes them difficult to use in practice. Since the appearance of Landau levels is, intrinsically, an orbital effect it is appealing to use orbital-dependent functionals. We have developed a CSDFT version of the optimized
A multiconfigurational hybrid density-functional theory
DEFF Research Database (Denmark)
Sharkas, Kamal; Savin, Andreas; Jensen, Hans Jørgen Aagaard
2012-01-01
We propose a multiconfigurational hybrid density-functional theory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the electron-electron interaction. This gives a straightforward extension ...
A multiconfigurational hybrid density-functional theory
DEFF Research Database (Denmark)
Sharkas, Kamal; Savin, Andreas; Jensen, Hans Jørgen Aagaard
2012-01-01
We propose a multiconfigurational hybrid density-functional theory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the electron-electron interaction. This gives a straightforward extension ...
Exact maps in density functional theory for lattice models
Dimitrov, Tanja; Appel, Heiko; Fuks, Johanna I.; Rubio, Angel
2016-08-01
In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and graphically illustrate the complete exact density-to-wavefunction map that underly the Hohenberg-Kohn theorem in density functional theory. Having the explicit wavefunction-to-density map at hand, we are able to construct arbitrary observables as functionals of the ground-state density. We analyze the density-to-potential map as the distance between the fragments of a system increases and the correlation in the system grows. We observe a feature that gradually develops in the density-to-potential map as well as in the density-to-wavefunction map. This feature is inherited by arbitrary expectation values as functional of the ground-state density. We explicitly show the excited-state energies, the excited-state densities, and the correlation entropy as functionals of the ground-state density. All of them show this exact feature that sharpens as the coupling of the fragments decreases and the correlation grows. We denominate this feature as intra-system steepening and discuss how it relates to the well-known inter-system derivative discontinuity. The inter-system derivative discontinuity is an exact concept for coupled subsystems with degenerate ground state. However, the coupling between subsystems as in charge transfer processes can lift the degeneracy. An important conclusion is that for such systems with a near-degenerate ground state, the corresponding cut along the particle number N of the exact density functionals is differentiable with a well-defined gradient near integer particle number.
Magnetic fields and density functional theory
Energy Technology Data Exchange (ETDEWEB)
Salsbury Jr., Freddie [Univ. of California, Berkeley, CA (United States)
1999-02-01
A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.
Tekarli, Sammer M; Williams, T Gavin; Cundari, Thomas R
2009-11-10
The kinetics and thermodynamics of copper-mediated nitrene insertion into C-H and H-H bonds (the former of methane) have been studied using several levels of theory: B3LYP/6-311++G(d,p), B97-1/cc-pVTZ, PBE1KCIS/cc-pVTZ, and ccCA (correlation consistent Composite Approach). The results show no significant difference among the DFT methods. All three DFT methods predict the ground state of the copper-nitrene model complex, L'Cu(NH), to be a triplet, while single reference ccCA predicts the singlet to be the ground state. The contributions to the total ccCA energy indicate that the singlet state is favored at the MP2/CBS level of theory, while electron correlation beyond this level (CCSD(T)) favors a triplet state, resulting in a close energetic balance between the two states. A multireference ccCA method is applied to the nitrene active species and supports the assignment of a singlet ground state. In general, the largest difference in the model reaction cycles between DFT and ccCA methods is for processes involving radicals and bond dissociation.
A Tryst With Density: Walter Kohn and Density Functional Theory
Indian Academy of Sciences (India)
Shobhana Narasimhan
2017-08-01
Walter Kohn transformed theoretical chemistry and solid statephysics with his development of density functional theory, forwhich he was awarded the Nobel Prize. This article tries toexplain, in simple terms, why this was an important advancein the field, and to describe precisely what it was that he (togetherwith his collaborators Pierre Hohenberg and Lu JeuSham) achieved.
Density functionals for the strong-interaction limit
Seidl, Michael; Perdew, John P.; Kurth, Stefan
2000-07-01
The strong-interaction limit of density-functional (DF) theory is simple and provides information required for an accurate resummation of DF perturbation theory. Here we derive the point-charge-plus-continuum (PC) model for that limit, and its gradient expansion. The exchange-correlation (xc) energy Exc[ρ]≡∫10dαWα[ρ] follows from the xc potential energies Wα at different interaction strengths α>=0 [but at fixed density ρ(r)]. For small α~0, the integrand Wα is obtained accurately from perturbation theory, but the perturbation expansion requires resummation for moderate and large α. For that purpose, we present density functionals for the coefficients in the asymptotic expansion Wα-->W∞+W'∞α-1/2 for α-->∞ in the PC model. WPC∞ arises from strict correlation, and W'PC∞ from zero-point vibration of the electrons around their strictly correlated distributions. The PC values for W∞ and W'∞ agree with those from a self-correlation-free meta-generalized gradient approximation, both for atoms and for atomization energies of molecules. We also (i) explain the difference between the PC cell and the exchange-correlation hole, (ii) present a density-functional measure of correlation strength, (iii) describe the electron localization and spin polarization energy in a highly stretched H2 molecule, and (iv) discuss the soft-plasmon instability of the low-density uniform electron gas.
Institute of Scientific and Technical Information of China (English)
Zhou Shi-Qi
2007-01-01
A universal theoretical approach is proposed which enables all hard sphere density functional approximations(DFAs) applicable to van der Waals fluids. The resultant DFA obtained by combining the universal theoretical approach with any hard sphere DFAs only needs as input a second-order direct correlation function (DCF) of a coexistence bulk fluid, and is applicable in both supercritical and subcritical temperature regions. The associated effective hard sphere density can be specified by a hard wall sum rule. It is indicated that the value of the effective hard sphere density so determined can be universal, i.e. can be applied to any external potentials different from the single hard wall. As an illustrating example, the universal theoretical approach is combined with a hard sphere bridge DFA to predict the density profile of a hard core attractive Yukawa model fluid influenced by diverse external fields; agreement between the present formalism's predictions and the corresponding simulation data is good or at least comparable to several previous DFT approaches. The primary advantage of the present theoretical approach combined with other hard sphere DFAs is discussed.
Energy Technology Data Exchange (ETDEWEB)
Benam, M.R., E-mail: m_benam@pnu.ac.ir [Department of Physics, Payame Noor University, P.O. BOX 19395-3697 (Iran, Islamic Republic of); Abdoshahi, N.; Majidiyan Sarmazdeh, M. [Department of Physics, Payame Noor University, P.O. BOX 19395-3697 (Iran, Islamic Republic of)
2014-08-01
In this paper the effect of pressure on the structural and electronic properties of cubic-LaAlO{sub 3} including the equilibrium lattice constant, bulk modulus, derivative of bulk modulus and band structure have been calculated by density functional theory (DFT) using GGA, LDA, and PBEsol exchange correlation potentials. It is found that the change of the lattice constant with pressure has an exponential behavior: with increasing pressure, the lattice constant decreases first sharply at low pressures, and then more slowly at high pressures. Furthermore, the lattice constant calculated by the PBEsol method and the bulk modulus calculated by LDA and PBEsol methods are closer to the available experimental values than those obtained using other exchange correlation potentials. Regarding the electronic properties, it is shown that an increase in pressure increases the band gap, the change being 0.26 eV at 34.00 GPa. The total density of state (t-DOS) calculations demonstrate that increasing pressure has a significant effect on the core and conduction band, but little effect on the valence band. The band structure calculations indicate that, in this material, the band gap changes from indirect to direct at a pressure of about 25 GPa. Also, increasing pressure produces a clear curvature in the band structure near the bottom of the conduction band, a behavior consistent with the strong pressure dependence of the transport properties.
Benam, M. R.; Abdoshahi, N.; Majidiyan Sarmazdeh, M.
2014-08-01
In this paper the effect of pressure on the structural and electronic properties of cubic-LaAlO3 including the equilibrium lattice constant, bulk modulus, derivative of bulk modulus and band structure have been calculated by density functional theory (DFT) using GGA, LDA, and PBEsol exchange correlation potentials. It is found that the change of the lattice constant with pressure has an exponential behavior: with increasing pressure, the lattice constant decreases first sharply at low pressures, and then more slowly at high pressures. Furthermore, the lattice constant calculated by the PBEsol method and the bulk modulus calculated by LDA and PBEsol methods are closer to the available experimental values than those obtained using other exchange correlation potentials. Regarding the electronic properties, it is shown that an increase in pressure increases the band gap, the change being 0.26 eV at 34.00 GPa. The total density of state (t-DOS) calculations demonstrate that increasing pressure has a significant effect on the core and conduction band, but little effect on the valence band. The band structure calculations indicate that, in this material, the band gap changes from indirect to direct at a pressure of about 25 GPa. Also, increasing pressure produces a clear curvature in the band structure near the bottom of the conduction band, a behavior consistent with the strong pressure dependence of the transport properties.
Boundary Anomalies and Correlation Functions
Huang, Kuo-Wei
2016-01-01
It was shown recently that boundary terms of conformal anomalies recover the universal contribution to the entanglement entropy and also play an important role in the boundary monotonicity theorem of odd-dimensional quantum field theories. Motivated by these results, we investigate relationships between boundary anomalies and the stress tensor correlation functions in conformal field theories. In particular, we focus on how the conformal Ward identity and the renormalization group equation are modified by boundary central charges. Renormalized stress tensors induced by boundary Weyl invariants are also discussed, with examples in spherical and cylindrical geometries.
Probability density functions of instantaneous Stokes parameters on weak scattering
Chen, Xi; Korotkova, Olga
2017-10-01
The single-point probability density functions (PDF) of the instantaneous Stokes parameters of a polarized plane-wave light field scattered from a three-dimensional, statistically stationary, weak medium with Gaussian statistics and Gaussian correlation function have been studied for the first time. Apart from the scattering geometry the PDF distributions of the scattered light have been related to the illumination's polarization state and the correlation properties of the medium.
Nucleation for Lennard-Jones Fluid by Density Functional Theory
Institute of Scientific and Technical Information of China (English)
FU Dong
2005-01-01
@@ A non-mean field density functional theory is employed to investigate the vapour-liquid nucleation. The excess Helmholtz free energy functional is formulated in terms of a local density approximation for short ranged repulsion and a density-gradient expansion for long-ranged attractions. An analytical expression for the direct correlation function of a Lennard-Jones fluid is utilized to take into account the effect of long-ranged attractions on intermolecular correlations. With the predicted bulk properties and surface tension as input, the nucleation properties including density profile, work of formation and number of particles at the reduced temperatures T* = 0.694 and 0.741 are inuestigated. The obtained number of particles in the critical nucleus agrees well with the simulation data.
Density-functional theory of thermoelectric phenomena.
Eich, F G; Di Ventra, M; Vignale, G
2014-05-16
We introduce a nonequilibrium density-functional theory of local temperature and associated local energy density that is suited for the study of thermoelectric phenomena. The theory rests on a local temperature field coupled to the energy-density operator. We identify the excess-energy density, in addition to the particle density, as the basic variable, which is reproduced by an effective noninteracting Kohn-Sham system. A novel Kohn-Sham equation emerges featuring a time-dependent and spatially varying mass which represents local temperature variations. The adiabatic contribution to the Kohn-Sham potentials is related to the entropy viewed as a functional of the particle and energy density. Dissipation can be taken into account by employing linear response theory and the thermoelectric transport coefficients of the electron gas.
Estimation of Correlation Functions by Random Decrement
DEFF Research Database (Denmark)
Asmussen, J. C.; Brincker, Rune
This paper illustrates how correlation functions can be estimated by the random decrement technique. Several different formulations of the random decrement technique, estimating the correlation functions are considered. The speed and accuracy of the different formulations of the random decrement...... and the length of the correlation functions. The accuracy of the estimates with respect to the theoretical correlation functions and the modal parameters are both investigated. The modal parameters are extracted from the correlation functions using the polyreference time domain technique....
Meson's Correlation Functions in a Nuclear Medium
Park, Chanyong
2016-01-01
We investigate meson's spectrum, decay constant and form factor in a nuclear medium through holographic two- and three-point correlation functions. To describe a nuclear medium composed of protons and neutrons, we consider a hard wall model on the thermal charged AdS geometry and show that due to the isospin interaction with a nuclear medium, there exist splittings of the meson's spectrum, decay constant and form factor relying on the isospin charge. In addition, we show that the rho-meson's form factor describing an interaction with pseudoscalar fluctuation decreases when the nuclear density increases, while the interaction with a longitudinal part of an axial vector meson increases.
Meson's correlation functions in a nuclear medium
Park, Chanyong
2016-09-01
We investigate meson's spectrum, decay constant and form factor in a nuclear medium through holographic two- and three-point correlation functions. To describe a nuclear medium composed of protons and neutrons, we consider a hard wall model on the thermal charged AdS geometry and show that due to the isospin interaction with a nuclear medium, there exist splittings of the meson's spectrum, decay constant and form factor relying on the isospin charge. In addition, we show that the ρ-meson's form factor describing an interaction with pseudoscalar fluctuation decreases when the nuclear density increases, while the interaction with a longitudinal part of an axial vector meson increases.
Indian Academy of Sciences (India)
Amit S Tiwary; Asok K Mukherjee
2013-07-01
The inductive effect of methyl group has been quantified by expressing highest occupied molecular orbital (HOMO) and HOMO-1 energies of indole and a series of methylated indoles using a combination of graph theory (GT) and the Coulson-Longuett-Higgins perturbation method. By correlating these expressions with the corresponding Kohn-Sham orbital energies of the indoles obtained by density functional theory (DFT) calculation at the B3LYP/6-31++G(d,p) and M06-2X/6-31++G(d,p) levels of theory, the inductive effect parameter ℎ has been estimated; the Coulomb integral of -conjugated carbon atom also comes out from the analysis. A correlation of the GT results with the HOMO and HOMO-1 energies obtained by the HF/STO-3G method yield almost the same values of ℎ and . Finally, when these estimated ℎ and are used to calculate the vertical ionization potentials of the methylated indoles in the series, an excellent correlation with experimental charge transfer transition energies of their molecular complexes with tetracyanoethylene is obtained which complies with Mulliken’s theory of charge transfer.
Relativistic density functional for nuclear structure
2016-01-01
This book aims to provide a detailed introduction to the state-of-the-art covariant density functional theory, which follows the Lorentz invariance from the very beginning and is able to describe nuclear many-body quantum systems microscopically and self-consistently. Covariant density functional theory was introduced in nuclear physics in the 1970s and has since been developed and used to describe the diversity of nuclear properties and phenomena with great success. In order to provide an advanced and updated textbook of covariant density functional theory for graduate students and nuclear physics researchers, this book summarizes the enormous amount of material that has accumulated in the field of covariant density functional theory over the last few decades as well as the latest developments in this area. Moreover, the book contains enough details for readers to follow the formalism and theoretical results, and provides exhaustive references to explore the research literature.
Nuclear Energy Density Functional for KIDS
Gil, Hana; Hyun, Chang Ho; Park, Tae-Sun; Oh, Yongseok
2016-01-01
The density functional theory (DFT) is based on the existence and uniqueness of a universal functional $E[\\rho]$, which determines the dependence of the total energy on single-particle density distributions. However, DFT says nothing about the form of the functional. Our strategy is to first look at what we know, from independent considerations, about the analytical density dependence of the energy of nuclear matter and then, for practical applications, to obtain an appropriate density-dependent effective interaction by reverse engineering. In a previous work on homogeneous matter, we identified the most essential terms to include in our "KIDS" functional, named after the early-stage participating institutes. We now present first results for finite nuclei, namely the energies and radii of $^{16,28}$O, $^{40,60}$Ca.
Energy Technology Data Exchange (ETDEWEB)
Goo, Hyun Woo; Yang, Dong Hyun; Seo, Joon Beom; Chae, Eun Jin; Lee, Jeongjin [University of Ulsan College of Medicine, Department of Radiology and Research Institute of Radiology, Asan Medical Center, Songpa-gu, Seoul (Korea); Hong, Soo-Jong; Yu, Jinho; Kim, Byoung-Ju [University of Ulsan College of Medicine, Department of Pediatrics, Asan Medical Center, Seoul (Korea); Krauss, Bernhard [Siemens Medical Solutions AG-Computed Tomography, Forchheim (Germany)
2010-09-15
Xenon ventilation CT using dual-source and dual-energy technique is a recently introduced, promising functional lung imaging method. To expand its clinical applications evidence of additional diagnostic value of xenon ventilation CT over conventional chest CT is required. To evaluate the usefulness of xenon ventilation CT using dual-source and dual-energy technique in children with bronchiolitis obliterans (BO). Seventeen children (age 7-18 years; 11 boys) with BO underwent xenon ventilation CT using dual-source and dual-energy technique. Xenon and CT density values were measured in normal and hyperlucent lung regions on CT and were compared between the two regions. Volumes of hyperlucent regions and ventilation defects were calculated with thresholds determined by visual and histogram-based analysis. Indexed volumes of hyperlucent lung regions and ventilation defects were correlated with pulmonary function test results. Effective doses of xenon CT were calculated. Xenon (14.6 {+-} 6.4 HU vs 26.1 {+-} 6.5 HU; P < 0.001) and CT density (-892.8 {+-} 25.4 HU vs -812.3 {+-} 38.7 HU; P < 0.001) values were significantly lower in hyperlucent regions than in normal lung regions. Xenon and CT density values showed significant positive correlation for the entire lung in 16 children ({gamma} = 0.55 {+-} 0.17, P < 0.001 or =0.017) and for hyperlucent regions in 13 children ({gamma} = 0.44 {+-} 0.16, P < 0.001 or =0.001-0.019). Indexed volumes and volume percentages of hyperlucent lung regions and ventilation defects showed strong negative correlations with forced expiratory volume [FEV1, ({gamma} = -0.64-0.85, P {<=} 0.006)], FEV1/forced vital capacity [FVC, ({gamma} = -0.63-0.84, P {<=} 0.008)], and forced midexpiratory flow rate [FEF{sub 25-75}, ({gamma} = -0.68-0.88, P {<=} 0.002). Volume percentages of xenon ventilation defects (35.0 {+-} 16.4%)] were not significantly different from those of hyperlucent lung regions (38.2 {+-} 18.6%). However, mismatches between the
Density Functional Theory and Materials Modeling at Atomistic Length Scales
Directory of Open Access Journals (Sweden)
Swapan K. Ghosh
2002-04-01
Full Text Available Abstract: We discuss the basic concepts of density functional theory (DFT as applied to materials modeling in the microscopic, mesoscopic and macroscopic length scales. The picture that emerges is that of a single unified framework for the study of both quantum and classical systems. While for quantum DFT, the central equation is a one-particle Schrodinger-like Kohn-Sham equation, the classical DFT consists of Boltzmann type distributions, both corresponding to a system of noninteracting particles in the field of a density-dependent effective potential, the exact functional form of which is unknown. One therefore approximates the exchange-correlation potential for quantum systems and the excess free energy density functional or the direct correlation functions for classical systems. Illustrative applications of quantum DFT to microscopic modeling of molecular interaction and that of classical DFT to a mesoscopic modeling of soft condensed matter systems are highlighted.
Schuetrumpf, B.; Nazarewicz, W.; Reinhard, P.-G.
2017-08-01
Background: The central depression of nucleonic density, i.e., a reduction of density in the nuclear interior, has been attributed to many factors. For instance, bubble structures in superheavy nuclei are believed to be due to the electrostatic repulsion. In light nuclei, the mechanism behind the density reduction in the interior has been discussed in terms of shell effects associated with occupations of s orbits. Purpose: The main objective of this work is to reveal mechanisms behind the formation of central depression in nucleonic densities in light and heavy nuclei. To this end, we introduce several measures of the internal nucleonic density. Through the statistical analysis, we study the information content of these measures with respect to nuclear matter properties. Method: We apply nuclear density functional theory with Skyrme functionals. Using the statistical tools of linear least square regression, we inspect correlations between various measures of central depression and model parameters, including nuclear matter properties. We study bivariate correlations with selected quantities as well as multiple correlations with groups of parameters. Detailed correlation analysis is carried out for 34Si for which a bubble structure has been reported recently, 48Ca, and N =82 , 126, and 184 isotonic chains. Results: We show that the central depression in medium-mass nuclei is very sensitive to shell effects, whereas for superheavy systems it is firmly driven by the electrostatic repulsion. An appreciable semibubble structure in proton density is predicted for 294Og, which is currently the heaviest nucleus known experimentally. Conclusion: Our correlation analysis reveals that the central density indicators in nuclei below 208Pb carry little information on parameters of nuclear matter; they are predominantly driven by shell structure. On the other hand, in the superheavy nuclei there exists a clear relationship between the central nucleonic density and symmetry energy.
Gritsenko, Oleg V; Baerends, Evert Jan
2009-06-14
Time-dependent density functional (response) theory (TDDF(R)T) is applied almost exclusively in its adiabatic approximation (ATDDFT), which is restricted to predominantly single electronic excitations and neglects additional roots of the TDDFT eigenvalue problem stemming from the interaction between single and double excitations. We incorporate the effect of the latter interaction into a non-adiabatic frequency-dependent and spatially non-local Hartree-exchange-correlation (Hxc) kernel fCEDAHxc (r1, r2, omega), the explicit analytical expression of which is derived for interacting single and double excitations well separated from the other excitations, within the common energy denominator approximation (CEDA) for the Kohn-Sham (KS) and interacting density response functions, chis and chi, respectively. The kernel fCEDAHxc (r1, r2, omega) obtained from the direct analytical inverse of chiCEDAs and chiCEDA is a sum of the delta-function and non-local orbital-dependent spatial terms with frequency-dependent factors, with which fCEDAHxc acquires a modulated quadratic dependence on omega. The effective incorporation in fCEDAHxc of the complete manifold of excited states (through the delta function term) represents an extension of the kernel reported by Maitra, Zhang, Cave, and Burke [J. Chem. Phys., 2004, 120, 5932]. In the TDDFT eigenvalue equations considered in the diagonal approximation, fCEDAHxc generates two excitation energies omegaq and omegaq+1, which both correspond to the same single KS excitation omegasq, thus producing the effect of the single-double excitation interaction.
Bao, Junwei Lucas; Odoh, Samuel O; Gagliardi, Laura; Truhlar, Donald G
2017-02-14
We study the performance of multiconfiguration pair-density functional theory (MC-PDFT) and multireference perturbation theory for the computation of the bond dissociation energies in 12 transition-metal-containing diatomic molecules and three small transition-metal-containing polyatomic molecules and in two transition-metal dimers. The first step is a multiconfiguration self-consistent-field calculation, for which two choices must be made: (i) the active space and (ii) its partition into subspaces, if the generalized active space formulation is used. In the present work, the active space is chosen systematically by using three correlated-participating-orbitals (CPO) schemes, and the partition is chosen by using the separated-pair (SP) approximation. Our calculations show that MC-PDFT generally has similar accuracy to CASPT2, and the active-space dependence of MC-PDFT is not very great for transition-metal-ligand bond dissociation energies. We also find that the SP approximation works very well, and in particular SP with the fully translated BLYP functional SP-ftBLYP is more accurate than CASPT2. SP greatly reduces the number of configuration state functions relative to CASSCF. For the cases of FeO and NiO with extended-CPO active space, for which complete active space calculations are unaffordable, SP calculations are not only affordable but also of satisfactory accuracy. All of the MC-PDFT results are significantly better than the corresponding results with broken-symmetry spin-unrestricted Kohn-Sham density functional theory. Finally we test a perturbation theory method based on the SP reference and find that it performs slightly worse than CASPT2 calculations, and for most cases of the nominal-CPO active space, the approximate SP perturbation theory calculations are less accurate than the much less expensive SP-PDFT calculations.
A molecular density functional theory to study solvation in water
Jeanmairet, Guillaume
2014-01-01
A classical density functional theory is applied to study solvation of solutes in water. An approx- imate form of the excess functional is proposed for water. This functional requires the knowledge of pure solvent direct correlation functions. Those functions can be computed by using molecular simulations such as molecular dynamic or Monte Carlo. It is also possible to use functions that have been determined experimentally. The functional minimization gives access to the solvation free energy and to the equilibrium solvent density. Some correction to the functional are also proposed to get the proper tetrahedral order of solvent molecules around a charged solute and to reproduce the correct long range hydrophobic behavior of big apolar solutes. To proceed the numerical minimization of the functional, the theory has been discretized on two tridimensional grids, one for the space coordinates, the other for the angular coordinates, in a functional minimization code written in modern Fortran, mdft. This program i...
Energy Density Functional for Nuclei and Neutron Stars
Energy Technology Data Exchange (ETDEWEB)
Erler, J. [UTK/ORNL/German Cancer Research Center-Heidelberg; Horowitz, C. J. [UTK/ORNL/Indiana University; Nazarewicz, Witold [UTK/ORNL/University of Warsaw; Rafalski, M. [UTK/ORNL; Reinhard, P.-G. [Universitat Erlangen, Germany
2013-01-01
Background: Recent observational data on neutron star masses and radii provide stringent constraints on the equation of state of neutron rich matter [ Annu. Rev. Nucl. Part. Sci. 62 485 (2012)]. Purpose: We aim to develop a nuclear energy density functional that can be simultaneously applied to finite nuclei and neutron stars. Methods: We use the self-consistent nuclear density functional theory (DFT) with Skyrme energy density functionals and covariance analysis to assess correlations between observables for finite nuclei and neutron stars. In a first step two energy functionals a high density energy functional giving reasonable neutron properties, and a low density functional fitted to nuclear properties are matched. In a second step, we optimize a new functional using exactly the same protocol as in earlier studies pertaining to nuclei but now including neutron star data. This allows direct comparisons of performance of the new functional relative to the standard one. Results: The new functional TOV-min yields results for nuclear bulk properties (energy, rms radius, diffraction radius, and surface thickness) that are of the same quality as those obtained with the established Skyrme functionals, including SV-min. When comparing SV-min and TOV-min, isoscalar nuclear matter indicators vary slightly while isovector properties are changed considerably. We discuss neutron skins, dipole polarizability, separation energies of the heaviest elements, and proton and neutron drip lines. We confirm a correlation between the neutron skin of 208Pb and the neutron star radius. Conclusions: We demonstrate that standard energy density functionals optimized to nuclear data do not carry information on the expected maximum neutron star mass, and that predictions can only be made within an extremely broad uncertainty band. For atomic nuclei, the new functional TOV-min performs at least as well as the standard nuclear functionals, but it also reproduces expected neutron star data
Correlation functions in stochastic inflation
Energy Technology Data Exchange (ETDEWEB)
Vennin, Vincent [University of Portsmouth, Institute of Cosmology and Gravitation, Portsmouth (United Kingdom); Starobinsky, Alexei A. [L.D. Landau Institute for Theoretical Physics RAS, Moscow (Russian Federation); Utrecht University, Department of Physics and Astronomy, Institute for Theoretical Physics, Utrecht (Netherlands)
2015-09-15
Combining the stochastic and δ N formalisms, we derive non-perturbative analytical expressions for all correlation functions of scalar perturbations in single-field, slow-roll inflation. The standard, classical formulas are recovered as saddle-point limits of the full results. This yields a classicality criterion that shows that stochastic effects are small only if the potential is sub-Planckian and not too flat. The saddle-point approximation also provides an expansion scheme for calculating stochastic corrections to observable quantities perturbatively in this regime. In the opposite regime, we show that a strong suppression in the power spectrum is generically obtained, and we comment on the physical implications of this effect. (orig.)
Density Functional Theory Embedding for Correlated Wavefunctions
2014-01-01
Van Barel, J. Comput. Appl. Math. 213, 268 (2008). [52] M. Gu and S. C. Eisenstat, SIAM J. Matrix Anal. Appl. 16, 172 (1995). [53] M. Schutz, R. Lindh ...Analysis and Methods , (Dover Pub- lishing, 2003). 93 [56] H.-J. Werner, P. J. Knowles, R. Lindh , F. R. Manby, M. Schütz et al. Molpro, ver- sion...43] T. M. Henderson, J. Chem. Phys. 125, 014105 (2006). [44] B. Swerts, L. F. Chibotaru, R. Lindh , L. Seijo, Z. Barandiaran, S. Clima, K. Pier- loot
Double-hybrid density-functional theory made rigorous
Sharkas, Kamal; Savin, Andreas
2010-01-01
We provide a rigorous derivation of a class of double-hybrid approximations, combining Hartree-Fock exchange and second-order Moller-Plesset correlation with a semilocal exchange-correlation density functional. These double-hybrid approximations contain only one empirical parameter and use a density-scaled correlation energy functional. Neglecting density scaling leads to an one-parameter version of the standard double-hybrid approximations. We assess the performance of these double-hybrid schemes on representative test sets of atomization energies and reaction barrier heights, and we compare to other hybrid approximations, including range-separated hybrids. Our best one-parameter double-hybrid approximation, called 1DH-BLYP, roughly reproduces the two parameters of the standard B2-PLYP or B2GP-PLYP double-hybrid approximations, which shows that these methods are not only empirically close to an optimum for general chemical applications but are also theoretically supported.
Energy Technology Data Exchange (ETDEWEB)
Hedegård, Erik Donovan, E-mail: erik.hedegard@phys.chem.ethz.ch; Knecht, Stefan; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch [Laboratorium für Physikalische Chemie, ETH Zürich, Vladimir-Prelog-Weg 2, CH-8093 Zürich (Switzerland); Kielberg, Jesper Skau; Jensen, Hans Jørgen Aagaard, E-mail: hjj@sdu.dk [Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, Odense (Denmark)
2015-06-14
We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electron-correlation effects in multiconfigurational electronic structure problems.
Hedegård, Erik Donovan; Kielberg, Jesper Skau; Jensen, Hans Jørgen Aagaard; Reiher, Markus
2015-01-01
We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electron-correlation effects in multiconfigurational electronic structure problems.
The correlations of ions density with geomagnetic activity and solar dynamic pressure in cusp region
Institute of Scientific and Technical Information of China (English)
GUO JianGuang; SHI JianKui; ZHANG TieLong; LIU ZhenXing; A. FAZAKERLEY; H. R(E)ME; Ⅰ. DANDOURAS; E. LUCEK
2007-01-01
A statistical study of the properties of ions (O+, He+ and H+) measured by the Cluster-Ⅱ in cusp region as a function of the solar wind dynamic pressure and geomagnetic index Kp respectively was made during the summer and fall of 2001 -2003. The main results are that: (1) O+ ion density responds in a significant way to geomagnetic index Kp, and He+ ion density is not correlated with geomagnetic index Kp,both of them have a significant positive correlation with solar wind dynamic pressure; (2) H+ ion density is also observed to increase with solar wind dynamic pressure, and not correlated with geomagnetic index Kp.
Density-Matrix Propagation Driven by Semiclassical Correlation
Elliott, Peter
2016-01-01
Methods based on propagation of the one-body reduced density-matrix hold much promise for the simulation of correlated many-electron dynamics far from equilibrium, but difficulties with finding good approximations for the interaction term in its equation of motion have so far impeded their application. These difficulties include the violation of fundamental physical principles such as energy conservation, positivity conditions on the density, or unchanging natural orbital occupation numbers. We review some of the recent efforts to confront these problems, and explore a semiclassical approximation for electron correlation coupled to time-dependent Hartree-Fock propagation. We find that this approach captures changing occupation numbers, and excitations to doubly-excited states, improving over TDHF and adiabatic approximations in density-matrix propagation. However, it does not guarantee $N$-representability of the density-matrix, consequently resulting sometimes in violation of positivity conditions, even thou...
Whitenack, Daniel L; Wasserman, Adam
2012-04-28
Aspects of density functional resonance theory (DFRT) [D. L. Whitenack and A. Wasserman, Phys. Rev. Lett. 107, 163002 (2011)], a recently developed complex-scaled version of ground-state density functional theory (DFT), are studied in detail. The asymptotic behavior of the complex density function is related to the complex resonance energy and system's threshold energy, and the function's local oscillatory behavior is connected with preferential directions of electron decay. Practical considerations for implementation of the theory are addressed including sensitivity to the complex-scaling parameter, θ. In Kohn-Sham DFRT, it is shown that almost all θ-dependence in the calculated energies and lifetimes can be extinguished via use of a proper basis set or fine grid. The highest occupied Kohn-Sham orbital energy and lifetime are related to physical affinity and width, and the threshold energy of the Kohn-Sham system is shown to be equal to the threshold energy of the interacting system shifted by a well-defined functional. Finally, various complex-scaling conditions are derived which relate the functionals of ground-state DFT to those of DFRT via proper scaling factors and a non-Hermitian coupling-constant system.
Tran, Fabien; Blaha, Peter
2017-05-04
Recently, exchange-correlation potentials in density functional theory were developed with the goal of providing improved band gaps in solids. Among them, the semilocal potentials are particularly interesting for large systems since they lead to calculations that are much faster than with hybrid functionals or methods like GW. We present an exhaustive comparison of semilocal exchange-correlation potentials for band gap calculations on a large test set of solids, and particular attention is paid to the potential HLE16 proposed by Verma and Truhlar. It is shown that the most accurate potential is the modified Becke-Johnson potential, which, most noticeably, is much more accurate than all other semilocal potentials for strongly correlated systems. This can be attributed to its additional dependence on the kinetic energy density. It is also shown that the modified Becke-Johnson potential is at least as accurate as the hybrid functionals and more reliable for solids with large band gaps.
Functional responses modified by predator density
Kratina, P.; Vos, M.; Bateman, A.W.; Anholt, B.R.
