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.
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.
Relativistic density functional theory for finite nuclei and neutron stars
Piekarewicz, J
2015-01-01
The main goal of the present contribution is a pedagogical introduction to the fascinating world of neutron stars by relying on relativistic density functional theory. Density functional theory provides a powerful--and perhaps unique--framework for the calculation of both the properties of finite nuclei and neutron stars. Given the enormous densities that may be reached in the core of neutron stars, it is essential that such theoretical framework incorporates from the outset the basic principles of Lorentz covariance and special relativity. After a brief historical perspective, we present the necessary details required to compute the equation of state of dense, neutron-rich matter. As the equation of state is all that is needed to compute the structure of neutron stars, we discuss how nuclear physics--particularly certain kind of laboratory experiments--can provide significant constrains on the behavior of neutron-rich matter.
Relativistic Cosmology Number Densities and the Luminosity Function
Iribarrem, Alvaro S; Ribeiro, Marcelo B; Stoeger, William R
2012-01-01
This paper studies the connection between the relativistic number density of galaxies down the past light cone in a Friedmann-Lemaitre-Robertson-Walker spacetime with non-vanishing cosmological constant and the galaxy luminosity function (LF) data. It extends the redshift range of previous results presented in Albani et al. (2007, arXiv:astro-ph/0611032) where the galaxy distribution was studied out to z=1. Observational inhomogeneities were detected at this range. This research also searches for LF evolution in the context of the framework advanced by Ribeiro and Stoeger (2003, arXiv:astro-ph/0304094), further developing the theory linking relativistic cosmology theory and LF data. Selection functions are obtained using the Schechter parameters and redshift parametrization of the galaxy luminosity functions obtained from an I-band selected dataset of the FORS Deep Field galaxy survey in the redshift range 0.5
Dohn, Asmus Ougaard; Møller, Klaus Braagaard; Sauer, Stephan P. A.
2013-01-01
The geometry of tetracyanoplatinate(II) (TCP) has been optimized with density functional theory (DFT) calculations in order to compare different computational strategies. Two approximate scalar relativistic methods, i.e. the scalar zeroth-order regular approximation (ZORA) and non-relativistic ca...
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...
Kullie, Ossama, E-mail: kullie@uni-kassel.de [Institute de Chimie de Strasbourg, CNRS et Université de Strasbourg, Laboratoire de Chimie Quantique, 4 rue Blaise Pascal, 67070 Strasbourg (France); Theoretical Physics, Institute for Physics, Department of Mathematics and Natural Science, University of Kassel (Germany)
2013-03-29
Highlights: ► The achievement of CAMB3LYP functional for excited states in framework of TD-DFT. ► Relativistic 4-components calculations for the excited states of the Cd{sub 2} dimer. ► Relativistic Spin-Free calculations for the excited states of Cd{sub 2} dimer. ► A comparison of the achievements of different types of DFT approximations upon Cd{sub 2}. - Abstract: In this paper we present a time-dependent density functional study for the ground-state as well the 20-lowest laying excited states of the cadmium dimer Cd{sub 2}, we analyze its spectrum obtained from all electrons calculations performed with time-depended density functional for the relativistic Dirac-Coulomb- and relativistic spin-free-Hamiltonian as implemented in DIRAC-PACKAGE. The calculations were obtained with different density functional approximations, and a comparison with the literature is given as far as available. Our result is very encouraging, especially for the lowest excited states of this dimer, and is expected to be enlightened for similar systems. The result shows that only long-range corrected functionals such as CAMB3LYP, gives the correct asymptotic behavior for the higher states. A comparable but less satisfactory results were obtained with B3LYP and PBE0 functionals. Spin-free-Hamiltonian is shown to be very efficient for systems containing heavy elements such as Cd{sub 2} in frameworks of (time-dependent) density functional without introducing large errors.
Time-dependent relativistic density functional study of Yb and YbO
XU WenHua; ZHANG Yong; LIU WenJian
2009-01-01
The low-lying electronic states of Yb and YbO are investigated by using time-dependent relativistic density functional theory,which is based on the newly developed exact two-component Hamiltonian resulting from symmetrized elimination of the small component.The nature of the excited states is analyzed by using the full molecular symmetry.The calculated results support the previous experimental assignment of the ground and excited states of YbO.
Magnetic properties of f-electron systems in spin-polarized relativistic density functional theory
Yamagami, H.; Mavromaras, A.; Kübler, J.
1997-12-01
The magnetic ground state of the series of lanthanide and actinide trivalent ions is investigated by means of spin-polarized relativistic spin-density functional theory. In the local density functional approximation (LDA) an internal effective magnetic field due to exchange and correlation couples to the spin degrees of freedom. The resulting set of coupled Dirac equations yields ground-state multiplets that obey the well-known Hund's rules. This remarkable result comes about by the coupling of the j = l + 1/2 with the j = l - 1/2 states due to the exchange - correlation potential that is, as usual, the functional derivative of the exchange - correlation energy with respect to the spin magnetic moment. The effect of the coupling is shown to depend on the varying relative strengths of spin - orbit coupling and exchange splitting within the f series. Since in the f levels the internal exchange splitting dominates rather than the spin - orbit splitting, the energy level scheme is that of the Paschen - Back effect, and thus features of the Russell - Saunders coupling persist in spite of relativistic effects.
A relativistic time-dependent density functional study of the excited states of the mercury dimer
Kullie, Ossama, E-mail: kullie@uni-kassel.de, E-mail: ossama.kullie@unistra.fr [Institute de Chimie de Strasbourg, CNRS et Université de Strasbourg, Laboratoire de Chimie Quantique, 4 rue Blaise Pascal, 67070 Strasbourg, France and Theoretical Physics, Institute for Physics, Department of Mathematics and Natural Science, University of Kassel, D-34127 Kassel (Germany)
2014-01-14
In previous works on Zn{sub 2} and Cd{sub 2} dimers we found that the long-range corrected CAMB3LYP gives better results than other density functional approximations for the excited states, especially in the asymptotic region. In this paper, we use it to present a time-dependent density functional (TDDFT) study for the ground-state as well as the excited states corresponding to the (6s{sup 2} + 6s6p), (6s{sup 2} + 6s7s), and (6s{sup 2} + 6s7p) atomic asymptotes for the mercury dimer Hg{sub 2}. We analyze its spectrum obtained from all-electron calculations performed with the relativistic Dirac-Coulomb and relativistic spinfree Hamiltonian as implemented in DIRAC-PACKAGE. A comparison with the literature is given as far as available. Our result is excellent for the most of the lower excited states and very encouraging for the higher excited states, it shows generally good agreements with experimental results and outperforms other theoretical results. This enables us to give a detailed analysis of the spectrum of the Hg{sub 2} including a comparative analysis with the lighter dimers of the group 12, Cd{sub 2}, and Zn{sub 2}, especially for the relativistic effects, the spin-orbit interaction, and the performance of CAMB3LYP and is enlightened for similar systems. The result shows, as expected, that spinfree Hamiltonian is less efficient than Dirac-Coulomb Hamiltonian for systems containing heavy elements such as Hg{sub 2}.
Bagayoko, Diola
In 2014, 50 years following the introduction of density functional theory (DFT), a rigorous understanding of it was published [AIP Advances, 4, 127104 (2014)]. This understanding included necessary steps ab initio electronic structure calculations have to take if their results are to possess the full physical content of DFT. These steps guarantee the fulfillment of conditions of validity of DFT; not surprisingly, they have led to accurate descriptions of several dozens of semiconductors, from first principle, without invoking derivative discontinuity or self-interaction correction. This presentation shows the mathematically and physically rigorous understanding of the relativistic extension of DFT by Rajagopal and Callaway {Phys. Rev. B 7, 1912 (1973)]. As in the non-relativistic case, the attainment of the absolute minima of the occupied energies is a necessary condition for the corresponding current density to be that of the ground state of the system and for computational results to agree with corresponding, experimental ones. Acknowledgments:This work was funded in part by the US National Science Foundation [NSF, Award Nos. EPS-1003897, NSF (2010-2015)-RII-SUBR, and HRD-1002541], the US Department of Energy, National Nuclear Security Administration (NNSA, Award No. DE-NA0002630), LaSPACE, and LONI-SUBR.
Komorovsky, Stanislav; Repisky, Michal; Malkin, Elena; Demissie, Taye B; Ruud, Kenneth
2015-08-11
We present an implementation of the nuclear spin-rotation (SR) constants based on the relativistic four-component Dirac-Coulomb Hamiltonian. This formalism has been implemented in the framework of the Hartree-Fock and Kohn-Sham theory, allowing assessment of both pure and hybrid exchange-correlation functionals. In the density-functional theory (DFT) implementation of the response equations, a noncollinear generalized gradient approximation (GGA) has been used. The present approach enforces a restricted kinetic balance condition for the small-component basis at the integral level, leading to very efficient calculations of the property. We apply the methodology to study relativistic effects on the spin-rotation constants by performing calculations on XHn (n = 1-4) for all elements X in the p-block of the periodic table and comparing the effects of relativity on the nuclear SR tensors to that observed for the nuclear magnetic shielding tensors. Correlation effects as described by the density-functional theory are shown to be significant for the spin-rotation constants, whereas the differences between the use of GGA and hybrid density functionals are much smaller. Our calculated relativistic spin-rotation constants at the DFT level of theory are only in fair agreement with available experimental data. It is shown that the scaling of the relativistic effects for the spin-rotation constants (varying between Z(3.8) and Z(4.5)) is as strong as for the chemical shieldings but with a much smaller prefactor.
Spectral line shifts of alkali atoms in liquid helium: a relativistic density functional approach
Anton, J [Universitaet Kassel, Institut fuer Physik, 34109 Kassel (Germany); Mukherjee, P K [Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700 032 (India); Fricke, B [Universitaet Kassel, Institut fuer Physik, 34109 Kassel (Germany); Fritzsche, S [Universitaet Kassel, Institut fuer Physik, 34109 Kassel (Germany)
2007-06-28
Excitation line shifts of the principal resonance transitions in alkali atoms sodium and cesium embedded inside the liquid helium environment have been calculated using four-component relativistic density functional theory. The effect of the liquid helium environment is assumed to be represented by a cluster of 14 atoms surrounding the central alkali atom. The estimated blue shift of the principal resonance line {sup 2}S {yields}{sup 2}P is 22.8 nm for Na and 16.7 nm for Cs. The result for Cs is in good agreement with the experimental shift of 18.2 nm. In the absence of the experimental data for Na, our result is compared with those of other theoretical estimates.
Ray, Rupashree Shyama
2009-02-10
In this work, the complexation of uranium in its most stable oxidation state VI in aqueous solution was studied computationally, within the framework of density functional (DF) theory. The thesis is divided into the following parts: Chapter 2 briefly summarizes the relevant general aspects of actinide chemistry and then focuses on actinide environmental chemistry. Experimental results on hydrolysis, actinide complexation by carboxylic acids, and humic substances are presented to establish a background for the subsequent discussion. Chapter 3 describes the computational method used in this work and the relevant features of the parallel quantum chemistry code PARAGAUSS employed. First, the most relevant basics of the applied density functional approach are presented focusing on relativistic effects. Then, the treatment of solvent effects, essential for an adequate modeling of actinide species in aqueous solution, will be introduced. At the end of this chapter, computational parameters and procedures will be summarized. Chapter 4 presents the computational results including a comparison to available experimental data. In the beginning, the mononuclear hydrolysis product of UO{sub 2}{sup 2+}, [UO{sub 2}OH]{sup +}, will be discussed. The second part deals with actinide complexation by carboxylate ligands. First of all the coordination number for uranylacetate will be discussed with respect to implications for the complexation of actinides by humic substances followed by the uranyl complexation of aromatic carboxylic acids in comparison to earlier results for aliphatic ones. In the end, the ternary uranyl-hydroxo-acetate are discussed, as models of uranyl humate complexation at ambient condition.