2009-01-01
Realistic functional responses are required for accurate model predictions at the community level. However, controversy remains regarding which types of dependencies need to be included in functional response models. Several studies have shown an effect of very high predator densities on per capita
Particle conservation in dynamical density functional theory.
de Las Heras, Daniel; Brader, Joseph M; Fortini, Andrea; Schmidt, Matthias
2016-06-22
We present the exact adiabatic theory for the dynamics of the inhomogeneous density distribution of a classical fluid. Erroneous particle number fluctuations of dynamical density functional theory are absent, both for canonical and grand canonical initial conditions. We obtain the canonical free energy functional, which yields the adiabatic interparticle forces of overdamped Brownian motion. Using an exact and one of the most advanced approximate hard core free energy functionals, we obtain excellent agreement with simulations. The theory applies to finite systems in and out of equilibrium.
Versatile Density Functionals for Computational Surface Science
DEFF Research Database (Denmark)
Wellendorff, Jess
Density functional theory (DFT) emerged almost 50 years ago. Since then DFT has established itself as the central electronic structure methodology for simulating atomicscale systems from a few atoms to a few hundred atoms. This success of DFT is due to a very favorable accuracy-to-computational c......Density functional theory (DFT) emerged almost 50 years ago. Since then DFT has established itself as the central electronic structure methodology for simulating atomicscale systems from a few atoms to a few hundred atoms. This success of DFT is due to a very favorable accuracy...... resampling techniques, thereby systematically avoiding problems with overfitting. The first ever density functional presenting both reliable accuracy and convincing error estimation is generated. The methodology is general enough to be applied to more complex functional forms with higher-dimensional fitting...
Prosenc, Marc Heinrich; Reddmann, Hauke; Amberger, Hanns-Dieter
2012-02-15
Previous empirical assignments of the normal modes of Ru(η(5)-C(5)H(5))(2) were checked against the results of a calculation applying density functional theory (DFT). After some reassignments, following those recently suggested for Fe(η(5)-C(5)H(5))(2) (after theoretical model calculations), a satisfactory agreement was observed. Recently communicated polarized Raman spectra of an oriented Ru(η(5)-C(5)Me(5))(2) single crystal were used here for the identification of the irreducible representations of a number of Raman active normal modes (assuming molecular D(5h) symmetry) which agree well with the results of the DFT calculation. The energies of IR active fundamental vibrations, extracted from recently communicated FIR/MIR spectra (pellets), were correlated with comparable energies of IR allowed irreducible representations of the DFT calculation and assigned. Both the skeletal and the intra-ligand normal modes could be correlated with the idealized standard motions (ν(i)s) of the model sandwich complex Ru(C(5)C(5))(2), and previous assignments had to be revised. Neglecting the νCH vibrations (which are off by ca. 50cm(-1)) an r.m.s. deviation of 9.8cm(-1) (for 47 assignments) of the remaining normal modes could be achieved.
Institute of Scientific and Technical Information of China (English)
周世琦
2002-01-01
In this Letter, we truncate the functional expansion of the non-uniform first-order direct correlation function (DCF) around the bulk density at the lowest order. But the truncation is performed formally and exactly by making use of functional counterpart of the Lagrangian theorem of differential calculus. Consequently the expansion coefficient, i.e. the uniform second-order DCF, is replaced by its non-uniform counterpart whose density argument is an appropriate mixture of calculated density distribution and the bulk density with a mixing parameter determined by a hard-wall sum rule. The non-uniform second-order DCF is then approximated by the uniform second-order DCF with an appropriate weighted density as its density argument. The present formally exact truncated functional expansion predicts the density distribution in good agreement with simulation data for hard sphere and Lennard-Jones fluid exerted by an external field.
Density functional for ternary non-additive hard sphere mixtures.
Schmidt, Matthias
2011-10-19
Based on fundamental measure theory, a Helmholtz free energy density functional for three-component mixtures of hard spheres with general, non-additive interaction distances is constructed. The functional constitutes a generalization of the previously given theory for binary non-additive mixtures. The diagrammatic structure of the spatial integrals in both functionals is of star-like (or tree-like) topology. The ternary diagrams possess a higher degree of complexity than the binary diagrams. Results for partial pair correlation functions, obtained via the Ornstein-Zernike route from the second functional derivatives of the excess free energy functional, agree well with Monte Carlo simulation data. © 2011 IOP Publishing Ltd
Orbital-Free Density Functional Theory for Molecular Structure Calculations
Institute of Scientific and Technical Information of China (English)
Huajie Chen; Aihui Zhou
2008-01-01
We give here an overview of the orbital-free density functional theory that is used for modeling atoms and molecules. We review typical approximations to the kinetic energy, exchange-correlation corrections to the kinetic and Hartree energies, and constructions of the pseudopotentials. We discuss numerical discretizations for the orbital-free methods and include several numerical results for illustrations.
Exact ensemble density-functional theory for excited states
Yang, Zeng-hui; Pribram-Jones, Aurora; Burke, Kieron; Needs, Richard J; Ullrich, Carsten A
2014-01-01
We construct exact Kohn-Sham potentials for the ensemble density-functional theory (EDFT) of excited states from the ground and excited states of helium. The exchange-correlation potential is compared with current approximations, which miss prominent features. The ensemble derivative discontinuity is tested, and the virial theorem is proven and illustrated.
Density functional theory and multiscale materials modeling
Indian Academy of Sciences (India)
Swapan K Ghosh
2003-01-01
One of the vital ingredients in the theoretical tools useful in materials modeling at all the length scales of interest is the concept of density. In the microscopic length scale, it is the electron density that has played a major role in providing a deeper understanding of chemical binding in atoms, molecules and solids. In the intermediate mesoscopic length scale, an appropriate picture of the equilibrium and dynamical processes has been obtained through the single particle number density of the constituent atoms or molecules. A wide class of problems involving nanomaterials, interfacial science and soft condensed matter has been addressed using the density based theoretical formalism as well as atomistic simulation in this regime. In the macroscopic length scale, however, matter is usually treated as a continuous medium and a description using local mass density, energy density and other related density functions has been found to be quite appropriate. A unique single unified theoretical framework that emerges through the density concept at these diverse length scales and is applicable to both quantum and classical systems is the so called density functional theory (DFT) which essentially provides a vehicle to project the many-particle picture to a single particle one. Thus, the central equation for quantum DFT is a one-particle Schrödinger-like Kohn–Sham equation, while the same for classical DFT consists of Boltzmann type distributions, both corresponding to a system of noninteracting particles in the field of a density-dependent effective potential. Selected illustrative applications of quantum DFT to microscopic modeling of intermolecular interaction and that of classical DFT to a mesoscopic modeling of soft condensed matter systems are presented.
Noncovalent Interactions in Density-Functional Theory
DiLabio, Gino A
2014-01-01
Non-covalent interactions are essential in the description of soft matter, including materials of technological importance and biological molecules. In density-functional theory, common approaches fail to describe dispersion forces, an essential component in noncovalent binding interactions. In the last decade, great progress has been made in the development of accurate and computationally-efficient methods to describe noncovalently bound systems within the framework of density-functional theory. In this review, we give an account of the field from a chemical and didactic perspective, describing different approaches to the calculation of dispersion energies and comparing their accuracy, complexity, popularity, and general availability. This review should be useful to the newcomer who wants to learn more about noncovalent interactions and the different methods available at present to describe them using density-functional theory.
Geological correlations with the interior density structure of Venus
Herrick, Robert R.; Phillips, Roger J.
1992-01-01
The paper develops a geophysical model for Venus that allows separation of topography supported by shallow density anomalies, e.g., crustal thickening, from that interpreted to be caused by mantle convection, and produces estimates of the planforms of lithospheric density anomalies and the mantle convection pattern. The topography caused by these two planforms is compared to several global data sets compiled from analysis of Magellan data. The mantle convection pattern agrees qualitatively with numerical simulations by Bercovici et al. (1989) and shows isolated upwellings amidst a network of downwellings. Crustal thickening does not exhibit a similar pattern. Impact crater density is nearly uniform and does not correlate with either crustal thickening or the mantle convection patterns. Large volcanic structures exhibit a good but imperfect correlation with mantle upwellings. Coronae locations are anticorrelated with large upwellings and large downwellings. A scenario is proposed for global tectonics on Venus and its relationship to mantle convection.
Basis convergence of range-separated density-functional theory.
Franck, Odile; Mussard, Bastien; Luppi, Eleonora; Toulouse, Julien
2015-02-21
Range-separated density-functional theory (DFT) is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with cardinal number X of the Dunning basis sets cc - p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.
Molecular Density Functional Theory of Water
Jeanmairet, Guillaume; Vuilleumier, Rodolphe; Borgis, Daniel; 10.1021/jz301956b
2013-01-01
Three dimensional implementations of liquid state theories offer an efficient alternative to computer simulations for the atomic-level description of aqueous solutions in complex environments. In this context, we present a (classical) molecular density functional theory (MDFT) of water that is derived from first principles and is based on two classical density fields, a scalar one, the particle density, and a vectorial one, the multipolar polarization density. Its implementation requires as input the partial charge distribution of a water molecule and three measurable bulk properties, namely the structure factor and the k-dependent longitudinal and transverse dielectric constants. It has to be complemented by a solute-solvent three-body term that reinforces tetrahedral order at short range. The approach is shown to provide the correct three-dimensional microscopic solvation profile around various molecular solutes, possibly possessing H-bonding sites, at a computer cost two-three orders of magnitude lower tha...
Density functional theory studies of etoricoxib
Sachdeva, Ritika; Kaur, Prabhjot; Singh, V. P.; Saini, G. S. S.
2016-05-01
Etoricoxib is a COX-2 selective inhibitor drug with molecular formula C18H15ClN2O2S. It is primarily used for the treatment of arthritis(rheumatoid, psoriatic, osteoarthritis), ankylosing spondylitis, gout and chronic low back pain. Theoretical studies of the molecule including geometry optimization and vibrational frequency calculations were carried out with the help of density functional theory calculations using 6-311++ g (d, p) basis set and B3LYP functional.
Energy Technology Data Exchange (ETDEWEB)
Yao, Yongxin [Iowa State Univ., Ames, IA (United States)
2009-01-01
also plays an important role, as it may directly track the movement of every atom. Simulation time is a major limit for molecular dynamics, not only because of “slow” computer speed, but also because of the accumulation error in the numerical treatment of the motion equations. There is also a great concern about the reliability of the emperical potentials if using classical molecular dynamics. Ab initio methods based on density functional theory(DFT) do not have this problem, however, it suffers from small simulation cells and is more demanding computationally. When crystal phase is involved, size effect of the simulation cell is more pronounced since long-range elastic energy would be established. Simulation methods which are more efficient in computation but yet have similar reliability as the ab initio methods, like tight-binding method, are highly desirable. While the complexity of metallic glasses comes from the atomistic level, there is also a large field which deals with the complexity from electronic level. The only “ab initio” method applicable to solid state systems is density functional theory with local density approximation( LDA) or generalized gradient approximation(GGA) for the exchange-correlation energy. It is very successful for simple sp element, where it reaches an high accuracy for determining the surface reconstruction. However, there is a large class of materials with strong electron correlation, where DFT based on LDA or GGA fails in a fundamental way. An “ab initio” method which can generally apply to correlated materials, as LDA for simple sp element, is still to be developed. The thesis is prepared to address some of the above problems.
Density Functional Simulation of a Breaking Nanowire
DEFF Research Database (Denmark)
Nakamura, A.; Brandbyge, Mads; Hansen, Lars Bruno
1999-01-01
We study the deformation and breaking of an atomic-sized sodium wire using density functional simulations. The wire deforms through sudden atomic rearrangements and smoother atomic displacements. The conductance of the wire exhibits plateaus at integer values in units of 2e(2)/h corresponding...
Density functional and neural network analysis
DEFF Research Database (Denmark)
Jalkanen, K. J.; Bohr, Henrik
1997-01-01
Density functional theory (DFT) calculations have been carried out for hydrated L-alanine, L-alanyl-L-alanine and N-acetyl L-alanine N'-methylamide and examined with respect to the effect of water on the structure, the vibrational frequencies, vibrational absorption (VA) and vibrational circular...
Density functional theory with quantum nuclei
Requist, Ryan
2016-01-01
It is proved that the ground state energy of an electron-nuclear system is a variational functional of the conditional electronic density n_R(r), the nuclear wavefunction \\chi(R) and the quantum geometric tensor of the conditional electronic wavefunction $T_{\\mu\
Current Developments in Nuclear Density Functional Methods
Dobaczewski, J
2010-01-01
Density functional theory (DFT) became a universal approach to compute ground-state and excited configurations of many-electron systems held together by an external one-body potential in condensed-matter, atomic, and molecular physics. At present, the DFT strategy is also intensely studied and applied in the area of nuclear structure. The nuclear DFT, a natural extension of the self-consistent mean-field theory, is a tool of choice for computations of ground-state properties and low-lying excitations of medium-mass and heavy nuclei. Over the past thirty-odd years, a lot of experience was accumulated in implementing, adjusting, and using the density-functional methods in nuclei. This research direction is still extremely actively pursued. In particular, current developments concentrate on (i) attempts to improve the performance and precision delivered by the nuclear density-functional methods, (ii) derivations of density functionals from first principles rooted in the low-energy chromodynamics and effective th...
Density functional theory: Fixing Jacob's ladder
Car, Roberto
2016-09-01
Density functional theory calculations can be carried out with different levels of accuracy, forming a hierarchy that is often represented by the rungs of a ladder. Now a new method has been developed that significantly improves the accuracy of the 'third rung' when calculating the properties of diversely bonded systems.
Incidence of histological prostatitis and its correlation with PSA density
Directory of Open Access Journals (Sweden)
Affonso Celso Piovesan
2009-11-01
Full Text Available OBJECTIVE: The aim of this study was to determine the incidence of asymptomatic, histologically proven prostatitis in men with symptoms of benign prostate hyperplasia and to observe the correlation between asymptomatic prostatitis and prostate specific antigen (PSA density. INTRODUCTION: The incidence of type IV prostatitis is unknown. There is a tendency to correlate the presence of inflammatory prostatitis with an elevation of PSA. MATERIALS AND METHODS: From August 2000 to January 2006, 183 patients who underwent surgical treatment for benign prostate hyperplasia as a result of obstructive or irritative symptoms were prospectively studied. In accordance with the histology findings, these patients were divided into two groups: group I included patients with the presence of histological prostatitis and group II included patients with the absence of histological prostatitis. The mean PSA densities were compared. RESULTS: Histological evidence of prostatitis was observed in 145 patients. In this group, the mean PSA density was 0.136 ± 0.095. In 38 cases, there was no evidence of inflammation upon histological examination of the surgical samples. In these 38 cases, the mean PSA density was 0.126 ± 0.129. No statistically significant differences were detected between the two groups; the p-value is 0.124. CONCLUSION: Abnormal PSA density should not be attributed to the inflammatory prostatitis process.
Meson's correlation functions in a nuclear medium
Directory of Open Access Journals (Sweden)
Chanyong Park
2016-09-01
Full Text Available We investigate meson's spectrum, decay constant and form factor in a nuclear medium through holographic two- and three-point correlation functions. To describe a nuclear medium composed of protons and neutrons, we consider a hard wall model on the thermal charged AdS geometry and show that due to the isospin interaction with a nuclear medium, there exist splittings of the meson's spectrum, decay constant and form factor relying on the isospin charge. In addition, we show that the ρ-meson's form factor describing an interaction with pseudoscalar fluctuation decreases when the nuclear density increases, while the interaction with a longitudinal part of an axial vector meson increases.
Ecological Correlates of Family Functioning.
Meyers, Steven A.; Varkey, Soji; Aguirre, Angela M.
2002-01-01
Explores how parents' psychological functioning, social relationships, and demographic characteristics relate to family functioning with a sample of 197 participants. Significant associations between predictor variables and family functioning were found as rated by mothers, caseworkers, and coders of family interaction tasks. (JDM)
A Probability Density Function for Neutrino Masses and Mixings
Fortin, Jean-François; Marleau, Luc
2016-01-01
The anarchy principle leading to the see-saw ensemble is studied analytically with the usual tools of random matrix theory. The probability density function for the see-saw ensemble of $N\\times N$ matrices is obtained in terms of a multidimensional integral. This integral involves all light neutrino masses, leading to a complicated probability density function. It is shown that the probability density function for the neutrino mixing angles and phases is the appropriate Haar measure. The decoupling of the light neutrino masses and neutrino mixings implies no correlation between the neutrino mass eigenstates and the neutrino mixing matrix, in contradiction with observations but in agreement with some of the claims found in the literature.
Probability density function for neutrino masses and mixings
Fortin, Jean-François; Giasson, Nicolas; Marleau, Luc
2016-12-01
The anarchy principle leading to the seesaw ensemble is studied analytically with the usual tools of random matrix theory. The probability density function for the seesaw ensemble of N ×N matrices is obtained in terms of a multidimensional integral. This integral involves all light neutrino masses, leading to a complicated probability density function. It is shown that the probability density function for the neutrino mixing angles and phases is the appropriate Haar measure. The decoupling of the light neutrino masses and neutrino mixings implies no correlation between the neutrino mass eigenstates and the neutrino mixing matrix and leads to a loss of predictive power when comparing with observations. This decoupling is in agreement with some of the claims found in the literature.
Wave-function and density functional theory studies of dihydrogen complexes
Fabiano, E; Della Sala, F
2014-01-01
We performed a benchmark study on a series of dihydrogen bond complexes and constructed a set of reference bond distances and interaction energies. The test set was employed to assess the performance of several wave-function correlated and density functional theory methods. We found that second-order correlation methods describe relatively well the dihydrogen complexes. However, for high accuracy inclusion of triple contributions is important. On the other hand, none of the considered density functional methods can simultaneously yield accurate bond lengths and interaction energies. However, we found that improved results can be obtained by the inclusion of non-local exchange contributions.
A Tale of Two Electrons: Correlation at High Density
Loos, Pierre-François
2010-01-01
We review our recent progress in the determination of the high-density correlation energy $\\Ec$ in two-electron systems. Several two-electron systems are considered, such as the well known helium-like ions (helium), and the Hooke's law atom (hookium). We also present results regarding two electrons on the surface of a sphere (spherium), and two electrons trapped in a spherical box (ballium). We also show that, in the large-dimension limit, the high-density correlation energy of two opposite-spin electrons interacting {\\em via} a Coulomb potential is given by $\\Ec \\sim -1/(8D^2)$ for any radial external potential $V(r)$, where $D$ is the dimensionality of the space. This result explains the similarity of $\\Ec$ in the previous two-electron systems for $D=3$.
Adiabatic density-functional perturbation theory
Gonze, Xavier
1995-08-01
The treatment of adiabatic perturbations within density-functional theory is examined, at arbitrary order of the perturbation expansion. Due to the extremal property of the energy functional, standard variation-perturbation theorems can be used. The different methods (Sternheimer equation, extremal principle, Green's function, and sum over state) for obtaining the perturbation expansion of the wave functions are presented. The invariance of the Hilbert space of occupied wave functions with respect to a unitary transformation leads to the definition of a ``parallel-transport-gauge'' and a ``diagonal-gauge'' perturbation expansion. Then, the general expressions are specialized for the second, third, and fourth derivative of the energy, with an example of application of the method up to third order.
Density functional theory a practical introduction
Sholl, David
2009-01-01
Demonstrates how anyone in math, science, and engineering can master DFT calculations Density functional theory (DFT) is one of the most frequently used computational tools for studying and predicting the properties of isolated molecules, bulk solids, and material interfaces, including surfaces. Although the theoretical underpinnings of DFT are quite complicated, this book demonstrates that the basic concepts underlying the calculations are simple enough to be understood by anyone with a background in chemistry, physics, engineering, or mathematics. The authors show how the widespread availability of powerful DFT codes makes it possible for students and researchers to apply this important computational technique to a broad range of fundamental and applied problems. Density Functional Theory: A Practical Introduction offers a concise, easy-to-follow introduction to the key concepts and practical applications of DFT, focusing on plane-wave DFT. The authors have many years of experience introducing DFT to studen...
Teaching Density Functional Theory Through Experiential Learning
Narasimhan, Shobhana
2015-09-01
Today, quantum mechanical density functional theory is often the method of choice for performing accurate calculations on atomic, molecular and condensed matter systems. Here, I share some of my experiences in teaching the necessary basics of solid state physics, as well as the theory and practice of density functional theory, in a number of workshops held in developing countries over the past two decades. I discuss the advantages of supplementing the usual mathematically formal teaching methods, characteristic of graduate courses, with the use of visual imagery and analogies. I also describe a successful experiment we carried out, which resulted in a joint publication co-authored by 67 lecturers and students participating in a summer school.
Is Density Functional Theory adequate for quantum transport?
Burke, Kieron
2007-03-01
Density functional calculations for the electronic conductance of single molecules attached to leads are now common. I'll examine the methodology from a rigorous point of view, discussing where it can be expected to work, and where it should fail. When molecules are weakly coupled to leads, local and gradient-corrected approximations fail, as the Kohn-Sham levels are misaligned. In the weak bias regime, XC corrections to the current are missed by the standard methodology. Finally, I will compare and contrast several new methodologies that go beyond the present standard approach of applying the Landauer formula to ground-state DFT. Self-interaction errors in density functional calculations of electronictransport, C. Toher, A. Filippetti, S. Sanvito, and K. Burke, Phys. Rev. Lett. 95, 146402 (2005) The Dramatic Role of the Exchange-Correlation Potential in ab initio Electron Transport Calculations, S-H. Ke, H.U. Baranger, and W. Yang, cond-mat/0609367. Zero-bias molecular electronics: Exchange-correlation corrections to Landauer's formula, M. Koentopp, K. Burke, and F. Evers, Phys. Rev. B Rapid Comm., 73, 121403 (2006). Density Functional Theory of the Electrical Conductivity of Molecular Devices, K. Burke, Roberto Car, and Ralph Gebauer, Phys. Rev. Lett. 94, 146803 (2005). Density functional calculations of nanoscale conductance, Connie Chang, Max Koentopp, Kieron Burke, and Roberto Car, in prep.
Pribram-Jones, Aurora
Warm dense matter (WDM) is a high energy phase between solids and plasmas, with characteristics of both. It is present in the centers of giant planets, within the earth's core, and on the path to ignition of inertial confinement fusion. The high temperatures and pressures of warm dense matter lead to complications in its simulation, as both classical and quantum effects must be included. One of the most successful simulation methods is density functional theory-molecular dynamics (DFT-MD). Despite great success in a diverse array of applications, DFT-MD remains computationally expensive and it neglects the explicit temperature dependence of electron-electron interactions known to exist within exact DFT. Finite-temperature density functional theory (FT DFT) is an extension of the wildly successful ground-state DFT formalism via thermal ensembles, broadening its quantum mechanical treatment of electrons to include systems at non-zero temperatures. Exact mathematical conditions have been used to predict the behavior of approximations in limiting conditions and to connect FT DFT to the ground-state theory. An introduction to FT DFT is given within the context of ensemble DFT and the larger field of DFT is discussed for context. Ensemble DFT is used to describe ensembles of ground-state and excited systems. Exact conditions in ensemble DFT and the performance of approximations depend on ensemble weights. Using an inversion method, exact Kohn-Sham ensemble potentials are found and compared to approximations. The symmetry eigenstate Hartree-exchange approximation is in good agreement with exact calculations because of its inclusion of an ensemble derivative discontinuity. Since ensemble weights in FT DFT are temperature-dependent Fermi weights, this insight may help develop approximations well-suited to both ground-state and FT DFT. A novel, highly efficient approach to free energy calculations, finite-temperature potential functional theory, is derived, which has the
General degeneracy in density functional perturbation theory
Palenik, Mark C
2016-01-01
Degenerate perturbation theory from quantum mechanics is inadequate in density functional theory (DFT) because of nonlinearity in the Kohn-Sham potential. We develop the fully general degenerate perturbation theory for DFT without assuming that the degeneracy is required by symmetry. The resulting methodology is applied to the iron atom ground state in order to demonstrate the effects of degeneracy that appears both due to symmetry requirements and accidentally, between different representations of the symmetry group.
Asymptotic Correction Schemes for Semilocal Exchange-Correlation Functionals
Pan, Chi-Ruei; Chai, Jeng-Da
2013-01-01
Aiming to remedy the incorrect asymptotic behavior of conventional semilocal exchange-correlation (XC) density functionals for finite systems, we propose an asymptotic correction scheme, wherein an exchange density functional whose functional derivative has the correct (-1/r) asymptote can be directly added to any semilocal density functional. In contrast to semilocal approximations, our resulting exchange kernel in reciprocal space exhibits the desirable singularity of the type O(-1/q^2) as q -> 0, which is a necessary feature for describing the excitonic effects in non-metallic solids. By applying this scheme to a popular semilocal density functional, PBE [J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)], the predictions of the properties that are sensitive to the asymptote are significantly improved, while the predictions of the properties that are insensitive to the asymptote remain essentially the same as PBE. Relative to the popular model XC potential scheme, our scheme is sig...
Computing dispersion interactions in density functional theory
Cooper, V. R.; Kong, L.; Langreth, D. C.
2010-02-01
In this article techniques for including dispersion interactions within density functional theory are examined. In particular comparisons are made between four popular methods: dispersion corrected DFT, pseudopotential correction schemes, symmetry adapted perturbation theory, and a non-local density functional - the so called Rutgers-Chalmers van der Waals density functional (vdW-DF). The S22 benchmark data set is used to evaluate the relative accuracy of these methods and factors such as scalability and transferability are also discussed. We demonstrate that vdW-DF presents an excellent compromise between computational speed and accuracy and lends most easily to full scale application in solid materials. This claim is supported through a brief discussion of a recent large scale application to H2 in a prototype metal organic framework material (MOF), Zn2BDC2TED. The vdW-DF shows overwhelming promise for first-principles studies of physisorbed molecules in porous extended systems; thereby having broad applicability for studies as diverse as molecular adsorption and storage, battery technology, catalysis and gas separations.
Excitations and benchmark ensemble density functional theory for two electrons
Pribram-Jones, Aurora; Trail, John R; Burke, Kieron; Needs, Richard J; Ullrich, Carsten A
2014-01-01
A new method for extracting ensemble Kohn-Sham potentials from accurate excited state densities is applied to a variety of two electron systems, exploring the behavior of exact ensemble density functional theory. The issue of separating the Hartree energy and the choice of degenerate eigenstates is explored. A new approximation, spin eigenstate Hartree-exchange (SEHX), is derived. Exact conditions that are proven include the signs of the correlation energy components, the virial theorem for both exchange and correlation, and the asymptotic behavior of the potential for small weights of the excited states. Many energy components are given as a function of the weights for two electrons in a one-dimensional flat box, in a box with a large barrier to create charge transfer excitations, in a three-dimensional harmonic well (Hooke's atom), and for the He atom singlet-triplet ensemble, singlet-triplet-singlet ensemble, and triplet bi-ensemble.
Nonequilibrium Anderson model made simple with density functional theory
Kurth, S.; Stefanucci, G.
2016-12-01
The single-impurity Anderson model is studied within the i-DFT framework, a recently proposed extension of density functional theory (DFT) for the description of electron transport in the steady state. i-DFT is designed to give both the steady current and density at the impurity, and it requires the knowledge of the exchange-correlation (xc) bias and on-site potential (gate). In this work we construct an approximation for both quantities which is accurate in a wide range of temperatures, gates, and biases, thus providing a simple and unifying framework to calculate the differential conductance at negligible computational cost in different regimes. Our results mark a substantial advance for DFT and may inform the construction of functionals applicable to other correlated systems.
Semilocal density functional theory with correct surface asymptotics
Constantin, Lucian A.; Fabiano, Eduardo; Pitarke, J. M.; Della Sala, Fabio
2016-03-01
Semilocal density functional theory is the most used computational method for electronic structure calculations in theoretical solid-state physics and quantum chemistry of large systems, providing good accuracy with a very attractive computational cost. Nevertheless, because of the nonlocality of the exchange-correlation hole outside a metal surface, it was always considered inappropriate to describe the correct surface asymptotics. Here, we derive, within the semilocal density functional theory formalism, an exact condition for the imagelike surface asymptotics of both the exchange-correlation energy per particle and potential. We show that this condition can be easily incorporated into a practical computational tool, at the simple meta-generalized-gradient approximation level of theory. Using this tool, we also show that the Airy-gas model exhibits asymptotic properties that are closely related to those at metal surfaces. This result highlights the relevance of the linear effective potential model to the metal surface asymptotics.
Linear density response function in the projector augmented wave method
DEFF Research Database (Denmark)
Yan, Jun; Mortensen, Jens Jørgen; Jacobsen, Karsten Wedel;
2011-01-01
We present an implementation of the linear density response function within the projector-augmented wave method with applications to the linear optical and dielectric properties of both solids, surfaces, and interfaces. The response function is represented in plane waves while the single......-particle eigenstates can be expanded on a real space grid or in atomic-orbital basis for increased efficiency. The exchange-correlation kernel is treated at the level of the adiabatic local density approximation (ALDA) and crystal local field effects are included. The calculated static and dynamical dielectric...... functions of Si, C, SiC, AlP, and GaAs compare well with previous calculations. While optical properties of semiconductors, in particular excitonic effects, are generally not well described by ALDA, we obtain excellent agreement with experiments for the surface loss function of graphene and the Mg(0001...
Neutron skin uncertainties of Skyrme energy density functionals
Kortelainen, M; Nazarewicz, W; Birge, N; Gao, Y; Olsen, E
2013-01-01
Background: Neutron-skin thickness is an excellent indicator of isovector properties of atomic nuclei. As such, it correlates strongly with observables in finite nuclei that depend on neutron-to-proton imbalance and the nuclear symmetry energy that characterizes the equation of state of neutron-rich matter. A rich worldwide experimental program involving studies with rare isotopes, parity violating electron scattering, and astronomical observations is devoted to pinning down the isovector sector of nuclear models. Purpose: We assess the theoretical systematic and statistical uncertainties of neutron-skin thickness and relate them to the equation of state of nuclear matter, and in particular to nuclear symmetry energy parameters. Methods: We use the nuclear superfluid Density Functional Theory with several Skyrme energy density functionals and density dependent pairing. To evaluate statistical errors and their budget, we employ the statistical covariance technique. Results: We find that the errors on neutron s...
Lovett, Ronald
1988-06-01
All predictive theories for the spatial variation of the density in an inhomogeneous system can be constructed by approximating exact, nonlinear integral equations which relate the density and pair correlation functions of the system. It is shown that the set of correct kernels in the exact integral equations for the density is on the boundary between the set of kernels for which the integral equations have no solution for the density and the set for which the integral equations have a multiplicity of solutions. Thus arbitrarily small deviations from the correct kernel can make these integral equations insoluble. A heuristic model equation is used to illustrate how the density functional problem can be so sensitive to the approximation made to the correlation function kernel and it is then shown explicitly that this behavior is realized in the relation between the density and the direct correlation function and in the lowest order BGYB equation. Functional equations are identified for the kernels in these equations which are satisified by the correct kernels, which guarantee a unique solution to the integral equations, and which provide a natural constraint on approximations which can be used in density functional theory. It is also shown that this sensitive behavior is a general property of density functional problems and that the methodology for constructing the constraints is equally general. A variety of applications of density functional theory are reviewed to illustrate practical consequences of this sensitivity.
RECONSTRUCTING THE SHAPE OF THE CORRELATION FUNCTION
Energy Technology Data Exchange (ETDEWEB)
Huffenberger, K. M.; Galeazzi, M.; Ursino, E. [Department of Physics, University of Miami, Coral Gables, FL 33146 (United States)
2013-06-01
We develop an estimator for the correlation function which, in the ensemble average, returns the shape of the correlation function, even for signals that have significant correlations on the scale of the survey region. Our estimator is general and works in any number of dimensions. We develop versions of the estimator for both diffuse and discrete signals. As an application, we apply them to Monte Carlo simulations of X-ray background measurements. These include a realistic, spatially inhomogeneous population of spurious detector events. We discuss applying the estimator to the averaging of correlation functions evaluated on several small fields, and to other cosmological applications.
Reconstructing the shape of the correlation function
Huffenberger, K M; Ursino, E
2012-01-01
We develop an estimator for the angular correlation function which, in the ensemble average, returns the shape of the correlation function, even for signals that have significant correlations on the scale of the survey region. We develop versions of the estimator for both diffuse and discrete signals, and apply them to Monte Carlo simulations of the diffuse X-ray background that include spatially inhomogeneous detector background events. The estimator is applied to data from the Chandra X-ray observatory in a companion paper, Galeazzi et al. 2012. We discuss applying the estimator to the averaging of correlation functions evaluated on several small fields, and to other cosmological applications.