Komorovsky, Stanislav; Repisky, Michal; Ruud, Kenneth; Malkina, Olga L; Malkin, Vladimir G
2013-12-27
A four-component relativistic method for the calculation of NMR shielding constants of paramagnetic doublet systems has been developed and implemented in the ReSpect program package. The method uses a Kramer unrestricted noncollinear formulation of density functional theory (DFT), providing the best DFT framework for property calculations of open-shell species. The evaluation of paramagnetic nuclear magnetic resonance (pNMR) tensors reduces to the calculation of electronic g tensors, hyperfine coupling tensors, and NMR shielding tensors. For all properties, modern four-component formulations were adopted. The use of both restricted kinetically and magnetically balanced basis sets along with gauge-including atomic orbitals ensures rapid basis-set convergence. These approaches are exact in the framework of the Dirac-Coulomb Hamiltonian, thus providing useful reference data for more approximate methods. Benchmark calculations on Ru(III) complexes demonstrate good performance of the method in reproducing experimental data and also its applicability to chemically relevant medium-sized systems. Decomposition of the temperature-dependent part of the pNMR tensor into the traditional contact and pseudocontact terms is proposed.
Kullie, Ossama [CNRS et Universite de Strasbourg, Institut de Chimie, Laboratoire de Chimie Quantique, 1 Rue Blaise Pascal, F- 67008 Strasbourg cedex (France)
2012-07-01
In this poster I present a (time-dependent) density functional study of the 20 low-lying excited states as well the ground states of the zinc dimer Zn{sub 2}. I analyze the spectrum of the dimer obtained form all electrons calculations which are performed using time-depended density functional with a relativistic 4-components-, and spin-free-Hamiltonian. I show results for different well-known density functional approximations, in comparing with literature and experimental values, the results are very encouraging, especially for the lowest excited states of these dimers. However, the results show that only the long-range corrected functionals such CAMB3LYP gives the correct asymptotic behavior for the higher states, for which the best result is obtained, and a comparable result is obtained from PBE0 functional.
Keith, Todd A; Frisch, Michael J
2011-11-17
Scalar-relativistic, all-electron density functional theory (DFT) calculations were done for free, neutral atoms of all elements of the periodic table using the universal Gaussian basis set. Each core, closed-subshell contribution to a total atomic electron density distribution was separately fitted to a spherical electron density function: a linear combination of s-type Gaussian functions. The resulting core subshell electron densities are useful for systematically and compactly approximating total core electron densities of atoms in molecules, for any atomic core defined in terms of closed subshells. When used to augment the electron density from a wave function based on a calculation using effective core potentials (ECPs) in the Hamiltonian, the atomic core electron densities are sufficient to restore the otherwise-absent electron density maxima at the nuclear positions and eliminate spurious critical points in the neighborhood of the atom, thus enabling quantum theory of atoms in molecules (QTAIM) analyses to be done in the neighborhoods of atoms for which ECPs were used. Comparison of results from QTAIM analyses with all-electron, relativistic and nonrelativistic molecular wave functions validates the use of the atomic core electron densities for augmenting electron densities from ECP-based wave functions. For an atom in a molecule for which a small-core or medium-core ECPs is used, simply representing the core using a simplistic, tightly localized electron density function is actually sufficient to obtain a correct electron density topology and perform QTAIM analyses to obtain at least semiquantitatively meaningful results, but this is often not true when a large-core ECP is used. Comparison of QTAIM results from augmenting ECP-based molecular wave functions with the realistic atomic core electron densities presented here versus augmenting with the limiting case of tight core densities may be useful for diagnosing the reliability of large-core ECP models in
Mahdi Afshar
2013-11-01
Full Text Available We have demonstrated electronic structure and magnetic properties of Cu3, Ag3 and Au3 trimers using a full potential local orbital method in the framework of relativistic density functional theory. We have also shown that the non-relativistic generalized gradient approximation for the exchange-correlation energy functional gives reliable magnetic properties in coinage metal trimers compared to experiment. In addition we have indicated that the spin-orbit coupling changes the structure and magnetic properties of gold trimer while the structure and magnetic properties of copper and silver trimers are marginally affected. A significant orbital moment of 0.21μB was found for most stable geometry of the gold trimer whereas orbital magnetism is almost quenched in the copper and silver trimers.
Density perturbations with relativistic thermodynamics
Maartens, R
1997-01-01
We investigate cosmological density perturbations in a covariant and gauge- invariant formalism, incorporating relativistic causal thermodynamics to give a self-consistent description. The gradient of density inhomogeneities splits covariantly into a scalar part, a rotational vector part that is determined by the vorticity, and a tensor part that describes the shape. We give the evolution equations for these parts in the general dissipative case. Causal thermodynamics gives evolution equations for viswcous stress and heat flux, which are coupled to the density perturbation equation and to the entropy and temperature perturbation equations. We give the full coupled system in the general dissipative case, and simplify the system in certain cases.
Ji, Min; Lan, Xin; Han, Zhenping; Hao, Ce; Qiu, Jieshan
2012-11-19
The electronically excited state and luminescence property of metal-organic framework MOF-5 were investigated using relativistic density functional theory (DFT) and time-dependent DFT (TDDFT). The geometry, IR spectra, and UV-vis spectra of MOF-5 in the ground state were calculated using relativistic DFT, leading to good agreement between the experimental and theoretical results. The frontier molecular orbitals and electronic configuration indicated that the luminescence mechanism in MOF-5 follows ligand-to-ligand charge transfer (LLCT), namely, π* → π, rather than emission with the ZnO quantum dot (QD) proposed by Bordiga et al. The geometry and IR spectra of MOF-5 in the electronically excited state have been calculated using the relativistic TDDFT and compared with those for the ground state. The comparison reveals that the Zn4O13 QD is rigid, whereas the ligands BDC(2-) are nonrigid. In addition, the calculated emission band of MOF-5 is in good agreement with the experimental result and is similar to that of the ligand H2BDC. The combined results confirmed that the luminescence mechanism for MOF-5 should be LLCT with little mixing of the ligand-to-metal charge transfer. The reason for the MOF-5 luminescence is explained by the excellent coplanarity between the six-membered ring consisting of zinc, oxygen, carbon, and the benzene ring.
Imamura, Yutaka; Kamiya, Muneaki; Nakajima, Takahito
2016-03-01
We study spin-forbidden transitions of Os polypyridyl sensitizers by two-component relativistic time-dependent density functional theory with the spin-orbit interaction based on Tamm-Dancoff approximation. The absorption spectra, including spin-forbidden-transition peaks, for the Os complexes are reasonably reproduced in comparison with the experimental ones. The extension of the conjugated lengths in the Os complexes is investigated and found to be effective to enhance photo absorption for spin-allowed transitions as well as spin-forbidden ones. This study provides fruitful information for a design of new dyes in terms of conjugation lengths.
Nakata, Ayako; Tsuneda, Takao; Hirao, Kimihiko
2011-12-14
A long-range corrected (LC) time-dependent density functional theory (TDDFT) incorporating relativistic effects with spin-orbit couplings is presented. The relativistic effects are based on the two-component zeroth-order regular approximation Hamiltonian. Before calculating the electronic excitations, we calculated the ionization potentials (IPs) of alkaline metal, alkaline-earth metal, group 12 transition metal, and rare gas atoms as the minus orbital (spinor) energies on the basis of Koopmans' theorem. We found that both long-range exchange and spin-orbit coupling effects are required to obtain Koopmans' IPs, i.e., the orbital (spinor) energies, quantitatively in DFT calculations even for first-row transition metals and systems containing large short-range exchange effects. We then calculated the valence excitations of group 12 transition metal atoms and the Rydberg excitations of rare gas atoms using spin-orbit relativistic LC-TDDFT. We found that the long-range exchange and spin-orbit coupling effects significantly contribute to the electronic spectra of even light atoms if the atoms have low-lying excitations between orbital spinors of quite different electron distributions.
A relativistic non-relativistic Goldstone theorem: gapped Goldstones at finite charge density
Nicolis, Alberto
2012-01-01
We adapt the Goldstone theorem to study spontaneous symmetry breaking in relativistic theories at finite charge density. It is customary to treat systems at finite density via non-relativistic Hamiltonians. Here we highlight the importance of the underlying relativistic dynamics. This leads to seemingly new results whenever the charge in question is spontaneously broken and does not commute with other broken charges. These would normally be associated with gapless Goldstone excitations. We find that, in fact, their currents interpolate gapped excitations. We derive exact non-perturbative expressions for their gaps, in terms of the chemical potential and of the symmetry algebra.
Lorentz covariant reduced-density-operator theory for relativistic quantum information processing
Ahn, D; Hwang, S W; Ahn, Doyeol; Lee, Hyuk-jae; Hwang, Sung Woo
2003-01-01
In this paper, we derived Lorentz covariant quantum Liouville equation for the density operator which describes the relativistic quantum information processing from Tomonaga-Schwinger equation and an exact formal solution for the reduced-density-operator is obtained using the projector operator technique and the functional calculus. When all the members of the family of the hypersurfaces become flat hyperplanes, it is shown that our results agree with those of non-relativistic case which is valid only in some specified reference frame. The formulation presented in this work is general and might be applied to related fields such as quantum electrodynamics and relativistic statistical mechanics.
董宇兵; 王翼展
2011-01-01
The transverse charge density of pions is calculated based on relativistic quantum mechanics, where the pion is regarded as a quark-antiquark bound state. Corrections from the two spin-1/2 constituents and from the wave function of a quark and antiquark i
Statistical Gauge Theory for Relativistic Finite Density Problems
YING Shu-Qian
2001-01-01
A relativistic quantum field theory is presented for finite density problems based on the principle of locality. It is shown that, in addition to the conventional ones, a local approach to the relativistic quantum field theories at both zero and finite densities consistent with the violation of Bell-like inequalities should contain and provide solutions to at least three additional problems, namely, i) the statistical gauge invariance; ii) the dark components of the local observables; and iii) the fermion statistical blocking effects, based upon an asymptotic nonthermal ensemble. An application to models is presented to show the importance of the discussions.
Relativistic dynamics, Green function and pseudodifferential operators
Cirilo-Lombardo, Diego Julio
2016-01-01
The central role played by pseudodifferential operators in relativistic dynamics is very well know. In this work, operators as the Schrodinger one (e.g: square root) are treated from the point of view of the non-local pseudodifferential Green functions. Starting from the explicit construction of the Green (semigroup) theoretical kernel, a theorem linking the integrability conditions and their dependence on the spacetime dimensions is given. Relativistic wave equations with arbitrary spin and the causality problem are discussed with the algebraic interpretation of the radical operator and their relation with coherent and squeezed states. Also we perform by mean of pure theoretical procedures (based in physical concepts and symmetry) the relativistic position operator which satisfies the conditions of integrability : it is non-local, Lorentz invariant and does not have the same problems as the "local"position operator proposed by Newton and Wigner. Physical examples, as Zitterbewegung and rogue waves, are prese...
Waves in relativistic electron beam in low-density plasma
Sheinman, I.; Sheinman (Chernenco, J.
2016-11-01
Waves in electron beam in low-density plasma are analyzed. The analysis is based on complete electrodynamics consideration. Dependencies of dispersion laws from system parameters are investigated. It is shown that when relativistic electron beam is passed through low-density plasma surface waves of two types may exist. The first type is a high frequency wave on a boundary between the beam and neutralization area and the second type wave is on the boundary between neutralization area and stationary plasma.
Yb、Ybo电子激发态的相对论含时密度泛函理论研究%Time-dependent relativistic density functional study of Yb and YbO
许文华; 张勇; 刘文剑
2009-01-01
The low-lying electronic states of Yb and YbO are investigated by using time-dependent relativistic density functional theory,which is based on the newly developed exact two-component Hamiltonian resulting from symmetrized elimination of the small component.The nature of the excited states is analyzed by using the fall molecular symmetry.The calculated results support the previous experimental assignment of the ground and excited states of YbO.%本文用基于精确二分量哈密顿(exact two-component Hamiltonian)的相对论含时密度泛函理论(time-dependent relativistic density functional theory)计算了Yb和YbO的电子激发态,并利用对称性、自然原子轨道对激发态性质和归属进行了详细分析,所得结果支持实验对YbO基态与激发态的指认.