Hazra, Susanta; Bhattacharya, Sagarika; Singh, Mukesh Kumar; Carrella, Luca; Rentschler, Eva; Weyhermueller, Thomas; Rajaraman, Gopalan; Mohanta, Sasankasekhar
2013-11-18
The bis(μ-phenoxo) Fe(III)Ni(II) compound [Fe(III)(N3)2LNi(II)(H2O)(CH3CN)](ClO4) (1) and the bis(μ-phenoxo)-μ-acetate/bis(μ-phenoxo)-bis(μ-acetate) Fe(III)Ni(II) compound {[Fe(III)(OAc)LNi(II)(H2O)(μ-OAc)](0.6)·[Fe(III)LNi(II)(μ-OAc)2](0.4)}(ClO4)·1.1H2O (2) have been synthesized from the Robson type tetraiminodiphenol macrocyclic ligand H2L, which is the [2 + 2] condensation product of 4-methyl-2,6-diformylphenol and 2,2'-dimethyl-1,3-diaminopropane. Single-crystal X-ray structures of both compounds have been determined. The cationic part of the dinuclear compound 2 is a cocrystal of the two species [Fe(III)(OAc)LNi(II)(H2O)(μ-OAc)](+) (2A) and [Fe(III)LNi(II)(μ-OAc)2](+) (2B) with weights of 60% of the former and 40% of the latter. While 2A is a triply bridged bis(μ-phenoxo)-μ-acetate system, 2B is a quadruply bridged bis(μ-phenoxo)-bis(μ-acetate) system. Variable-temperature (2-300 K) magnetic studies reveal antiferromagnetic interaction in 1 and ferromagnetic interaction in 2 with J values of -3.14 and 7.36 cm(-1), respectively (H = -2JS1·S2). Broken-symmetry density functional calculations of exchange interaction have been performed on complexes 1 and 2 and also on previously published related compounds, providing good numerical estimates of J values in comparison to experiments. The electronic origin of the difference in magnetic behavior of 1 and 2 has been well understood from MO analyses and computed overlap integrals of BS empty orbitals. The role of acetate and thus its complementarity/countercomplementarity effect on the magnetic properties of diphenoxo-bridged Fe(III)Ni(II) compounds have been determined on computing J values of model compounds by replacing bridging acetate and nonbridging acetate ligand(s) by water ligands in the model compounds derived from 2A,B. The DFT calculations have also been extended to develop several magneto-structural correlations in these types of complexes, and the correlations focus on the role of Fe
Covariance and correlation estimation in electron-density maps.
Altomare, Angela; Cuocci, Corrado; Giacovazzo, Carmelo; Moliterni, Anna; Rizzi, Rosanna
2012-03-01
Quite recently two papers have been published [Giacovazzo & Mazzone (2011). Acta Cryst. A67, 210-218; Giacovazzo et al. (2011). Acta Cryst. A67, 368-382] which calculate the variance in any point of an electron-density map at any stage of the phasing process. The main aim of the papers was to associate a standard deviation to each pixel of the map, in order to obtain a better estimate of the map reliability. This paper deals with the covariance estimate between points of an electron-density map in any space group, centrosymmetric or non-centrosymmetric, no matter the correlation between the model and target structures. The aim is as follows: to verify if the electron density in one point of the map is amplified or depressed as an effect of the electron density in one or more other points of the map. High values of the covariances are usually connected with undesired features of the map. The phases are the primitive random variables of our probabilistic model; the covariance changes with the quality of the model and therefore with the quality of the phases. The conclusive formulas show that the covariance is also influenced by the Patterson map. Uncertainty on measurements may influence the covariance, particularly in the final stages of the structure refinement; a general formula is obtained taking into account both phase and measurement uncertainty, valid at any stage of the crystal structure solution.
Density Functional Theory An Advanced Course
Dreizler, Reiner M
2011-01-01
Density Functional Theory (DFT) has firmly established itself as the workhorse for the atomic-level simulation of condensed matter phases, pure or composite materials and quantum chemical systems. The present book is a rigorous and detailed introduction to the foundations up to and including such advanced topics as orbital-dependent functionals and both time-dependent and relativistic DFT. Given the many ramifications of contemporary DFT, this text concentrates on the self-contained presentation of the basics of the most widely used DFT variants. This implies a thorough discussion of the corresponding existence theorems and effective single particle equations, as well as of key approximations utilized in implementations. The formal results are complemented by selected quantitative results, which primarily aim at illustrating strengths and weaknesses of a particular approach or functional. DFT for superconducting or nuclear and hadronic systems are not addressed in this work. The structure and material contain...
Correlation functions of one-dimensional bosons at low temperature
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Maillet, J.M. [CNRS, ENS Lyon (France). Lab. de Physique; Slavnov, N.A. [Steklov Mathematical Institute, Moscow (Russian Federation)
2010-12-15
We consider the low-temperature limit of the long-distance asymptotic behavior of the finite temperature density-density correlation function in the one-dimensional Bose gas derived recently in the algebraic Bethe Ansatz framework. Our results confirm the predictions based on the Luttinger liquid and conformal field theory approaches. We also demonstrate that the amplitudes arising in this asymptotic expansion at low-temperature coincide with the amplitudes associated with the so-called critical form factors. (orig.)
Density ripples in expanding low-dimensional gases as a probe of correlations
DEFF Research Database (Denmark)
Imambekov, A.; Mazets, I. E.; Petrov, D. S.
2009-01-01
fluctuations. For the case of free ballistic expansion relevant to current experiments, we present simple analytical relations between the spectrum of "density ripples" and the correlation functions of the original confined systems. We analyze several physical regimes, including weakly and strongly interacting...
Covariant density functional theory for nuclear matter
Energy Technology Data Exchange (ETDEWEB)
Badarch, U.
2007-07-01
The present thesis is organized as follows. In Chapter 2 we study the Nucleon-Nucleon (NN) interaction in Dirac-Brueckner (DB) approach. We start by considering the NN interaction in free-space in terms of the Bethe-Salpeter (BS) equation to the meson exchange potential model. Then we present the DB approach for nuclear matter by extending the BS equation for the in-medium NN interaction. From the solution of the three-dimensional in-medium BS equation, we derive the DB self-energies and total binding energy which are the main results of the DB approach, which we later incorporate in the field theoretical calculation of the nuclear equation of state. In Chapter 3, we introduce the basic concepts of density functional theory in the context of Quantum Hadrodynamics (QHD-I). We reach the main point of this work in Chapter 4 where we introduce the DDRH approach. In the DDRH theory, the medium dependence of the meson-nucleon vertices is expressed as functionals of the baryon field operators. Because of the complexities of the operator-valued functionals we decide to use the mean-field approximation. In Chapter 5, we contrast microscopic and phenomenological approaches to extracting density dependent meson-baryon vertices. Chapter 6 gives the results of our studies of the EOS of infinite nuclear matter in detail. Using formulas derived in Chapters 4 and 5 we calculate the properties of symmetric and asymmetric nuclear matter and pure neutron matter. (orig.)
Density functional and neural network analysis
DEFF Research Database (Denmark)
Jalkanen, K. J.; Bohr, Henrik
1997-01-01
Density functional theory (DFT) calculations have been carried out for hydrated L-alanine, L-alanyl-L-alanine and N-acetyl L-alanine N'-methylamide and examined with respect to the effect of water on the structure, the vibrational frequencies, vibrational absorption (VA) and vibrational circular...... dichroism (VCD) intensities. The large changes due to hydration on the structures, relative stability of conformers, and in the VA and VCD spectra observed experimentally are reproduced by the DFT calculations. Furthermore a neural network was constructed for reproducing the inverse scattering data (infer...
Modulation Based on Probability Density Functions
Williams, Glenn L.
2009-01-01
A proposed method of modulating a sinusoidal carrier signal to convey digital information involves the use of histograms representing probability density functions (PDFs) that characterize samples of the signal waveform. The method is based partly on the observation that when a waveform is sampled (whether by analog or digital means) over a time interval at least as long as one half cycle of the waveform, the samples can be sorted by frequency of occurrence, thereby constructing a histogram representing a PDF of the waveform during that time interval.
Spin projection with double hybrid density functional theory.
Thompson, Lee M; Hratchian, Hrant P
2014-07-21
A spin projected double-hybrid density functional theory is presented that accounts for different scaling of opposite and same spin terms in the second order correction. This method is applied to three dissociation reactions which in the unprojected formalism exhibit significant spin contamination with higher spin states. This gives rise to a distorted potential surface and can lead to poor geometries and energies. The projected method presented is shown to improve the description of the potential over unprojected double hybrid density functional theory. Comparison is made with the reference states of the two double hybrid functionals considered here (B2PLYP and mPW2PLYP) in which the projected potential surface is degraded by an imbalance in the description of dynamic and static correlation.
Performance of one-body reduced density-matrix functionals for the homogeneous electron gas
Lathiotakis, N. N.; Helbig, N.; Gross, E. K. U.
2007-05-01
The subject of this study is the exchange-correlation-energy functional of reduced density-matrix functional theory. Approximations of this functional are tested by applying them to the homogeneous electron gas. We find that two approximations recently proposed by Gritsenko , [J. Chem. Phys. 122, 204102 (2005)] yield considerably better correlation energies and momentum distributions than previously known functionals. We introduce modifications to these functionals, which, by construction, reproduce the exact correlation energy of the homogeneous electron gas.
An improved density matrix functional by physically motivated repulsive corrections.
Gritsenko, Oleg; Pernal, Katarzyna; Baerends, Evert Jan
2005-05-22
An improved density matrix functional [correction to Buijse and Baerends functional (BBC)] is proposed, in which a hierarchy of physically motivated repulsive corrections is employed to the strongly overbinding functional of Buijse and Baerends (BB). The first correction C1 restores the repulsive exchange-correlation (xc) interaction between electrons in weakly occupied natural orbitals (NOs) as it appears in the exact electron pair density rho(2) for the limiting two-electron case. The second correction C2 reduces the xc interaction of the BB functional between electrons in strongly occupied NOs to an exchange-type interaction. The third correction C3 employs a similar reduction for the interaction of the antibonding orbital of a dissociating molecular bond. In addition, C3 applies a selective cancellation of diagonal terms in the Coulomb and xc energies (not for the frontier orbitals). With these corrections, BBC still retains a correct description of strong nondynamical correlation for the dissociating electron pair bond. BBC greatly improves the quality of the BB potential energy curves for the prototype few-electron molecules and in several cases BBC reproduces very well the benchmark ab initio potential curves. The average error of the self-consistent correlation energies obtained with BBC3 for prototype atomic systems and molecular systems at the equilibrium geometry is only ca. 6%.
Exact factorization of correlation functions in 2-D critical percolation
Simmons, Jacob J H; Ziff, Robert M
2007-01-01
By use of conformal field theory, we discover several exact factorizations of higher-order density correlation functions in critical two-dimensional percolation. Our formulas are valid in the upper half-plane, or any conformally equivalent region. We find excellent agreement of our results with high-precision computer simulations. There are indications that our formulas hold more generally.
Implementation Strategies for Orbital-dependent Density Functionals
Bento, Marsal E.; Vieira, Daniel
2016-12-01
The development of density functional theory (DFT) has been focused primarily on two main pillars: (1) the pursuit of more accurate exchange-correlation (XC) density functionals; (2) the feasibility of computational implementation when dealing with many-body systems. In this context, this work is aimed on using one-dimensional quantum systems as theoretical laboratories to investigate the implementation of orbital functionals (OFs) of density. By definition, OFs are those which depend only implicitly on the density, via an explicit formulation in terms of Kohn-Sham orbitals. Typical examples are the XC functionals arising from the Perdew-Zunger self-interaction correction (PZSIC). Formally, via Kohn-Sham equations, the implementation of OFs must be performed by means of the optimized effective potential method (OEP), which is known by requiring an excessive computational effort even when dealing with few electrons systems. Here, we proceed a systematical investigation aiming to simplify or avoid the OEP procedure, taking as reference the implementation of the PZSIC correction applied to one-dimensional Hubbard chains.
Implementation Strategies for Orbital-dependent Density Functionals
Bento, Marsal E.; Vieira, Daniel
2016-10-01
The development of density functional theory (DFT) has been focused primarily on two main pillars: (1) the pursuit of more accurate exchange-correlation (XC) density functionals; (2) the feasibility of computational implementation when dealing with many-body systems. In this context, this work is aimed on using one-dimensional quantum systems as theoretical laboratories to investigate the implementation of orbital functionals (OFs) of density. By definition, OFs are those which depend only implicitly on the density, via an explicit formulation in terms of Kohn-Sham orbitals. Typical examples are the XC functionals arising from the Perdew-Zunger self-interaction correction (PZSIC). Formally, via Kohn-Sham equations, the implementation of OFs must be performed by means of the optimized effective potential method (OEP), which is known by requiring an excessive computational effort even when dealing with few electrons systems. Here, we proceed a systematical investigation aiming to simplify or avoid the OEP procedure, taking as reference the implementation of the PZSIC correction applied to one-dimensional Hubbard chains.
Estimating purity in terms of correlation functions
Prosen, T; Znidaric, M; Prosen, Tomaz; Seligman, Thomas H.; Znidaric, Marko
2003-01-01
We prove a rigorous inequality estimating the purity of a reduced density matrix of a composite quantum system in terms of cross-correlation of the same state and an arbitrary product state. Various immediate applications of our result are proposed, in particular concerning Gaussian wave-packet propagation under classically regular dynamics.
Bayesian error estimation in density-functional theory
DEFF Research Database (Denmark)
Mortensen, Jens Jørgen; Kaasbjerg, Kristen; Frederiksen, Søren Lund
2005-01-01
We present a practical scheme for performing error estimates for density-functional theory calculations. The approach, which is based on ideas from Bayesian statistics, involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies...... for molecules and solids. Fluctuations within the ensemble can then be used to estimate errors relative to experiment on calculated quantities such as binding energies, bond lengths, and vibrational frequencies. It is demonstrated that the error bars on energy differences may vary by orders of magnitude...
Formation energies of rutile metal dioxides using density functional theory
DEFF Research Database (Denmark)
Martinez, Jose Ignacio; Hansen, Heine Anton; Rossmeisl, Jan
2009-01-01
We apply standard density functional theory at the generalized gradient approximation (GGA) level to study the stability of rutile metal oxides. It is well known that standard GGA exchange and correlation in some cases is not sufficient to address reduction and oxidation reactions. Especially...... and due to a more accurate description of exchange for this particular GGA functional compared to PBE. Furthermore, we would expect the self-interaction problem to be largest for the most localized d orbitals; that means the late 3d metals and since Co, Fe, Ni, and Cu do not form rutile oxides...
Pernal, Katarzyna
2012-05-14
Time-dependent density functional theory (TD-DFT) in the adiabatic formulation exhibits known failures when applied to predicting excitation energies. One of them is the lack of the doubly excited configurations. On the other hand, the time-dependent theory based on a one-electron reduced density matrix functional (time-dependent density matrix functional theory, TD-DMFT) has proven accurate in determining single and double excitations of H(2) molecule if the exact functional is employed in the adiabatic approximation. We propose a new approach for computing excited state energies that relies on functionals of electron density and one-electron reduced density matrix, where the latter is applied in the long-range region of electron-electron interactions. A similar approach has been recently successfully employed in predicting ground state potential energy curves of diatomic molecules even in the dissociation limit, where static correlation effects are dominating. In the paper, a time-dependent functional theory based on the range-separation of electronic interaction operator is rigorously formulated. To turn the approach into a practical scheme the adiabatic approximation is proposed for the short- and long-range components of the coupling matrix present in the linear response equations. In the end, the problem of finding excitation energies is turned into an eigenproblem for a symmetric matrix. Assignment of obtained excitations is discussed and it is shown how to identify double excitations from the analysis of approximate transition density matrix elements. The proposed method used with the short-range local density approximation (srLDA) and the long-range Buijse-Baerends density matrix functional (lrBB) is applied to H(2) molecule (at equilibrium geometry and in the dissociation limit) and to Be atom. The method accounts for double excitations in the investigated systems but, unfortunately, the accuracy of some of them is poor. The quality of the other
Density functional calculations on hydrocarbon isodesmic reactions
Fortunelli, Alessandro; Selmi, Massimo
1994-06-01
Hartree—Fock, Hartree—Fock-plus-correlation and self-consistent Kohn—Sham calculations are performed on a set of hydrocarbon isodesmic reactions, i.e. reactions among hydrocarbons in which the number and type of carbon—carbon and carbon—hydrogen bonds is conserved. It is found that neither Hartree—Fock nor Kohn—Sham methods correctly predict standard enthalpies, Δ Hr(298 K), of these reactions, even though — for reactions involving molecules containing strained double bonds — the agreement between the theoretical estimates and the experimental values of Δ Hr seems to be improved by the self-consistent solution of the Kohn—Sham equations. The remaining discrepancies are attributed to intramolecular dispersion effects, that are not described by ordinary exchange—correlation functionals, and are eliminated by introducing corrections based on a simple semi-empirical model.
Universality principle and the development of classical density functional theory
Institute of Scientific and Technical Information of China (English)
周世琦; 张晓琪
2002-01-01
The universality principle of the free energy density functional and the ‘test particle' trick by Percus are combined to construct the approximate free energy density functional or its functional derivative. Information about the bulk fluid ralial distribution function is integrated into the density functional approximation directly for the first time in the present methodology. The physical foundation of the present methodology also applies to the quantum density functional theory.
Anero, Jesús G; Español, Pep; Tarazona, Pedro
2013-07-21
We present a generalization of Density Functional Theory (DFT) to non-equilibrium non-isothermal situations. By using the original approach set forth by Gibbs in his consideration of Macroscopic Thermodynamics (MT), we consider a Functional Thermo-Dynamics (FTD) description based on the density field and the energy density field. A crucial ingredient of the theory is an entropy functional, which is a concave functional. Therefore, there is a one to one connection between the density and energy fields with the conjugate thermodynamic fields. The connection between the three levels of description (MT, DFT, FTD) is clarified through a bridge theorem that relates the entropy of different levels of description and that constitutes a generalization of Mermin's theorem to arbitrary levels of description whose relevant variables are connected linearly. Although the FTD level of description does not provide any new information about averages and correlations at equilibrium, it is a crucial ingredient for the dynamics in non-equilibrium states. We obtain with the technique of projection operators the set of dynamic equations that describe the evolution of the density and energy density fields from an initial non-equilibrium state towards equilibrium. These equations generalize time dependent density functional theory to non-isothermal situations. We also present an explicit model for the entropy functional for hard spheres.
Nitrogenase structure and function relationships by density functional theory.
Harris, Travis V; Szilagyi, Robert K
2011-01-01
Modern density functional theory has tremendous potential with matching popularity in metalloenzymology to reveal the unseen atomic and molecular details of structural data, spectroscopic measurements, and biochemical experiments by providing insights into unobservable structures and states, while also offering theoretical justifications for observed trends and differences. An often untapped potential of this theoretical approach is to bring together diverse experimental structural and reactivity information and allow for these to be critically evaluated at the same level. This is particularly applicable for the tantalizingly complex problem of the structure and molecular mechanism of biological nitrogen fixation. In this chapter we provide a review with extensive practical details of the compilation and evaluation of experimental data for an unbiased and systematic density functional theory analysis that can lead to remarkable new insights about the structure-function relationships of the iron-sulfur clusters of nitrogenase.
Steady-State Density Functional Theory for Finite Bias Conductances.
Stefanucci, G; Kurth, S
2015-12-09
In the framework of density functional theory, a formalism to describe electronic transport in the steady state is proposed which uses the density on the junction and the steady current as basic variables. We prove that, in a finite window around zero bias, there is a one-to-one map between the basic variables and both local potential on as well as bias across the junction. The resulting Kohn-Sham system features two exchange-correlation (xc) potentials, a local xc potential, and an xc contribution to the bias. For weakly coupled junctions the xc potentials exhibit steps in the density-current plane which are shown to be crucial to describe the Coulomb blockade diamonds. At small currents these steps emerge as the equilibrium xc discontinuity bifurcates. The formalism is applied to a model benzene junction, finding perfect agreement with the orthodox theory of Coulomb blockade.
Comparison of density estimators. [Estimation of probability density functions
Energy Technology Data Exchange (ETDEWEB)
Kao, S.; Monahan, J.F.
1977-09-01
Recent work in the field of probability density estimation has included the introduction of some new methods, such as the polynomial and spline methods and the nearest neighbor method, and the study of asymptotic properties in depth. This earlier work is summarized here. In addition, the computational complexity of the various algorithms is analyzed, as are some simulations. The object is to compare the performance of the various methods in small samples and their sensitivity to change in their parameters, and to attempt to discover at what point a sample is so small that density estimation can no longer be worthwhile. (RWR)
Bartelmann, Matthias; Kozlikin, Elena; Lilow, Robert; Dombrowski, Johannes; Mildenberger, Julius
2016-01-01
In earlier work, we have developed a Kinetic Field Theory (KFT) for cosmological structure formation and showed that the non-linear density-fluctuation power spectrum known from numerical simulations can be reproduced quite well even if particle interactions are taken into account to first order only. Besides approximating gravitational interactions, we had to truncate the initial correlation hierarchy of particle momenta at the second order. Here, we substantially simplify KFT. We show that its central object, the free generating functional, can be factorized, taking the full hierarchy of momentum correlations into account. The factors appearing in the generating functional have a universal form and can thus be tabulated for fast access in perturbation schemes. Our results show that the complete hierarchy of initial momentum correlations is responsible for a characteristic deformation in the density-fluctuation power spectrum, caused by mode transport independent of the particle interaction. At the present e...
Characterization of maximally random jammed sphere packings: Voronoi correlation functions.
Klatt, Michael A; Torquato, Salvatore
2014-11-01
We characterize the structure of maximally random jammed (MRJ) sphere packings by computing the Minkowski functionals (volume, surface area, and integrated mean curvature) of their associated Voronoi cells. The probability distribution functions of these functionals of Voronoi cells in MRJ sphere packings are qualitatively similar to those of an equilibrium hard-sphere liquid and partly even to the uncorrelated Poisson point process, implying that such local statistics are relatively structurally insensitive. This is not surprising because the Minkowski functionals of a single Voronoi cell incorporate only local information and are insensitive to global structural information. To improve upon this, we introduce descriptors that incorporate nonlocal information via the correlation functions of the Minkowski functionals of two cells at a given distance as well as certain cell-cell probability density functions. We evaluate these higher-order functions for our MRJ packings as well as equilibrium hard spheres and the Poisson point process. It is shown that these Minkowski correlation and density functions contain visibly more information than the corresponding standard pair-correlation functions. We find strong anticorrelations in the Voronoi volumes for the hyperuniform MRJ packings, consistent with previous findings for other pair correlations [A. Donev et al., Phys. Rev. Lett. 95, 090604 (2005)PRLTAO0031-900710.1103/PhysRevLett.95.090604], indicating that large-scale volume fluctuations are suppressed by accompanying large Voronoi cells with small cells, and vice versa. In contrast to the aforementioned local Voronoi statistics, the correlation functions of the Voronoi cells qualitatively distinguish the structure of MRJ sphere packings (prototypical glasses) from that of not only the Poisson point process but also the correlated equilibrium hard-sphere liquids. Moreover, while we did not find any perfect icosahedra (the locally densest possible structure in which a
On the measurability of quantum correlation functions
Energy Technology Data Exchange (ETDEWEB)
Lima Bernardo, Bertúlio de, E-mail: bertulio.fisica@gmail.com; Azevedo, Sérgio; Rosas, Alexandre
2015-05-15
The concept of correlation function is widely used in classical statistical mechanics to characterize how two or more variables depend on each other. In quantum mechanics, on the other hand, there are observables that cannot be measured at the same time; the so-called incompatible observables. This prospect imposes a limitation on the definition of a quantum analog for the correlation function in terms of a sequence of measurements. Here, based on the notion of sequential weak measurements, we circumvent this limitation by introducing a framework to measure general quantum correlation functions, in principle, independently of the state of the system and the operators involved. To illustrate, we propose an experimental configuration to obtain explicitly the quantum correlation function between two Pauli operators, in which the input state is an arbitrary mixed qubit state encoded on the polarization of photons.
A Stochastic Wave Model Interpretation of Correlation Functions for Turbulent Shear Flows.
narrow band (frequency filtered) correlation function data. Next, the power spectral density function is identified as the appropriate frequency weighting... density function which agrees with the observed data is taken to be the superposition of a strong, unorganized background turbulence (Markoff noise...function with which to synthesize the broad band (unfiltered) from the narrow band correlation functions. The functional form of the power spectral
Uncertainty propagation with functionally correlated quantities
Giordano, Mosè
2016-01-01
Many uncertainty propagation software exist, written in different programming languages, but not all of them are able to handle functional correlation between quantities. In this paper we review one strategy to deal with uncertainty propagation of quantities that are functionally correlated, and introduce a new software offering this feature: the Julia package Measurements.jl. It supports real and complex numbers with uncertainty, arbitrary-precision calculations, mathematical and linear algebra operations with matrices and arrays.
Correlation Functions for Lattice Integrable Models
Directory of Open Access Journals (Sweden)
F. Smirnov
2008-01-01
Full Text Available In this lectures I consider the problem of calculating the correlation functions for XXZ spin chain. First, I explain in details the free fermion case. Then I show that for generic coupling constant the fermionic operators acting on the space of quasi-local fields can be introduced. In the basis generated by these fermionic operators the correlation functions are given by determinants as in the free fermion case.
Inequalities for electron-field correlation functions
Tyc, T
2000-01-01
I show that there exists a class of inequalities between correlation functions of different orders of a chaotic electron field. These inequalities lead to the antibunching effect and are a consequence of the fact that electrons are fermions -- indistinguishable particles with antisymmetric states. The derivation of the inequalities is based on the known form of the correlation functions for the chaotic state and on the properties of matrices and determinants.
A density functional for liquid [sup 3]He
Energy Technology Data Exchange (ETDEWEB)
Barranco, M. (Dept. de Estructura y Constituyentes de la Materia, Barcelona Univ. (Spain)); Jezek, D.M. (Dept. de Estructura y Constituyentes de la Materia, Barcelona Univ. (Spain)); Hernandez, E.S. (Dept. de Fisica, Univ. de Buenos Aires (Argentina)); Navarro, J. (Dept. de Fisica Atomica, Molecular y Nuclear, Valencia Univ. (Spain)); Serra, Ll. (Dipt. di Fisica, Milan Univ. (Italy))
1993-11-01
We present a density functional for the description of liquid [sup 3]He properties at zero temperture in a mean field approximation. Its basic ingredients are a zero-range, particle- and spin-density dependent effective interaction of Skyrme type, and a long-range effective interaction of Lennard-Jones type supplemented with a weighted density approximation similar to the one used in the study of classical fluids, to phenomenologically account for short range correlations. After fixing the value of its parameters, the functional yields a good desription of the equation of state and Landau parameters (spin symmetric and spin antisymmetric as well) from saturation to solidification densities. The zero sound propagation at finite momentum transfer is quantitatively reproduced up to the Fermi momentum, and qualitatively above it. The surface tension is in agreement with experiment, which makes the functional well suited for [sup 3]He drop calculations. We describe the structure of drops made of up to 516 atoms. As a novel application, we discuss the possible appearance of triplet pairing in a nl-shell of a drop applying the formalism to the 1j-shell holding up to 30 atoms from N=169 to 198. (orig.)
Excitations and benchmark ensemble density functional theory for two electrons
Energy Technology Data Exchange (ETDEWEB)
Pribram-Jones, Aurora; Burke, Kieron [Department of Chemistry, University of California-Irvine, Irvine, California 92697 (United States); Yang, Zeng-hui; Ullrich, Carsten A. [Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211 (United States); Trail, John R.; Needs, Richard J. [Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE (United Kingdom)
2014-05-14
A new method for extracting ensemble Kohn-Sham potentials from accurate excited state densities is applied to a variety of two-electron systems, exploring the behavior of exact ensemble density functional theory. The issue of separating the Hartree energy and the choice of degenerate eigenstates is explored. A new approximation, spin eigenstate Hartree-exchange, is derived. Exact conditions that are proven include the signs of the correlation energy components and the asymptotic behavior of the potential for small weights of the excited states. Many energy components are given as a function of the weights for two electrons in a one-dimensional flat box, in a box with a large barrier to create charge transfer excitations, in a three-dimensional harmonic well (Hooke's atom), and for the He atom singlet-triplet ensemble, singlet-triplet-singlet ensemble, and triplet bi-ensemble.
Time-dependent density-functional description of nuclear dynamics
Nakatsukasa, Takashi; Matsuo, Masayuki; Yabana, Kazuhiro
2016-01-01
We present the basic concepts and recent developments in the time-dependent density functional theory (TDDFT) for describing nuclear dynamics at low energy. The symmetry breaking is inherent in nuclear energy density functionals (EDFs), which provides a practical description of important correlations at the ground state. Properties of elementary modes of excitation are strongly influenced by the symmetry breaking and can be studied with TDDFT. In particular, a number of recent developments in the linear response calculation have demonstrated their usefulness in description of collective modes of excitation in nuclei. Unrestricted real-time calculations have also become available in recent years, with new developments for quantitative description of nuclear collision phenomena. There are, however, limitations in the real-time approach; for instance, it cannot describe the many-body quantum tunneling. Thus, we treat the quantum fluctuations associated with slow collective motions assuming that time evolution of...
Chemistry by Way of Density Functional Theory
Bauschlicher, Charles W., Jr.; Ricca, Alessandra; Partridge, Harry; Langohff, Stephen R.; Arnold, James O. (Technical Monitor)
1996-01-01
In this work we demonstrate that density functional theory (DFT) methods make an important contribution to understanding chemical systems and are an important additional method for the computational chemist. We report calibration calculations obtained with different functionals for the 55 G2 molecules to justify our selection of the B3LYP functional. We show that accurate geometries and vibrational frequencies obtained at the B3LYP level can be combined with traditional methods to simplify the calculation of accurate heats of formation. We illustrate the application of the B3LYP approach to a variety of chemical problems from the vibrational frequencies of polycyclic aromatic hydrocarbons to transition metal systems. We show that the B3LYP method typically performs better than the MP2 method at a significantly lower computational cost. Thus the B3LYP method allows us to extend our studies to much larger systems while maintaining a high degree of accuracy. We show that for transition metal systems, the B3LYP bond energies are typically of sufficient accuracy that they can be used to explain experimental trends and even differentiate between different experimental values. We show that for boron clusters the B3LYP energetics are not as good as for many of the other systems presented, but even in this case the B3LYP approach is able to help understand the experimental trends.
Fromager, Emmanuel
2014-01-01
The exact formulation of multi-configuration density-functional theory (DFT) is discussed in this work. As an alternative to range-separated methods, where electron correlation effects are split in the coordinate space, the combination of Configuration Interaction methods with orbital occupation functionals is explored at the formal level through the separation of correlation effects in the orbital space. When applied to model Hamiltonians, this approach leads to an exact Site-Occupation Embedding Theory (SOET). An adiabatic connection expression is derived for the complementary bath functional and a comparison with Density Matrix Embedding Theory (DMET) is made. Illustrative results are given for the simple two-site Hubbard model. SOET is then applied to a quantum chemical Hamiltonian, thus leading to an exact Complete Active Space Site-Occupation Functional Theory (CASSOFT) where active electrons are correlated explicitly within the CAS and the remaining contributions to the correlation energy are described...
General degeneracy in density functional perturbation theory
Palenik, Mark C.; Dunlap, Brett I.
2017-07-01
Degenerate perturbation theory from quantum mechanics is inadequate in density functional theory (DFT) because of nonlinearity in the Kohn-Sham potential. Herein, we develop the fully general perturbation theory for open-shell, degenerate systems in Kohn-Sham DFT, without assuming the presence of symmetry or equal occupation of degenerate orbitals. To demonstrate the resulting methodology, we apply it to the iron atom in the central field approximation, perturbed by an electric quadrupole. This system was chosen because it displays both symmetry required degeneracy, between the five 3 d orbitals, as well as accidental degeneracy, between the 3 d and 4 s orbitals. The quadrupole potential couples the degenerate 3 d and 4 s states, serving as an example of the most general perturbation.
Phases of Polonium via Density Functional Theory
Verstraete, Matthieu J.
2010-01-01
The thermodynamical properties of the main phases of metallic polonium are examined using density functional theory. The exceptional nature of the solid-solid phase transition of α to β Po is underlined: it induces a lowering in symmetry, from cubic to rhombohedral, with increasing temperature. This is explained as the result of a delicate balance between bonding and entropic effects. Overall agreement with existing experimental data is good by state-of-the-art standards. The phonons of Po present Kohn anomalies, and it is shown that the effect of spin-orbit interactions is the inverse of that in normal metals: due to the nonspherical nature of the Fermi Surface, spin-orbit effects reduce nesting and harden most phonon frequencies.
Effective potential in density matrix functional theory.
Nagy, A; Amovilli, C
2004-10-01
In the previous paper it was shown that in the ground state the diagonal of the spin independent second-order density matrix n can be determined by solving a single auxiliary equation of a two-particle problem. Thus the problem of an arbitrary system with even electrons can be reduced to a two-particle problem. The effective potential of the two-particle equation contains a term v(p) of completely kinetic origin. Virial theorem and hierarchy of equations are derived for v(p) and simple approximations are proposed. A relationship between the effective potential u(p) of the shape function equation and the potential v(p) is established.
Multitime correlation functions in nonclassical stochastic processes
Krumm, F.; Sperling, J.; Vogel, W.
2016-06-01
A general method is introduced for verifying multitime quantum correlations through the characteristic function of the time-dependent P functional that generalizes the Glauber-Sudarshan P function. Quantum correlation criteria are derived which identify quantum effects for an arbitrary number of points in time. The Magnus expansion is used to visualize the impact of the required time ordering, which becomes crucial in situations when the interaction problem is explicitly time dependent. We show that the latter affects the multi-time-characteristic function and, therefore, the temporal evolution of the nonclassicality. As an example, we apply our technique to an optical parametric process with a frequency mismatch. The resulting two-time-characteristic function yields full insight into the two-time quantum correlation properties of such a system.