Bast, Radovan; Juselius, Jonas [Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Tromso, N-9037 Tromso (Norway); Saue, Trond [Institut de Chimie de Strasbourg, CNRS et Universite Louis Pasteur, Laboratoire de Chimie Quantique, 4, rue Blaise Pascal, BP 1032, F-67070 Strasbourg (France)], E-mail: tsaue@chimie.u-strasbg.fr
2009-02-17
We present a 4-component relativistic implementation for calculating the magnetically induced current density within Hartree-Fock and Kohn-Sham linear response theory using a common gauge origin. We demonstrate how the current density can be decomposed into paramagnetic and diamagnetic contributions by calculating separately the contributions from rotations between positive-energy orbitals and contributions from rotations between the occupied positive-energy orbitals and the virtual negative-energy orbitals, respectively. This methodology is applied to the study of the magnetically induced current density in benzene and the group 15 heteroaromatic compounds C{sub 5}H{sub 5}E (E = N, P, As, Sb, Bi). Quantitative values for the magnetically induced ring currents are obtained by numerical integration over the current flow. We have found that the diatropic ring current is sustained for the entire series of the group 15 heteroaromatic compounds-the induced ring current susceptibility of bismabenzene being 76% of the benzene result. Having employed two hybrid and two nonhybrid generalized gradient approximation functionals, the results are found to be rather insensitive to the choice of the density functional approximation. The relativistic effect is relatively small, reaching its maximum of 8% for bismabenzene. The presented 4-component relativistic methodology opens up the possibility to visualize magnetically induced current densities of aromatic heavy-element systems with both scalar relativistic and spin-orbit effects included.
Mitin, Alexander V; van Wüllen, Christoph
2006-02-14
A two-component quasirelativistic Hamiltonian based on spin-dependent effective core potentials is used to calculate ionization energies and electron affinities of the heavy halogen atom bromine through the superheavy element 117 (eka-astatine) as well as spectroscopic constants of the homonuclear dimers of these atoms. We describe a two-component Hartree-Fock and density-functional program that treats spin-orbit coupling self-consistently within the orbital optimization procedure. A comparison with results from high-order Douglas-Kroll calculations--for the superheavy systems also with zeroth-order regular approximation and four-component Dirac results--demonstrates the validity of the pseudopotential approximation. The density-functional (but not the Hartree-Fock) results show very satisfactory agreement with theoretical coupled cluster as well as experimental data where available, such that the theoretical results can serve as an estimate for the hitherto unknown properties of astatine, element 117, and their dimers.
Zhou Dai Mei; Sá Ben-Hao; Li Zhong Dao
2002-01-01
Using a hadron and string cascade model, JPCIAE, and the corresponding Monte Carlo events generator, the energy and centrality dependences of charged particle pseudorapidity density in relativistic nuclear collisions were studied. Within the framework of this model, both the relativistic p anti p experimental data and the PHOBOS and PHENIX Au + Au data could be reproduced fairly well without retuning the model parameters. The author shows that since is not a well defined physical variable both experimentally and theoretically, the charged particle pseudorapidity density per participant pair can increase and also can decrease with increasing of , so it may be hard to use charged particle pseudorapidity density per participant pair as a function of to distinguish various theoretical models for particle production
Relativistic analysis of nuclear ground state densities at 135 to 200 MeV
M A Suhail; N Neeloffer; Z A Khan
2005-12-01
A relativistic analysis of p + 40Ca elastic scattering with different nuclear ground state target densities at 135 to 200 MeV is presented in this paper. It is found that the IGO densities are more consistent in reproducing the data over the energy range considered here. The reproduction of spin-rotation-function data with the simultaneous fitting of differential cross-section and analyzing power, and the appearance of wine-bottle-bottom shaped Re eff() in the transition energy region, sensitively depends on the input nuclear ground state densities and are not solely the relativistic characteristic signatures. We also found that the wine-bottle-bottom shaped Re eff() is preferred by the spin observables in the transition energy region (i.e. 181 MeV to 200 MeV).
Charged Multiplicity Density and Number of Participant Nucleons in Relativistic Nuclear Collisions
SA Ben-Hao; CAI Xu; ZHOU Dai-Mei
2003-01-01
The energy and centrality dependencies of charged particle pseudorapidity density in relativistic nuclearcollisions were studied using a hadron and string cascade model, JPCIAE. Both the relativistic p+p experimental dataand the PHOBOS and PHENIX Au+Au data at RHIC energy could be fairly reproduced within the framework ofJPCIAE model and without retuning the model parameters. The predictions for Pb + Pb collisions at the LHC energywere also given. We computed the participant nucleon distributions using different methods. It was found that thenumber of participant nucleons is not a well defined variable both experimentally and theoretically. Thus it may beinappropriate to use the charged particle pseudorapidity density per participant pair .as a function of the number ofparticipant nucleons for distinguishing various theoretical models.
On the relativistic mass function and averaging in cosmology
Ostrowski, Jan J; Roukema, Boudewijn F
2016-01-01
The general relativistic description of cosmological structure formation is an important challenge from both the theoretical and the numerical point of views. In this paper we present a brief prescription for a general relativistic treatment of structure formation and a resulting mass function on galaxy cluster scales in a highly generic scenario. To obtain this we use an exact scalar averaging scheme together with the relativistic generalization of Zel'dovich's approximation (RZA) that serves as a closure condition for the averaged equations.
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 and Centrality Dependences of Charged Multiplicity Density in Relativistic Nuclear Collisions
SA; Ben-hao; Bonasera; A; TAI; An
2002-01-01
Using a hadron and string cascade model, JPCIAE, the energy and centrality dependences of chargedparticle pseudo rapidity density in relativistic nuclear collisions were studied. Within the framework ofthis model, both the relativistic p + p experimental data and the PHOBOS and PHENIX Au + Au data at
A study of transverse charge density of pions in relativistic quantum mechanics
DONG Yu-Bing; WANG Yi-Zhan
2011-01-01
The transverse charge density of pions is calculated based on relativistic quantum mechanics,where the pion is regarded as a quark-antiquark bound state. Corrections from the two spin-1/2 constituents and from the wave function of a quark and antiquark inside the bound system are discussed. The calculated results are compared to the results with a realistic effective Lagrangian approach as well as to that with a simple covariant model where the pion is regarded as a composite system with two scalar particles.
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.
Relativistic correction to gluon fragmentation function into pseudoscalar quarkonium
Gao, Xiangrui; Li, LiuJi; Xiong, Xiaonu
2016-01-01
Inspired by the recent measurements of the $\\eta_c$ meson production at LHC, we investigate the relativistic correction effect for the fragmentation function of the gluon into $\\eta_c$, which constitutes the crucial nonperturbative elements to understand $\\eta_c$ production at high $p_T$. Employing three distinct methods, we calculate the leading relativistic correction to the $g\\to\\eta_c$ fragmentation function in the NRQCD factorization framework, as well as verify the existing NLO result for the $c\\to \\eta_c$ fragmentation function. We also study the evolution behavior of these fragmentation functions with the aid of DGLAP equation.
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.
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...
Relativistic Kinetic-Balance Condition for Explicitly Correlated Basis Functions
Simmen, Benjamin; Reiher, Markus
2015-01-01
This paper presents the derivation of a kinetic-balance condition for explicitly correlated basis functions employed in semi-classical relativistic calculations. Such a condition is important to ensure variational stability in algorithms based on the first-quantized Dirac theory of 1/2-fermions. We demonstrate that the kinetic-balance condition can be obtained from the row reduction process commonly applied to solve systems of linear equations. The resulting form of kinetic balance establishes a relation for the $4^N$ components of the spinor of an $N$-fermion system to the non-relativistic limit, which is in accordance with recent developments in the field of exact decoupling in relativistic orbital-based many-electron theory.
The effect of density gradient on the growth rate of relativistic Weibel instability
Mahdavi, M., E-mail: m.mahdavi@umz.ac.ir [Physics Department, University of Mazandaran, P.O. Box 47415-416, Babolsar (Iran, Islamic Republic of); Khodadadi Azadboni, F., E-mail: f.khodadadi@stu.umz.ac.ir [Physics Department, University of Mazandaran, P.O. Box 47415-416, Babolsar (Iran, Islamic Republic of); Young Researchers Club, Sari Branch, Islamic Azad University, P.O. Box 48161-194, Sari (Iran, Islamic Republic of)
2014-02-15
In this paper, the effect of density gradient on the Weibel instability growth rate is investigated. The density perturbations in the near corona fuel, where temperature anisotropy, η, is larger than the critical temperature anisotropy, η{sub c}, (η > η{sub c}), enhances the growth rate of Weibel instability due to the sidebands coupled with the electron oscillatory velocity. But for η < η{sub c}, the thermal spread of the energetic electrons reduces the growth rate. Also, the growth rate can be reduced if the relativistic parameter (Lorentz factor) is sufficiently large, γ > 2. The analysis shows that relativistic effects and density gradient tend to stabilize the Weibel instability. The growth rate can be reduced by 88% by reducing η by a factor of 100 and increasing relativistic parameter by a factor of 3.
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.
Green's function relativistic mean field theory for Λ hypernuclei
Ren, S.-H.; Sun, T.-T.; Zhang, W.
2017-05-01
The relativistic mean field theory with the Green's function method is extended to study Λ hypernuclei. Taking the hypernucleus Ca61Λ as an example, the single-particle resonant states for Λ hyperons are investigated by analyzing the density of states, and the corresponding energies and widths are given. Different behaviors are observed for the resonant states, i.e., the distributions of the very narrow 1 f5 /2 and 1 f7 /2 states are very similar to bound states while those of the wide 1 g7 /2 and 1 g9 /2 states are like scattering states. Besides, the impurity effect of Λ hyperons on the single-neutron resonant states is investigated. For most of the resonant states, both the energies and widths decrease with adding more Λ hyperons due to the attractive Λ N interaction. Finally, the energy level structure of Λ hyperons in the Ca hypernucleus isotopes with mass number A =53 -73 are studied; obvious shell structure and small spin-orbit splitting are found for the single-Λ spectrum.
Initial energy density of quark-gluon plasma in relativistic heavy-ion collisions
Wong, C.Y.
1984-01-01
Recently, there has been considerable interest in the central rapidity region of highly relativistic heavy-ion collisions. Such an interest stems from the possibility of creating hadron matter of high energy density which may exceed the critical energy density for a phase transition between ordinary confined matter and the unconfined quark-gluon plasma. The experimental searches and identification of the quark-gluon plasma may provide a new insight into the question of quark confinement. The estimate of the initial energy density is quite uncertain. The initial energy density is nonetheless an important physical quantity. It is one of the factors which determines whether the produced matter can undergo phase transition or not. The energy density has been estimated previously by using the color neutralization model of Brodsky et al. However, the color neutralization model gives a central rapidity multiplicity in heavy-ion collision too low by a factor of two. For this reason, we wish to obtain a better estimate of the energy density (in the central rapidity region). As is well known, a simple Glauber-type multiple collision model can reproduce the total multiplicity and multiplicity plateau near the central rapidity region to within 30%. The simple multiple collision model has an approximate validity as a gross description of the reaction process. We shall adopt a semiempirical approach. Using the multiple collision model and the thickness function of Glauber, we obtain analytical functional form for all the quantities in question. A single parameter, r/sub rms/, is adjusted to fit the experimental central rapidity multiplicity data. The semi-empirical results provide a useful tool to extrapolate to the unknown central rapidity region of heavy-ion collisions.
Net baryon density in Au+Au collisions at the Relativistic Heavy Ion Collider
Bass, S A; Srivastava, D K; Bass, Steffen A.; Müller, Berndt; Srivastava, Dinesh K.
2003-01-01
We calculate the net baryon rapidity distribution in Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC) in the framework of the Parton Cascade Model (PCM). Parton rescattering and fragmentation leads to a substantial increase in the net baryon density at mid-rapidity over the density produced by initial primary parton-parton scatterings. The PCM is able to describe the measured net baryon density at RHIC.
Zaitsevskii, Andréi V
2012-01-01
Interactions of Cn (element 112) atoms with small Au clusters are studied using accurate ab initio scalar relativistic coupled cluster method for correlation treatment and two-component relativistic density functional theory (RDFT) to account for spin-dependent relativistic effect. The results demonstrate the failure of RDFT with simple generalized-gradient and hybrid functionals in describing Cn--Au bonds in complex systems.
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.