Out-of-Time-Ordered Density Correlators in Luttinger Liquids
Dóra, Balázs; Moessner, Roderich
2017-07-01
Information scrambling and the butterfly effect in chaotic quantum systems can be diagnosed by out-of-time-ordered (OTO) commutators through an exponential growth and large late time value. We show that the latter feature shows up in a strongly correlated many-body system, a Luttinger liquid, whose density fluctuations we study at long and short wavelengths, both in equilibrium and after a quantum quench. We find rich behavior combining robustly universal and nonuniversal features. The OTO commutators display temperature- and initial-state-independent behavior and grow as t2 for short times. For the short-wavelength density operator, they reach a sizable value after the light cone only in an interacting Luttinger liquid, where the bare excitations break up into collective modes. This challenges the common interpretation of the OTO commutator in chaotic systems. We benchmark our findings numerically on an interacting spinless fermion model in 1D and find persistence of central features even in the nonintegrable case. As a nonuniversal feature, the short-time growth exhibits a distance-dependent power.
Spontaneous symmetry breaking in correlated wave functions
Kaneko, Ryui; Tocchio, Luca F.; Valentí, Roser; Becca, Federico; Gros, Claudius
2016-03-01
We show that Jastrow-Slater wave functions, in which a density-density Jastrow factor is applied onto an uncorrelated fermionic state, may possess long-range order even when all symmetries are preserved in the wave function. This fact is mainly related to the presence of a sufficiently strong Jastrow term (also including the case of full Gutzwiller projection, suitable for describing spin models). Selected examples are reported, including the spawning of Néel order and dimerization in spin systems, and the stabilization of charge and orbital order in itinerant electronic systems.
Time-dependent density functional theory: Causality and other problems
Energy Technology Data Exchange (ETDEWEB)
Ruggenthaler, Michael; Bauer, Dieter [Max-Planck-Inst. fuer Kernphysik, Heidelberg (Germany)
2007-07-01
Time-dependent density functional theory (TDDFT) is a reformulation of the time dependent many-body problem in quantum mechanics which is capable of reducing the computational cost to calculate, e.g., strongly driven many-electron systems enormously. Recent developments were able to overcome fundamental problems associated with ionization processes. Still vital issues have to be clarified. Besides the construction of the underlying functionals we investigate the causality problem of TDDFT by general considerations and by studying a exactly solvable system of two correlated electrons in an intense laser-pulse. For the latter system, the two alternative approaches to the construction of the action functional or a constrained functional derivative by van Leeuwen and Gal, respectively, are explored.
Building a Universal Nuclear Energy Density Functional
Energy Technology Data Exchange (ETDEWEB)
Carlson, Joe A. [Michigan State Univ., East Lansing, MI (United States); Furnstahl, Dick; Horoi, Mihai; Lust, Rusty; Nazaewicc, Witek; Ng, Esmond; Thompson, Ian; Vary, James
2012-12-30
During the period of Dec. 1 2006 – Jun. 30, 2012, the UNEDF collaboration carried out a comprehensive study of all nuclei, based on the most accurate knowledge of the strong nuclear interaction, the most reliable theoretical approaches, the most advanced algorithms, and extensive computational resources, with a view towards scaling to the petaflop platforms and beyond. The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: First, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties; Second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data; Third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory.
Building a Universal Nuclear Energy Density Functional
Energy Technology Data Exchange (ETDEWEB)
Carlson, Joe A. [Michigan State University; Furnstahl, Dick; Horoi, Mihai; Lust, Rusty; Nazaewicc, Witek; Ng, Esmond; Thompson, Ian; Vary, James
2012-12-30
During the period of Dec. 1 2006 – Jun. 30, 2012, the UNEDF collaboration carried out a comprehensive study of all nuclei, based on the most accurate knowledge of the strong nuclear interaction, the most reliable theoretical approaches, the most advanced algorithms, and extensive computational resources, with a view towards scaling to the petaflop platforms and beyond. The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: First, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties; Second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data; Third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory.
Charge transfer in time-dependent density functional theory
Maitra, Neepa T.
2017-10-01
Charge transfer plays a crucial role in many processes of interest in physics, chemistry, and bio-chemistry. In many applications the size of the systems involved calls for time-dependent density functional theory (TDDFT) to be used in their computational modeling, due to its unprecedented balance between accuracy and efficiency. However, although exact in principle, in practise approximations must be made for the exchange-correlation functional in this theory, and the standard functional approximations perform poorly for excitations which have a long-range charge-transfer component. Intense progress has been made in developing more sophisticated functionals for this problem, which we review. We point out an essential difference between the properties of the exchange-correlation kernel needed for an accurate description of charge-transfer between open-shell fragments and between closed-shell fragments. We then turn to charge-transfer dynamics, which, in contrast to the excitation problem, is a highly non-equilibrium, non-perturbative, process involving a transfer of one full electron in space. This turns out to be a much more challenging problem for TDDFT functionals. We describe dynamical step and peak features in the exact functional evolving over time, that are missing in the functionals currently used. The latter underestimate the amount of charge transferred and manifest a spurious shift in the charge transfer resonance position. We discuss some explicit examples.
Correlation of Density Pedestal Width and Neutral Penetration
Xu, X. Q.; Nevins, W. M.; Cohen, R. H.; Rognlien, T. D.; Umansky, M. V.
2003-10-01
Pedestal studies in DIII-D and C-Mod find a good correlation between the width of the H-mode density barrier and the neutral penetration length.[1][2] These results suggest that the width may be set by the combined effects of neutral and plasma transport. This paper is a report on fluid simulations of boundary plasma using BOUT code [3] with neutral source added. Thus both neutral and plasma physics are treated. The plasma transport is self-consistently driven by boundary turbulence due to the resistive X-point mode, while neutral is described by a simple fluid diffusive model. The plasma profiles are evolved on the same time scale as the turbulence for the given heat source from the core plasma and particle source from the neutrals. For prescribed neutral profiles, we find the formation of a density pedestal inside the separatrix in the L-mode even though the calculated plasma diffusion coefficients are almost radially constant and without the formation of a temperature pedestal. These results support the hypothesis that particle fueling can provide the dominant control for the size of the H-mode density barrier. The width of the density barrier, and its relationship to pedestal height and neutral penetration length at the midplane, will be given by using hyperbolic-tangent fit to the simulation data. [1] R.J.Groebner, M.A.Mahdavi, A.W.Leonard, 19th IAEA Fusion Energy Conference(Lyon, France, 14 to 19 October 2002), IAEA-CN-94/EX/C2-3. [2] D.Mossessian, J.W.Hughes, M.Greenwald, et al., ``Local dimensionless identity method as a tool for studying H-mode pedestal'', The 9th Joint US-European TTF workshop (Madison, Wisconsin, April 2nd - 5th, 2003). [3] X.Q.Xu, R.H.Cohen, T.D.Rognlien and J.R.Myra, Physics of Plasma, Vol. 7, 1951-1958 (2000).
Correlation Functions in Open Quantum-Classical Systems
Directory of Open Access Journals (Sweden)
Chang-Yu Hsieh
2013-12-01
Full Text Available Quantum time correlation functions are often the principal objects of interest in experimental investigations of the dynamics of quantum systems. For instance, transport properties, such as diffusion and reaction rate coefficients, can be obtained by integrating these functions. The evaluation of such correlation functions entails sampling from quantum equilibrium density operators and quantum time evolution of operators. For condensed phase and complex systems, where quantum dynamics is difficult to carry out, approximations must often be made to compute these functions. We present a general scheme for the computation of correlation functions, which preserves the full quantum equilibrium structure of the system and approximates the time evolution with quantum-classical Liouville dynamics. Several aspects of the scheme are discussed, including a practical and general approach to sample the quantum equilibrium density, the properties of the quantum-classical Liouville equation in the context of correlation function computations, simulation schemes for the approximate dynamics and their interpretation and connections to other approximate quantum dynamical methods.
Tailoring correlations of the local density of states in disordered photonic materials
Riboli, F; Monaco, G; Caselli, N; Intonti, F; Gurioli, M; Skipetrov, S E
2016-01-01
We present experimental evidence for the different mechanisms driving the fluctuations of the local density of states (LDOS) in disordered photonic systems. We establish a clear link between the microscopic structure of the material and the frequency correlation function of LDOS accessed by a near-field hyperspectral imaging technique. We show, in particular, that short- and long-range frequency correlations of LDOS are controlled by different physical processes (multiple or single scattering processes, respectively) that can be---to some extent---manipulated independently. We also demonstrate that the single scattering contribution to the LDOS fluctuations is sensitive to subwavelength features of the material and, in particular, to the correlation length of its dielectric function. Our work paves the way towards a complete control of statistical properties of disordered photonic systems, allowing for designing materials with predefined LDOS correlations.
Molecular Kohn-Sham exchange-correlation potential from the correlated ab initio electron density
Gritsenko, Oleg V.; van Leeuwen, Robert; Baerends, Evert Jan
1995-09-01
The molecular Kohn-Sham (KS) exchange-correlation potential vxc has been constructed for LiH from the correlated ab initio density ρ by means of the simple iterative procedure developed by van Leeuwen and Baerends [Phys. Rev. A 49, 2421 (1994)]. The corresponding KS energy characteristics, such as the kinetic energy of noninteracting particles Ts, kinetic part of the exchange-correlation energy Tc, and energy of the highest occupied molecular orbital ɛN, have been obtained with reasonable accuracy. A relation between the form of vxc and the electronic structure of LiH has been discussed. Test calculations for the two-electron H2 molecule have shown the efficiency of the procedure.
Time-dependent density-functional theory for extended systems
Energy Technology Data Exchange (ETDEWEB)
Botti, Silvana [European Theoretical Spectroscopy Facility (ETSF) (Country Unknown); Schindlmayr, Arno [European Theoretical Spectroscopy Facility (ETSF) (Country Unknown); Del Sole, Rodolfo [European Theoretical Spectroscopy Facility (ETSF) (Country Unknown); Reining, Lucia [European Theoretical Spectroscopy Facility (ETSF) (Country Unknown)
2007-03-15
For the calculation of neutral excitations, time-dependent density functional theory (TDDFT) is an exact reformulation of the many-body time-dependent Schroedinger equation, based on knowledge of the density instead of the many-body wavefunction. The density can be determined in an efficient scheme by solving one-particle non-interacting Schroedinger equations-the Kohn-Sham equations. The complication of the problem is hidden in the-unknown-time-dependent exchange and correlation potential that appears in the Kohn-Sham equations and for which it is essential to find good approximations. Many approximations have been suggested and tested for finite systems, where even the very simple adiabatic local-density approximation (ALDA) has often proved to be successful. In the case of solids, ALDA fails to reproduce optical absorption spectra, which are instead well described by solving the Bethe-Salpeter equation of many-body perturbation theory (MBPT). On the other hand, ALDA can lead to excellent results for loss functions (at vanishing and finite momentum transfer). In view of this and thanks to recent successful developments of improved linear-response kernels derived from MBPT, TDDFT is today considered a promising alternative to MBPT for the calculation of electronic spectra, even for solids. After reviewing the fundamentals of TDDFT within linear response, we discuss different approaches and a variety of applications to extended systems.
Covariant density functional theory: Reexamining the structure of superheavy nuclei
Agbemava, S E; Nakatsukasa, T; Ring, P
2015-01-01
A systematic investigation of even-even superheavy elements in the region of proton numbers $100 \\leq Z \\leq 130$ and in the region of neutron numbers from the proton-drip line up to neutron number $N=196$ is presented. For this study we use five most up-to-date covariant energy density functionals of different types, with a non-linear meson coupling, with density dependent meson couplings, and with density-dependent zero-range interactions. Pairing correlations are treated within relativistic Hartree-Bogoliubov (RHB) theory based on an effective separable particle-particle interaction of finite range and deformation effects are taken into account. This allows us to assess the spread of theoretical predictions within the present covariant models for the binding energies, deformation parameters, shell structures and $\\alpha$-decay half-lives. Contrary to the previous studies in covariant density functional theory, it was found that the impact of $N=172$ spherical shell gap on the structure of superheavy elemen...
Afanasjev, A V
2015-01-01
The assessment of the global performance of the state-of-the-art covariant energy density functionals and related theoretical uncertainties in the description of ground state observables has recently been performed. Based on these results, the correlations between global description of binding energies and nuclear matter properties of covariant energy density functionals have been studied in this contribution.
Probing heterogeneous dynamics from spatial density correlation in glass-forming liquids
Li, Yan-Wei; Zhu, You-Liang; Sun, Zhao-Yan
2016-12-01
We numerically investigate the connection between spatial density correlation and dynamical heterogeneity in glass-forming liquids. We demonstrate that the cluster size defined by the spatial aggregation of densely packed particles (DPPs) can better capture the difference between the dynamics of the Lennard-Jones glass model and the Weeks-Chandler-Andersen truncation model than the commonly used pair correlation functions. More interestingly, we compare the mobility of DPPs and loosely packed particles, and we find that high local density correlates well with slow dynamics in systems with relatively hard repulsive interactions but links to mobile ones in the system with soft repulsive interactions at one relaxation time scale. Our results show clear evidence that the above model dependence behavior stems from the hopping motion of DPPs at the end of the caging stage due to the compressive nature of soft repulsive spheres, which activates the dynamics of DPPs in the α relaxation stage.
Ghosh, Soumen; Sonnenberger, Andrew L; Hoyer, Chad E; Truhlar, Donald G; Gagliardi, Laura
2015-08-11
The correct description of charge transfer in ground and excited states is very important for molecular interactions, photochemistry, electrochemistry, and charge transport, but it is very challenging for Kohn-Sham (KS) density functional theory (DFT). KS-DFT exchange-correlation functionals without nonlocal exchange fail to describe both ground- and excited-state charge transfer properly. We have recently proposed a theory called multiconfiguration pair-density functional theory (MC-PDFT), which is based on a combination of multiconfiguration wave function theory with a new type of density functional called an on-top density functional. Here we have used MC-PDFT to study challenging ground- and excited-state charge-transfer processes by using on-top density functionals obtained by translating KS exchange-correlation functionals. For ground-state charge transfer, MC-PDFT performs better than either the PBE exchange-correlation functional or CASPT2 wave function theory. For excited-state charge transfer, MC-PDFT (unlike KS-DFT) shows qualitatively correct behavior at long-range with great improvement in predicted excitation energies.
Spectral density function mapping using 15N relaxation data exclusively.
Farrow, N A; Zhang, O; Szabo, A; Torchia, D A; Kay, L E
1995-09-01
A method is presented for the determination of values of the spectral density function, J(omega), describing the dynamics of amide bond vectors from 15N relaxation parameters alone. Assuming that the spectral density is given by the sum of Lorentzian functions, the approach allows values of J(omega) to be obtained at omega = 0, omega N and 0.870 omega H, where omega N and omega H are Larmor frequencies of nitrogen and proton nuclei, respectively, from measurements of 15N T1, T2 and 1H-15N steady-state NOE values at a single spectrometer frequency. Alternatively, when measurements are performed at two different spectrometer frequencies of i and j MHz, J(omega) can be mapped at omega = 0, omega iN, omega jN, 0.870 omega iH and 0.870 omega iH, where omega iN, for example, is the 15N Larmor frequency for a spectrometer operating at 1 MHz. Additionally, measurements made at two different spectrometer frequencies enable contributions to transverse relaxation from motions on millisecond-microsecond time scales to be evaluated and permit assessment of whether a description of the internal dynamics is consistent with a correlation function consisting of a sum of exponentials. No assumptions about the specific form of the spectral density function describing the dynamics of the 15N-NH bond vector are necessary, provided that dJ(omega)/d omega is relatively constant between omega = omega H + omega N to omega = omega H - omega N. Simulations demonstrate that the method is accurate for a wide range of protein motions and correlation times, and experimental data establish the validity of the methodology. Results are presented for a folded and an unfolded form of the N-terminal SH3 domain of the protein drk.
Triplet correlation functions in liquid water
Energy Technology Data Exchange (ETDEWEB)
Dhabal, Debdas; Chakravarty, Charusita, E-mail: charus@chemistry.iitd.ac.in [Department of Chemistry, Indian Institute of Technology-Delhi, New Delhi 110016 (India); Singh, Murari [School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067 (India); Wikfeldt, Kjartan Thor [Science Institute, University of Iceland, 107 Reykjavik (Iceland)
2014-11-07
Triplet correlations have been shown to play a crucial role in the transformation of simple liquids to anomalous tetrahedral fluids [M. Singh, D. Dhabal, A. H. Nguyen, V. Molinero, and C. Chakravarty, Phys. Rev. Lett. 112, 147801 (2014)]. Here we examine triplet correlation functions for water, arguably the most important tetrahedral liquid, under ambient conditions, using configurational ensembles derived from molecular dynamics (MD) simulations and reverse Monte Carlo (RMC) datasets fitted to experimental scattering data. Four different RMC data sets with widely varying hydrogen-bond topologies fitted to neutron and x-ray scattering data are considered [K. T. Wikfeldt, M. Leetmaa, M. P. Ljungberg, A. Nilsson, and L. G. M. Pettersson, J. Phys. Chem. B 113, 6246 (2009)]. Molecular dynamics simulations are performed for two rigid-body effective pair potentials (SPC/E and TIP4P/2005) and the monatomic water (mW) model. Triplet correlation functions are compared with other structural measures for tetrahedrality, such as the O–O–O angular distribution function and the local tetrahedral order distributions. In contrast to the pair correlation functions, which are identical for all the RMC ensembles, the O–O–O triplet correlation function can discriminate between ensembles with different degrees of tetrahedral network formation with the maximally symmetric, tetrahedral SYM dataset displaying distinct signatures of tetrahedrality similar to those obtained from atomistic simulations of the SPC/E model. Triplet correlations from the RMC datasets conform closely to the Kirkwood superposition approximation, while those from MD simulations show deviations within the first two neighbour shells. The possibilities for experimental estimation of triplet correlations of water and other tetrahedral liquids are discussed.
2012-01-01
We investigate on the procedure of extracting a "spectral density" from mixed QM/MM calculations and employing it in open quantum systems models. In particular, we study the connection between the energy gap correlation function extracted from ground state QM/MM and the bath spectral density used as input in open quantum system approaches. We introduce a simple model which can give intuition on when the ground state QM/MM propagation will give the correct energy gap. We also discuss the role ...
Density functional theory in the solid state.
Hasnip, Philip J; Refson, Keith; Probert, Matt I J; Yates, Jonathan R; Clark, Stewart J; Pickard, Chris J
2014-03-13
Density functional theory (DFT) has been used in many fields of the physical sciences, but none so successfully as in the solid state. From its origins in condensed matter physics, it has expanded into materials science, high-pressure physics and mineralogy, solid-state chemistry and more, powering entire computational subdisciplines. Modern DFT simulation codes can calculate a vast range of structural, chemical, optical, spectroscopic, elastic, vibrational and thermodynamic phenomena. The ability to predict structure-property relationships has revolutionized experimental fields, such as vibrational and solid-state NMR spectroscopy, where it is the primary method to analyse and interpret experimental spectra. In semiconductor physics, great progress has been made in the electronic structure of bulk and defect states despite the severe challenges presented by the description of excited states. Studies are no longer restricted to known crystallographic structures. DFT is increasingly used as an exploratory tool for materials discovery and computational experiments, culminating in ex nihilo crystal structure prediction, which addresses the long-standing difficult problem of how to predict crystal structure polymorphs from nothing but a specified chemical composition. We present an overview of the capabilities of solid-state DFT simulations in all of these topics, illustrated with recent examples using the CASTEP computer program.
Combining Molecular Dynamics and Density Functional Theory
Kaxiras, Efthimios
2015-03-01
The time evolution of a system consisting of electrons and ions is often treated in the Born-Oppenheimer approximation, with electrons in their instantaneous ground state. This approach cannot capture many interesting processes that involved excitation of electrons and its effects on the coupled electron-ion dynamics. The time scale needed to accurately resolve the evolution of electron dynamics is atto-seconds. This poses a challenge to the simulation of important chemical processes that typically take place on time scales of pico-seconds and beyond, such as reactions at surfaces and charge transport in macromolecules. We will present a methodology based on time-dependent density functional theory for electrons, and classical (Ehrenfest) dynamics for the ions, that successfully captures such processes. We will give a review of key features of the method and several applications. These illustrate how the atomic and electronic structure evolution unravels the elementary steps that constitute a chemical reaction. In collaboration with: G. Kolesov, D. Vinichenko, G. Tritsaris, C.M. Friend, Departments of Physics and of Chemistry and Chemical Biology.
Bone mineral density, adiposity and cognitive functions
Directory of Open Access Journals (Sweden)
Hamid R Sohrabi
2015-02-01
Full Text Available Cognitive decline and dementia due to Alzheimer’s disease have been associated with genetic, lifestyle, and environmental factors. A number of potentially modifiable risk factors should be taken into account when preventive or ameliorative interventions targeting dementia and its preclinical stages are investigated. Bone mineral density (BMD and body composition are two such potentially modifiable risk factors, and their association with cognitive decline was investigated in this study. 164 participants, aged 34 to 87 years old (62.78±9.27, were recruited for this longitudinal study and underwent cognitive and clinical examinations at baseline and after three years. Blood samples were collected for apolipoprotein E (APOE genotyping and dual energy x-ray absorptiometry (DXA was conducted at the same day as cognitive assessment. Using hierarchical regression analysis, we found that BMD and lean body mass, as measured using DXA were significant predictors of episodic memory. Age, gender, APOE status and premorbid IQ were controlled for. Specifically, the List A learning from California Verbal Learning Test was significantly associated with BMD and lean mass both at baseline and at follow up assessment. Our findings indicate that there is a significant association between BMD and lean body mass and episodic verbal learning. While the involvement of modifiable lifestyle factors in human cognitive function has been examined in different studies, there is a need for further research to understand the potential underlying mechanisms.
Dynamic density functional theory of solid tumor growth: Preliminary models
Directory of Open Access Journals (Sweden)
Arnaud Chauviere
2012-03-01
Full Text Available Cancer is a disease that can be seen as a complex system whose dynamics and growth result from nonlinear processes coupled across wide ranges of spatio-temporal scales. The current mathematical modeling literature addresses issues at various scales but the development of theoretical methodologies capable of bridging gaps across scales needs further study. We present a new theoretical framework based on Dynamic Density Functional Theory (DDFT extended, for the first time, to the dynamics of living tissues by accounting for cell density correlations, different cell types, phenotypes and cell birth/death processes, in order to provide a biophysically consistent description of processes across the scales. We present an application of this approach to tumor growth.
Equation of State in a Generalized Relativistic Density Functional Approach
Typel, Stefan
2015-01-01
The basic concepts of a generalized relativistic density functional approach to the equation of state of dense matter are presented. The model is an extension of relativistic mean-field models with density-dependent couplings. It includes explicit cluster degrees of freedom. The formation and dissolution of nuclei is described with the help of mass shifts. The model can be adapted to the description of finite nuclei in order to study the effect of $\\alpha$-particle correlations at the nuclear surface on the neutron skin thickness of heavy nuclei. Further extensions of the model to include quark degrees of freedom or an energy dependence of the nucleon self-energies are outlined.
Design of exchange-correlation functionals through the correlation factor approach
Energy Technology Data Exchange (ETDEWEB)
Pavlíková Přecechtělová, Jana, E-mail: j.precechtelova@gmail.com, E-mail: Matthias.Ernzerhof@UMontreal.ca [Département de Chimie, Université de Montréal, C.P. 6128 Succursale A, Montréal, Québec H3C 3J7 (Canada); Institut für Chemie, Theoretische Chemie / Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin (Germany); Bahmann, Hilke; Kaupp, Martin [Institut für Chemie, Theoretische Chemie / Quantenchemie, Sekr. C7, Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin (Germany); Ernzerhof, Matthias, E-mail: j.precechtelova@gmail.com, E-mail: Matthias.Ernzerhof@UMontreal.ca [Département de Chimie, Université de Montréal, C.P. 6128 Succursale A, Montréal, Québec H3C 3J7 (Canada)
2015-10-14
The correlation factor model is developed in which the spherically averaged exchange-correlation hole of Kohn-Sham theory is factorized into an exchange hole model and a correlation factor. The exchange hole model reproduces the exact exchange energy per particle. The correlation factor is constructed in such a manner that the exchange-correlation energy correctly reduces to exact exchange in the high density and rapidly varying limits. Four different correlation factor models are presented which satisfy varying sets of physical constraints. Three models are free from empirical adjustments to experimental data, while one correlation factor model draws on one empirical parameter. The correlation factor models are derived in detail and the resulting exchange-correlation holes are analyzed. Furthermore, the exchange-correlation energies obtained from the correlation factor models are employed to calculate total energies, atomization energies, and barrier heights. It is shown that accurate, non-empirical functionals can be constructed building on exact exchange. Avenues for further improvements are outlined as well.
Non-Parametric Estimation of Correlation Functions
DEFF Research Database (Denmark)
Brincker, Rune; Rytter, Anders; Krenk, Steen
In this paper three methods of non-parametric correlation function estimation are reviewed and evaluated: the direct method, estimation by the Fast Fourier Transform and finally estimation by the Random Decrement technique. The basic ideas of the techniques are reviewed, sources of bias are pointed...... out, and methods to prevent bias are presented. The techniques are evaluated by comparing their speed and accuracy on the simple case of estimating auto-correlation functions for the response of a single degree-of-freedom system loaded with white noise....
Semiclassical approximations to quantum time correlation functions
Egorov, S. A.; Skinner, J. L.
1998-09-01
Over the last 40 years several ad hoc semiclassical approaches have been developed in order to obtain approximate quantum time correlation functions, using as input only the corresponding classical time correlation functions. The accuracy of these approaches has been tested for several exactly solvable gas-phase models. In this paper we test the accuracy of these approaches by comparing to an exactly solvable many-body condensed-phase model. We show that in the frequency domain the Egelstaff approach is the most accurate, especially at high frequencies, while in the time domain one of the other approaches is more accurate.
Exact Exchange-Correlation Functional for the Infinitely Stretched Hydrogen Molecule
Matito, Eduard; Lopez, Xabier; Ugalde, Jesus M
2016-01-01
The exchange-correlation hole density of the infinitely stretched (dissociated) hydrogen molecule can be cast into a closed analytical form by using its exact wave function. This permits to obtain an explicit exchange-correlation energy functional of the electron density which allows for its functional derivation to yield the corresponding Kohh-Sham effective exchange-correlation potential. We have shown that this exchange-correlation functional is exact for the dissociated hydrogen molecule, yields its dissociation energy correctly, and its corresponding exchange-correlation potential has the correct $-1/r$ asymptotic behavior.
Hoyer, Chad E; Gagliardi, Laura; Truhlar, Donald G
2015-11-05
Time-dependent Kohn-Sham density functional theory (TD-KS-DFT) is useful for calculating electronic excitation spectra of large systems, but the low-energy spectra are often complicated by artificially lowered higher-energy states. This affects even the lowest energy excited states. Here, by calculating the lowest energy spin-conserving excited state for atoms from H to K and for formaldehyde, we show that this problem does not occur in multiconfiguration pair-density functional theory (MC-PDFT). We use the tPBE on-top density functional, which is a translation of the PBE exchange-correlation functional. We compare to a robust multireference method, namely, complete active space second-order perturbation theory (CASPT2), and to TD-KS-DFT with two popular exchange-correlation functionals, PBE and PBE0. We find for atoms that the mean unsigned error (MUE) of MC-PDFT with the tPBE functional improves from 0.42 to 0.40 eV with a double set of diffuse functions, whereas the MUEs for PBE and PBE0 drastically increase from 0.74 to 2.49 eV and from 0.45 to 1.47 eV, respectively.
THE NORMAL BIVARIATE DENSITY FUNCTION AND ITS APPLICATIONS TO WEAPON SYSTEMS ANALYSIS, A REVIEW
The normal bivariate density function is derived from a priori considerations. It is discussed in terms of probability area in a plane, and as a...correlation surface. Several numerical methods of solving the normal bivariate distribution double integral are presented, and a curve is included for...given specific mathematical treatment. An Appendix examines the elliptical properties of normally correlated distributions. The investigation has resulted in a reference paper for the normal bivariate density function.
Correlation Function and Simplified TBA Equations for XXZ Chain
Directory of Open Access Journals (Sweden)
Minoru Takahashi
2011-01-01
Full Text Available The calculation of the correlation functions of Bethe ansatz solvable models is very difficult problem. Among these solvable models spin 1/2 XXX chain has been investigated for a long time. Even for this model only the nearest neighbor and the second neighbor correlations were known. In 1990's multiple integral formula for the general correlations is derived. But the integration of this formula is also very difficult problem. Recently these integrals are decomposed to products of one dimensional integrals and at zero temperature, zero magnetic field and isotropic case, correlation functions are expressed by log 2 and Riemann's zeta functions with odd integer argument ς(3,ς(5,ς(7,.... We can calculate density sub-matrix of successive seven sites. Entanglement entropy of seven sites is calculated. These methods can be extended to XXZ chain up to n=4. Correlation functions are expressed by the generalized zeta functions. Several years ago I derived new thermodynamic Bethe ansatz equation for XXZ chain. This is quite different with Yang-Yang type TBA equations and contains only one unknown function. This equation is very useful to get the high temperature expansion. In this paper we get the analytic solution of this equation at Δ=0.
A marked correlation function for constraining modified gravity models
White, Martin
2016-01-01
Future large scale structure surveys will provide increasingly tight constraints on our cosmological model. These surveys will report results on the distance scale and growth rate of perturbations through measurements of Baryon Acoustic Oscillations and Redshift-Space Distortions. It is interesting to ask: what further analyses should become routine, so as to test as-yet-unknown models of cosmic acceleration? Models which aim to explain the accelerated expansion rate of the Universe by modifications to General Relativity often invoke screening mechanisms which can imprint a non-standard density dependence on their predictions. This suggests density-dependent clustering as a `generic' constraint. This paper argues that a density-marked correlation function provides a density-dependent statistic which is easy to compute and report and requires minimal additional infrastructure beyond what is routinely available to such survey analyses. We give one realization of this idea and study it using low order perturbati...
Correlations of the density and of the current in non-equilibrium diffusive systems
Sadhu, Tridib; Derrida, Bernard
2016-11-01
We use fluctuating hydrodynamics to analyze the dynamical properties in the non-equilibrium steady state of a diffusive system coupled with reservoirs. We derive the two-time correlations of the density and of the current in the hydrodynamic limit in terms of the diffusivity and the mobility. Within this hydrodynamic framework we discuss a generalization of the fluctuation dissipation relation in a non-equilibrium steady state where the response function is expressed in terms of the two-time correlations. We compare our results to an exact solution of the symmetric exclusion process. This exact solution also allows one to directly verify the fluctuating hydrodynamics equation.
Density functional theory investigation of antiproton-helium collisions
Henkel, N; Lüdde, H J; Kirchner, T; 10.1103/PhysRevA.80.032704
2011-01-01
We revisit recent developments in the theoretical foundations of time-dependent density functional theory (TDDFT). TDDFT is then applied to the calculation of total cross sections for ionization processes in the antiproton-Helium collision system. The Kohn-Sham potential is approximated as the sum of the Hartree-exchange potential and a correlation potential that was proposed in the context of laser-induced ionization. Furthermore, some approaches to the problem of calculating the ionization probabilities from the density are discussed. Small projectile energies below 5keV are considered as well as those in the range from 5 to 1000 keV. Results are compared with former calculations and with experimental data. We find that the correlation potential yields no obvious improvement of the results over the exchange-only approximation where the correlation potential is neglected. Furthermore, we find the problem of calculating the desired observables crucial, introducing errors of at least the same order of magnitud...
Green's function formalism for highly correlated systems
Directory of Open Access Journals (Sweden)
F.Mancini
2006-01-01
Full Text Available We present the Composite Operator Method (COM as a modern approach to the study of strongly correlated electronic systems, based on the equation of motion and Green's function method. COM uses propagators of composite operators as building blocks at the basis of approximate calculations and algebra constrains to fix the representation of Green's functions in order to maintain the algebraic and symmetry properties.
Wave-function inspired density functional applied to the H$_2$/H$_2^+$ challenge
Zhang, Igor Ying; Scheffler, Matthias
2016-01-01
We start from the Bethe-Goldstone equation (BGE) to derive a simple orbital-dependent correlation functional -- BGE2 -- which terminates the BGE expansion at the second-order, but retains the self-consistent coupling of electron-pair orrelations. We demonstrate that BGE2 is size consistent and one-electron "self-correlation" free. The electron-pair correlation coupling ensures the correct H$_2$ dissociation limit and gives a finite correlation energy for any system even if it has a no energy gap. BGE2 provides a good description of both H$_2$ and H$_2^+$ dissociation, which is regarded as a great challenge in density functional theory (DFT). We illustrate the behavior of BGE2 analytically by considering H$_2$ in a minimal basis. Our analysis shows that BGE2 captures essential features of the adiabatic connection path that current state-of-the-art DFT approximations do not.
Cluster density functional theory for lattice models based on the theory of Möbius functions
Lafuente, Luis; Cuesta, José A.