Interacting relativistic quantum dynamics for multi-time wave functions
Lienert Matthias
2016-01-01
Full Text Available In this paper, we report on recent progress about a rigorous and manifestly covariant interacting model for two Dirac particles in 1+1 dimensions [9, 10]. It is formulated using the multi-time formalism of Dirac, Tomonaga and Schwinger. The mechanism of interaction is a relativistic generalization of contact interactions, and it is achieved going beyond the usual functional-analytic Hamiltonian method.
Interacting relativistic quantum dynamics for multi-time wave functions
Lienert, Matthias
2016-11-01
In this paper, we report on recent progress about a rigorous and manifestly covariant interacting model for two Dirac particles in 1+1 dimensions [9, 10]. It is formulated using the multi-time formalism of Dirac, Tomonaga and Schwinger. The mechanism of interaction is a relativistic generalization of contact interactions, and it is achieved going beyond the usual functional-analytic Hamiltonian method.
On relativistically invariant method of constructing one- and two-parton density matrix
Shchelkachev, A V
2001-01-01
Hadron is considered as a system of one or two partons and a nucleus that contains many partons, but is described as a parton with variable mass. By integration over this mass the relativistically invariant density matrix is constructed. Using this method one can obtained simple relationships between the density matrix elements and to check or give a better interpretation of the hypotheses proposed by the parton models of various authors
A Relativistic Conical Function and its Whittaker Limits
Simon Ruijsenaars
2011-11-01
Full Text Available In previous work we introduced and studied a function R(a+,a−,c;v,vˆ that is a generalization of the hypergeometric function _2F_1 and the Askey-Wilson polynomials. When the coupling vector c∈C^4 is specialized to (b,0,0,0, b∈C, we obtain a function R(a+,a−,b;v,2vˆ that generalizes the conical function specialization of _2F_1 and the q-Gegenbauer polynomials. The function R is the joint eigenfunction of four analytic difference operators associated with the relativistic Calogero-Moser system of A_1 type, whereas the function R corresponds to BC_1, and is the joint eigenfunction of four hyperbolic Askey-Wilson type difference operators. We show that the R-function admits five novel integral representations that involve only four hyperbolic gamma functions and plane waves. Taking their nonrelativistic limit, we arrive at four representations of the conical function. We also show that a limit procedure leads to two commuting relativistic Toda Hamiltonians and two commuting dual Toda Hamiltonians, and that a similarity transform of the function R converges to a joint eigenfunction of the latter four difference operators.
Relativistic plasma optics enabled by near-critical density nanostructured material
Bin, J H; Wang, H Y; Streeter, M J V; Kreuzer, C; Kiefer, D; Yeung, M; Cousens, S; Foster, P S; Dromey, B; Yan, X Q; Meyer-ter-Vehn, J; Zepf, M; Schreiber, J
2014-01-01
The nonlinear optical properties of a plasma due to the relativistic electron motion in an intense laser field are of fundamental importance for current research and the generation of brilliant laser-driven sources of particles and photons1-15. Yet, one of the most interesting regimes, where the frequency of the laser becomes resonant with the plasma, has remained experimentally hard to access. We overcome this limitation by utilizing ultrathin carbon nanotube foam16 (CNF) targets allowing the strong relativistic nonlinearities at near- critical density (NCD) to be exploited for the first time. We report on the experimental realization of relativistic plasma optics to spatio-temporally compress the laser pulse within a few micrometers of propagation, while maintaining about half its energy. We also apply the enhanced laser pulses to substantially improve the properties of an ion bunch accelerated from a secondary target. Our results provide first insights into the rich physics of NCD plasmas and the opportuni...
Relativistic Spin-Isospin Dependent Response Function of Nucleus
LIU Liang-Gang; CHEN Wei; AI Bao-Quan; ZHENG Xiao-Ping; Masahiro Nakano
2000-01-01
A full relativistic formalism is employed to derive the relativistic particle-hole and delta-hole excitation polariza tion insertion of pion propagator in nuclear matter. The spin-isospin-dependent response function of nucleus at high energy-momentum transfer is calculated with the nuclear matter approximation. The short range correlation effect, two-nucleon absorption and nucleus form factor effects are included in the calculation. The position and width of the resonance peak of the spin-isospin mode are reproduced and found to be coincident with experiment data. The position of the peak and its width is sensitive to Landau-Migdal parameter g＇ which is about 0.6.
Correlation function and electronic spectral line broadening in relativistic plasmas
Douis S.
2013-01-01
Full Text Available The electrons dynamics and the time autocorrelation function Cee(t for the total electric microfield of the electrons on positive charge impurity embedded in a plasma are considered when the relativistic dynamic of the electrons is taken into account. We have, at first, built the effective potential governing the electrons dynamics. This potential obeys a nonlinear integral equation that we have solved numerically. Regarding the electron broadening of the line in plasma, we have found that when the plasma parameters change, the amplitude of the collision operator changes in the same way as the time integral of Cee(t. The electron-impurity interaction is taken at first time as screened Deutsh interaction and at the second time as Kelbg interaction. Comparisons of all interesting quantities are made with respect to the previous interactions as well as between classical and relativistic dynamics of electrons.
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).
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...
Relativistic Remnants of Non-Relativistic Electrons
Kashiwa, Taro
2015-01-01
Electrons obeying the Dirac equation are investigated under the non-relativistic $c \\mapsto \\infty$ limit. General solutions are given by derivatives of the relativistic invariant functions whose forms are different in the time- and the space-like region, yielding the delta function of $(ct)^2 - x^2$. This light-cone singularity does survive to show that the charge and the current density of electrons travel with the speed of light in spite of their massiveness.
Larchenkova, T. I.; Lutovinov, A. A.; Lyskova, N. S.
2011-01-01
The images of relativistic jets from extragalactic sources produced by gravitational lensing by galaxies with different mass surface density distributions are modeled. In particular, the following models of the gravitational lens mass distribution are considered: a singular isothermal ellipsoid, an isothermal ellipsoid with a core, two- and three-component models with a galactic disk, halo, and bulge. The modeled images are compared both between themselves and with available observations. Dif...
Baryon Wave Functions in Covariant Relativistic Quark Models
Dillig, M
2002-01-01
We derive covariant baryon wave functions for arbitrary Lorentz boosts. Modeling baryons as quark-diquark systems, we reduce their manifestly covariant Bethe-Salpeter equation to a covariant 3-dimensional form by projecting on the relative quark-diquark energy. Guided by a phenomenological multigluon exchange representation of a covariant confining kernel, we derive for practical applications explicit solutions for harmonic confinement and for the MIT Bag Model. We briefly comment on the interplay of boosts and center-of-mass corrections in relativistic quark models.
Casarin, Maurizio; Finetti, Paola; Vittadini, Andrea; Wang, Fan; Ziegler, Tom
2007-06-21
Time-dependent density functional theory (TDDFT) coupled to the relativistic two-component zeroth-order regular approximation, both available in the last version of the ADF package, have been successfully used to simulate X-ray absorption spectra of TiCl4, Ti(eta5-C5H5)Cl3, and Ti(eta5-C5H5)2Cl2 in terms of their oscillator strength distributions. Besides allowing a first principle assignment of Ti 1s, Cl 1s, and Ti 2p (L2,3 edges) core excitation spectra, theoretical outcomes provide a rationale for deviations from the expected L3/L2 branching ratio.
Sahai, Aakash; Ettlinger, Oliver; Hicks, George; Ditter, Emma-Jane; Najmudin, Zulfikar
2016-10-01
We investigate proton and light-ion acceleration driven by the interaction of relativistic CO2 laser pulses with overdense Argon or other heavy-ion gas targets doped with lighter-ion species. Optically shaping the gas targets allows tuning of the pre-plasma scale-length from a few to several laser wavelengths, allowing the laser to efficiently drive a propagating snowplow through the bunching in the electron density. Preliminary PIC-based modeling shows that the lighter-ion species is accelerated even without any significant motion of the heavier ions which is a signature of the Relativistically Induced Transparency Acceleration mechanism. Some outlines of possible experiments at the TW CO2 laser at the Accelerator Test Facility at Brookhaven National Laboratory are presented.
Relativistic effects in model calculations of double parton distribution function
Rinaldi, Matteo
2016-01-01
In this paper we consider double parton distribution functions (dPDFs) which are the main non perturbative ingredients appearing in the double parton scattering cross section formula in hadronic collisions. By using recent calculation of dPDFs by means of constituent quark models within the so called Light-Front approach, we investigate the role of relativistic effects on dPDFs. We find, in particular, that the so called Melosh operators, which allow to properly convert the LF spin into the canonical one and incorporate a proper treatment of boosts, produce sizeable effects on dPDFs. We discuss specific partonic correlations induced by these operators in transverse plane which are relevant to the proton structure and study under which conditions these results are stable against variations in the choice of the proton wave function.
Entropy density of an adiabatic relativistic Bose-Einstein condensate star
Khaidir, Ahmad Firdaus; Kassim, Hasan Abu; Yusof, Norhasliza [Theoretical Physics Lab., Department of Physics, Faculty of Science Building, University of Malaya, 50603 Kuala Lumpur (Malaysia)
2015-04-24
Inspired by recent works, we investigate how the thermodynamics parameters (entropy, temperature, number density, energy density, etc) of Bose-Einstein Condensate star scale with the structure of the star. Below the critical temperature in which the condensation starts to occur, we study how the entropy behaves with varying temperature till it reaches its own stability against gravitational collapse and singularity. Compared to photon gases (pressure is described by radiation) where the chemical potential, μ is zero, entropy of photon gases obeys the Stefan-Boltzmann Law for a small values of T while forming a spiral structure for a large values of T due to general relativity. The entropy density of Bose-Einstein Condensate is obtained following the similar sequence but limited under critical temperature condition. We adopt the scalar field equation of state in Thomas-Fermi limit to study the characteristics of relativistic Bose-Einstein condensate under varying temperature and entropy. Finally, we obtain the entropy density proportional to (σT{sup 3}-3T) which obeys the Stefan-Boltzmann Law in ultra-relativistic condition.
Rocca, J.; Bargsten, C.; Hollinger, R.; Shylaptsev, V.; Wang, S.; Rockwood, A.; Wang, Y.; Keiss, D.; Capeluto, M.; Kaymak, V.; Pukhov, A.; Tommasini, R.; London, R.; Park, J.
2016-10-01
Ultra-high-energy-density (UHED) plasmas, characterized by energy densities >1 x 108 J cm-3 and pressures greater than a gigabar are encountered in the center of stars and in inertial confinement fusion capsules driven by the world's largest lasers. Similar conditions can be obtained with compact, ultra-high contrast, femtosecond lasers focused to relativistic intensities onto aligned nanowire array targets. Here we report the measurement of the key physical process in determining the energy density deposited in high aspect ratio nanowire array plasmas: the energy penetration. By monitoring the x-ray emission from buried Co tracer segments in Ni nanowire arrays irradiated at an intensity of 4 x 1019 W cm-2, we demonstrate energy penetration depths of several μm, leading to UHED plasmas of that size. Relativistic 3D particle-in-cell-simulations validated by these measurements predict that irradiation of nanostructures at increased intensity will lead to a virtually unexplored extreme UHED plasma regime characterized by energy densities in excess of 8 x 1010 J cm-3, equivalent to a pressure of 0.35 Tbar. This work was supported by the Fusion Energy Program, Office of Science of the U.S Department of Energy, and by the Defense Threat Reduction Agency.
Relativistic central--field Green's functions for the RATIP package
Koval, P; Koval, Peter; Fritzsche, Stephan
2004-01-01
From perturbation theory, Green's functions are known for providing a simple and convenient access to the (complete) spectrum of atoms and ions. Having these functions available, they may help carry out perturbation expansions to any order beyond the first one. For most realistic potentials, however, the Green's functions need to be calculated numerically since an analytic form is known only for free electrons or for their motion in a pure Coulomb field. Therefore, in order to facilitate the use of Green's functions also for atoms and ions other than the hydrogen--like ions, here we provide an extension to the Ratip program which supports the computation of relativistic (one--electron) Green's functions in an -- arbitrarily given -- central--field potential $\\rV(r)$. Different computational modes have been implemented to define these effective potentials and to generate the radial Green's functions for all bound--state energies $E < 0$. In addition, care has been taken to provide a user--friendly component...