2005-08-01
Rosenfeld's fundamental-measure theory for lattice models is given a rigorous formulation in terms of the theory of Möbius functions of partially ordered sets. The free-energy density functional is expressed as an expansion in a finite set of lattice clusters. This set is endowed with a partial order, so that the coefficients of the cluster expansion are connected to its Möbius function. Because of this, it is rigorously proven that a unique such expansion exists for any lattice model. The low-density analysis of the free-energy functional motivates a redefinition of the basic clusters (zero-dimensional cavities) which guarantees a correct zero-density limit of the pair and triplet direct correlation functions. This new definition extends Rosenfeld's theory to lattice models with any kind of short-range interaction (repulsive or attractive, hard or soft, one or multicomponent ...). Finally, a proof is given that these functionals have a consistent dimensional reduction, i.e. the functional for dimension d' can be obtained from that for dimension d (d' < d) if the latter is evaluated at a density profile confined to a d'-dimensional subset.
Cluster density functional theory for lattice models based on the theory of Moebius functions
Energy Technology Data Exchange (ETDEWEB)
Lafuente, Luis; Cuesta, Jose A [Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matematicas, Universidad Carlos III de Madrid, 28911 Leganes, Madrid (Spain)
2005-08-26
Rosenfeld's fundamental-measure theory for lattice models is given a rigorous formulation in terms of the theory of Moebius functions of partially ordered sets. The free-energy density functional is expressed as an expansion in a finite set of lattice clusters. This set is endowed with a partial order, so that the coefficients of the cluster expansion are connected to its Moebius function. Because of this, it is rigorously proven that a unique such expansion exists for any lattice model. The low-density analysis of the free-energy functional motivates a redefinition of the basic clusters (zero-dimensional cavities) which guarantees a correct zero-density limit of the pair and triplet direct correlation functions. This new definition extends Rosenfeld's theory to lattice models with any kind of short-range interaction (repulsive or attractive, hard or soft, one or multicomponent ...). Finally, a proof is given that these functionals have a consistent dimensional reduction, i.e. the functional for dimension d' can be obtained from that for dimension d (d' < d) if the latter is evaluated at a density profile confined to a d'-dimensional subset.
Institute of Scientific and Technical Information of China (English)
黄鼎祥
2011-01-01
Objective To investigate the correlation between lung density measured by MSCT and pulmonary function tests in patients with pulmonary emphysema. Methods The lung density and pulmonary function of 45 patients with pulmonary emphysema and 40 cases in control group were detected. The results of lung density measured by MSCT and pulmonary function tests were compared in the research. Results The VD of total lung measured by MSCT with pulmonary emphysema in expiratory and inspiratory time were significantly correlated to TLC, FEV1 and FEV1/FVC ( P ＜ 0. 01 ), but significantly negatively correlated to RV/TLC ( P ＜ 0. 01 ). The MLD of the total lung in the inspiratory time showed no correlation with PFT indices ( P ＞ 0. 05 ). Conclusion The lung density measured by MSCT was closely related to pulmonary function tests in pulmonary emphysema disease.%目的 探讨多层螺旋CT肺密度测定与肺气肿患者肺功能的相互关系.方法 对45例肺气肿患者及40例对照组人员的CT肺密度和肺功能进行测定,并将CT肺密度测定结果与肺功能结果进行对照研究.结果 肺气肿患者CT呼、吸气相 VD与TLC、FEV1及FEV1/FVC呈显著正相关(P0.05).结论 对于肺气肿疾病多层螺旋CT肺密度测定与肺功能检测有着密切的关系.
Greisch, Jean-François; Chmela, Jiří; Harding, Michael E; Wunderlich, Dirk; Schäfer, Bernhard; Ruben, Mario; Klopper, Wim; Schooss, Detlef; Kappes, Manfred M
2017-02-22
We report a combined investigation of europium(iii)9-oxo-phenalen-1-one (PLN) coordination complexes, [Eu(PLN)4AE](+) with AE = Mg, Ca, and Sr, using gas-phase photoluminescence, trapped ion-mobility spectrometry and density-functional computations. In order to sort out the structural impact of the alkali earth dications on the photoluminescence spectra, the experimental data are compared to the predicted ligand-field splittings as well as to the collision cross-sections for different isomers of [Eu(PLN)4AE](+). The best fitting interpretation is that one isomer family predominantly contributes to the recorded luminescence. The present work demonstrates the complexity of the coordination patterns of multicenter lanthanoid chelates involved in dynamical equilibria and the pertinence of using isolation techniques to elucidate their photophysical properties.
Density-dependence of functional spiking networks in vitro
Energy Technology Data Exchange (ETDEWEB)
Ham, Michael I [Los Alamos National Laboratory; Gintautuas, Vadas [Los Alamos National Laboratory; Rodriguez, Marko A [Los Alamos National Laboratory; Bettencourt, Luis M A [Los Alamos National Laboratory; Bennett, Ryan [UNIV OF NORTH TEXAS; Santa Maria, Cara L [UNIV OF NORTH TEXAS
2008-01-01
During development, the mammalian brain differentiates into specialized regions with unique functional abilities. While many factors contribute to this functional specialization, we explore the effect neuronal density can have on neuronal interactions. Two types of networks, dense (50,000 neurons and glia support cells) and sparse (12,000 neurons and glia support cells), are studied. A competitive first response model is applied to construct activation graphs that represent pairwise neuronal interactions. By observing the evolution of these graphs during development in vitro we observe that dense networks form activation connections earlier than sparse networks, and that link-!llltropy analysis of the resulting dense activation graphs reveals that balanced directional connections dominate. Information theoretic measures reveal in addition that early functional information interactions (of order 3) are synergetic in both dense and sparse networks. However, during development in vitro, such interactions become redundant in dense, but not sparse networks. Large values of activation graph link-entropy correlate strongly with redundant ensembles observed in the dense networks. Results demonstrate differences between dense and sparse networks in terms of informational groups, pairwise relationships, and activation graphs. These differences suggest that variations in cell density may result in different functional specialization of nervous system tissue also in vivo.
Hydrodynamic correlation functions in nematic liquid crystals
Lekkerkerker, H.N.W.; Carle, D.; Laidlaw, W.G.
1976-01-01
The result, recently discovered by Forster, that the strength factors of the nonpropagating modes in certain hydrodynamic correlation functions in nematic liquid crystals are not fully determined by the hydrodynamic matrix is reconsidered. Using time reversal and space inversion symmetry one finds t
Hydrodynamic correlation functions in nematic liquid crystals
Lekkerkerker, H.N.W.; Carle, D.; Laidlaw, W.G.
1976-01-01
The result, recently discovered by Forster, that the strength factors of the nonpropagating modes in certain hydrodynamic correlation functions in nematic liquid crystals are not fully determined by the hydrodynamic matrix is reconsidered. Using time reversal and space inversion symmetry one finds t
Ions in solution: density corrected density functional theory (DC-DFT).
Kim, Min-Cheol; Sim, Eunji; Burke, Kieron
2014-05-14
Standard density functional approximations often give questionable results for odd-electron radical complexes, with the error typically attributed to self-interaction. In density corrected density functional theory (DC-DFT), certain classes of density functional theory calculations are significantly improved by using densities more accurate than the self-consistent densities. We discuss how to identify such cases, and how DC-DFT applies more generally. To illustrate, we calculate potential energy surfaces of HO·Cl(-) and HO·H2O complexes using various common approximate functionals, with and without this density correction. Commonly used approximations yield wrongly shaped surfaces and/or incorrect minima when calculated self consistently, while yielding almost identical shapes and minima when density corrected. This improvement is retained even in the presence of implicit solvent.
Ions in solution: Density Corrected Density Functional Theory (DC-DFT)
Kim, Min-Cheol; Burke, Kieron
2014-01-01
Standard density functional approximations often give questionable results for odd-electron radical complexes, with the error typically attributed to self-interaction. In density corrected density functional theory (DC-DFT), certain classes of density functional theory calculations are significantly improved by using densities more accurate than the self-consistent densities. We discuss how to identify such cases, and how DC-DFT applies more generally. To illustrate, we calculate potential energy surfaces of HO$\\cdot$Cl$^-$ and HO$\\cdot$H$_2$O complexes using various common approximate functionals, with and without this density correction. Commonly used approximations yield wrongly shaped surfaces and/or incorrect minima when calculated self consistently, while yielding almost identical shapes and minima when density corrected. This improvement is retained even in the presence of implicit solvent.
Graphene on metals: A van der Waals density functional study
DEFF Research Database (Denmark)
Vanin, Marco; Mortensen, Jens Jørgen; Kelkkanen, Kari André;
2010-01-01
We use density functional theory (DFT) with a recently developed van der Waals density functional (vdW-DF) to study the adsorption of graphene on Co, Ni, Pd, Ag, Au, Cu, Pt, and Al(111) surfaces. In contrast to the local-density approximation (LDA) which predicts relatively strong binding for Ni...
Semilocal exchange hole with an application to range-separation density functional
Tao, Jianmin; Scuseria, Gustavo E
2016-01-01
Exchange-correlation hole is a central concept in density functional theory. It not only provides justification for an exchange-correlation energy functional, but also serves as a local ingredient in nonlocal range-separation density functional. However, due to the nonlocal nature, modelig the conventional exact exchange hole presents a great challenge to density functional theory. In this work, we propose a semilocal exchange hole underlying the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA functional. The present model is distinct from previous models at small separation between an electron and the hole around the electron. It is also different in the way it interpolates between the rapidly varying iso-orbital density and the slowly varying density, which is determined by the wave vector analysis based on the exactly solvable infinite barrier model for jellium surface. Our numerical tests show that the exchange hole generated from this model mimics the conventional exact exchange hole quite well for atoms....
Mean Spherical Approximation-Based Partitioned Density Functional Theory
Institute of Scientific and Technical Information of China (English)
ZHOU Shi-Qi
2003-01-01
Previous literature claims that the density functional theory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0(3)(r1, r2, r3) =ζ∫ dr4a(r4 - r1)a(r4 - r2)a(r4 - r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ζ and the short range of the a kernel function.Improvement over the previous theories is proposed and tested.
Mean Spherical Approximation-Based Partitioned Density Functional Theory
Institute of Scientific and Technical Information of China (English)
ZHOUShi-Qi
2003-01-01
Previous literature claims that the density functional theory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0(3)(r1, r2, r3) =(∫dr4a(r4-r1)a(r4-r2)a(r4-r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ξ and the short range of the a kernel function.Improvement over the previous theories is proposed and tested.
Towards reliable calculations of the correlation function
Maj, Radoslaw; 10.1142/S0218301307009221
2008-01-01
The correlation function of two identical pions interacting via Coulomb potential is computed for a general case of anisotropic particle's source of finite life time. The effect of halo is taken into account as an additional particle's source of large spatial extension. Due to the Coulomb interaction, the effect of halo is not limited to very small relative momenta but it influences the correlation function in a relatively large domain. The relativistic effects are discussed in detail and it is argued that the calculations have to be performed in the center-of-mass frame of particle's pair where the (nonrelativistic) wave function of particle's relative motion is meaningful. The Bowler-Sinyukov procedure to remove the Coulomb interaction is tested and it is shown to significantly underestimate the source's life time.
Exact four-spinon dynamical correlation function
Abada, A; Si-Lakhal, B; Seba, S; Abada, As
1998-01-01
We discuss some properties of the exact four-spinon dynamical correlation function in the antiferromagnetic spin 1/2 XXX-model the expression of which we derived recently. We show that the region in which it is not identically zero is different from and larger than the spin-wave continuum. We discuss its behavior as a function of the neutron momentum transfer $k$ for fixed values of the neutron energy $\\omega$ and compare it to the one corresponding to the exact two-spinon dynamical correlation function. We show that the overall shapes are quite similar but there are differences that we discuss. Particular is the fact that the symmetry about the axis $k=\\pi$ present in the two-spinon case seems to be lost in the four-spinon one. We finish with concluding remarks.
Polymer density functional approach to efficient evaluation of path integrals
DEFF Research Database (Denmark)
Brukhno, Andrey; Vorontsov-Velyaminov, Pavel N.; Bohr, Henrik
2005-01-01
A polymer density functional theory (P-DFT) has been extended to the case of quantum statistics within the framework of Feynman path integrals. We start with the exact P-DFT formalism for an ideal open chain and adapt its efficient numerical solution to the case of a ring. We show that, similarly......, the path integral problem can, in principle, be solved exactly by making use of the two-particle pair correlation function (2p-PCF) for the ends of an open polymer, half of the original. This way the exact data for one-dimensional quantum harmonic oscillator are reproduced in a wide range of temperatures......-consistent iteration so as to correctly account for the interparticle interactions. The algorithm is speeded up by taking convolutions with the aid of fast Fourier transforms. We apply this approximate path integral DFT (PI-DFT) method to systems within spherical symmetry: 3D harmonic oscillator, atoms of hydrogen...
Energetics of cyclohexane isomers: a density-functional study
Lee, C Y
1999-01-01
The binding energies and the geometric structures of conformational isomers of cyclohexane (C sub 6 H sub 1 sub 2) are determined from the density-functional theory combined with ultrasoft pseudopotentials and gradient-corrected nonlocal exchange-correlation functionals. The ground-state chair conformation is found to have a binding energy of 99.457 eV, and the metastable twist-boat conformation has 99.161 eV. The chair conformation converts to another conformation via a half-chair conformation with an energy barrier of 0.507 eV whereas the twist-boat conformation converts to another twist-boat conformation via a boat conformation with a much smaller energy barrier of 0.015 eV.
Geometry-based density functional theory an overview
Schmidt, M
2003-01-01
An overview of recent developments and applications of a specific density functional approach that originates from Rosenfeld's fundamental measure theory for hard spheres is given. Model systems that were treated include penetrable spheres that interact with a step function pair potential, the Widom-Rowlinson model, the Asakura-Oosawa colloid-polymer mixture, ternary mixtures of spheres, needles, and globular polymers, hard-body amphiphilic mixtures, fluids in porous media, and random sequential adsorption that describes non-equilibrium processes such as colloidal deposition and random car parking. In these systems various physical phenomena were studied, such as correlations in liquids, freezing and demixing phase behaviour, the properties of fluid interfaces with and without orientational order, and wetting and layering phenomena at walls.
Stretched hydrogen molecule from a constrained-search density-functional perspective
Energy Technology Data Exchange (ETDEWEB)
Valone, Steven M [Los Alamos National Laboratory; Levy, Mel [DIKE UNIV.
2009-01-01
Constrained-search density functional theory gives valuable insights into the fundamentals of density functional theory. It provides exact results and bounds on the ground- and excited-state density functionals. An important advantage of the theory is that it gives guidance in the construction of functionals. Here they engage constrained search theory to explore issues associated with the functional behavior of 'stretched bonds' in molecular hydrogen. A constrained search is performed with familiar valence bond wavefunctions ordinarily used to describe molecular hydrogen. The effective, one-electron hamiltonian is computed and compared to the corresponding uncorrelated, Hartree-Fock effective hamiltonian. Analysis of the functional suggests the need to construct different functionals for the same density and to allow a competition among these functions. As a result the correlation energy functional is composed explicitly of energy gaps from the different functionals.
Correlated Strength in Nuclear Spectral Function
Rohe, D; Asaturyan, R; Baker, O K; Bültmann, S; Carasco, C C; Day, D; Ent, R; Fenker, H C; Garrow, K; Gasparian, A; Gueye, P; Hauger, M; Honegger, A; Jourdan, J; Keppel, C E; Kubon, G; Lindgren, R; Lung, A; Mack, D J; Mitchell, J H; Mkrtchyan, H G; Mocelj, D; Normand, K; Petitjean, T; Rondon, Oscar A; Segbefia, E; Sick, I; Stepanyan, S; Tang, L; Tiefenbacher, F; Vulcan, W F; Warren, G; Wood, S A; Yuan, L; Zeier, M; Zhu, H; Zihlmann, B
2004-01-01
We have carried out an (e,e'p) experiment at high momentum transfer and in parallel kinematics to measure the strength of the nuclear spectral function S(k,E) at high nucleon momenta k and large removal energies E. This strength is related to the presence of short-range and tensor correlations, and was known hitherto only indirectly and with considerable uncertainty from the lack of strength in the independent-particle region. This experiment confirms by direct measurement the correlated strength predicted by theory.
Correlated Strength in the Nuclear Spectral Function
Energy Technology Data Exchange (ETDEWEB)
D. Rohe; C. S. Armstrong; R. Asaturyan; O. K. Baker; S. Bueltmann; C. Carasco; D. Day; R. Ent; H. C. Fenker; K. Garrow; A. Gasparian; P. Gueye; M. Hauger; A. Honegger; J. Jourdan; C. E. Keppel; G. Kubon; R. Lindgren; A. Lung; D. J. Mack; J. H. Mitchell; H. Mkrtchyan; D. Mocelj; K. Normand; T. Petitjean; O. Rondon; E. Segbefia; I. Sick; S. Stepanyan; L. Tang; F. Tiefenbacher; W. F. Vulcan; G. Warren; S. A. Wood; L. Yuan; M. Zeier; H. Zhu; B. Zihlmann
2004-10-01
We have carried out an (e,ep) experiment at high momentum transfer and in parallel kinematics to measure the strength of the nuclear spectral function S(k,E) at high nucleon momenta k and large removal energies E. This strength is related to the presence of short-range and tensor correlations, and was known hitherto only indirectly and with considerable uncertainty from the lack of strength in the independent-particle region. This experiment locates by direct measurement the correlated strength predicted by theory.
Correlation functions in theories with Lifshitz scaling
Keranen, Ville; Szepietowski, Phillip; Thorlacius, Larus
2016-01-01
The 2+1 dimensional quantum Lifshitz model can be generalised to a class of higher dimensional free field theories that exhibit Lifshitz scaling. When the dynamical critical exponent equals the number of spatial dimensions, equal time correlation functions of scaling operators in the generalised quantum Lifshitz model are given by a d-dimensional higher-derivative conformal field theory. Autocorrelation functions in the generalised quantum Lifshitz model in any number of dimensions can on the other hand be expressed in terms of autocorrelation functions of a two-dimensional conformal field theory. This also holds for autocorrelation functions in a strongly coupled Lifshitz field theory with a holographic dual of Einstein-Maxwell-dilaton type. The map to a two-dimensional conformal field theory extends to autocorrelation functions in thermal states and out- of-equilbrium states preserving symmetry under spatial translations and rotations in both types of Lifshitz models. Furthermore, the spectrum of quasinorma...
Dynamic density functional theory with hydrodynamic interactions and fluctuations
Energy Technology Data Exchange (ETDEWEB)
Donev, Aleksandar, E-mail: donev@courant.nyu.edu; Vanden-Eijnden, Eric, E-mail: eve2@courant.nyu.edu [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
2014-06-21
We derive a closed equation for the empirical concentration of colloidal particles in the presence of both hydrodynamic and direct interactions. The ensemble average of our functional Langevin equation reproduces known deterministic Dynamic Density Functional Theory (DDFT) [M. Rex and H. Löwen, “Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps,” Phys. Rev. Lett. 101(14), 148302 (2008)], and, at the same time, it also describes the microscopic fluctuations around the mean behavior. We suggest separating the ideal (non-interacting) contribution from additional corrections due to pairwise interactions. We find that, for an incompressible fluid and in the absence of direct interactions, the mean concentration follows Fick's law just as for uncorrelated walkers. At the same time, the nature of the stochastic terms in fluctuating DDFT is shown to be distinctly different for hydrodynamically-correlated and uncorrelated walkers. This leads to striking differences in the behavior of the fluctuations around Fick's law, even in the absence of pairwise interactions. We connect our own prior work [A. Donev, T. G. Fai, and E. Vanden-Eijnden, “A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law,” J. Stat. Mech.: Theory Exp. (2014) P04004] on fluctuating hydrodynamics of diffusion in liquids to the DDFT literature, and demonstrate that the fluid cannot easily be eliminated from consideration if one wants to describe the collective diffusion in colloidal suspensions.
Energy Technology Data Exchange (ETDEWEB)
Ahuja, B.L., E-mail: blahuja@yahoo.ik [Department of Physics, M.L. Sukhadia University, Udaipur 313001, Rajasthan (India); Raykar, Veera; Joshi, Ritu [Department of Physics, M.L. Sukhadia University, Udaipur 313001, Rajasthan (India); Tiwari, Shailja [Department of Physics, Govt. Women Engineering College, Ajmer 305001, Rajasthan (India); Talreja, Sonal [Department of Computer Science, M.L. Sukhadia University, Udaipur 313001 (India); Choudhary, Gopal [Department of Physics, Techno India NJR Institute of Technology, Udaipur 313001, Rajasthan (India)
2015-05-15
We report Compton profiles of SnS and SnTe at a momentum resolution of 0.34 a.u. using a 20 Ci {sup 137}Cs Compton spectrometer. To compare our experimental data, we have also computed the theoretical Compton profiles using density functional theory within linear combination of atomic orbitals (LCAO) method. To interpret the relative nature of bonding in these compounds, we have scaled the experimental and theoretical Compton profiles on equal-valence-electron-density (EVED). On the basis of EVED profiles, it is seen that SnTe shows more covalent character than SnS. To rectify the substantial disagreement between experimental and theoretical band gaps, we have also presented the energy bands and density of states of both the compounds using full-potential linearized augmented plane wave method (FP-LAPW) including spin–orbit interaction within the PBEsol exchange-correlation potential.
Accurate Semilocal Density Functional for Condensed-Matter Physics and Quantum Chemistry.
Tao, Jianmin; Mo, Yuxiang
2016-08-12
Most density functionals have been developed by imposing the known exact constraints on the exchange-correlation energy, or by a fit to a set of properties of selected systems, or by both. However, accurate modeling of the conventional exchange hole presents a great challenge, due to the delocalization of the hole. Making use of the property that the hole can be made localized under a general coordinate transformation, here we derive an exchange hole from the density matrix expansion, while the correlation part is obtained by imposing the low-density limit constraint. From the hole, a semilocal exchange-correlation functional is calculated. Our comprehensive test shows that this functional can achieve remarkable accuracy for diverse properties of molecules, solids, and solid surfaces, substantially improving upon the nonempirical functionals proposed in recent years. Accurate semilocal functionals based on their associated holes are physically appealing and practically useful for developing nonlocal functionals.
Accurate Semilocal Density Functional for Condensed-Matter Physics and Quantum Chemistry
Tao, Jianmin; Mo, Yuxiang
2016-08-01
Most density functionals have been developed by imposing the known exact constraints on the exchange-correlation energy, or by a fit to a set of properties of selected systems, or by both. However, accurate modeling of the conventional exchange hole presents a great challenge, due to the delocalization of the hole. Making use of the property that the hole can be made localized under a general coordinate transformation, here we derive an exchange hole from the density matrix expansion, while the correlation part is obtained by imposing the low-density limit constraint. From the hole, a semilocal exchange-correlation functional is calculated. Our comprehensive test shows that this functional can achieve remarkable accuracy for diverse properties of molecules, solids, and solid surfaces, substantially improving upon the nonempirical functionals proposed in recent years. Accurate semilocal functionals based on their associated holes are physically appealing and practically useful for developing nonlocal functionals.
Green's Dyadic, Spectral Function, Local Density of States, and Fluctuation Dissipation Theorem
Chew, W C; Dai, Q I
2015-01-01
The spectral functions are studied in conjunction with the dyadic Green's functions for various media. The dyadic Green's functions are found using the eigenfunction expansion method for homogeneous, inhomogeneous, periodic, lossless, lossy, and anisotropic media, guided by the Bloch- Floquet theorem. For the lossless media cases, the spectral functions can be directly related to the photon local density of states, and hence, to the electromagnetic energy density. For the lossy case, the spectral function can be related to the ?eld correlation function. Because of these properties, one can derive properties for ?eld correlations and the Langevin-source correlations without resorting to the uctuation dissipation theorem. The results are corroborated by the uctuation dissipation theorem. An expression for the local density of states for lossy, inhomogeneous, and dispersive media has also been suggested.
Bioinorganic Chemistry Modeled with the TPSSh Density Functional
DEFF Research Database (Denmark)
Kepp, Kasper Planeta
2008-01-01
In this work, the TPSSh density functional has been benchmarked against a test set of experimental structures and bond energies for 80 transition-metal-containing diatomics. It is found that the TPSSh functional gives structures of the same quality as other commonly used hybrid and nonhybrid func...... promising density functional for use and further development within the field of bioinorganic chemistry....
Multiple Soft Limits of Cosmological Correlation Functions
Joyce, Austin; Simonović, Marko
2015-01-01
We derive novel identities satisfied by inflationary correlation functions in the limit where two external momenta are taken to be small. We derive these statements in two ways: using background-wave arguments and as Ward identities following from the fixed-time path integral. Interestingly, these identities allow us to constrain some of the O(q^2) components of the soft limit, in contrast to their single-soft analogues. We provide several nontrivial checks of our identities both in the context of resonant non-Gaussianities and in small sound speed models. Additionally, we extend the relation at lowest order in external momenta to arbitrarily many soft legs, and comment on the many-soft extension at higher orders in the soft momentum. Finally, we consider how higher soft limits lead to identities satisfied by correlation functions in large-scale structure.
Multiple soft limits of cosmological correlation functions
Energy Technology Data Exchange (ETDEWEB)
Joyce, Austin [Enrico Fermi Institute and Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637 (United States); Khoury, Justin [Center for Particle Cosmology, Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104 (United States); Simonović, Marko, E-mail: ajoy@uchicago.edu, E-mail: jkhoury@sas.upenn.edu, E-mail: msimonov@sissa.it [SISSA, via Bonomea 265, 34136, Trieste (Italy)
2015-01-01
We derive novel identities satisfied by inflationary correlation functions in the limit where two external momenta are taken to be small. We derive these statements in two ways: using background-wave arguments and as Ward identities following from the fixed-time path integral. Interestingly, these identities allow us to constrain some of the O(q{sup 2}) components of the soft limit, in contrast to their single-soft analogues. We provide several nontrivial checks of our identities both in the context of resonant non-Gaussianities and in small sound speed models. Additionally, we extend the relation at lowest order in external momenta to arbitrarily many soft legs, and comment on the many-soft extension at higher orders in the soft momentum. Finally, we consider how higher soft limits lead to identities satisfied by correlation functions in large-scale structure.
Equilibrium time correlation functions in open systems
Zhu, Jinglong; Agarwal, Animesh; Site, Luigi Delle
2014-01-01
We study equilibrium time correlation functions for liquid water at room temperature employing the Molecular Dynamics (MD) adaptive resolution method AdResS in its Grand Canonical formulation (GC-AdResS). This study introduces two technical innovations: the employment of a local thermostat that acts only in the reservoir and the consequent construction of an "ideal" Grand Canonical reservoir of particles and energy. As a consequence the artificial action of a thermostat in the calculation of equilibrium time correlation functions of standard NVT simulations is efficiently removed. The success of the technical innovation provides the basis for formulating a profound conceptual problem, that is the extension of Liouville theorem to open systems (Grand Canonical ensemble), a question, so far, treated neither in MD nor (in general) in statistical physics.
Total Correlation Function Integrals and Isothermal Compressibilities from Molecular Simulations
DEFF Research Database (Denmark)
Wedberg, Rasmus; Peters, Günther H.j.; Abildskov, Jens
2008-01-01
Generation of thermodynamic data, here compressed liquid density and isothermal compressibility data, using molecular dynamics simulations is investigated. Five normal alkane systems are simulated at three different state points. We compare two main approaches to isothermal compressibilities: (1...... in approximately the same amount of time. This suggests that computation of total correlation function integrals is a route to isothermal compressibility, as accurate and fast as well-established benchmark techniques. A crucial step is the integration of the radial distribution function. To obtain sensible results...
Thyroid function and bone mineral density among Indian subjects
Directory of Open Access Journals (Sweden)
Raman K Marwaha
2012-01-01
Full Text Available Background : Thyroid hormones affect bone remodeling in patients with thyroid disease by acting directly or indirectly on bone cells. In view of limited information on correlation of thyroid function with bone mineral density (BMD in euthyroid subjects, we undertook this study to evaluate the correlation between thyroid function with BMD in subjects with normal thyroid function and subclinical hypothyroidism. Material and Methods : A total of 1290 subjects included in this cross sectional study, were divided in Group-1 with normal thyroid function and Group-2 with subclinical hypothyroidism. Fasting blood samples were drawn for the estimation of serum 25(OHD, intact parathyroid hormone, total and ionized calcium, inorganic phosphorus, and alkaline phosphatase. BMD at lumbar spine, femur, and forearm was measured. Results : BMD at all sites (radius, femur, and spine were comparable in both groups. There was no difference in BMD when subjects were divided in tertiles of TSH in either group. In group-1, FT4 and TSH were positively associated with BMD at 33% radius whereas FT3 was negatively associated with BMD at femoral neck in multiple regression analysis after adjustment for age, sex, BMI, 25(OHD and PTH levels. In group-2, there was no association observed between TSH and BMD at any site. Amongst all study subjects FT4 and FT3 were positively correlated with BMD at lumbar spine and radius respectively among all subjects. Conclusion: TSH does not affect BMD in euthyroid subjects and subjects with subclinical hypothyroidism. Thyroid hormones appear to have more pronounced positive effect on cortical than trabecular bone in euthyroid subjects.
Energy Technology Data Exchange (ETDEWEB)
Zobelli, Alberto [Laboratoire de Physique des Solides, Univ. Paris Sud, CNRS UMR, Orsay (France); Ivanovskaya, Viktoria; Wagner, Philipp; Yaya, Abu; Ewels, Chris P. [Institut des Materiaux Jean Rouxel (IMN), CNRS UMR, University of Nantes (France); Suarez-Martinez, Irene [Nanochemistry Research Institute, Curtin University of Technology, Perth, Western Australia (Australia)
2012-02-15
The density functional tight binding approach (DFTB) is well adapted for the study of point and line defects in graphene based systems. After briefly reviewing the use of DFTB in this area, we present a comparative study of defect structures, energies, and dynamics between DFTB results obtained using the dftb+ code, and density functional results using the localized Gaussian orbital code, AIMPRO. DFTB accurately reproduces structures and energies for a range of point defect structures such as vacancies and Stone-Wales defects in graphene, as well as various unfunctionalized and hydroxylated graphene sheet edges. Migration barriers for the vacancy and Stone-Wales defect formation barriers are accurately reproduced using a nudged elastic band approach. Finally we explore the potential for dynamic defect simulations using DFTB, taking as an example electron irradiation damage in graphene. DFTB-MD derived sputtering energy threshold map for a carbon atom in a graphene plane. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Mo, Yuxiang; Car, Roberto; Staroverov, Viktor N.; Scuseria, Gustavo E.; Tao, Jianmin
2017-01-01
Recently, Tao and Mo developed a semilocal exchange-correlation density functional. The exchange part of this functional is derived from a density-matrix expansion corrected to reproduce the fourth-order gradient expansion of the exchange energy in the slowly-varying-density limit, while the correlation part is based on the Tao-Perdew-Staroverov-Scuseria (TPSS) correlation functional, with a modification for the low-density limit. In the present paper, the Tao-Mo (TM) functional is assessed by computing various properties of solids and jellium surfaces. This includes 22 lattice constants and bulk moduli, 30 band gaps, seven cohesive energies, and jellium surface exchange and correlation energies for the density parameter rs in the range from 2 to 3 bohr. Our calculations show that the TM approximation can yield consistently high accuracy for most properties considered here, with mean absolute errors (MAEs) of 0.025 Å for lattice constants, 7.0 GPa for bulk moduli, 0.08 eV/atom for cohesive energies, and 35 erg /c m2 for surface exchange-correlation energies. The MAE in band gaps is larger than that of TPSS, but slightly smaller than the errors of the local spin-density approximation, Perdew-Burke-Ernzerhof generalized gradient approximation, and revised TPSS. However, band gaps are still underestimated, particularly for large-gap semiconductors, compared to the Heyd-Scuseria-Ernzerhof nonlocal screened hybrid functional.
Fattoyev, F J; Li, Bao-An
2014-01-01
According to the Hugenholtz-Van Hove theorem, the nuclear symmetry energy $S(\\rho)$ and its slope $L(\\rho)$ at arbitrary densities can be decomposed in terms of the density and momentum dependence of the single-nucleon potentials in isospin-asymmetric nuclear matter which are potentially accessible to experiment. We quantify the correlations between several well-known isovector observables and $L(\\rho)$ to locate the density range in which each isovector observable is most sensitive to the density dependence of the $S(\\rho)$. We then study the correlation coefficients between those isovector observables and all the components of the $L(\\rho)$. The neutron skin thickness of $^{208}$Pb is found to be strongly correlated with the $L(\\rho)$ at a subsaturation density of $\\rho = 0.59 \\rho_0$ through the density dependence of the first-order symmetry potential. Neutron star radii are found to be strongly correlated with the $L(\\rho)$ over a wide range of supra-saturation densities mainly through both the density an...
Nusser, Adi
2017-09-01
The peculiar velocity of a mass tracer is on average aligned with the dipole modulation of the surrounding mass density field. We present a first measurement of the correlation between radial peculiar velocities of objects in the cosmicflows-3 catalogue and the dipole moment of the 2MRS galaxy distribution in concentric spherical shells centred on these objects. Limiting the analysis to cosmicflows-3 objects with distances of 100h-1 Mpc, the correlation function is detected at a confidence level of ≳ 4σ. The measurement is found consistent with the standard ΛCDM model at the ≲ 1.7σ level. We formally derive the constraints 0.32 confidence level) or equivalently 0.34 type of correlations.
Multicomponent density-functional theory for time-dependent systems
Butriy, O.; Ebadi, H.; de Boeij, P. L.; van Leeuwen, R.; Gross, E. K. U.