Kullie, Ossama [Institute de Chimie de Strasbourg, CNRS et Universite de Strasbourg, Laboratoire de Chimie Quantique, 4 rue Blaise Pascal, 67070 Strasbourg (France); Saue, Trond, E-mail: trond.saue@isamc.ups-tlse.fr [Laboratoire de Chimie et Physique Quantique (UMR 5626), CNRS/Universite de Toulouse 3 (Paul Sabatier), 118 route de Narbonne, 31062 Toulouse (France)
2012-02-20
Highlights: Black-Right-Pointing-Pointer First implementation of 4-component relativistic long-range MP2/short-range DFT. Black-Right-Pointing-Pointer First complete study of spectroscopic constants of the rare gas dimers He{sub 2}-Uuo{sub 2}. Black-Right-Pointing-Pointer MP2-srLDA has a performance similar to pure MP2, but the overbinding of MP2 can be tuned by the range-separation parameter. - Abstract: We report the implementation of long-range second-order Moller-Plesset perturbation theory coupled with short-range density functional theory (MP2-srDFT) based on the 4-component relativistic Dirac-Coulomb Hamiltonian. The range separation of the two-electron interaction is based on the error function, such that the long-range interaction, to be handled by wave function theory, corresponds to the potential of finite electrons with a Gaussian charge distribution. We argue that the interelectronic distance associated with the range-separation parameter should accordingly be determined from a Gaussian rather than a hard-sphere model. As a first application of our relativistic MP2-srDFT implementation we calculate spectroscopic constants of the complete series of homoatomic rare gas dimers, from helium to the superheavy element 118 and with bonding dominated by dispersion forces. We find that the MP2-srDFT method is less sensitive to the basis set quality than pure MP2, but for the heavier rare gas dimers the computational cost is approximately the same as for pure MP2 if one seeks convergence with respect to both basis set and number of correlated electrons. The inclusion of a short-range DFT contribution allows to dampen the tendency of pure MP2 to overbind the heavier dimers, but it is difficult to find an optimal range-separation parameter for the whole series of diatomics. Interestingly, MP2-srLDA shows better performance than MP2-srPBE for the selected molecules.
The Beam-Density Effect on Energy Loss of a Relativistic Charged Particle Beam.
1983-09-01
media. t iU NSWC TR 83-348 Folloving the method developed by Sternheimer 24 in his calculations of the Fermi density effect, i l L2 -2in.v-v 2 (2.16...where Z 2v 2 + f.. The Sternheimer factor P is chosen so that the i i i value of the Bethe logarithm, InI, obtained in non-relativistic experiments, is...first three eigenfrequencies were taken from Reference 25. A more recent set has been given by Sternheimer and Peierls,2 6 but the ones of Reference 25
High density ultrashort relativistic positron beam generation by laser-plasma interaction
Gu, Y. J.; Klimo, O.; Weber, S.; Korn, G.
2016-11-01
A mechanism of high energy and high density positron beam creation is proposed in ultra-relativistic laser-plasma interaction. Longitudinal electron self-injection into a strong laser field occurs in order to maintain the balance between the ponderomotive potential and the electrostatic potential. The injected electrons are trapped and form a regular layer structure. The radiation reaction and photon emission provide an additional force to confine the electrons in the laser pulse. The threshold density to initiate the longitudinal electron self-injection is obtained from analytical model and agrees with the kinetic simulations. The injected electrons generate γ-photons which counter-propagate into the laser pulse. Via the Breit-Wheeler process, well collimated positron bunches in the GeV range are generated of the order of the critical plasma density and the total charge is about nano-Coulomb. The above mechanisms are demonstrated by particle-in-cell simulations and single electron dynamics.
Study of reaction and decay using densities from relativistic mean field theory
Gangopadhyay, G
2012-01-01
Relativistic mean field calculations have been performed to obtain nuclear density pro- file. Microscopic interactions have been folded with the calculated densities of finite nuclei to obtain a semi-microscopic potential. Life time values for the emission of proton, alpha particles and complex clusters have been calculated in the WKB approach assum- ing a tunneling process through the potential barrier. Elastic scattering cross sections have been estimated for proton-nucleus scattering in light neutron rich nuclei. Low en- ergy proton reactions have been studied and their astrophysical implications have been discussed. The success of the semi-microscopic potentials obtained in the folding model with RMF densities in explaining nuclear decays and reactions has been emphasized.
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.
Density Functionals of Chemical Bonding
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.
Δ (1232 ) effects in density-dependent relativistic Hartree-Fock theory and neutron stars
Zhu, Zhen-Yu; Li, Ang; Hu, Jin-Niu; Sagawa, Hiroyuki
2016-10-01
The density-dependent relativistic Hartree-Fock (DDRHF) theory is extended to include Δ isobars for the study of dense nuclear matter and neutron stars. To this end, we solve the Rarita-Schwinger equation for spin-3/2 particle. Both the direct and exchange terms of the Δ isobars' self-energies are evaluated in detail. In comparison with the relativistic mean field theory (Hartree approximation), a weaker parameter dependence is found for DDRHF. An early appearance of Δ isobars is recognized at ρB˜0.28 fm-3, comparable with that of hyperons. Also, we find that the Δ isobars' softening of the equation of state is mainly due to the reduced Fock contributions from the coupling of the isoscalar mesons, while the pion contributions are negligibly small. We finally conclude that with typical parameter sets, neutron stars with Δ isobars in their interiors could be as heavy as the two massive pulsars whose masses are precisely measured, with slightly smaller radii than normal neutron stars.
$\\Delta$ (1232) effects in density-dependent relativistic Hartree-Fock theory and neutron stars
Zhu, Zhen-Yu; Hu, Jin-Niu; Sagawa, Hiroyuki
2016-01-01
The density-dependent relativistic Hartree-Fock (DDRHF) theory is extended to include $\\Delta$-isobars for the study of dense nuclear matter and neutron stars. To this end, we solve the Rarita-Schwinger equation for spin-3/2 particle. Both the direct and exchange terms of the $\\Delta$-isobars' self-energies are evaluated in details. In comparison with the relativistic mean field theory (Hartree approximation), a weaker parameter dependence is found for DDRHF. An early appearance of $\\Delta$-isobars is recognized at $\\rho_B\\sim0.27$fm$^{-3}$, comparable with that of hyperons. Also, we find that the $\\Delta$-isobars' softening of the equation of state is found to be mainly due to the reduced Fock contributions from the coupling of the isoscalar mesons, while the pion contributions are found negligibly small. We finally conclude that with typical parameter sets, neutron stars with $\\Delta$-isobars in their interiors could be as heavy as the two massive pulsars whose masses are precisely measured, with slightly s...
Arpita Ghosh; Somenath Chakrabarty
2011-09-01
Following an extremely interesting idea (Schieber 1984), published long ago, the work function associated with the emission of ultra-relativistic electrons from magnetically deformed metallic crystal (mainly iron) at the outer crust of a magnetar is obtained using relativistic version of Thomas–Fermi type model for electron distribution around the nuclei in this region. In the present scenario, surprisingly, the work function becomes anisotropic; the longitudinal part is an increasing function of magnetic field strength, whereas the transverse part diverges.
Relativistic equation of state at subnuclear densities in the Thomas-Fermi approximation
Zhang, Z W
2014-01-01
We study the non-uniform nuclear matter using the self-consistent Thomas--Fermi approximation with a relativistic mean-field model. The non-uniform matter is assumed to be composed of a lattice of heavy nuclei surrounded by dripped nucleons. At each temperature $T$, proton fraction $Y_p$, and baryon mass density $\\rho_B$, we determine the thermodynamically favored state by minimizing the free energy with respect to the radius of the Wigner--Seitz cell, while the nucleon distribution in the cell can be determined self-consistently in the Thomas--Fermi approximation. A detailed comparison is made between the present results and previous calculations in the Thomas--Fermi approximation with a parameterized nucleon distribution that has been adopted in the widely used Shen EOS.
Larchenkova, T I; Lyskova, N S
2011-01-01
The images of relativistic jets from extragalactic sources produced by gravitational lensing by galaxies with different mass surface density distributions are modeled. In particular, the following models of the gravitational lens mass distribution are considered: a singular isothermal ellipsoid, an isothermal ellipsoid with a core, two- and three-component models with a galactic disk, halo, and bulge. The modeled images are compared both between themselves and with available observations. Different sets of parameters are shown to exist for the gravitationally lensed system B0218+357 in multicomponent models. These sets allow the observed geometry of the system and the intensity ratio of the compact core images to be obtained, but they lead to a significant variety in the Hubble constant determined from the modeling results.
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
Sahai, Aakash A; Tableman, A R; Mori, W B; Katsouleas, T C
2014-01-01
The relativistically induced transparency acceleration (RITA) scheme of proton and ion acceleration using laser-plasma interactions is introduced, modeled, and compared to the existing schemes. Protons are accelerated with femtosecond relativistic pulses to produce quasimonoenergetic bunches with controllable peak energy. The RITA scheme works by a relativistic laser inducing transparency to densities higher than the cold-electron critical density, while the background heavy ions are stationary. The rising laser pulse creates a traveling acceleration structure at the relativistic critical density by ponderomotively driving a local electron density inflation, creating an electron snowplow and a co-propagating electrostatic potential. The snowplow advances with a velocity determined by the rate of the rise of the laser's intensity envelope and the heavy-ion-plasma density gradient scale length. The rising laser is incrementally rendered transparent to higher densities such that the relativistic-electron plasma ...
Sahai, Aakash A.; Tsung, Frank S.; Tableman, Adam R.; Mori, Warren B.; Katsouleas, Thomas C.
2013-10-01
The relativistically induced transparency acceleration (RITA) scheme of proton and ion acceleration using laser-plasma interactions is introduced, modeled, and compared to the existing schemes. Protons are accelerated with femtosecond relativistic pulses to produce quasimonoenergetic bunches with controllable peak energy. The RITA scheme works by a relativistic laser inducing transparency [Akhiezer and Polovin, Zh. Eksp. Teor. Fiz 30, 915 (1956); Kaw and Dawson, Phys. FluidsPFLDAS0031-917110.1063/1.1692942 13, 472 (1970); Max and Perkins, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.27.1342 27, 1342 (1971)] to densities higher than the cold-electron critical density, while the background heavy ions are stationary. The rising laser pulse creates a traveling acceleration structure at the relativistic critical density by ponderomotively [Lindl and Kaw, Phys. FluidsPFLDAS0031-917110.1063/1.1693437 14, 371 (1971); Silva , Phys. Rev. E1063-651X10.1103/PhysRevE.59.2273 59, 2273 (1999)] driving a local electron density inflation, creating an electron snowplow and a co-propagating electrostatic potential. The snowplow advances with a velocity determined by the rate of the rise of the laser's intensity envelope and the heavy-ion-plasma density gradient scale length. The rising laser is incrementally rendered transparent to higher densities such that the relativistic-electron plasma frequency is resonant with the laser frequency. In the snowplow frame, trace density protons reflect off the electrostatic potential and get snowplowed, while the heavier background ions are relatively unperturbed. Quasimonoenergetic bunches of velocity equal to twice the snowplow velocity can be obtained and tuned by controlling the snowplow velocity using laser-plasma parameters. An analytical model for the proton energy as a function of laser intensity, rise time, and plasma density gradient is developed and compared to 1D and 2D PIC OSIRIS [Fonseca , Lect. Note Comput. Sci.9783
Chen, Y.; Friedel, R. H. W.; Reeves, G. D.; Cayton, T. E.; Christensen, R.