2007-01-01
We derive the basic formalism of density functional theory for time-dependent electron-nuclear systems. The basic variables of this theory are the electron density in body-fixed frame coordinates and the diagonal of the nuclear N-body density matrix. The body-fixed frame transformation is carried ou
Insight into Structural Phase Transitions from Density Functional Theory
Ruzsinszky, Adrienn
2014-03-01
Structural phase transitions caused by high pressure or temperature are very relevant in materials science. The high pressure transitions are essential to understand the interior of planets. Pressure or temperature induced phase transitions can be relevant to understand other phase transitions in strongly correlated systems or molecular crystals.Phase transitions are important also from the aspect of method development. Lower level density functionals, LSDA and GGAs all fail to predict the lattice parameters of different polymorphs and the phase transition parameters at the same time. At this time only nonlocal density functionals like HSE and RPA have been proved to resolve the geometry-energy dilemma to some extent in structural phase transitions. In this talk I will report new results from the MGGA_MS family of meta-GGAs and give an insight why this type of meta-GGAs can give a systematic improvement of the geometry and phase transition parameters together. I will also present results from the RPA and show a possible way to improve beyond RPA.
Numerical Methods for a Kohn-Sham Density Functional Model Based on Optimal Transport.
Chen, Huajie; Friesecke, Gero; Mendl, Christian B
2014-10-14
In this paper, we study numerical discretizations to solve density functional models in the "strictly correlated electrons" (SCE) framework. Unlike previous studies, our work is not restricted to radially symmetric densities. In the SCE framework, the exchange-correlation functional encodes the effects of the strong correlation regime by minimizing the pairwise Coulomb repulsion, resulting in an optimal transport problem. We give a mathematical derivation of the self-consistent Kohn-Sham-SCE equations, construct an efficient numerical discretization for this type of problem for N = 2 electrons, and apply it to the H2 molecule in its dissociating limit.
Energy Technology Data Exchange (ETDEWEB)
Zhou, Yongxi; Ernzerhof, Matthias, E-mail: Matthias.Ernzerhof@UMontreal.ca [Département de Chimie, Université de Montréal, C.P. 6128, Succursale A, Montréal, Québec H3C 3J7 (Canada); Bahmann, Hilke [Department of Chemistry, Technische Universität Berlin, Strasse des 17 Juni, Berlin (Germany)
2015-09-28
Drawing on the adiabatic connection of density functional theory, exchange-correlation functionals of Kohn-Sham density functional theory are constructed which interpolate between the extreme limits of the electron-electron interaction strength. The first limit is the non-interacting one, where there is only exchange. The second limit is the strong correlated one, characterized as the minimum of the electron-electron repulsion energy. The exchange-correlation energy in the strong-correlation limit is approximated through a model for the exchange-correlation hole that is referred to as nonlocal-radius model [L. O. Wagner and P. Gori-Giorgi, Phys. Rev. A 90, 052512 (2014)]. Using the non-interacting and strong-correlated extremes, various interpolation schemes are presented that yield new approximations to the adiabatic connection and thus to the exchange-correlation energy. Some of them rely on empiricism while others do not. Several of the proposed approximations yield the exact exchange-correlation energy for one-electron systems where local and semi-local approximations often fail badly. Other proposed approximations generalize existing global hybrids by using a fraction of the exchange-correlation energy in the strong-correlation limit to replace an equal fraction of the semi-local approximation to the exchange-correlation energy in the strong-correlation limit. The performance of the proposed approximations is evaluated for molecular atomization energies, total atomic energies, and ionization potentials.
Significance of input correlations in striatal function.
Directory of Open Access Journals (Sweden)
Man Yi Yim
2011-11-01
Full Text Available The striatum is the main input station of the basal ganglia and is strongly associated with motor and cognitive functions. Anatomical evidence suggests that individual striatal neurons are unlikely to share their inputs from the cortex. Using a biologically realistic large-scale network model of striatum and cortico-striatal projections, we provide a functional interpretation of the special anatomical structure of these projections. Specifically, we show that weak pairwise correlation within the pool of inputs to individual striatal neurons enhances the saliency of signal representation in the striatum. By contrast, correlations among the input pools of different striatal neurons render the signal representation less distinct from background activity. We suggest that for the network architecture of the striatum, there is a preferred cortico-striatal input configuration for optimal signal representation. It is further enhanced by the low-rate asynchronous background activity in striatum, supported by the balance between feedforward and feedback inhibitions in the striatal network. Thus, an appropriate combination of rates and correlations in the striatal input sets the stage for action selection presumably implemented in the basal ganglia.
The correlation function of radio sources
Loan, A J; Lahav, O
1996-01-01
We investigate the large-scale clustering of radio sources in the Green Bank and Parkes-MIT-NRAO 4.85 GHz surveys by measuring the angular two-point correlation function w(\\theta). Excluding contaminated areas, the two surveys together cover 70 per cent of the whole sky. We find both surveys to be reasonably complete above 50 mJy. On the basis of previous studies, the radio sources are galaxies and radio-loud quasars lying at redshifts up to z \\sim 4, with a median redshift z \\sim 1. This provides the opportunity to probe large-scale structures in a volume far larger than that within the reach of present optical and infrared surveys. We detect a clustering signal w(\\theta) correlation function in comoving coordinates \\xi(r_c,z) = ( r_c / r_0 )^{-\\gamma} (1+z)^{\\gamma-(3+\\epsilon)}, where \\gamma = 1.8, and the redshift distribution N(z) of the radio galaxies, we constrain the r_0--\\epsilon parameter space. For `stable clustering' (\\epsilon = 0), we find the correlation length r_0 \\approx 18 Mpc/h, larger than ...
Dipole polarizability of 120Sn and nuclear energy density functionals
Hashimoto, T; Reinhard, P -G; Tamii, A; von Neumann-Cosel, P; Adachi, T; Aoi, N; Bertulani, C A; Fujita, H; Fujita, Y; Ganioǧlu, E; Hatanaka, K; Iwamoto, C; Kawabata, T; Khai, N T; Krugmann, A; Martin, D; Matsubara, H; Miki, K; Neveling, R; Okamura, H; Ong, H J; Poltoratska, I; Ponomarev, V Yu; Richter, A; Sakaguchi, H; Shimbara, Y; Shimizu, Y; Simonis, J; Smit, F D; Süsoy, G; Thies, J H; Suzuki, T; Yosoi, M; Zenihiro, J
2015-01-01
The electric dipole strength distribution in 120Sn between 5 and 22 MeV has been determined at RCNP Osaka from a polarization transfer analysis of proton inelastic scattering at E_0 = 295 MeV and forward angles including 0{\\deg}. Combined with photoabsorption data an electric dipole polarizability alpha_D(120Sn) = 8.93(36) fm^3 is extracted. The correlation of this value with alpha_D for 208Pb serves as a test of energy density functionals (EDFs). The majority of models based on Skyrme interactions can describe the data while relativistic approaches fail. The accuracy of the experimental results provides important constraints on the static isovector properties of EDFs used to predict symmetry energy parameters and the neutron skin thickness of nuclei.
Band Anticrossing in Dilute Germanium Carbides Using Hybrid Density Functionals
Stephenson, Chad A.; O'brien, William A.; Qi, Meng; Penninger, Michael; Schneider, William F.; Wistey, Mark A.
2016-04-01
Dilute germanium carbides (Ge1- x C x ) offer a direct bandgap for compact silicon photonics, but widely varying properties have been reported. This work reports improved band structure calculations for Ge1- x C x using ab initio simulations that employ the HSE06 exchange-correlation density functional. Contrary to Vegard's law, the conduction band minimum at Γ is consistently found to decrease with increasing C content, while L and X valleys change much more slowly. The calculated Ge bandgap is within 11% of experimental values. A decrease in energy at the Γ conduction band valley of (170 meV ± 50)/%C is predicted, leading to a direct bandgap for x > 0.008. These results indicate a promising material for Group IV lasers.
New angles on energy correlation functions
Moult, Ian; Necib, Lina; Thaler, Jesse
2016-12-01
Jet substructure observables, designed to identify specific features within jets, play an essential role at the Large Hadron Collider (LHC), both for searching for signals beyond the Standard Model and for testing QCD in extreme phase space regions. In this paper, we systematically study the structure of infrared and collinear safe substructure observables, defining a generalization of the energy correlation functions to probe n-particle correlations within a jet. These generalized correlators provide a flexible basis for constructing new substructure observables optimized for specific purposes. Focusing on three major targets of the jet substructure community — boosted top tagging, boosted W/Z/H tagging, and quark/gluon discrimination — we use power-counting techniques to identify three new series of powerful discriminants: M i , N i , and U i . The M i series is designed for use on groomed jets, providing a novel example of observables with improved discrimination power after the removal of soft radiation. The N i series behave parametrically like the N -subjettiness ratio observables, but are defined without respect to subjet axes, exhibiting improved behavior in the unresolved limit. Finally, the U i series improves quark/gluon discrimination by using higher-point correlators to simultaneously probe multiple emissions within a jet. Taken together, these observables broaden the scope for jet substructure studies at the LHC.
Indian Academy of Sciences (India)
Paul W Ayers; Mel Levy
2005-09-01
Using the constrained search and Legendre-transform formalisms, one can derive ``generalized” density-functional theories, in which the fundamental variable is either the electron pair density or the second-order reduced density matrix. In both approaches, the -representability problem is solved by the functional, and the variational principle is with respect to all pair densities (density matrices) that are nonnegative and appropriately normalized. The Legendre-transform formulation provides a lower bound on the constrained-search functional. Noting that experience in density-functional and density-matrix theories suggests that it is easier to approximate functionals than it is to approximate the set of -representable densities sheds some light on the significance of this work.
Correlation of Critical Current Density with Cu3+ Concentration and Density in YBa2Cu3O7-x
Dou, S. X.; Liu, H. K.; Zhou, J. P.; Bourdillon, A. J.; Savvides, N.; Apperley, M.; Gouch, A.; Sorrell, C. C.
Superconducting YBa2Cu3O7 wires and tapes were fabricated by cold drawing, rolling and extrusion processes. It was found that the critical current density, after O2 equilibration, correlates both with density and Cu3+ concentration. Full density was achieved by using a special heat treatment, but the critical current density was low owing to the low Cu3+ concentration present in this heavily twinned material. The best critical current density results were obtained for material with density of 92-95% of the theoretical value. The low critical current density of the porous specimens is attributed not only to a poor connectivity between grains but also to a low Cu3+ concentration due to the instability of Cu3+ at crystallite surfaces which increase in area with specimen porosity.
Karasiev, V.; López-Boada, R.
1998-09-01
The line-integral method developed by van Leeuwen and Baerends [Phys. Rev. A 51, 170 (1995)] is applied to the calculation of the differences of correlation energy functional values ΔEDFTc=EDFTc[ρHF]- EDFTc[ρexact], where ρHF is the Hartree-Fock density and ρexact is the near-exact one (DFT is density-functional theory). From the Kohn-Sham wave functions yielding Hartree-Fock and the near-exact densities, the corresponding noninteracting kinetic energies and the exchange energies are calculated. An approximate relation between EDFTc[ρHF] and the conventional quantum chemistry correlation energy is presented, accurate to <=4μ hartree for the isoelectronic series of He, and Li, and for the Be atom.
A density functional for sparse matter
DEFF Research Database (Denmark)
Langreth, D.C.; Lundqvist, Bengt; Chakarova-Kack, S.D.;
2009-01-01
forces in molecules, to adsorbed molecules, like benzene, naphthalene, phenol and adenine on graphite, alumina and metals, to polymer and carbon nanotube (CNT) crystals, and hydrogen storage in graphite and metal-organic frameworks (MOFs), and to the structure of DNA and of DNA with intercalators......Sparse matter is abundant and has both strong local bonds and weak nonbonding forces, in particular nonlocal van der Waals (vdW) forces between atoms separated by empty space. It encompasses a broad spectrum of systems, like soft matter, adsorption systems and biostructures. Density...
First-principles derivation of density-functional formalism for quenched-annealed systems
Lafuente, Luis; Cuesta, José A.
2006-10-01
We derive from first principles (without resorting to the replica trick) a density-functional theory for fluids in quenched disordered matrices (QA-DFT). We show that the disorder-averaged free energy of the fluid is a functional of the average density profile of the fluid as well as the pair correlation of the fluid and matrix particles. For practical reasons it is preferable to use another functional: the disorder-averaged free energy plus the fluid-matrix interaction energy, which, for fixed fluid-matrix interaction potential, is a functional only of the average density profile of the fluid. When the matrix is created as a quenched configuration of another fluid, the functional can be regarded as depending on the density profile of the matrix fluid as well. In this situation, the replica Ornstein-Zernike equations which do not contain the blocking parts of the correlations can be obtained as functional identities in this formalism, provided the second derivative of this functional is interpreted as the connected part of the direct correlation function. The blocking correlations are totally absent from QA-DFT, but nevertheless the thermodynamics can be entirely obtained from the functional. We apply the formalism to obtain the exact functional for an ideal fluid in an arbitrary matrix, and discuss possible approximations for nonideal fluids.
Introduction to Classical Density Functional Theory by a Computational Experiment
Jeanmairet, Guillaume; Levy, Nicolas; Levesque, Maximilien; Borgis, Daniel
2014-01-01
We propose an in silico experiment to introduce the classical density functional theory (cDFT). Density functional theories, whether quantum or classical, rely on abstract concepts that are nonintuitive; however, they are at the heart of powerful tools and active fields of research in both physics and chemistry. They led to the 1998 Nobel Prize in…
Density Functional Theory with Spatial-Symmetry Breaking and Configuration Mixing
Lesinski, Thomas
2013-01-01
This article generalizes the notion of the local density of a many-body system to introduce collective coordinates as explicit degrees of freedom. It is shown that the energy of the system can be expressed as a functional of this object. The latter can in turn be factorized as the product of the square of a collective wave function and a normalized collective-coordinate-dependent density. Energy minimization translates into a set of coupled equations, i.e. a local Schr\\"odinger equation for the collective wave function and a set of Kohn-Sham equations for optimizing the normalized density at each point in the collective space. These equations reformulate the many-body problem exactly provided one is able to determine density- and collective-wave-function-dependent terms of the collective mass and potential which play a similar role to the exchange-correlation term in electronic Kohn-Sham density functional theory.
Ramos, J G G S; Barbosa, A L R; Carlson, B V; Frederico, T; Hussein, M S
2016-01-01
We derive analytical expressions for the correlation functions of the electronic conductance fluctuations of an open quantum dot under several conditions. Both the variation of energy and that of an external parameter, such as an applied perpendicular or parallel magnetic fields, are considered in the general case of partial openness. These expressions are then used to obtain the ensemble-averaged density of maxima, a measure recently suggested to contain invaluable information concerning the correlation widths of chaotic systems. The correlation width is then calculated for the case of energy variation, and a significant deviation from the Weisskopf estimate is found in the case of two terminals. The results are extended to more than two terminals. All of our results are analytical. The use of these results in other fields, such as nuclei, where the system can only be studied through a variation of the energy, is then discussed.
High Temperature, high pressure equation of state density correlations and viscosity correlations
Energy Technology Data Exchange (ETDEWEB)
Tapriyal, D.; Enick, R.; McHugh, M.; Gamwo, I.; Morreale, B.
2012-07-31
Global increase in oil demand and depleting reserves has derived a need to find new oil resources. To find these untapped reservoirs, oil companies are exploring various remote and harsh locations such as deep waters in Gulf of Mexico, remote arctic regions, unexplored deep deserts, etc. Further, the depth of new oil/gas wells being drilled has increased considerably to tap these new resources. With the increase in the well depth, the bottomhole temperature and pressure are also increasing to extreme values (i.e. up to 500 F and 35,000 psi). The density and viscosity of natural gas and crude oil at reservoir conditions are critical fundamental properties required for accurate assessment of the amount of recoverable petroleum within a reservoir and the modeling of the flow of these fluids within the porous media. These properties are also used to design appropriate drilling and production equipment such as blow out preventers, risers, etc. With the present state of art, there is no accurate database for these fluid properties at extreme conditions. As we have begun to expand this experimental database it has become apparent that there are neither equations of state for density or transport models for viscosity that can be used to predict these fundamental properties of multi-component hydrocarbon mixtures over a wide range of temperature and pressure. Presently, oil companies are using correlations based on lower temperature and pressure databases that exhibit an unsatisfactory predictive capability at extreme conditions (e.g. as great as {+-} 50%). From the perspective of these oil companies that are committed to safely producing these resources, accurately predicting flow rates, and assuring the integrity of the flow, the absence of an extensive experimental database at extreme conditions and models capable of predicting these properties over an extremely wide range of temperature and pressure (including extreme conditions) makes their task even more daunting.
Computing a Function of Correlated Sources
Sefidgaran, Milad
2011-01-01
A receiver wants to compute a function f of two correlated sources X and Y and side information Z. What is the minimum number of bits that needs to be communicated by each transmitter? In this paper, we derive inner and outer bounds to the rate region of this problem which coincide in the cases where f is partially invertible and where the sources are independent given the side information. From the former case we recover the Slepian-Wolf rate region and from the latter case we recover Orlitsky and Roche's single source result.
Nuclear correlation functions in lattice QCD
Detmold, William
2012-01-01
We consider the problem of calculating the large number of Wick contractions necessary to compute states with the quantum numbers of many baryons in lattice QCD. We consider a constructive approach and a determinant-based approach and show that these methods allow the required contractions to be performed in computationally manageable amount of time for certain choices of interpolating operators. Examples of correlation functions computed using these techniques are shown for the quantum numbers of the light nuclei, He, Be, C, O and Si.
Pair correlation function for spin glasses
Fernández, Julio F.; Alonso, Juan J.
2012-10-01
We extract a pair correlation function (PCF) from probability distributions of the spin-overlap parameter q. The distributions come from Monte Carlo simulations. A measure, w, of the thermal fluctuations of magnetic patterns follows from the PCFs. We also obtain rms deviations (over different system samples) δp away from average probabilities for q. For the linear system sizes L that we have studied, w and δp are independent of L in the Edwards-Anderson model but scale as 1/L and L, respectively, in the Sherrington-Kirkpatrick model.
Molecular density functional theory of water including density-polarization coupling.
Jeanmairet, Guillaume; Levy, Nicolas; Levesque, Maximilien; Borgis, Daniel
2016-06-22
We present a three-dimensional molecular density functional theory of water derived from first-principles that relies on the particle's density and multipolar polarization density and includes the density-polarization coupling. This brings two main benefits: (i) scalar density and vectorial multipolar polarization density fields are much more tractable and give more physical insight than the full position and orientation densities, and (ii) it includes the full density-polarization coupling of water, that is known to be non-vanishing but has never been taken into account. Furthermore, the theory requires only the partial charge distribution of a water molecule and three measurable bulk properties, namely the structure factor and the Fourier components of the longitudinal and transverse dielectric susceptibilities.
Molecular density functional theory of water including density-polarization coupling
Jeanmairet, Guillaume; Levesque, Maximilien; Borgis, Daniel
2016-01-01
We present a three-dimensional molecular density functional theory (MDFT) of water derived from first-principles that relies on the particle's density and multipolar polarization density and includes the density-polarization coupling. This brings two main benefits: ($i$) a scalar density and a vectorial multipolar polarization density fields are much more tractable and give more physical insight than the full position and orientation densities, and ($ii$) it includes the full density-polarization coupling of water, that is known to be non-vanishing but has never been taken into account. Furthermore, the theory requires only the partial charge distribution of a water molecule and three measurable bulk properties, namely the structure factor and the Fourier components of the longitudinal and transverse dielectric susceptibilities.
Spin constraints on nuclear energy density functionals
Robledo, L M; Bertsch, G F
2013-01-01
The Gallagher-Moszkowski rule in the spectroscopy of odd-odd nuclei imposes a new spin constraint on the energy functionals for self-consistent mean field theory. The commonly used parameterization of the effective three-body interaction in the Gogny and Skyrme families of energy functionals is ill-suited to satisfy the spin constraint. In particular, the Gogny parameterization of the three-body interaction has the opposite spin dependence to that required by the observed spectra. The two-body part has a correct sign, but in combination the rule is violated as often as not. We conclude that a new functional form is needed for the effective three-body interaction that can take into better account the different spin-isospin channels of the interaction.
Development and testing of new exchange correlation functionals
DEFF Research Database (Denmark)
Lundgård, Keld Troen
, selectivity or similar of current chemical processes, or to make new technologies economical feasible. Kohn-Sham density functional theory (KS-DFT) has proven to be a powerful theory to find trends in current catalytic materials, which can empower a more informed search for better alternatives. KS-DFT relies...... generally applicable models; a robust MM-estimator loss function, for ensuring resistance to outliers in data; and a hierarchical bootstrap resampling estimating prediction error validation method, for selecting the model complexity that provide best transferability outside the training data. Three new semi...... on accurate and efficient approximations to the exchange correlation functional, yet these functional approximations have lacked a systematic way to estimate the underlying uncertainties. A Bayesian error estimation approach provides a mechanism for calculating approximative uncertainties, and so accurate...
Institute of Scientific and Technical Information of China (English)
周世琦
2003-01-01
Based on the functional integral procedure, a recently proposed bridge density function [J. Chem. Phys. 112 (2000) 8079] is developed to calculate global thermodynamic properties of non-uniform fluids. The resulting surface tension of a hard wall-hard sphere interface as a function of the bulk hard sphere fluid density is in good agreement with the available simulation data. The proposed numerical procedure from the approximation of non-uniform first=order direct correlation function to a non=uniform system with excess Helmholtz free energy is of fundamental importance for phase behaviour under the confined condition due to the fact that many available simple approximations in classical density functional theory are for non=uniform first=order direct correlation function.
Carlson, Rebecca K; Li Manni, Giovanni; Sonnenberger, Andrew L; Truhlar, Donald G; Gagliardi, Laura
2015-01-13
Kohn-Sham density functional theory, resting on the representation of the electronic density and kinetic energy by a single Slater determinant, has revolutionized chemistry, but for open-shell systems, the Kohn-Sham Slater determinant has the wrong symmetry properties as compared to an accurate wave function. We have recently proposed a theory, called multiconfiguration pair-density functional theory (MC-PDFT), in which the electronic kinetic energy and classical Coulomb energy are calculated from a multiconfiguration wave function with the correct symmetry properties, and the rest of the energy is calculated from a density functional, called the on-top density functional, that depends on the density and the on-top pair density calculated from this wave function. We also proposed a simple way to approximate the on-top density functional by translation of Kohn-Sham exchange-correlation functionals. The method is much less expensive than other post-SCF methods for calculating the dynamical correlation energy starting with a multiconfiguration self-consistent-field wave function as the reference wave function, and initial tests of the theory were quite encouraging. Here, we provide a broader test of the theory by applying it to bond energies of main-group molecules and transition metal complexes, barrier heights and reaction energies for diverse chemical reactions, proton affinities, and the water dimerization energy. Averaged over 56 data points, the mean unsigned error is 3.2 kcal/mol for MC-PDFT, as compared to 6.9 kcal/mol for Kohn-Sham theory with a comparable density functional. MC-PDFT is more accurate on average than complete active space second-order perturbation theory (CASPT2) for main-group small-molecule bond energies, alkyl bond dissociation energies, transition-metal-ligand bond energies, proton affinities, and the water dimerization energy.
Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Maillet, J.M. [UMR 5672 du CNRS, ENS Lyon (France). Lab. de Physique; Slavnov, N.A. [Steklov Mathematical Institute, Moscow (Russian Federation)
2010-12-15
We describe a Bethe ansatz based method to derive, starting from a multiple integral representation, the long-distance asymptotic behavior at finite temperature of the density-density correlation function in the interacting onedimensional Bose gas. We compute the correlation lengths in terms of solutions of non-linear integral equations of the thermodynamic Bethe ansatz type. Finally, we establish a connection between the results obtained in our approach with the correlation lengths stemming from the quantum transfer matrix method. (orig.)
Detecting correlations among functional-sequence motifs
Pirino, Davide; Rigosa, Jacopo; Ledda, Alice; Ferretti, Luca
2012-06-01
Sequence motifs are words of nucleotides in DNA with biological functions, e.g., gene regulation. Identification of such words proceeds through rejection of Markov models on the expected motif frequency along the genome. Additional biological information can be extracted from the correlation structure among patterns of motif occurrences. In this paper a log-linear multivariate intensity Poisson model is estimated via expectation maximization on a set of motifs along the genome of E. coli K12. The proposed approach allows for excitatory as well as inhibitory interactions among motifs and between motifs and other genomic features like gene occurrences. Our findings confirm previous stylized facts about such types of interactions and shed new light on genome-maintenance functions of some particular motifs. We expect these methods to be applicable to a wider set of genomic features.
Matrix elements from moments of correlation functions
Bouchard, Chris; Orginos, Kostas; Richards, David
2016-01-01
Momentum-space derivatives of matrix elements can be related to their coordinate-space moments through the Fourier transform. We derive these expressions as a function of momentum transfer $Q^2$ for asymptotic in/out states consisting of a single hadron. We calculate corrections to the finite volume moments by studying the spatial dependence of the lattice correlation functions. This method permits the computation of not only the values of matrix elements at momenta accessible on the lattice, but also the momentum-space derivatives, providing {\\it a priori} information about the $Q^2$ dependence of form factors. As a specific application we use the method, at a single lattice spacing and with unphysically heavy quarks, to directly obtain the slope of the isovector form factor at various $Q^2$, whence the isovector charge radius. The method has potential application in the calculation of any hadronic matrix element with momentum transfer, including those relevant to hadronic weak decays.
Matrix elements from moments of correlation functions
Energy Technology Data Exchange (ETDEWEB)
Chang, Chia Cheng [SLAC National Accelerator Lab., Menlo Park, CA (United States); Bouchard, Chris [College of William and Mary, Williamsburg, VA (United States); Orginos, Konstantinos [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States); Richards, David G. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
2016-10-01
Momentum-space derivatives of matrix elements can be related to their coordinate-space moments through the Fourier transform. We derive these expressions as a function of momentum transfer Q2 for asymptotic in/out states consisting of a single hadron. We calculate corrections to the finite volume moments by studying the spatial dependence of the lattice correlation functions. This method permits the computation of not only the values of matrix elements at momenta accessible on the lattice, but also the momentum-space derivatives, providing {\\it a priori} information about the Q2 dependence of form factors. As a specific application we use the method, at a single lattice spacing and with unphysically heavy quarks, to directly obtain the slope of the isovector form factor at various Q2, whence the isovector charge radius. The method has potential application in the calculation of any hadronic matrix element with momentum transfer, including those relevant to hadronic weak decays.
Time-dependent density functional theory for strong-field ionization by circularly polarized pulses
Chirilă, Ciprian C.; Lein, Manfred
2017-03-01
By applying time-dependent density functional theory to a two-dimensional multielectron atom subject to strong circularly polarized light pulses, we confirm that the ionization of p orbitals with defined angular momentum depends on the sense of rotation of the applied field. A simple ad-hoc modification of the adiabatic local-density exchange-correlation functional is proposed to remedy its unphysical behavior under orbital depletion.
New Angles on Energy Correlation Functions
Moult, Ian; Thaler, Jesse
2016-01-01
Jet substructure observables, designed to identify specific features within jets, play an essential role at the Large Hadron Collider (LHC), both for searching for signals beyond the Standard Model and for testing QCD in extreme phase space regions. In this paper, we systematically study the structure of infrared and collinear safe substructure observables, defining a generalization of the energy correlation functions to probe $n$-particle correlations within a jet. These generalized correlators provide a flexible basis for constructing new substructure observables optimized for specific purposes. Focusing on three major targets of the jet substructure community---boosted top tagging, boosted $W/Z/H$ tagging, and quark/gluon discrimination---we use power-counting techniques to identify three new series of powerful discriminants: $M_i$, $N_i$, and $U_i$. The $M_i$ series is designed for use on groomed jets, providing a novel example of observables with improved discrimination power after the removal of soft ra...
Density Functional Theory Based on the Electron Distribution on the Energy Coordinate
Takahashi, Hideaki
2016-01-01
We introduced a new electron density n({\\epsilon}) by projecting the spatial electron density n(r) onto the energy coordinate {\\epsilon} defined with the external potential \\upsion (r) of interest. Then, a density functional theory (DFT) was formulated, where n({\\epsilon}) serves as a fundamental variable for the electronic energy. It was demonstrated that the Kohn-Sham equation can also be adapted to the DFT that employs the density n({\\epsilon}) as an argument to the exchange energy functional. An important attribute of the energy density is that it involves the spatially non-local population of the spin-adapted density n(r) at the bond dissociation. By taking advantage of this property we developed a prototype of the static correlation functional employing no empirical parameters, which realized a reasonable dissociation curve for H2 molecule.
Efficient Density Functional Approximation for Electronic Properties of Conjugated Systems
Caldas, Marília J.; Pinheiro, José Maximiano, Jr.; Blum, Volker; Rinke, Patrick
2014-03-01
There is on-going discussion about reliable prediction of electronic properties of conjugated oligomers and polymers, such as ionization potential IP and energy gap. Several exchange-correlation (XC) functionals are being used by the density functional theory community, with different success for different properties. In this work we follow a recent proposal: a fraction α of exact exchange is added to the semi-local PBE XC aiming consistency, for a given property, with the results obtained by many-body perturbation theory within the G0W0 approximation. We focus the IP, taken as the negative of the highest occupied molecular orbital energy. We choose α from a study of the prototype family trans-acetylene, and apply this same α to a set of oligomers for which there is experimental data available (acenes, phenylenes and others). Our results indicate we can have excellent estimates, within 0,2eV mean ave. dev. from the experimental values, better than through complete EN - 1 -EN calculations from the starting PBE functional. We also obtain good estimates for the electrical gap and orbital energies close to the band edge. Work supported by FAPESP, CNPq, and CAPES, Brazil, and DAAD, Germany.
Curvature and Frontier Orbital Energies in Density Functional Theory.
Stein, Tamar; Autschbach, Jochen; Govind, Niranjan; Kronik, Leeor; Baer, Roi
2012-12-20
Perdew et al. discovered two different properties of exact Kohn-Sham density functional theory (DFT): (i) The exact total energy versus particle number is a series of linear segments between integer electron points. (ii) Across an integer number of electrons, the exchange-correlation potential "jumps" by a constant, known as the derivative discontinuity (DD). Here we show analytically that in both the original and the generalized Kohn-Sham formulation of DFT the two properties are two sides of the same coin. The absence of a DD dictates deviation from piecewise linearity, but the latter, appearing as curvature, can be used to correct for the former, thereby restoring the physical meaning of orbital energies. A simple correction scheme for any semilocal and hybrid functional, even Hartree-Fock theory, is shown to be effective on a set of small molecules, suggesting a practical correction for the infamous DFT gap problem. We show that optimally tuned range-separated hybrid functionals can inherently minimize both DD and curvature, thus requiring no correction, and that this can be used as a sound theoretical basis for novel tuning strategies.
Scaling laws for density correlations and fluctuations in multiparticle dynamics
Energy Technology Data Exchange (ETDEWEB)
Wolf, E.A. de [Universitaire Instelling Antwerpen, Wilrijk (Belgium). Dept. of Physics]|[Interuniversity Inst. for High Energies, Brussels (Belgium); Dremin, I.M. [Rossijskaya Akademiya Nauk, Moscow (Russian Federation). Fizicheskij Inst.; Kittel, W. [Nationaal Inst. voor Kernfysica en Hoge-Energiefysica (NIKHEF), Nijmegen (Netherlands)
1996-05-01
Experimental data on particle correlations and fluctuations in various high-energy multiparticle collisions are presented, with special emphasis on evidence for scaling-law evolution in small phase-space domains. The notions of intermittency and fractality as related to the above findings are described. Phenomenological and theoretical work on the subject is reviewed. (orig.).
Exact density functional and wave function embedding schemes based on orbital localization
Hégely, Bence; Nagy, Péter R.; Ferenczy, György G.; Kállay, Mihály
2016-08-01
Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.
Capillary waves and the decay of density correlations at liquid surfaces
Hernández-Muñoz, Jose; Chacón, Enrique; Tarazona, Pedro
2016-12-01
Wertheim predicted strong density-density correlations at free liquid surfaces, produced by capillary wave fluctuations of the interface [M. S. Wertheim, J. Chem. Phys. 65, 2377 (1976), 10.1063/1.433352]. That prediction has been used to search for a link between capillary wave (CW) theory and density functional (DF) formalism for classical fluids. In particular, Parry et al. have recently analyzed the decaying tails of these CW effects moving away from the interface as a clue for the extended CW theory [A. O. Parry et al., J. Phys.: Condens. Matter 28, 244013 (2016), 10.1088/0953-8984/28/24/244013], beyond the strict long-wavelength limit studied by Wertheim. Some apparently fundamental inconsistencies between the CW and the DF theoretical views of the fluid interfaces arose from the asymptotic analysis of the CW signal. In this paper we revisit the problem of the CW asymptotic decay with a separation of local non-CW surface correlation effects from those that are a truly nonlocal propagation of the CW fluctuations from the surface towards the liquid bulk.
The Keldysh formalism applied to time-dependent current-density-functional theory
Gidopoulos, NI; Wilson, S
2003-01-01
In this work we demonstrate how to derive the Kohn-Sham equations of time-dependent current-density functional theory from a generating action functional defined on a Keldysh time contour. These Kohn-Sham equations contain an exchange-correlation contribution to the vector potential. For this
Ronca, Enrico; Angeli, Celestino; Belpassi, Leonardo; De Angelis, Filippo; Tarantelli, Francesco; Pastore, Mariachiara
2014-09-09
Making use of the recently developed excited state charge displacement analysis [E. Ronca et al., J. Chem. Phys. 140, 054110 (2014)], suited to quantitatively characterize the charge fluxes coming along an electronic excitation, we investigate the role of the density relaxation effects in the overall description of electronically excited states of different nature, namely, valence, ionic, and charge transfer (CT), considering a large set of prototypical small and medium-sized molecular systems. By comparing the response densities provided by time-dependent density functional theory (TDDFT) and the corresponding relaxed densities obtained by applying the Z-vector postlinear-response approach [N. C. Handy and H. F. Schaefer, J. Chem. Phys. 81, 5031 (1984)] with those obtained by highly correlated state-of-the-art wave function calculations, we show that the inclusion of the relaxation effects is imperative to get an accurate description of the considered excited states. We also examine what happens at the quality of the response function when an increasing amount of Hartree-Fock (HF) exchange is included in the functional, showing that the usually improved excitation energies in the case of CT states are not always the consequence of an improved description of their overall properties. Remarkably, we find that the relaxation of the response densities is always able to reproduce, independently of the extent of HF exchange in the functional, the benchmark wave function densities. Finally, we propose a novel and computationally convenient strategy, based on the use of the natural orbitals derived from the relaxed TDDFT density to build zero-order wave function for multireference perturbation theory calculations. For a significant set of different excited states, the proposed approach provided accurate excitation energies, comparable to those obtained by computationally demanding ab initio calculations.
Correlation between the High Density Lipoprotein and its Subtypes in Coronary Heart Disease
Directory of Open Access Journals (Sweden)
Fen Gao
2016-05-01
Full Text Available Background/Aims: To detect the changes of high density lipoprotein (HDL and its subtypes in serum of patients with coronary heart disease (CHD. Methods: 337 hospitalized patients were selected from our hospital during August, 2014 - January, 2015, and divided into CHD group (n = 190 and control group (n = 127. Lipoprint lipoprotein analyzer was used to classify low density lipoprotein (LDL particle size and its sub-components, as well as HDL particle size and its sub-components. The changes of the subtypes in patients with CHD were statistically analyzed. The possible mechanism was explored. Results: (1 Compared with the control group, the concentration of HDL in CHD patients reduced, HDLL significantly decreased (P S increased (P L had the most significant decreased; (3 HDL and all HDL subtypes were positively correlated with apolipoprotein A-I (apoA-I, of which, HDLL had the biggest correlation with apoA-I (P M had a maximum correlation with HDL (P Conclusion: HDL maturation disorders existed in the serum of CHD patients, HDLL may be protected factor for CHD, whose decrease was closely related wit the risk increase of CHD. The cardiovascular protection function of HDLL may be related with apoA-I content.
DEFF Research Database (Denmark)
Johnston, Karen; Kleis, Jesper; Lundqvist, Bengt
2008-01-01
Two different adsorption configurations of benzene on the Si(001)-(2×1) surface, the tight-bridge and butterfly structures, were studied using density functional theory. Several exchange and correlation functionals were used, including the recently developed van der Waals density functional (vdW-...
Codis, Sandrine; Pichon, Christophe
2016-01-01
In order to quantify the error budget in the measured probability distribution functions of cell densities, the two-point statistics of cosmic densities in concentric spheres is investigated. Bias functions are introduced as the ratio of their two-point correlation function to the two-point correlation of the underlying dark matter distribution. They describe how cell densities are spatially correlated. They are computed here via the so-called large deviation principle in the quasi-linear regime. Their large-separation limit is presented and successfully compared to simulations for density and density slopes: this regime is shown to be rapidly reached allowing to get sub-percent precision for a wide range of densities and variances. The corresponding asymptotic limit provides an estimate of the cosmic variance of standard concentric cell statistics applied to finite surveys. More generally, no assumption on the separation is required for some specific moments of the two-point statistics, for instance when pre...
A Joint Density Function in the Renewal Risk Model
Institute of Scientific and Technical Information of China (English)
XU HUAI; TANG LING; Wang De-hui
2013-01-01
In this paper,we consider a general expression for (Φ)(u,x,y),the joint density function of the surplus prior to ruin and the deficit at ruin when the initial surplus is u.In the renewal risk model,this density function is expressed in terms of the corresponding density function when the initial surplus is 0.In the compound Poisson risk process with phase-type claim size,we derive an explicit expression for (Φ)(u,x,y).Finally,we give a numerical example to illustrate the application of these results.
Density scaling as a property of strongly correlating viscous liquids
Schrøder, Thomas; Pedersen, Ulf Rørbæk; Bailey, Nicholas; Toxværd, Søren; Dyre, J.C.
2008-01-01
Results from molecular dynamics simulations of two viscous molecular model liquids -- the Lewis-Wahnstrom model of ortho-terphenyl and an asymmetric dumbbell model -- are reported. We demonstrate that the liquids have a ``hidden'' approximate scale invariance: Equilibrium potential energy fluctuations are accurately described by inverse power law (IPL) potentials, the radial distribution functions are accurately reproduced by the IPL's, and the radial distribution functions obey the IPL predi...
Sum rule of the correlation function
Maj, R; Maj, Radoslaw; Mrowczynski, Stanislaw
2004-01-01
We discuss a sum rule satisfied by the correlation function of two particles with small relative momenta. The sum rule, which results from the completeness condition of the quantum states of the two particles, is first derived and then we check how it works in practice. The sum rule is shown to be trivially satisfied by free particle pair, and then there are considered three different systems of interacting particles. We discuss a pair of neutron and proton in the s-wave approximation and the case of the so-called hard spheres with the phase shifts taken into account up to l=4. Finally, the Coulomb system of two charged particles is analyzed.
Hilbert Space of Probability Density Functions Based on Aitchison Geometry
Institute of Scientific and Technical Information of China (English)
J. J. EGOZCUE; J. L. D(I)AZ-BARRERO; V. PAWLOWSKY-GLAHN
2006-01-01
The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison's ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.
Kinetic theory of time correlation functions for a dense one-component plasma in a magnetic field
Schoolderman, A.J.; Suttorp, L.G.
1988-01-01
The time-dependent correlations of a one-component plasma in a uniform magnetic field are studied with the help of kinetic theory. The time correlation functions of the particle density, the momentum density, and the kinetic energy density are evaluated for large time intervals. In the collision-dom
Hybrid density functional theory band structure engineering in hematite.
Pozun, Zachary D; Henkelman, Graeme
2011-06-14
We present a hybrid density functional theory (DFT) study of doping effects in α-Fe(2)O(3), hematite. Standard DFT underestimates the band gap by roughly 75% and incorrectly identifies hematite as a Mott-Hubbard insulator. Hybrid DFT accurately predicts the proper structural, magnetic, and electronic properties of hematite and, unlike the DFT+U method, does not contain d-electron specific empirical parameters. We find that using a screened functional that smoothly transitions from 12% exact exchange at short ranges to standard DFT at long range accurately reproduces the experimental band gap and other material properties. We then show that the antiferromagnetic symmetry in the pure α-Fe(2)O(3) crystal is broken by all dopants and that the ligand field theory correctly predicts local magnetic moments on the dopants. We characterize the resulting band gaps for hematite doped by transition metals and the p-block post-transition metals. The specific case of Pd doping is investigated in order to correlate calculated doping energies and optical properties with experimentally observed photocatalytic behavior.
Assessment of density functional methods with correct asymptotic behavior
Tsai, Chen-Wei; Li, Guan-De; Chai, Jeng-Da
2012-01-01
Long-range corrected (LC) hybrid functionals and asymptotically corrected (AC) model potentials are two distinct density functional methods with correct asymptotic behavior. They are known to be accurate for properties that are sensitive to the asymptote of the exchange-correlation potential, such as the highest occupied molecular orbital energies and Rydberg excitation energies of molecules. To provide a comprehensive comparison, we investigate the performance of the two schemes and others on a very wide range of applications, including the asymptote problems, self-interaction-error problems, energy-gap problems, charge-transfer problems, and many others. The LC hybrid scheme is shown to consistently outperform the AC model potential scheme. In addition, to be consistent with the molecules collected in the IP131 database [Y.-S. Lin, C.-W. Tsai, G.-D. Li, and J.-D. Chai, J. Chem. Phys. 136, 154109 (2012)], we expand the EA115 and FG115 databases to include, respectively, the vertical electron affinities and f...
Density functional theory of the crystal field in dioxides
Diviš, M.; Kuriplach, J.; Richter, M.; Steinbeck, L.
1996-04-01
Presented are the results of ab-initio density functional calculations for PrO2 and UO2 using the general potential LAPW and optimized LCAO method in the local density approximation. The crystal field splitting of ionic Pr4+ and U4+ ground states was calculated and compared with predictions of a superposition model.
Charge and spin fluctuations in the density functional theory
Energy Technology Data Exchange (ETDEWEB)
Gyoerffy, B.L.; Barbieri, A. (Bristol Univ. (UK). H.H. Wills Physics Lab.); Staunton, J.B. (Warwick Univ., Coventry (UK). Dept. of Physics); Shelton, W.A.; Stocks, G.M. (Oak Ridge National Lab., TN (USA))
1990-01-01
We introduce a conceptual framework which allow us to treat charge and spin fluctuations about the Local density Approximation (LDA) to the Density Functional Theory (DFT). We illustrate the approach by explicit study of the Disordered Local Moment (DLM) state in Fe above the Curie Temperature {Tc} and the Mott insulating state in MnO. 27 refs., 6 figs.
Excitation Spectra of Nucleobases with Multiconfigurational Density Functional Theory
DEFF Research Database (Denmark)
Hubert, Mickaël; Jensen, Hans Jørgen Aa; Hedegård, Erik D.
2016-01-01
Range-separated hybrid methods between wave function theory and density functional theory (DFT) can provide high-accuracy results, while correcting some of the inherent flaws of both the underlying wave function theory and DFT. We here assess the accuracy for excitation energies of the nucleobases...
Applications and validations of the Minnesota density functionals
Zhao, Yan; Truhlar, Donald G.
2011-01-01
We discuss and review selected recent applications and validations of the Minnesota density functionals, especially the M06 family, emphasizing nanochemistry, organic, inorganic, and biological chemistry, and catalysis and highlighting the broad accuracy of these functionals as compared to previous popular functionals for thermochemistry, kinetics, and noncovalent interactions.
Pulmonary alveolar proteinosis: Quantitative CT and pulmonary functional correlations
Energy Technology Data Exchange (ETDEWEB)
Guan, Yubao, E-mail: yubaoguan@163.com [Department of Radiology, the First Affiliated Hospital of Guangzhou Medical College, Guangzhou 510120 (China); State Key Laboratory of Respiratory Disease, Guangzhou 510120 (China); Zeng, Qingsi [Department of Radiology, the First Affiliated Hospital of Guangzhou Medical College, Guangzhou 510120 (China); Yang, Haihong; Zheng, Jinping; Li, Shiyue; Gao, Yi [State Key Laboratory of Respiratory Disease, Guangzhou 510120 (China); Deng, Yu [Department of Radiology, the First Affiliated Hospital of Guangzhou Medical College, Guangzhou 510120 (China); Mei, Jiang [State Key Laboratory of Respiratory Disease, Guangzhou 510120 (China); He, Jianxing, E-mail: jianxing63@163.com [State Key Laboratory of Respiratory Disease, Guangzhou 510120 (China); Zhong, Nanshan, E-mail: nanshan@vip.163.com [State Key Laboratory of Respiratory Disease, Guangzhou 510120 (China)
2012-09-15
Objective: We assessed the relationship between quantitative computer tomography (qCT) and the pulmonary function test (PFT) or blood gas analysis in pulmonary alveolar proteinosis (PAP) patients, as well as the utility of these analyses to monitor responses to whole lung lavage (WLL) therapy. Methods: Thirty-eight PAP patients simultaneously received a CT scan and PFT. Fifteen of these patients, undergoing sequential WLL for a total of 20 lavages, also underwent chest CT scans and blood gas analysis before and after WLL, and 14 of 15 patients underwent simultaneous PFT analysis. Differences between the qCT and PFT results were analyzed by canonical correlation. Results: PAP patients with low predicted values for FVC, FEV1, D{sub LCO} and D{sub LCO}/VA indicated small airspace volume and mean lung inflation, low airspace volume/total lung volume ratio and high mean lung density. Correlation and regression analysis revealed a strong correlation between D{sub LCO} and PaO{sub 2} values with CT results. The qCT results indicated that WLL significantly decreased lung weights and mean lung densities, and improved the total airspace volume/total lung volume ratios and mean lung inflations. Conclusion: Quantitative CT may be a sensitive tool for measuring the response of PAP patients to medical interventions such as WLL.
Density Functional Calculations for the Neutron Star Matter at Subnormal Density
Kashiwaba, Yu; Nakatsukasa, Takashi
The pasta phases of nuclear matter, whose existence is suggested at low density, may influence observable properties of neutron stars. In order to investigate properties of the neutron star matter, we calculate self-consistent solutions for the ground states of slab-like phase using the microscopic density functional theory with Bloch wave functions. The calculations are performed at each point of fixed average density and proton fraction (\\bar{ρ },Yp), varying the lattice constant of the unit cell. For small Yp values, the dripped neutrons emerge in the ground state, while the protons constitute the slab (crystallized) structure. The shell effect of protons affects the thickness of the slab nuclei.
FUNCTIONAL CORRELATION OF FP AND DC METHODS
Directory of Open Access Journals (Sweden)
Marin Kaluža
2013-02-01
Full Text Available Most of organizations today use information-communication technologies (ICT for building an information system (IS. IS is assembled of hardware, software, network resources, organizational and human resources. In IS development process, complexity is crucial for evaluating quantities of resources needed (time, people, money, equipment. Complexity of an IS can be evaluated and/or measured in different phases of development. There are many methods for measuring complexity, but mostly used and thoroughly described method is Function Point Analysis (FP. The opposite method, Database Complexity (DC, does not measure all the aspects of IS, but it could evaluate system complexity depending on the database complexity. DC method is intended to be used for measuring semantic complexity of the IS database, and can be shown by counting attributes A and foreign keys F. This paper describes a very high correlation between FP and DC methods, and defines a function which can in 95% of accuracy express FP values from measured DC values.
DEFF Research Database (Denmark)
Bast, Radovan; Jensen, Hans Jørgen Aagaard; Saue, Trond
2009-01-01
We report an implementation of adiabatic time-dependent density functional theory based on the 4-component relativistic Dirac-Coulomb Hamiltonian and a closed-shell reference. The implementation includes noncollinear spin magnetization and full derivatives of functionals, including hybrid...... and time reversal symmetry on trial vectors to obtain even better reductions in terms of memory and run time, and without invoking approximations. Further reductions are obtained by exploiting point group symmetries for D2h and subgroups in a symmetry scheme where symmetry reductions translate...... into reduction of algebra from quaternion to complex or real. For hybrid GGAs with noncollinear spin magnetization we derive a new computationally advantageous equation for the full second variational derivatives of such exchange-correlation functionals. We apply our implementation to calculations on the ns2...
Reflection-asymmetric nuclear deformations within the Density Functional Theory
Olsen, E; Nazarewicz, W; Stoitsov, M; 10.1088/1742-6596/402/1/012034
2013-01-01
Within the nuclear density functional theory (DFT) we study the effect of reflection-asymmetric shapes on ground-state binding energies and binding energy differences. To this end, we developed the new DFT solver AxialHFB that uses an approximate second-order gradient to solve the Hartree-Fock-Bogoliubov equations of superconducting DFT with the quasi-local Skyrme energy density functionals. Illustrative calculations are carried out for even-even isotopes of radium and thorium.
Density Functional Theory with Dissipation: Transport through Single Molecules
Energy Technology Data Exchange (ETDEWEB)
Kieron Burke
2012-04-30
A huge amount of fundamental research was performed on this grant. Most of it focussed on fundamental issues of electronic structure calculations of transport through single molecules, using density functional theory. Achievements were: (1) First density functional theory with dissipation; (2) Pseudopotential plane wave calculations with master equation; (3) Weak bias limit; (4) Long-chain conductance; and (5) Self-interaction effects in tunneling.
Universal correlations of one-dimensional electrons at low density
Göhmann, F.
2000-01-01
We summarize results on the asymptotics of the two-particle Green functions of interacting electrons in one dimension. Below a critical value of the chemical potential the Fermi surface vanishes, and the system can no longer be described as a Luttinger liquid. Instead, the non-relativistic Fermi gas with infinite point-like repulsion becomes the universal model for the long-wavelength, low temperature physics of the one-dimensional electrons. This model, which we call the impenetrable electro...
Non-Local Density Functional Description of Poly-Para-Phenylene Vinylene
Institute of Scientific and Technical Information of China (English)
ZHENG Guang; Clark S. J.; Brand S.; Abram R. A.
2007-01-01
A fully non-local exchange-correlation formalism within the framework of density functional theory, known as the weighted density approximation (WDA), has been applied to the conjugated polymer poly-para-phenylene vinylene (PPV) and is shown to lead to a marked improvement in the agreement of theory and experiment for the electronic band structure of the conjugated polymer. In particular, some new model WDA functions are developed, which substantially increase the electronic band gap of the polymer relative to those obtained with the local density approximation and generalized gradient approximation. The calculated band gap of PPV is quantitatively or at 1east semiquantitatively in agreement with the experimental data.
Impact of ATLAS Data on Parton Density Functions
Newman, PR; The ATLAS collaboration
2014-01-01
Various measurements provided by the ATLAS collaboration have significant impact on parton density functions. The production of W and Z bosons inclusively or in association with charm-quark have are found to constraint the strange-quark density at medium and low Bjorken-x. Multi-Jet and photon production processes show impact on the gluon density. Off-resonance Drell Yan production at large lepton pair masses may be used to constrain anti-quark density at high x. A qualitative comparison of the ATLAS measurements to predictions based on different PDFs is presented.
Łazarski, Roman; Burow, Asbjörn Manfred; Grajciar, Lukáš; Sierka, Marek
2016-10-30
A full implementation of analytical energy gradients for molecular and periodic systems is reported in the TURBOMOLE program package within the framework of Kohn-Sham density functional theory using Gaussian-type orbitals as basis functions. Its key component is a combination of density fitting (DF) approximation and continuous fast multipole method (CFMM) that allows for an efficient calculation of the Coulomb energy gradient. For exchange-correlation part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097) is extended to energy gradients. Computational efficiency and asymptotic O(N) scaling behavior of the implementation is demonstrated for various molecular and periodic model systems, with the largest unit cell of hematite containing 640 atoms and 19,072 basis functions. The overall computational effort of energy gradient is comparable to that of the Kohn-Sham matrix formation. © 2016 Wiley Periodicals, Inc.
Ground state of medium-heavy doubly-closed shell nuclei in correlated basis function theory
Bisconti, C; Có, G; Fabrocini, A
2006-01-01
The correlated basis function theory is applied to the study of medium-heavy doubly closed shell nuclei with different wave functions for protons and neutrons and in the jj coupling scheme. State dependent correlations including tensor correlations are used. Realistic two-body interactions of Argonne and Urbana type, together with three-body interactions have been used to calculate ground state energies and density distributions of the 12C, 16O, 40Ca, 48Ca and 208Pb nuclei.
Basis convergence of range-separated density-functional theory
Franck, Odile; Luppi, Eleonora; Toulouse, Julien
2014-01-01
Range-separated density-functional theory is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components, and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whe...
Density functional theory for polymeric systems in 2D.
Słyk, Edyta; Roth, Roland; Bryk, Paweł
2016-06-22
We propose density functional theory for polymeric fluids in two dimensions. The approach is based on Wertheim's first order thermodynamic perturbation theory (TPT) and closely follows density functional theory for polymers proposed by Yu and Wu (2002 J. Chem. Phys. 117 2368). As a simple application we evaluate the density profiles of tangent hard-disk polymers at hard walls. The theoretical predictions are compared against the results of the Monte Carlo simulations. We find that for short chain lengths the theoretical density profiles are in an excellent agreement with the Monte Carlo data. The agreement is less satisfactory for longer chains. The performance of the theory can be improved by recasting the approach using the self-consistent field theory formalism. When the self-avoiding chain statistics is used, the theory yields a marked improvement in the low density limit. Further improvements for long chains could be reached by going beyond the first order of TPT.
Improving the accuracy of the nonlocal van der Waals density functional with minimal empiricism.
Vydrov, Oleg A; Van Voorhis, Troy
2009-03-14
The nonlocal van der Waals density functional (vdW-DF) captures the essential physics of the dispersion interaction not only in the asymptotic regime but also for a general case of overlapping fragment densities. A balanced treatment of other energetic contributions, such as exchange, is crucial if we aim for accurate description of various properties of weakly bound systems. In this paper, the vdW-DF correlation functional is modified to make it better compatible with accurate exchange functionals. We suggest a slightly simplified construction of the nonlocal correlation, yielding more accurate asymptotic C(6) coefficients. We also derive a gradient correction, containing a parameter that can be adjusted to suit an exchange functional of choice. We devise a particularly apt combination of exchange and correlation terms, which satisfies many important constraints and performs well for our benchmark tests.
Linear response of homogeneous nuclear matter with energy density functionals
Energy Technology Data Exchange (ETDEWEB)
Pastore, A. [Institut d’Astronomie et d’Astrophysique, CP 226, Université Libre de Bruxelles, B-1050 Bruxelles (Belgium); Davesne, D., E-mail: davesne@ipnl.in2p3.fr [Institut de Physique Nucléaire de Lyon, CNRS-IN2P3, UMR 5822, Université Lyon 1, F-69622 Villeurbanne (France); Navarro, J. [IFIC (CSIC University of Valencia), Apdo. Postal 22085, E-46071 Valencia (Spain)
2015-03-01
Response functions of infinite nuclear matter with arbitrary isospin asymmetry are studied in the framework of the random phase approximation. The residual interaction is derived from a general nuclear Skyrme energy density functional. Besides the usual central, spin–orbit and tensor terms it could also include other components as new density-dependent terms or three-body terms. Algebraic expressions for the response functions are obtained from the Bethe–Salpeter equation for the particle–hole propagator. Applications to symmetric nuclear matter, pure neutron matter and asymmetric nuclear matter are presented and discussed. Spin–isospin strength functions are analyzed for varying conditions of density, momentum transfer, isospin asymmetry, and temperature for some representative Skyrme functionals. Particular attention is paid to the discussion of instabilities, either real or unphysical, which could manifest in finite nuclei.
Inclusion of Dispersion Effects in Density Functional Theory
DEFF Research Database (Denmark)
Møgelhøj, Andreas
In this thesis, applications and development will be presented within the field of van der Waals interactions in density functional theory. The thesis is based on the three projects: i) van der Waals interactions effect on the structure of liquid water at ambient conditions, ii) development...... and benchmarking of a new van der Waals density functional, and iii) the application of the newly developed functional to CO desorption from Ru(0001). The effect of van der Waals interactions in water was studied by performing ab initio molecular dynamics simulations using PBE and the two recent van der Waals...... density functionals optPBE-vdW and vdW-DF2 with identical computational setup. The two van der Waals functionals have been found to give excellent descriptions of the constituents of water (e.g., water dimers and hexamers). Including van der Waals interactions gives a softer water structure as seen from...
Introduction to Classical Density Functional Theory by Computational Experiment
Jeanmairet, Guillaume; Levesque, Maximilien; Borgis, Daniel
2014-01-01
We present here an introductory practical course to classical density functional theory (cDFT). Density functional theories, whether quantum or classical, rely largely on nonintuitive abstract concepts and applied mathematics. They are nevertheless a powerful tool and an active field of research in physics and chemistry that led to the 1998 Nobel prize in chemistry. We here illustrate the DFT in its most mathematically simple and yet physically relevant form: the classical density functional theory of an ideal fluid in an external field, as applied to the prediction of the structure of liquid neon at the molecular scale. This introductory course is built around the production of a cDFT code written by students using the Mathematica language. In this way, they are brought to deal with (i) the cDFT theory itself, (ii) some basic concepts around the statistical mechanics of simple fluids, (iii) the underlying mathematical and numerical problem of functional minimization, and (iv) a functional programming languag...
Sloppy nuclear energy density functionals: effective model reduction
Niksic, Tamara
2016-01-01
Concepts from information geometry are used to analyse parameter sensitivity for a nuclear energy density functional, representative of a class of semi-empirical functionals that start from a microscopically motivated ansatz for the density dependence of the energy of a system of protons and neutrons. It is shown that such functionals are sloppy, characterized by an exponential range of sensitivity to parameter variations. Responsive to only a few stiff parameter combinations, they exhibit an exponential decrease of sensitivity to variations of the remaining soft parameters. By interpreting the space of model predictions as a manifold embedded in the data space, with the parameters of the functional as coordinates on the manifold, it is also shown that the exponential distribution of model manifold widths corresponds to the distribution of parameter sensitivity. Using the Manifold Boundary Approximation Method, we illustrate how to systematically construct effective nuclear density functionals of successively...
The Role of the Basis Set: Assessing Density Functional Theory
Boese, A D; Handy, N C; Martin, Jan M. L.; Handy, Nicholas C.
2003-01-01
When developing and assessing density functional theory methods, a finite basis set is usually employed. In most cases, however, the issue of basis set dependency is neglected. Here, we assess several basis sets and functionals. In addition, the dependency of the semiempirical fits to a given basis set for a generalised gradient approximation and a hybrid functional is investigated. The resulting functionals are then tested for other basis sets, evaluating their errors and transferability.
Mewes, Stefanie A; Plasser, Felix; Dreuw, Andreas
2015-11-01
Excited-state descriptors based on the one-particle transition density matrix referring to the exciton picture have been implemented for time-dependent density functional theory. State characters such as local, extended ππ(∗), Rydberg, or charge transfer can be intuitively classified by simple comparison of these descriptors. Strong effects of the choice of the exchange-correlation kernel on the physical nature of excited states can be found and decomposed in detail leading to a new perspective on functional performance and the design of new functionals.
Density-functional study of U-Mo alloys
Landa, Alexander; Soderlind, Per; Turchi, Patrice E. A.
2011-03-01
The U-Mo and U-Zr alloys proved to be very promising fuels for advanced fast nuclear reactors. According to numerous experiments, the main advantages of U-Mo fuels over U-Zr fuels lies in a much lower constituent redistribution due to the existence a single γ -U-Mo phase with body-centered cubic structure over typical fuel operation temperatures. Density-functional theory (EMTO-CPA technique) previously used to describe phase equilibria in U-Zr alloys [A. Landa, P. Söderlind, P. E. A. Turchi, Journal of Alloys and Compounds, 478 (2009) 103] is extended to investigate the ground-state properties of U-Mo solid solutions. Calculated heats of formation of bcc U-Zr and U-Mo alloys are compared with CALPHAD assessments. We discuss how the heat of formation in both alloys correlates with the charge transfer between the alloy components, and how the specific behavior of the density of states in the vicinity of the Fermi level promotes the stabilization of the U2 Mo compound. Our calculations prove that, due to the existence of a single γ -phase over the typical fuel operation temperatures, γ -U-Mo alloys should indeed have much lower constituent redistribution than γ -U-Zr alloys for which binodal decomposition causes a high degree of constituent redistribution. This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Error estimates for density-functional theory predictions of surface energy and work function
De Waele, Sam; Lejaeghere, Kurt; Sluydts, Michael; Cottenier, Stefaan
2016-12-01
Density-functional theory (DFT) predictions of materials properties are becoming ever more widespread. With increased use comes the demand for estimates of the accuracy of DFT results. In view of the importance of reliable surface properties, this work calculates surface energies and work functions for a large and diverse test set of crystalline solids. They are compared to experimental values by performing a linear regression, which results in a measure of the predictable and material-specific error of the theoretical result. Two of the most prevalent functionals, the local density approximation (LDA) and the Perdew-Burke-Ernzerhof parametrization of the generalized gradient approximation (PBE-GGA), are evaluated and compared. Both LDA and GGA-PBE are found to yield accurate work functions with error bars below 0.3 eV, rivaling the experimental precision. LDA also provides satisfactory estimates for the surface energy with error bars smaller than 10%, but GGA-PBE significantly underestimates the surface energy for materials with a large correlation energy.
Hybrid density functional theory LCAO calculations on phonons in Ba (Ti,Zr,Hf) O3
Evaestov, Robert A
2010-01-01
Phonon frequencies at {\\Gamma},X,M,R-points of Brilloin zone in cubic phase of Ba(Ti,Zr,Hf)O3 were first time calculated by frozen phonon method using density functional theory (DFT) with hybrid exchange correlation functional PBE0. The calculations use linear combination of atomic orbitals (LCAO) basis functions as implemented in CRYSTAL09 computer code. The Powell algorithm was applied for basis set optimization. In agreement with the experimental observations the structural instability via...
Filtered density function approach for reactive transport in groundwater
Suciu, Nicolae; Schüler, Lennart; Attinger, Sabine; Knabner, Peter
2016-04-01
Spatial filtering may be used in coarse-grained simulations (CGS) of reactive transport in groundwater, similar to the large eddy simulations (LES) in turbulence. The filtered density function (FDF), stochastically equivalent to a probability density function (PDF), provides a statistical description of the sub-grid, unresolved, variability of the concentration field. Besides closing the chemical source terms in the transport equation for the mean concentration, like in LES-FDF methods, the CGS-FDF approach aims at quantifying the uncertainty over the whole hierarchy of heterogeneity scales exhibited by natural porous media. Practically, that means estimating concentration PDFs on coarse grids, at affordable computational costs. To cope with the high dimensionality of the problem in case of multi-component reactive transport and to reduce the numerical diffusion, FDF equations are solved by particle methods. But, while trajectories of computational particles are modeled as stochastic processes indexed by time, the concentration's heterogeneity is modeled as a random field, with multi-dimensional, spatio-temporal sets of indices. To overcome this conceptual inconsistency, we consider FDFs/PDFs of random species concentrations weighted by conserved scalars and we show that their evolution equations can be formulated as Fokker-Planck equations describing stochastically equivalent processes in concentration-position spaces. Numerical solutions can then be approximated by the density in the concentration-position space of an ensemble of computational particles governed by the associated Itô equations. Instead of sequential particle methods we use a global random walk (GRW) algorithm, which is stable, free of numerical diffusion, and practically insensitive to the increase of the number of particles. We illustrate the general FDF approach and the GRW numerical solution for a reduced complexity problem consisting of the transport of a single scalar in groundwater
Specification of Density Functional Approximation by Radial Distribution Function of Bulk Fluid
Institute of Scientific and Technical Information of China (English)
ZHOUShi－Qi
2002-01-01
A systematic methodology is proposed to deal with the weighted density approximation version of classical density functional theory by employing the knowledge of radial distribution function of bulk fluid.The present methodology results from the concept of universality of the free energy density functional combined with the test particle method.It is shown that the new method is very accurate for the predictions of density distribution of a hard sphere fluid at different confining geometries.The physical foundation of the present methodology is also applied to the quantum density functional theory.
A real-space stochastic density matrix approach for density functional electronic structure.
Beck, Thomas L
2015-12-21
The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and density functional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for density functional problems if localized orbitals are used to represent the Kohn-Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman-Kac functional integral as opposed to the extensive matrix operations in traditional approaches.
A Density Functional Study of Bare and Hydrogenated Platinum Clusters
Sebetci, A
2006-01-01
We perform density functional theory calculations using Gaussian atomic-orbital methods within the generalized gradient approximation for the exchange and correlation to study the interactions in the bare and hydrogenated platinum clusters. The minimum-energy structures, binding energies, relative stabilities, vibrational frequencies and the highest occupied and lowest unoccupied molecular-orbital gaps of Pt_nH_m (n=1-5, m=0-2) clusters are calculated and compared with previously studied pure platinum and hydrogenated platinum clusters. We investigate any magic behavior in hydrogenated platinum clusters and find that Pt_4H_2 is more stable than its neighboring sizes. Our results do not agree with a previous conclusion that 3D geometries of Pt tetramer and pentamer are unfavored. On the contrary, the lowest energy structure of Pt_4 is found to be a distorted tetrahedron and that of Pt_5 is found to be a bridge site capped tetrahedron which is a new global minimum for Pt_5 cluster. The successive addition of H ...
Metal catalyzed ethylene epoxidation: A comparative density functional theory study
Institute of Scientific and Technical Information of China (English)
Ruipeng Ren; Yongkang Lü; Xianyong Pang; Guichang Wang
2011-01-01
Ethylene epoxidation on Ag(111), Pt(111), Rh(111) and Mo(100) has been studied by density functional theory (DFT) calculations. The results show that the adsorption energies of possible adsorbed species involved in the ethylene epoxidation increase in the order: Ag＜Pt＜Rh＜Mo, and the activation energies of the formation of epoxide (EtO) and acetaldehyde (Ac) follow the same order. Moreover, it is found that the smallest difference in the activation energies between EtO formation and Ac formation is shown on Ag. These results indicate that the metallic Ag shows the highest between activity and selectivity for ethylene epoxidation among the studied metal surfaces. Perhaps, the stability of OMME intermediate is the crucial factor in controlling the activity and selectivity. And the stronger the binding of OMME, the lower the activity and selectivity are. In addition, the relationships between the reaction enthalpy and activation energy on these four metal surfaces are investigated,and it is found that such a correlation is only applied for OMME(a) → EtO(a) and OMME(a) → Ac(a), while invalid for the case of C2H4(a) +O(a) → OMME(a).
U(1 )×SU (2 ) gauge invariance made simple for density functional approximations
Pittalis, S.; Vignale, G.; Eich, F. G.