2007-11-01
An integrated investigation method, which can study the relativistic electron phase space density distribution and check the reliability of employed magnetic field models simultaneously, is developed and applied to the geosynchronous orbit region for 53 geomagnetic storms during a ˜190-d period. First, to test how the magnetospheric magnetic field affects the study of phase space density, two approaches are taken on handling the magnetic field model: One is to use an existing empirical model through the whole storm period; the other is to select one from a list of existing magnetic field models for each time bin during the period by fitting to multipoint in situ measurements. The magnetic field models in both approaches are again tested by Liouville's theorem, which requires the conserved phase space density for fixed phase space coordinates given no local losses and sources. Then on the basis of the selected magnetic field model, the phase space density is calculated by transforming the flux data from three Los Alamos National Laboratory geosynchronous satellites. By following the procedure developed here and using the cross-satellite calibration achieved in previous work, we deduce the storm time electron phase space density distribution for the region near geosynchronous orbit, covering a range of L shells with L* centered ˜6. This work establishes the radial phase space density gradient at constant adiabatic invariants as a function of universal time during storm times, and three types of geomagnetic storms are defined according to the degree of energy-dependent enhancements of energetic electrons during recovery phases. Initial results from this study suggest a source outside geosynchronous orbit for low-energy electrons and a major source inside for high-energy electrons.
Angular function for the Compton scattering in mildly and ultra relativistic astrophysical plasmas
Sazonov, S Y; Sazonov, Sergei Y.; Sunyaev, Rashid A.
1999-01-01
Compton scattering of low-frequency radiation by an isotropic distribution of(i) mildly and (ii) ultra relativistic electrons is considered. It is shownthat the ensemble-averaged differential cross-section in this case isnoticeably different from the Rayleigh phase function. The scattering by anensemble of ultra-relativistic electrons obeys the law p=1-cos(alpha), wherealpha is the scattering angle; hence photons are preferentially scatteredbackwards. This contrasts the forward scattering behaviour in the Klein-Nishinaregime. Analytical formulae describing first-order Klein-Nishina andfinite-electron-energy corrections to the simple relation above are given forvarious energy distributions of electrons: monoenergetic,relativistic-Maxwellian, and power-law. A similar formula is also given for themildly relativistic (with respect to the photon energy and electrontemperature) corrections to the Rayleigh angular function. One ofmanifestations of the phenomenon under consideration is that hot plasma is morereflecti...
Density functional theory: Foundations reviewed
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
Guided by the above motto (quotation), we review a broad range of issues lying at the foundations of Density Functional Theory, DFT, a theory which is currently omnipresent in our everyday computational study of atoms and molecules, solids and nano-materials, and which lies at the heart of modern many-body computational technologies. The key goal is to demonstrate that there are definitely the ways to improve DFT. We start by considering DFT in the larger context provided by reduced density matrix theory (RDMT) and natural orbital functional theory (NOFT), and examine the implications that N-representability conditions on the second-order reduced density matrix (2-RDM) have not only on RDMT and NOFT but, also, by extension, on the functionals of DFT. This examination is timely in view of the fact that necessary and sufficient N-representability conditions on the 2-RDM have recently been attained. In the second place, we review some problems appearing in the original formulation of the first Hohenberg–Kohn theorem which is still a subject of some controversy. In this vein we recall Lieb’s comment on this proof and the extension to this proof given by Pino et al. (2009), and in this context examine the conditions that must be met in order that the one-to-one correspondence between ground-state densities and external potentials remains valid for finite subspaces (namely, the subspaces where all Kohn–Sham solutions are obtained in practical applications). We also consider the issue of whether the Kohn–Sham equations can be derived from basic principles or whether they are postulated. We examine this problem in relation to ab initio DFT. The possibility of postulating arbitrary Kohn–Sham-type equations, where the effective potential is by definition some arbitrary mixture of local and non-local terms, is discussed. We also deal with the issue of whether there exists a universal functional, or whether one should advocate instead the construction of problem
Orbital functionals in density-matrix- and current-density-functional theory
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
L.S. Ferreira
2016-02-01
Full Text Available Proton radioactivity from deformed nuclei is described for the first time by a self-consistent calculation based on covariant relativistic density functionals derived from meson exchange and point coupling models. The calculation provides an important new test to these interactions at the limits of stability, since the mixing of different angular momenta in the single particle wave functions is probed.
Ferreira, L.S., E-mail: flidia@tecnico.ulisboa.pt [Center of Physics and Engineering of Advanced Materials, CeFEMA, and Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, P1049-001 Lisbon (Portugal); Maglione, E. [Dipartimento di Fisica e Astronomia “G. Galilei”, Via Marzolo 8, I-35131 Padova (Italy); Istituto Nazionale di Fisica Nucleare, Padova (Italy); Ring, P. [Physik Department der Technischen Universität München, D-85748 Garching (Germany)
2016-02-10
Proton radioactivity from deformed nuclei is described for the first time by a self-consistent calculation based on covariant relativistic density functionals derived from meson exchange and point coupling models. The calculation provides an important new test to these interactions at the limits of stability, since the mixing of different angular momenta in the single particle wave functions is probed.
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.
Shvets, Gennady
2014-05-09
In summary, an analytical model describing the self-pinching of a relativistic charge-neutralized electron beam undergoing the collisionless Weibel instability in an overdense plasma has been developed. The model accurately predicts the final temperature and size of the self-focused filament. It is found that the final temperature is primarily defined by the total beam’s current, while the filament’s radius is shown to be smaller than the collisionless skin depth in the plasma and primarily determined by the beam’s initial size. The model also accurately predicts the repartitioning ratio of the initial energy of the beam’s forward motion into the magnetic field energy and the kinetic energy of the surrounding plasma. The density profile of the final filament is shown to be a superposition of the standard Bennett pinch profile and a wide halo surrounding the pinch, which contains a significant fraction of the beam’s electrons. PIC simulations confirm the key assumption of the analytic theory: the collisionless merger of multiple current filaments in the course of the Weibel Instability provides the mechanism for Maxwellization of the beam’s distribution function. Deviations from the Maxwell-Boltzmann distribution are explained by incomplete thermalization of the deeply trapped and halo electrons. It is conjectured that the simple expression derived here can be used for understanding collsionless shock acceleration and magnetic field amplification in astrophysical plasmas.
Nuclear charge radii: Density functional theory meets Bayesian neural networks
Utama, Raditya; Piekarewicz, Jorge
2016-01-01
The distribution of electric charge in atomic nuclei is fundamental to our understanding of the complex nuclear dynamics and a quintessential observable to validate nuclear structure models. We explore a novel approach that combines sophisticated models of nuclear structure with Bayesian neural networks (BNN) to generate predictions for the charge radii of thousands of nuclei throughout the nuclear chart. A class of relativistic energy density functionals is used to provide robust predictions for nuclear charge radii. In turn, these predictions are refined through Bayesian learning for a neural network that is trained using residuals between theoretical predictions and the experimental data. Although predictions obtained with density functional theory provide a fairly good description of experiment, our results show significant improvement (better than 40%) after BNN refinement. Moreover, these improved results for nuclear charge radii are supplemented with theoretical error bars. We have successfully demonst...
A Density Functional study of Covalency in the Trihalides of Lutetium and Lawrencium
Kullie, Ossama
2016-01-01
In this work we present a four component relativistic theoretical investigation of the trihalides of lutetium and lawrencium, LuX3, LrX3 (X= F, Cl, Br, I) respectively using density functional theory (DFT) with different density functional and a geometrical optimisation procedure as implemented in DIRAC-package. The results show the trend of bonding from lighter to the heavier halide atoms and between 4f/5f atoms Lu and Lr.
Tachyonic quantum densities of relativistic electron plasmas: Cherenkov spectra of γ-ray pulsars
Tomaschitz, Roman, E-mail: tom@geminga.org
2014-06-27
Tachyonic Cherenkov radiation in second quantization can explain the subexponential spectral tails of GeV γ-ray pulsars (Crab pulsar, PSR J1836+5925, PSR J0007+7303, PSR J2021+4026) recently observed with the Fermi-LAT, VERITAS and MAGIC telescopes. The radiation is emitted by a thermal ultra-relativistic electron plasma. The Cherenkov effect is derived from a Maxwell–Proca field with negative mass-square in a dispersive spacetime. The frequency variation of the tachyon mass results in exp(−β{sup ^}ω{sup 1−ρ}) attenuation of the asymptotic Cherenkov energy flux, where β{sup ^} is a decay constant related to the electron temperature and ρ is the frequency scaling exponent of the tachyon mass. An exponent in the range 0<ρ<1 can reproduce the observed subexponential decay of the energy flux. For the Crab pulsar, we find ρ=0.81±0.02, inferred from the substantially weaker-than-exponential decay of its spectral tail measured by MAGIC over an extended energy range. The scaling exponent ρ determines whether the group velocity of the tachyonic γ-rays is sub- or superluminal. - Highlights: • Quantized tachyonic Cherenkov densities lead to subexponential spectral decay. • γ-Ray spectral fits to Crab pulsar, PSR J1836+5925, PSR J0007+7303, PSR J2021+4026. • The polarization of γ-rays is analyzed in the quasiclassical regime and quantum limit. • Three degrees of polarization due to the negative mass-square of the Maxwell–Proca field. • Weibull decay of spectral tails caused by frequency scaling of the tachyon mass.
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.
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...
Relativistic effects in Lyman-alpha forest
Iršič, Vid; Viel, Matteo
2015-01-01
We present the calculation of the Lyman-alpha (Lyman-$\\alpha$) transmitted flux fluctuations with full relativistic corrections to the first order. Even though several studies exist on relativistic effects in galaxy clustering, this is the first study to extend the formalism to a different tracer of underlying matter at unique redshift range ($z = 2 - 5$). Furthermore, we show a comprehensive application of our calculations to the Quasar- Lyman-$\\alpha$ cross-correlation function. Our results indicate that the signal of relativistic effects can be as large as 30% at Baryonic Acoustic Oscillation (BAO) scale, which is much larger than anticipated and mainly due to the large differences in density bias factors of our tracers. We construct an observable, the anti-symmetric part of the cross- correlation function, that is dominated by the relativistic signal and offers a new way to measure the relativistic terms at relatively small scales. The analysis shows that relativistic effects are important when considerin...
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.
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
Estimates on Functional Integrals of Quantum Mechanics and Non-relativistic Quantum Field Theory
Bley, Gonzalo A.; Thomas, Lawrence E.
2017-01-01
We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantum mechanics and non-relativistic quantum field theory, functionals of the form {E[{exp}(A_T)]} , the (effective) action {A_T} being a function of particle trajectories up to time T. The estimates in turn yield rigorous lower bounds for ground state energies, via the Feynman-Kac formula. The upper bounds are obtained by writing the action for these functional integrals in terms of stochastic integrals. The method is illustrated in familiar quantum mechanical settings: for the hydrogen atom, for a Schrödinger operator with {1/|x|^2} potential with small coupling, and, with a modest adaptation of the method, for the harmonic oscillator. We then present our principal applications of the method, in the settings of non-relativistic quantum field theories for particles moving in a quantized Bose field, including the optical polaron and Nelson models.
Typel, S.; Wolter, H.H. [Sektion Physik, Univ. Muenchen, Garching (Germany)
1998-06-01
Nuclear matter and ground state properties for (proton and neutron) semi-closed shell nuclei are described in relativistic mean field theory with coupling constants which depend on the vector density. The parametrization of the density dependence for {sigma}-, {omega}- and {rho}-mesons is obtained by fitting to properties of nuclear matter and some finite nuclei. The equation of state for symmetric and asymmetric nuclear matter is discussed. Finite nuclei are described in Hartree approximation, including a charge and an improved center-of-mass correction. Pairing is considered in the BCS approximation. Special attention is directed to the predictions for properties at the neutron and proton driplines, e.g. for separation energies, spin-orbit splittings and density distributions. (orig.)
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.
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...
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.
Meliani, Z; Giacomazzo, B
2008-01-01
The deceleration mechanisms for relativistic jets in active galactic nuclei remain an open question, and in this paper we propose a model which could explain sudden jet deceleration, invoking density discontinuities. This is particularly motivated by recent indications from HYMORS. Exploiting high resolution, numerical simulations, we demonstrate that for both high and low energy jets, always at high Lorentz factor, a transition to a higher density environment can cause a significant fraction of the directed jet energy to be lost on reflection. This can explain how one-sided jet deceleration and a transition to FR I type can occur in HYMORS, which start as FR II (and remain so on the other side). For that purpose, we implemented in the relativistic hydrodynamic grid-adaptive AMRVAC code, the Synge-type equation of state introduced in the general polytropic case by Meliani et al. (2004). We present results for 10 model computations, varying the inlet Lorentz factor from 10 to 20, including uniform or decreasin...