2017-07-01
A semirelativistic density-functional theory that includes spin-orbit couplings and Zeeman fields on equal footing with the electromagnetic potentials, is an appealing framework to develop a unified first-principles computational approach for noncollinear magnetism, spintronics, orbitronics, and topological states. The basic variables of this theory include the paramagnetic current and the spin-current density, besides the particle and the spin density, and the corresponding exchange-correlation (xc) energy functional is invariant under local U (1 )×SU (2 ) gauge transformations. The xc-energy functional must be approximated to enable practical applications, but, contrary to the case of the standard density functional theory, finding simple approximations suited to deal with realistic atomistic inhomogeneities has been a long-standing challenge. Here we propose a way out of this impasse by showing that approximate gauge-invariant functionals can be easily generated from existing approximate functionals of ordinary density-functional theory by applying a simple minimal substitution on the kinetic energy density, which controls the short-range behavior of the exchange hole. Our proposal opens the way to the construction of approximate, yet nonempirical functionals, which do not assume weak inhomogeneity and therefore may have a wide range of applicability in atomic, molecular, and condensed matter physics.
Higher-accuracy van der Waals density functional
DEFF Research Database (Denmark)
Lee, Kyuho; Murray, Éamonn D.; Kong, Lingzhu
2010-01-01
We propose a second version of the van der Waals density functional of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)], employing a more accurate semilocal exchange functional and the use of a large-N asymptote gradient correction in determining the vdW kernel. The predicted binding energy...
Wigner Function of Density Operator for Negative Binomial Distribution
Institute of Scientific and Technical Information of China (English)
HE Min-Hua; XU Xing-Lei; ZHANG Duan-Ming; LI Hong-Qi; PAN Gui-Jun; YIN Yan-Ping; CHEN Zhi-Yuan
2008-01-01
By using the technique of integration within an ordered product (IWOP) of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator.
Density-functional perturbation theory goes time-dependent
Gebauer, Ralph; Rocca, Dario; Baroni, Stefano
2009-01-01
The scope of time-dependent density-functional theory (TDDFT) is limited to the lowest portion of the spectrum of rather small systems (a few tens of atoms at most). In the static regime, density-functional perturbation theory (DFPT) allows one to calculate response functions of systems as large as currently dealt with in ground-state simulations. In this paper we present an effective way of combining DFPT with TDDFT. The dynamical polarizability is first expressed as an off-diagonal matrix e...
Density Functional Theory for General Hard-Core Lattice Gases
Lafuente, Luis; Cuesta, José A.
2004-09-01
We put forward a general procedure to obtain an approximate free-energy density functional for any hard-core lattice gas, regardless of the shape of the particles, the underlying lattice, or the dimension of the system. The procedure is conceptually very simple and recovers effortlessly previous results for some particular systems. Also, the obtained density functionals belong to the class of fundamental measure functionals and, therefore, are always consistent through dimensional reduction. We discuss possible extensions of this method to account for attractive lattice models.
The Bloch-Okounkov correlation functions of negative levels
Cheng, Shun-Jen; Taylor, David G.; Wang, Weiqiang
2007-01-01
Bloch and Okounkov introduced an $n$-point correlation function on the fermionic Fock space and found a closed formula in terms of theta functions. This function affords several distinguished interpretations and in particular can be formulated as correlation functions on irreducible $\\hat{gl}_\\infty$-modules of level one. These correlation functions have been generalized for irreducible integrable modules of $\\hat{gl}_\\infty$ and its classical Lie subalgebras of positive levels by the authors...
Exchange-correlation functionals via local interpolation along the adiabatic connection
Vuckovic, Stefan; Savin, Andreas; Teale, Andrew M; Gori-Giorgi, Paola
2016-01-01
The construction of density-functional approximations is explored by modeling the adiabatic connection em locally, using energy densities defined in terms of the electrostatic potential of the exchange-correlation hole. These local models are more amenable to the construction of size-consistent approximations than their global counterparts. In this work we use accurate input local ingredients to assess the accuracy of range of local interpolation models against accurate exchange-correlation energy densities. The importance of the strictly-correlated electrons (SCE) functional describing the strong coupling limit is emphasized, enabling the corresponding interpolated functionals to treat strong correlation effects. In addition to exploring the performance of such models numerically for the helium and beryllium isoelectronic series and the dissociation of the hydrogen molecule, an approximate analytic model is presented for the initial slope of the local adiabatic connection. Comparisons are made with approache...
Correlations in Many-Body systems from two-time Greens functions
Energy Technology Data Exchange (ETDEWEB)
Morawetz, K. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France); Kohler, H.S. [Arizona Univ., Tucson, AZ (United States). Dept. of Physics
2000-07-01
The Kadanoff-Baym (KB) equations are solved numerically for infinite nuclear matter. In particular we calculate correlation energies and correlation times. Approximating the Green's functions in the KB collision kernel by the free Green's functions the Levinson equation is obtained. This approximation is valid for weak interactions and/or low densities. It relates to the extended quasi-particle approximation for the spectral function. The Levinson correlation energy reduces for large times to a second order Born approximation for the energy. Comparing the Levinson, Born and KB calculations allows for an estimate of higher order spectral corrections to the correlations. (authors)
Multistate Density Functional Theory for Effective Diabatic Electronic Coupling.
Ren, Haisheng; Provorse, Makenzie R; Bao, Peng; Qu, Zexing; Gao, Jiali
2016-06-16
Multistate density functional theory (MSDFT) is presented to estimate the effective transfer integral associated with electron and hole transfer reactions. In this approach, the charge-localized diabatic states are defined by block localization of Kohn-Sham orbitals, which constrain the electron density for each diabatic state in orbital space. This differs from the procedure used in constrained density functional theory that partitions the density within specific spatial regions. For a series of model systems, the computed transfer integrals are consistent with experimental data and show the expected exponential attenuation with the donor-acceptor separation. The present method can be used to model charge transfer reactions including processes involving coupled electron and proton transfer.
Nuclear Energy Density Functionals: What do we really know?
Bulgac, Aurel; Jin, Shi
2015-01-01
We present the simplest nuclear energy density functional (NEDF) to date, determined by only 4 significant phenomenological parameters, yet capable of fitting measured nuclear masses with better accuracy than the Bethe-Weizs\\"acker mass formula, while also describing density structures (charge radii, neutron skins etc.) and time-dependent phenomena (induced fission, giant resonances, low energy nuclear collisions, etc.). The 4 significant parameters are necessary to describe bulk nuclear properties (binding energies and charge radii); an additional 2 to 3 parameters have little influence on the bulk nuclear properties, but allow independent control of the density dependence of the symmetry energy and isovector excitations, in particular the Thomas-Reiche-Kuhn sum rule. This Hohenberg-Kohn-style of density functional theory successfully realizes Weizs\\"acker's ideas and provides a computationally tractable model for a variety of static nuclear properties and dynamics, from finite nuclei to neutron stars, where...
Systematic of Nuclear Ground State Properties in Sr Isotope by Covariant Density Functional Theory
Institute of Scientific and Technical Information of China (English)
TIAN; Yuan
2012-01-01
<正>The hyperfine structure and isotope shifts of Sr-isotopes, both even-even and odd-even nuclei, are studied in the covariant density functional theory (DFT) with the new parameter set DD-PC1. Pairing correlation is treated by using the Bogoliubov with a separable form of the pairing interaction. Spin-parity,
In this study density functional theory (DFT) was used to study the adsorption of guaiacol and its initial hydrodeoxygenation (HDO) reactions on Pt(111). Previously reported Brønsted–Evans–Polanyi (BEP) correlations for small open chain molecules are found to be inadequate in estimating the reaction...
Metal-insulator transition and local moment formation: A spin-density functional approach
Ghazali, A.; Leroux-Hugon, P.
1980-01-01
A more thorough description of the metal-insulator transition in correlated systems including local moment formation may be achieved through the spin-density functional method when compared to the Hubbard model. We have applied this method to doped semiconductors and found a transition between an insulating phase with local moments and a metallic one without moments.
On soft limits of large-scale structure correlation functions
Energy Technology Data Exchange (ETDEWEB)
Ben-Dayan, Ido; Konstandin, Thomas; Porto, Rafael A.; Sagunski, Laura [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2014-11-15
We study soft limits of correlation functions for the density and velocity fields in the theory of structure formation. First, we rederive the (resummed) consistency conditions at unequal times using the eikonal approximation. These are solely based on symmetry arguments and are therefore universal. Then, we explore the existence of equal-time relations in the soft limit which, on the other hand, depend on the interplay between soft and hard modes. We scrutinize two approaches in the literature: The time-flow formalism, and a background method where the soft mode is absorbed into a locally curved cosmology. The latter has been recently used to set up (angular averaged) 'equal-time consistency relations'. We explicitly demonstrate that the time-flow relations and 'equal-time consistency conditions' are only fulfilled at the linear level, and fail at next-to-leading order for an Einstein de-Sitter universe. While applied to the velocities both proposals break down beyond leading order, we find that the 'equal-time consistency conditions' quantitatively approximates the perturbative results for the density contrast. Thus, we generalize the background method to properly incorporate the effect of curvature in the density and velocity fluctuations on short scales, and discuss the reasons behind this discrepancy. We conclude with a few comments on practical implementations and future directions.
Spectral density of the correlation matrix of factor models: a random matrix theory approach.
Lillo, F; Mantegna, R N
2005-07-01
We studied the eigenvalue spectral density of the correlation matrix of factor models of multivariate time series. By making use of the random matrix theory, we analytically quantified the effect of statistical uncertainty on the spectral density due to the finiteness of the sample. We considered a broad range of models, ranging from one-factor models to hierarchical multifactor models.
$\\eta^\\prime$ meson mass from topological charge density correlator in QCD
Fukaya, H; Cossu, G; Hashimoto, S; Kaneko, T; Noaki, J
2015-01-01
The flavor-singlet component of the eta prime meson is related to the topological structure of the SU(3) gauge field through the chiral anomaly. We perform a 2+1-flavor lattice QCD calculation and demonstrate that the two-point function of a gluonically defined topological charge density after a short Yang-Mills gradient flow contains the propagation of the eta prime meson, by showing that its mass in the chiral and continuum limit is consistent with the experimental value. The gluonic correlator does not suffer from the contamination of the pion contribution, and the clean signal is obtained at significantly lower numerical cost compared to the conventional method with the quark bilinear operators.
Global and local curvature in density functional theory
Zhao, Qing; Ioannidis, Efthymios I.; Kulik, Heather J.
2016-08-01
Piecewise linearity of the energy with respect to fractional electron removal or addition is a requirement of an electronic structure method that necessitates the presence of a derivative discontinuity at integer electron occupation. Semi-local exchange-correlation (xc) approximations within density functional theory (DFT) fail to reproduce this behavior, giving rise to deviations from linearity with a convex global curvature that is evidence of many-electron, self-interaction error and electron delocalization. Popular functional tuning strategies focus on reproducing piecewise linearity, especially to improve predictions of optical properties. In a divergent approach, Hubbard U-augmented DFT (i.e., DFT+U) treats self-interaction errors by reducing the local curvature of the energy with respect to electron removal or addition from one localized subshell to the surrounding system. Although it has been suggested that DFT+U should simultaneously alleviate global and local curvature in the atomic limit, no detailed study on real systems has been carried out to probe the validity of this statement. In this work, we show when DFT+U should minimize deviations from linearity and demonstrate that a "+U" correction will never worsen the deviation from linearity of the underlying xc approximation. However, we explain varying degrees of efficiency of the approach over 27 octahedral transition metal complexes with respect to transition metal (Sc-Cu) and ligand strength (CO, NH3, and H2O) and investigate select pathological cases where the delocalization error is invisible to DFT+U within an atomic projection framework. Finally, we demonstrate that the global and local curvatures represent different quantities that show opposing behavior with increasing ligand field strength, and we identify where these two may still coincide.
Time dependent density functional calculation of plasmon response in clusters
Institute of Scientific and Technical Information of China (English)
Wang Feng(王锋); Zhang Feng-Shou(张丰收); Eric Suraud
2003-01-01
We have introduced a theoretical scheme for the efficient description of the optical response of a cluster based on the time-dependent density functional theory. The practical implementation is done by means of the fully fledged timedependent local density approximation scheme, which is solved directly in the time domain without any linearization.As an example we consider the simple Na2 cluster and compute its surface plasmon photoabsorption cross section, which is in good agreement with the experiments.
Density functional calculations of spin-wave dispersion curves.
Kleinman, Leonard; Niu, Qian
1998-03-01
Extending the density functional method of Kubler et al( J. Kubler et al, J. Phys. F 18, 469 (1983) and J. Phys. Condens. Matter 1, 8155 (1989). ) for calcuating spin density wave ground states (but not making their atomic sphere approximation which requires a constant spin polarization direction in each WS sphere) we dicuss the calculation of frozen spin-wave eigenfunctions and their total energies. From these and the results of Niu's talk, we describe the calculation of spin-wave frequencies.
Methane dissociation on Pt(111): Searching for a specific reaction parameter density functional
Energy Technology Data Exchange (ETDEWEB)
Nattino, Francesco, E-mail: f.nattino@chem.leidenuniv.nl; Migliorini, Davide; Kroes, Geert-Jan [Leiden Institute of Chemistry, Leiden University, Gorlaeus Laboratories, P.O. Box 9502, 2300 RA Leiden (Netherlands); Bonfanti, Matteo [Dipartimento di Chimica, Università degli Studi di Milano, via Golgi 19, 20133 Milano (Italy)
2016-01-28
The theoretical description of methane dissociating on metal surfaces is a current frontier in the field of gas-surface dynamics. Dynamical models that aim at achieving a highly accurate description of this reaction rely on potential energy surfaces based on density functional theory calculations at the generalized gradient approximation. We focus here on the effect that the exchange-correlation functional has on the reactivity of methane on a metal surface, using CHD{sub 3} + Pt(111) as a test case. We present new ab initio molecular dynamics calculations performed with various density functionals, looking also at functionals that account for the van der Waals (vdW) interaction. While searching for a semi-empirical specific reaction parameter density functional for this system, we find that the use of a weighted average of the PBE and the RPBE exchange functionals together with a vdW-corrected correlation functional leads to an improved agreement with quantum state-resolved experimental data for the sticking probability, compared to previous PBE calculations. With this semi-empirical density functional, we have also investigated the surface temperature dependence of the methane dissociation reaction and the influence of the rotational alignment on the reactivity, and compared our results with experiments.
Estimation of Correlation Functions by the Random Decrement Technique
DEFF Research Database (Denmark)
Brincker, Rune; Krenk, S.; Jensen, Jakob Laigaard
1993-01-01
The Random Decrement (RDD) Technique is a versatile technique for characterization of random signals in the time domain. In this paper a short review of the theoretical basis is given, and the technique is illustrated by estimating auto-correlation functions and cross-correlation functions on modal...... from smaller estimation errors than the corresponding FFT estimates. However, in the case of estimating cross-correlations functions for stochastic processes with low mutual correlation, the FFT technique might be more accurate....
Estimation of Correlation Functions by the Random Decrement Technique
DEFF Research Database (Denmark)
Brincker, Rune; Krenk, Steen; Jensen, Jakob Laigaard
The Random Decrement (RDD) Technique is a versatile technique for characterization of random signals in the time domain. In this paper a short review of the theoretical basis is given, and the technique is illustrated by estimating auto-correlation functions and cross-correlation functions on modal...... from smaller estimation errors than the corresponding FFT estimates. However, in the case of estimating cross-correlations functions for stochastic processes with low mutual correlation, the FFT technique might be more accurate....
Correlation of densities with shear wave velocities and SPT N values
Anbazhagan, P.; Uday, Anjali; Moustafa, Sayed S. R.; Al-Arifi, Nassir S. N.
2016-06-01
Site effects primarily depend on the shear modulus of subsurface layers, and this is generally estimated from the measured shear wave velocity (V s) and assumed density. Very rarely, densities are measured for amplification estimation because drilling and sampling processes are time consuming and expensive. In this study, an attempt has been made to derive the correlation between the density (dry and wet density) and V s/SPT (standard penetration test) N values using measured data. A total of 354 measured V s and density data sets and 364 SPT N value and density data sets from 23 boreholes have been used in the study. Separate relations have been developed for all soil types as well as fine-grained and coarse-grained soil types. The correlations developed for bulk density were compared with the available data and it was found that the proposed relation matched well with the existing data. A graphical comparison and validation based on the consistency ratio and cumulative frequency curves was performed and the newly developed relations were found to demonstrate good prediction performance. An attempt has also been made to propose a relation between the bulk density and shear wave velocity applicable for a wide range of soil and rock by considering data from this study as well as that of previous studies. These correlations will be useful for predicting the density (bulk and dry) of sites having measured the shear wave velocity and SPT N values.
Pressure and surface tension of soild-liquid interface using Tarazona density functional theory
Directory of Open Access Journals (Sweden)
M. M.
2000-12-01
Full Text Available The weighted density functional theory proposed by Tarazona is applied to study the solid-liquid interface. In the last two decades the weighted density functional became a useful tool to consider the properties of inhomogeneous liquids. In this theory, the role of the size of molecules or the particles of which the matter is composed, was found to be important. In this resarch we study a hard sphere fluid beside a hard wall. For this study the liquid is an inhomogeneous system. We use the definition of the direct correlation function as a second derivative of free energy with respect to the density. We use this definition and the definition of the weighting function, then we minimize the grand potential with respect to the density to get the Euler Lagrange equation and we obtain an integral equation to find the inhomogeneous density profile. The obtained density profile as a function of the distance from the wall, for different bulk density is plotted in three dimensions. We also calculate the pressure and compare it with the Carnahan-starling results, and finally we obtained the surface tension at liquid-solid interface and compared it with the results of Monte Carlo simulation.
Nuclear energy density functional inspired by an effective field theory
Papakonstantinou, Panagiota; Lim, Yeunhwan; Hyun, Chang Ho
2016-01-01
Inspired by an effective field theory (EFT) for Fermi systems, we write the nuclear energy density functional (EDF) as an expansion in powers of the Fermi momentum $k_F$, or the cubic root of the density $\\rho^{1/3}$. With the help of pseudodata from microscopic calculations we fit the coefficients of the functional within a wide range of densities relevant for nuclei and neutron stars. The functional already at low order can reproduce known or adopted values of nuclear matter near saturation, a range of existing microscopic results on asymmetric matter, and a neutron-star mass-radius relation consistent with observations. Our approach leads to a transparent expansion of Skyrme-type EDFs and opens up many possibilities for future explorations in nuclei and homogeneous matter.
Density functional approach to the many-body problem : Key concepts and exact functionals
2003-01-01
We give an overview of the fundamental concepts of density functional theory. We give a careful discussion of the several density functionals and their differentiability properties. We show that for nondegenerate ground states we can calculate the necessary functional derivatives by means of linear
Multireference spin-adapted variant of density functional theory.
Khait, Yuriy G; Hoffmann, Mark R
2004-03-15
A new Kohn-Sham formalism is developed for studying the lowest molecular electronic states of given space and spin symmetry whose densities are represented by weighted sums of several reference configurations. Unlike standard spin-density functional theory, the new formalism uses total spin conserving spin-density operators and spin-invariant density matrices so that the method is fully spin-adapted and solves the so-called spin-symmetry dilemma. The formalism permits the use of an arbitrary set of reference (noninteracting) configurations with any number of open shells. It is shown that the requirement of degeneracy of the total noninteracting energies of the reference configurations (or configuration state functions) is equivalent to the stationary condition of the exact energy relative to the weights of the configurations (or configuration state functions). Consequently, at any molecular geometry, the weights can be determined by minimization of the energy, and, for given reference weights, the Kohn-Sham orbitals can be determined. From this viewpoint, the developed theory can be interpreted as an analog of the multiconfiguration self-consistent field approach within density functional theory.
Peverati, Roberto; Truhlar, Donald G
2014-03-13
Kohn-Sham density functional theory is in principle an exact formulation of quantum mechanical electronic structure theory, but in practice we have to rely on approximate exchange-correlation (xc) functionals. The objective of our work has been to design an xc functional with broad accuracy across as wide an expanse of chemistry and physics as possible, leading--as a long-range goal--to a functional with good accuracy for all problems, i.e. a universal functional. To guide our path towards that goal and to measure our progress, we have developed-building on earlier work of our group-a set of databases of reference data for a variety of energetic and structural properties in chemistry and physics. These databases include energies of molecular processes, such as atomization, complexation, proton addition and ionization; they also include molecular geometries and solid-state lattice constants, chemical reaction barrier heights, and cohesive energies and band gaps of solids. For this paper, we gather many of these databases into four comprehensive databases, two with 384 energetic data for chemistry and solid-state physics and another two with 68 structural data for chemistry and solid-state physics, and we test two wave function methods and 77 density functionals (12 Minnesota meta functionals and 65 others) in a consistent way across this same broad set of data. We especially highlight the Minnesota density functionals, but the results have broader implications in that one may see the successes and failures of many kinds of density functionals when they are all applied to the same data. Therefore, the results provide a status report on the quest for a universal functional.
Correlation between thyroid function and nodular goiter accompanied with gallstone
Institute of Scientific and Technical Information of China (English)
Shihong Ma; Qinjiang Liu; Xiaofeng Hou
2014-01-01
The-purpose-of-the-study-wass-to-explore-the-correlation-between-thyroid-function-and-nodular-goiter-accompanied-with-gal-stone.-Methods:We-col-ected-120-cases-about-nodular-goiter-accompanied-with-gal-stone-and-128-cases-about-nodular-goiter-and-establish-50-healthy-control-groups.-Detected-t-level-of-hyrotropic-hormone-(TSH),-total-tri-o-dothyronine-(TT3),-total-thyroxine-in-the-peripheral-venous-blood-of-these-cases-in-the-three-groups-by-using-electrochemilu-minescence-immunoassay,-measure-level-of-total-cholesterol-(TC),-high-density-lipoprotein-cholesterol-(HDL-C),-low-density-lipoprotein-cholesterol-(LDL-C)-and-total-bile-acid-(TBA)-levels-by-using-enzymic-method,-and-observed-the-changes-of-thyroid-function-and-blood-lipid-among-the-three-groups.-Results:The-serum-TT3-level-in-nodular-goiter-accompanied-with-gal-stone-group-and-the-nodular-goiter-group-was-significantly-lower-than-that-in-control-group-(P0.05).-Accordingly,-TC-and-LDL-C-level-in-nodular-goiter-accompanied-with-gal-stone-group-was-significantly-higher-than-that-in-nodular-goiter-and-control-group-(P0.05).-The-HDL-C-level-in-nodular-goiter-accompanied-with-gal-stone-group-and-control-group-was-higher-than-that-in-simple-nodular-goiter-group-(P<0.01).-Conclusion:The-originating-etiologic-factor-of-nodular-goiter-accompanied-with-gal-stone-may-be-related-to-that-the-decreased-TT3-induced-sub-clinical-hypothyroidism.
Ultra-nonlocality in density functional theory for photo-emission spectroscopy.
Uimonen, A-M; Stefanucci, G; van Leeuwen, R
2014-05-14
We derive an exact expression for the photocurrent of photo-emission spectroscopy using time-dependent current density functional theory (TDCDFT). This expression is given as an integral over the Kohn-Sham spectral function renormalized by effective potentials that depend on the exchange-correlation kernel of current density functional theory. We analyze in detail the physical content of this expression by making a connection between the density-functional expression and the diagrammatic expansion of the photocurrent within many-body perturbation theory. We further demonstrate that the density functional expression does not provide us with information on the kinetic energy distribution of the photo-electrons. Such information can, in principle, be obtained from TDCDFT by exactly modeling the experiment in which the photocurrent is split into energy contributions by means of an external electromagnetic field outside the sample, as is done in standard detectors. We find, however, that this procedure produces very nonlocal correlations between the exchange-correlation fields in the sample and the detector.
Usui, Kouta
2012-01-01
It will be proved that a model of lattice field theories which satisfies (A1) Hermiticity, (A2) translational invariance, (A3) reflection positivity, and (A4) polynomial boundedness of correlations, permits the Kallen-Lehmann representation of two point correlation functions with positive spectral density function. Then, we will also argue that positivity of spectral density functions is necessary for a lattice theory to satisfy conditions (A1) - (A4). As an example, a lattice overlap scalar boson model will be discussed. We will find that the overlap scalar boson violates the reflection positivity.
Exploration of a modified density dependence in the Skyrme functional
Erler, J; Reinhard, P -G
2010-01-01
A variant of the basic Skyrme-Hartree-Fock (SHF) functional is considered dealing with a new form of density dependence. It employs only integer powers and thus will allow a more sound basis for projection schemes (particle number, angular momentum). We optimize the new functional with exactly the same adjustment strategy as used in an earlier study with a standard Skyrme functional. This allows direct comparisons of the performance of the new functional relative to the standard one. We discuss various observables: bulk properties of finite nuclei, nuclear matter, giant resonances, super-heavy elements, and energy systematics. The new functional performs at least as well as the standard one, but offers a wider range of applicability (e.g. for projection) and more flexibility in the regime of high densities.
Choosing a density functional for static molecular polarizabilities
Wu, Taozhe; Thakkar, Ajit J
2015-01-01
Coupled-cluster calculations of static electronic dipole polarizabilities for 145 organic molecules are performed to create a reference data set. The molecules are composed from carbon, hydrogen, nitrogen, oxygen, fluorine, sulfur, chlorine, and bromine atoms. They range in size from triatomics to 14 atoms. The Hartree-Fock and 2nd-order M{\\o}ller-Plesset methods and 34 density functionals, including local functionals, global hybrid functionals, and range-separated functionals of the long-range-corrected and screened-exchange varieties, are tested against this data set. On the basis of the test results, detailed recommendations are made for selecting density functionals for polarizability computations on relatively small organic molecules.
Probability distribution functions in the finite density lattice QCD
Ejiri, S; Aoki, S; Kanaya, K; Saito, H; Hatsuda, T; Ohno, H; Umeda, T
2012-01-01
We study the phase structure of QCD at high temperature and density by lattice QCD simulations adopting a histogram method. We try to solve the problems which arise in the numerical study of the finite density QCD, focusing on the probability distribution function (histogram). As a first step, we investigate the quark mass dependence and the chemical potential dependence of the probability distribution function as a function of the Polyakov loop when all quark masses are sufficiently large, and study the properties of the distribution function. The effect from the complex phase of the quark determinant is estimated explicitly. The shape of the distribution function changes with the quark mass and the chemical potential. Through the shape of the distribution, the critical surface which separates the first order transition and crossover regions in the heavy quark region is determined for the 2+1-flavor case.
Maccione, Alessandro; Garofalo, Matteo; Nieus, Thierry; Tedesco, Mariateresa; Berdondini, Luca; Martinoia, Sergio
2012-06-15
We used electrophysiological signals recorded by CMOS Micro Electrode Arrays (MEAs) at high spatial resolution to estimate the functional-effective connectivity of sparse hippocampal neuronal networks in vitro by applying a cross-correlation (CC) based method and ad hoc developed spatio-temporal filtering. Low-density cultures were recorded by a recently introduced CMOS-MEA device providing simultaneous multi-site acquisition at high-spatial (21 μm inter-electrode separation) as well as high-temporal resolution (8 kHz per channel). The method is applied to estimate functional connections in different cultures and it is refined by applying spatio-temporal filters that allow pruning of those functional connections not compatible with signal propagation. This approach permits to discriminate between possible causal influence and spurious co-activation, and to obtain detailed maps down to cellular resolution. Further, a thorough analysis of the links strength and time delays (i.e., amplitude and peak position of the CC function) allows characterizing the inferred interconnected networks and supports a possible discrimination of fast mono-synaptic propagations, and slow poly-synaptic pathways. By focusing on specific regions of interest we could observe and analyze microcircuits involving connections among a few cells. Finally, the use of the high-density MEA with low density cultures analyzed with the proposed approach enables to compare the inferred effective links with the network structure obtained by staining procedures.
Crystallization induced by multiple seeds: dynamical density functional approach.
Neuhaus, T; Schmiedeberg, M; Löwen, H
2013-12-01
Using microscopic dynamical density functional theory, we calculate the dynamical formation of polycrystals by following the crystal growth around multiple crystalline seeds imposed to an undercooled fluid. Depending on the undercooling and the size ratio as well as the relative crystal orientation of two neighboring seeds, three possibilities of the final state emerge, namely no crystallization at all, formation of a monocrystal, or two crystallites separated by a curved grain boundary. Our results, which are obtained for two-dimensional hard disk systems using a fundamental-measure density functional, shed new light on the particle-resolved structure and growth of polycrystalline material in general.
Signatures of charmonium modification in spatial correlation functions
Karsch, F; Mukherjee, Swagato; Petreczky, P
2012-01-01
We study spatial correlation functions of charmonium in 2+1 flavor QCD using an improved staggered formulation. Contrary to the temporal correlation functions the spatial correlation functions exhibit a strong temperature dependence above the QCD transition temperature. Above this temperature they are sensitive to temporal boundary conditions. Both features become significant at a temperature close to 1.5 Tc and suggest corresponding modifications of charmonium spectral functions.
Gordon, David M; Ash, Stephen R
2009-01-01
The purpose of this research project was to determine whether the glucose level of a blood plasma sample from a diabetic patient could be predicted by measuring the density and conductivity of ultrafiltrate of plasma created by a 30,000 m.w. cutoff membrane. Conductivity of the plasma filtrate measures electrolyte concentration and should correct density measurements for changes in electrolytes and water concentration. In vitro studies were performed measuring conductivity and density of solutions of varying glucose and sodium chloride concentrations. Plasma from seven hospitalized patients with diabetes was filtered across a 30,000 m.w. cutoff membrane. The filtrate density and conductivity were measured and correlated to glucose levels. In vitro studies confirmed the ability to predict glucose from density and conductivity measurements, in varying concentrations of glucose and saline. In plasma filtrate, the conductivity and density measurements of ultrafiltrate allowed estimation of glucose in some patients with diabetes but not others. The correlation coefficient for the combined patient data was 0.45 which was significant but only explained 20% of the variability in the glucose levels. Individually, the correlation was significant in only two of the seven patients with correlation coefficients of 0.79 and 0.88. The reasons for lack of correlation are not clear, and cannot be explained by generation of idiogenic osmoles, effects of alcohol dehydrogenase, water intake, etc. This combination of physical methods for glucose measurement is not a feasible approach to measuring glucose in plasma filtrate.
Specification of Density Functional Approximation by Radial Distribution Function of Bulk Fluid
Institute of Scientific and Technical Information of China (English)
ZHOU Shi-Qi
2002-01-01
A systematic methodology is proposed to deal with the weighted density approximation version of clas-sical density functional theory by employing the knowledge of radial distribution function of bulk fluid. The presentmethodology results from the concept of universality of the free energy density functional combined with the test particlemethod. It is shown that the new method is very accurate for the predictions of density distribution ofa hard sphere fluidat different confining geometries. The physical foundation of the present methodology is also applied to the quantumdensity functional theory.
Semilocal exchange hole with an application to range-separated density functionals
Tao, Jianmin; Bulik, Ireneusz W.; Scuseria, Gustavo E.
2017-03-01
The exchange-correlation hole is a central concept in density functional theory. It not only provides justification for an exchange-correlation energy functional but also serves as a local ingredient for nonlocal range-separated density functionals. However, due to the nonlocal nature, modeling the conventional exact exchange hole presents a great challenge to density functional theory. In this work, we propose a semilocal exchange hole underlying the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-generalized gradient approximation functional. Our model is distinct from previous ones not only at small separation between an electron and the hole around the electron but also in the way it interpolates between rapidly varying and slowly varying densities. Here the interpolation is determined by the wave-vector analysis on the infinite-barrier model for a jellium surface. Numerical tests show that our exchange-hole model mimics the conventional exact one quite well for atoms. As a simple application, we apply the hole model to construct a TPSS-based range-separated functional. We find that this range-separated functional can substantially improve the band gaps and barrier heights of TPSS, without losing much accuracy for atomization energies.
Role of Wigner function in studying quantum correlations
Siyouri, F.; El Baz, M.; Hassouni, Y.
2016-09-01
In this paper, we investigate the possibility to use the Wigner function to detect and quantify quantum correlations in general. We study these quantum correlations for two quasi-Werner states formed with two general bipartite superposed squeezed states. We find then that the Wigner function is not sensitive to all kinds of quantum correlations but it only witnesses entanglement.
The importance of current contributions to shielding constants in density-functional theory.
Reimann, Sarah; Ekström, Ulf; Stopkowicz, Stella; Teale, Andrew M; Borgoo, Alex; Helgaker, Trygve
2015-07-28
The sources of error in the calculation of nuclear-magnetic-resonance shielding constants determined by density-functional theory are examined. Highly accurate Kohn-Sham wave functions are obtained from coupled-cluster electron density functions and used to define accurate-but current independent-density-functional shielding constants. These new reference values, in tandem with high-accuracy coupled-cluster shielding constants, provide a benchmark for the assessment of errors in common density-functional approximations. In particular the role of errors arising in the diamagnetic and paramagnetic terms is investigated, with particular emphasis on the role of current-dependence in the latter. For carbon and nitrogen the current correction is found to be, in some cases, larger than 10 ppm. This indicates that the absence of this correction in general purpose exchange-correlation functionals is one of the main sources of error in shielding calculations using density functional theory. It is shown that the current correction improves the shielding performance of many popular approximate DFT functionals.