HU Xiangqian; LI Lemin
2004-01-01
The regionalized computational method is extended to the non-relativistic, scalar and 2-component relativistic density functional calculation of large systems containing transition series or heavy main-group metal elements. A large system is divided into several regions which can be considered as relatively independent quantum mechanical subsystems. Taking into account the Coulomb and exchange-correlation potentials as well as the Pauli repulsion exerted by the other subsystems, the Kohn-Sham equation related to subsystem K can be written as: (FK+FKP)CK =SKCKεK K=A,B,C,…，where FK,CK,SK,εK are the Fock matrix, the matrix of combination coefficients of orbitals, the overlap matrix of basis sets and the energy eigenvalue matrix, respectively. The matrix FKP reflects the Pauli repulsion from the other subsystems.FK may be non-relativistic, scalar or 2-component relativistic Fock matrix determined by the theoretical method related to the density functional calculations. The other matrices are mated with FK. Solving the Kohn-Sham equation for every subsystem and combining the results from the subsystem calculations, the electronic structural information of the whole system is derived. The density functional calculation of several molecules containing transition metal Ni or heavy main-group metal Tl or Bi is performed by the afore-mentioned regionalization algorithm. The obtained results for each molecule are compared with those from the density functional calculation of that molecule in its entirety in order to check the feasibility of the regionalization algorithm. It is found that with sufficiently large regional basis set in the subsystem calculation the accuracy of the results calculated by the regionalization algorithm is essentially the same as that from the calculation of the molecule in its entirety. With proper smaller regional basis sets the accuracy of the results calculated with the regionalization algorithm can still match the actual accuracy of the
A multiconfigurational hybrid density-functional theory
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
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 ...
Touil, B.; Bendib, A.; Bendib-Kalache, K.
2017-02-01
The longitudinal dielectric function is derived analytically from the relativistic Vlasov equation for arbitrary values of the relevant parameters z = m c 2 / T , where m is the rest electron mass, c is the speed of light, and T is the electron temperature in energy units. A new analytical approach based on the Legendre polynomial expansion and continued fractions was used. Analytical expression of the electron distribution function was derived. The real part of the dispersion relation and the damping rate of electron plasma waves are calculated both analytically and numerically in the whole range of the parameter z . The results obtained improve significantly the previous results reported in the literature. For practical purposes, explicit expressions of the real part of the dispersion relation and the damping rate in the range z > 30 and strongly relativistic regime are also proposed.
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.
Magnetic fields and density functional theory
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.
Franz Gross, Alfred Stadler
2010-09-01
We present the effective range expansions for the 1S0 and 3S1 scattering phase shifts, and the relativistic deuteron wave functions that accompany our recent high precision fits (with \\chi^2/N{data} \\simeq 1) to the 2007 world np data below 350 MeV. The wave functions are expanded in a series of analytical functions (with the correct asymptotic behavior at both large and small arguments) that can be Fourier-transformed from momentum to coordinate space and are convenient to use in any application. A fortran subroutine to compute these wave functions can be obtained from the authors.
Sarkadi, L.
2017-03-01
The program MTRDCOUL [1] calculates the matrix elements of the Coulomb interaction between a charged particle and an atomic electron, ∫ ψf∗ (r) ∣ R - r∣-1ψi(r) d r. Bound-free transitions are considered, and relativistic hydrogenic wave functions are used. In this revised version a bug discovered in the F3Y CPC Program Library subprogram [2] is fixed.
A Tryst With Density: Walter Kohn and Density Functional Theory
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.
Relativistic Covariance and Quark-Diquark Wave Functions
Dillig, M
2006-01-01
We derive covariant wave functions for hadrons composed of two constituents for arbitrary Lorentz boosts. Focussing explicitly on baryons as quark-diquark systems, we reduce their manifestly covariant Bethe-Salpeter equation to covariant 3-dimensional forms by projecting on the relative quark-diquark energy. Guided by a phenomenological multi gluon exchange representation of covariant confining kernels, we derive explicit solutions for harmonic confinement and for the MIT Bag Model. We briefly sketch implications of breaking the spherical symmetry of the ground state and the transition from the instant form to the light cone via the infinite momentum frame.
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 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.
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.
Zhang, Ruili; He, Yang; Xiao, Jianyuan; Liu, Jian; Qin, Hong; Tang, Yifa
2016-01-01
Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. It is often multi-scale and requires accurate long-term numerical simulations using symplectic integrators. For modern large-scale particle simulations in complex, time-dependent electromagnetic field, explicit symplectic algorithms are much more preferable. In this paper, we treat the relativistic dynamics of a particle as a Hamiltonian system on the cotangent space of the space-time, and construct for the first time explicit symplectic algorithms for relativistic charged particles of order 2 and 3 using the sum-split technique and generating functions.
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.
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.
Radial Density Statistics of the Galaxy Distribution and the Luminosity Function
Iribarrem, Alvaro S; Stoeger, William R
2012-01-01
This paper discusses a connection between the relativistic number counts of cosmological sources and the observed galaxy luminosity function (LF). Observational differential number densities are defined and obtained from published LF data using such connection. We observe a distortion in the observational quantities that increases with higher redshift values as compared to the theoretical predictions. The use of different cosmological distance measures plays a role in such a distortion
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.
Differential Density Statistics of Galaxy Distribution and the Luminosity Function
Albani, V V L; Ribeiro, M B; Stöger, W R; Albani, Vinicius V. L.; Iribarrem, Alvaro S.; Ribeiro, Marcelo B.; Stoeger, William R.
2006-01-01
This paper uses data obtained from the galaxy luminosity function (LF) to calculate two types of radial number densities statistics of the galaxy distribution as discussed in Ribeiro (2005), namely the differential density $\\gamma$ and the integral differential density $\\gamma^\\ast$. By applying the theory advanced by Ribeiro and Stoeger (2003), which connects the relativistic cosmology number counts with the astronomically derived LF, the differential number counts $dN/dz$ are extracted from the LF and used to calculate both $\\gamma$ and $\\gamma^\\ast$ with various cosmological distance definitions, namely the area distance, luminosity distance, galaxy area distance and redshift distance. LF data are taken from the CNOC2 galaxy redshift survey and $\\gamma$ and $\\gamma^\\ast$ are calculated for two cosmological models: Einstein-de Sitter and an $\\Omega_{m_0}=0.3$, $\\Omega_{\\Lambda_0}=0.7$ standard cosmology. The results confirm the strong dependency of both statistics on the distance definition, as predicted in...
Potekhin, A Yu
2000-01-01
The analytic equation of state of nonideal Coulomb plasmas consisting of pointlike ions immersed in a polarizable electron background (physics/9807042) is improved, and its applicability range is considerably extended. First, the fit of the electron screening contribution in the free energy of the Coulomb liquid is refined at high densities where the electrons are relativistic. Second, we calculate the screening contribution for the Coulomb solid (bcc and fcc) and derive an analytic fitting expression. Third, we propose a simple approximation to the internal and free energy of the liquid one-component plasma of ions, accurate within the numerical errors of the most recent Monte Carlo simulations. We obtain an updated value of the coupling parameter at the solid-liquid phase transition for the one-component plasma: Gamma_m = 175.0 (+/- 0.4).
Relativistic RPA in axial symmetry
Arteaga, D Pena; 10.1103/PhysRevC.77.034317
2009-01-01
Covariant density functional theory, in the framework of self-consistent Relativistic Mean Field (RMF) and Relativistic Random Phase approximation (RPA), is for the first time applied to axially deformed nuclei. The fully self-consistent RMF+RRPA equations are posed for the case of axial symmetry and non-linear energy functionals, and solved with the help of a new parallel code. Formal properties of RPA theory are studied and special care is taken in order to validate the proper decoupling of spurious modes and their influence on the physical response. Sample applications to the magnetic and electric dipole transitions in $^{20}$Ne are presented and analyzed.
Relativistic field theories have no `sign problem' with DMRG
Weir, David J
2010-01-01
The density matrix renormalization group (DMRG) is applied to a relativistic complex scalar field at finite chemical potential. The two-point function and various bulk quantities are studied. It is seen that bulk quantities do not change with the chemical potential until it is larger than the minimum excitation energy. The technical limitations of DMRG for treating bosons in relativistic field theories are discussed. Applications to other relativistic models and to non-topological solitons are also suggested.
Nuclear charge radii: density functional theory meets Bayesian neural networks
Utama, R.; Chen, Wei-Chia; Piekarewicz, J.
2016-11-01
The distribution of electric charge in atomic nuclei is fundamental to our understanding of the complex nuclear dynamics and a quintessential observable to validate nuclear structure models. The aim of this study is to explore a novel approach that combines sophisticated models of nuclear structure with Bayesian neural networks (BNN) to generate predictions for the charge radii of thousands of nuclei throughout the nuclear chart. A class of relativistic energy density functionals is used to provide robust predictions for nuclear charge radii. In turn, these predictions are refined through Bayesian learning for a neural network that is trained using residuals between theoretical predictions and the experimental data. Although predictions obtained with density functional theory provide a fairly good description of experiment, our results show significant improvement (better than 40%) after BNN refinement. Moreover, these improved results for nuclear charge radii are supplemented with theoretical error bars. We have successfully demonstrated the ability of the BNN approach to significantly increase the accuracy of nuclear models in the predictions of nuclear charge radii. However, as many before us, we failed to uncover the underlying physics behind the intriguing behavior of charge radii along the calcium isotopic chain.
Romaniello, P; de Boeij, P L
2005-04-22
We included relativistic effects in the formulation of the time-dependent current-density-functional theory for the calculation of linear response properties of metals [P. Romaniello and P. L. de Boeij, Phys. Rev. B (to be published)]. We treat the dominant scalar-relativistic effects using the zeroth-order regular approximation in the ground-state density-functional theory calculations, as well as in the time-dependent response calculations. The results for the dielectric function of gold calculated in the spectral range of 0-10 eV are compared with experimental data reported in literature and recent ellipsometric measurements. As well known, relativistic effects strongly influence the color of gold. We find that the onset of interband transitions is shifted from around 3.5 eV, obtained in a nonrelativistic calculation, to around 1.9 eV when relativity is included. With the inclusion of the scalar-relativistic effects there is an overall improvement of both real and imaginary parts of the dielectric function over the nonrelativistic ones. Nevertheless some important features in the absorption spectrum are not well reproduced, but can be explained in terms of spin-orbit coupling effects. The remaining deviations are attributed to the underestimation of the interband gap (5d-6sp band gap) in the local-density approximation and to the use of the adiabatic local-density approximation in the response calculation.
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.
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.
Ahmad, Ali [National Centre for Physics, Shahdara Valley Road, Islamabad (Pakistan); Masood, W. [National Centre for Physics, Shahdara Valley Road, Islamabad (Pakistan); COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad (Pakistan)
2016-05-15
Linear and nonlinear electrostatic ion acoustic waves in a weakly relativistic magnetorotating plasma in the presence of non-Maxwellian electrons and warm ions have been examined. The system under consideration has yielded two solutions, namely, the fast and slow acoustic modes which have been observed to depend on the streaming velocity, ion to electron temperature ratio, and the nonthermality parameter of the non-Maxwellian electrons. Using the multiple time scale analysis, we have derived the three dimensional nonlinear Zakharov–Kuznetsov equation and also presented its solution. Both compressive and rarefactive solitary structures have been found in consonance with the satellite observations. It has been observed that although the linear dispersion relation gives both fast and slow ion acoustic waves, the solitary structures form only for the fast acoustic mode. The dependence of the characteristics of the solitary structures on several plasma parameters has also been explored. The present investigation may be beneficial to understanding the rotating plasma environments such as those found in the planetary magnetospheres of Saturn and Jupiter.
Thomson backscattering from laser generated, relativistically moving high-density electron layers
Paz, Athena E; Rödel, Christian; Schnell, Michael; Jäckel, Oliver; Kaluza, Malte C; Paulus, Gerhard G
2012-01-01
We show experimentally that XUV radiation is produced when a laser pulse is Thomson backscattered from sheets of relativistic electrons which are formed at the rear-surface of a foil irradiated on its front side by a high-intensity laser. An all-optical setup is realized using the Jena Titanium:Sapphire TW laser system (JETI). The main pulse is split into two pulses: one to accelerate electrons from thin aluminum foil targets to energies of the order of some MeV and the other, counterpropagating probe pulse is Thomson-backscattered off these electrons when they exit the target rear side. The process produced photons within a wide spectral range of some tens of eV as a result of the broad electron energy distribution. The highest scattering intensity is observed when the probe pulse arrives at the target rear surface 100 fs after the irradiation of the target front side by the pump pulse, corresponding to the maximum flux of hot electrons at the interaction region. These results can provide time-resolved infor...
Versatile Density Functionals for Computational Surface Science
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...
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.
Herrera, L
2011-01-01
We identify the factors responsible for the appearance of energy-density inhomogeneities in a self-gravitating fluid, and describe the evolution of those factors from an initially homogeneous distribution. It is shown that a specific combination of the Weyl tensor and/or local anisotropy of pressure and/or dissipative fluxes entails the formation of energy-density inhomogeneities. Different cases are analyzed in detail and in the particular case of dissipative fluids, the role of relaxational processes as well as non-local effects are brought out.
Hyperon effects in covariant density functional theory with recent astrophysical observations
Long, W H; Hagino, K; Sagawa, H; Tamura, H
2011-01-01
Motivated by recent observational data, the equations of state with the inclusion of strangeness-bearing $\\Lambda$-hyperons and the corresponding properties of neutron stars are studied, based on the covariant density functional (CDF) theory. To this end, we specifically employ the density dependent relativistic Hartree-Fock (DDRHF) theory and the relativistic mean field theory (RMF). The inclusion of $\\Lambda$-hyperons in neutron stars shows substantial effects in softening the equation of state. Because of the extra suppression effect originated from the Fock channel, large reductions on both the star mass and radius are predicted by the DDRHF calculations. It is also found that the mass-radius relations of neutron stars with $\\Lambda$-hyperons determined by DDRHF with the PKA1 parameter set are in fairly good agreement with the observational data where a relatively small neutron stars radius is required. Therefore, it is expected that the exotic degrees of freedom such as the strangeness-bearing structure ...
Density functional theory and multiscale materials modeling
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.
Density Functionals with Broad Applicability in Chemistry
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
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 functional calculations of nanoscale conductance
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)
Bubin, Sergiy; Stanke, Monika; Adamowicz, Ludwik
2017-06-01
In our previous work S. Bubin et al., Chem. Phys. Lett. 647, 122 (2016), 10.1016/j.cplett.2016.01.056, it was established that complex explicitly correlated one-center all-particle Gaussian functions (CECGs) provide effective basis functions for very accurate nonrelativistic molecular non-Born-Oppenheimer calculations. In this work, we advance the molecular CECGs approach further by deriving and implementing algorithms for calculating the leading relativistic corrections within this approach. The algorithms are tested in the calculations of the corrections for all 23 bound pure vibrational states of the HD+ ion.
Density and expansion effects on pion spectra in relativistic heavy-ion collisions
Ayala, A P; Montaño-Zetina, L M; Ayala, Alejandro; Barreiro, Julio; Montano, Luis M.
1999-01-01
We compute the pion inclusive momentum distribution in heavy-ion collisions at AGS energies, assuming thermal equilibrium and accounting for density and expansion effects at the time of decoupling. We compare to data on mid rapidity charged pions produced in central Au + Au collisions and find a very good agreement. The shape of the distribution at low m_t-m is explained in part as an effect arising from the high mean pion density achieved in these reactions. The difference between the positive and negative pion distributions in the same region is attributed in part to the different average yields of each kind of charged pions.
Phase-matched relativistic second harmonic generation in clusters with density ripple
Vij, Shivani; Aggarwal, Munish; Kant, Niti
2017-01-01
An intense short-pulse laser obliquely incident on a clustered gas quickly converts the atomic clusters into hot plasma balls. The laser beam produces a second harmonic due to nonlinear response of cluster and plasma electrons. For enhancement of efficiency of second harmonic generation, there should be appropriate phase-matching between the incident laser beam and the generated harmonic. To achieve the required phase-matching, the ripple in cluster density and plasma electron density outside the cluster is introduced. The efficiency of second harmonic generation is sensitive to the angle between ripple wave vector k→o and the direction of the incident laser beam.
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.
Density Functional Simulation of a Breaking Nanowire
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
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.
Nanda, Vikas; Kant, Niti, E-mail: nitikant@yahoo.com [Department of Physics, Lovely Professional University, Phagwara 144411, Punjab (India)
2014-04-15
Enhanced and early relativistic self-focusing of Hermite-cosh-Gaussian (HChG) beam in the plasmas under density transition has been investigated theoretically using Wentzel-Kramers-Brillouin and paraxial ray approximation for mode indices m=0, 1, and 2. The variation of beam width parameter with normalized propagation distance for m=0, 1, and 2 is reported, and it is observed that strong self-focusing occurs as the HChG beam propagates deeper inside the nonlinear medium as spot size shrinks due to highly dense plasmas and the results are presented graphically. A comparative study between self-focusing of HChG beam in the presence and absence of plasmas density transition is reported. The dependency of beam width parameter on the normalized propagation distance for different values of decentered parameter “b” has also been presented graphically. For m=0 and 1, strong self-focusing is reported for b=1.8, and for m=2 and b=1.8, beam gets diffracted. The results obtained indicate the dependency of the self-focusing of the HChG beam on the selected values of decentered parameter. Moreover, proper selection of decentered parameter results strong self-focusing of HChG beam. Stronger self-focusing of laser beam is observed due to the presence of plasma density transition which might be very useful in the applications like the generation of inertial fusion energy driven by lasers, laser driven accelerators, etc.
Jankowska, Marzena; Kupka, Teobald; Stobiński, Leszek
2016-01-01
Hartree-Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange-correlation functionals were used for non-relativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton and xenon dimers and free atoms. Relativistic...
Aharonovich, I
2011-01-01
In previous papers the authors have presented derivations of the Green function for the 5D offshell electrodynamics in the framework of the manifestly covariant relativistic dynamics of Stueckelberg. In this paper, we reconcile these derivations with previously published Green functions which have different forms. We relate our results to the conventional fundamental solutions of 5D wave equations published in the mathematical literature.
Mode conversion of large-amplitude electromagnetic waves in relativistic critical density plasmas
Pesch, T.C.; Kull, H.J. [Aachen Univ., Institute of Theoretical Physics A, RWTH (Germany)
2009-01-15
The propagation of linearly polarized large-amplitude electromagnetic waves in critical density plasmas is studied in the framework of the Akiezer-Polovin model. A new mechanism of mode conversion is presented. The well-known periodic solutions are generalized to quasiperiodic solutions taking into account additional electrostatic oscillations. Nearly periodic circle-like solutions are found to be stabilized by intrinsic mode coupling whereas for nearly periodic eight-like solutions an effective mode conversion mechanism is discovered. Finally, the modulation timescales are considered. (authors)
Al-Hashimi, M H
2015-01-01
We study the relativistic version of Schr\\"odinger equation for a point particle in 1-d with potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultra-violet divergent, and the resultant expression cannot be renormalized in the usual sense. Therefore a general procedure has been developed to derive different physical properties of the system. The procedure is used first on the non-relativistic case for the purpose of clarification and comparisons. The results from the relativistic case show that this system behaves exactly like the delta function potential, which means it also shares the same features with quantum field theories, like being asymptotically free, and in the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point.
Chen, Shaohao; Qing, Bo; Li, Jiaming
2007-10-01
Using the multiconfiguration Dirac-Fock method, including the quantum electrodynamics corrections, especially with the Breit interactions, we calculate the electric quadrupole (E2) and magnetic dipole (M1) transition rates for the two transitions D5/2,3/2o2→S3/2o4 of OII . We show systematically that the correlation effects owing to core electron excitations and the Breit interactions are vitally important for the transition rates. We present a benchmark for the intensity ratio between the two transitions in the limit of high electron density in planetary nebulas, i.e., r(∞)=0.345-0.014+0.028 , which is in good agreement with modern astronomical observations.
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.
Haba, Z
2009-02-01
We discuss relativistic diffusion in proper time in the approach of Schay (Ph.D. thesis, Princeton University, Princeton, NJ, 1961) and Dudley [Ark. Mat. 6, 241 (1965)]. We derive (Langevin) stochastic differential equations in various coordinates. We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form. We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution. We discuss drag terms leading to an equilibrium distribution. The relativistic analog of the Ornstein-Uhlenbeck process is not unique. We show that if the drag comes from a diffusion approximation to the master equation then its form is strongly restricted. The drag leading to the Tsallis equilibrium distribution satisfies this restriction whereas the one of the Jüttner distribution does not. We show that any function of the relativistic energy can be the equilibrium distribution for a particle in a static electric field. A preliminary study of the time evolution with friction is presented. It is shown that the problem is equivalent to quantum mechanics of a particle moving on a hyperboloid with a potential determined by the drag. A relation to diffusions appearing in heavy ion collisions is briefly discussed.
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...
Fauad Rami
2003-05-01
Charged particle pseudorapidity distributions have been measured in Au + Au collisions using the BRAHMS detector at RHIC. The results are presented as a function of the collision centrality and the center of mass energy. They are compared to the predictions of different parton scattering models and the important role of hard scattering processes at RHIC energies is discussed.
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 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.
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.
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.
Semiclassical models for uniform-density Cosmic Strings and Relativistic Stars
Campanelli, M; Campanelli, Manuela; Lousto, Carlos O.
1996-01-01
In this paper we show how quantum corrections, although perturbatively small, may play an important role in the analysis of the existence of some classical models. This, in fact, appears to be the case of static, uniform--density models of the interior metric of cosmic strings and neutron stars. We consider the fourth order semiclassical equations and first look for perturbative solutions in the coupling constants $\\alpha$ and $\\beta$ of the quadratic curvature terms in the effective gravitational Lagrangian. We find that there is not a consistent solution; neither for strings nor for spherical stars. We then look for non--perturbative solutions and find an explicit approximate metric for the case of straight cosmic strings. We finally analyse the contribution of the non--local terms to the renormalized energy--momentum tensor and the possibility of this terms to allow for a perturbative solution. We explicitly build up a particular renormalized energy--momentum tensor to fulfill that end. These state--depend...
Nonequilibrium distribution functions of nucleons in relativistic nucleus-nucleus collisions
Anchishkin, D; Cleymans, J; 10.5488/CMP.16.13201
2013-01-01
The collision smearing of the nucleon momenta about their initial values during relativistic nucleus-nucleus collisions is investigated. To a certain degree, our model belongs to the transport type, and we investigate the evolution of the nucleon system created at a nucleus-nucleus collision. However, we parameterize this development by the number of collisions of every particle during evolution rather than by the time variable. It is assumed that the group of nucleons which leave the system after the same number of collisions can be joined in a particular statistical ensemble. The nucleon nonequilibrium distribution functions, which depend on a certain number of collisions of a nucleon before freeze-out, are derived.
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.
Covariant density functional theory for nuclear matter
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 Approach Based on Numerically Obtained Bridge Functional
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.
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.
Density functional and neural network analysis
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.
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.
Density Functional Approach Based on Numerically Obtained Bridge Functional
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.
Density-functional calculations for rare-earth atoms and ions
Forstreuter, J.; Steinbeck, L.; Richter, M.; Eschrig, H.
1997-04-01
Relativistic local-spin-density (RLSD) and self-interaction-corrected (SIC) RLSD calculations were performed for the whole series of the rare-earth elements. Ionization potentials and radial expectation values with 4f wave functions were calculated. Improvement on nearly all quantities is found for SIC calculations. Comparison with other calculational methods shows that for a description of rare-earth elements SIC-RLSD competes well in accuracy with all of them, including the most accurate quantum-chemical approach. This is important since the SIC calculation has the advantage of being suited for a description of localized f states in solids with a comparatively moderate effort.
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.
Quantal density functional theory. 2. ed.
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.
Ohsaku, T; Yamaki, D; Yamaguchi, K
2002-01-01
For studying the group theoretical classification of the solutions of the density functional theory in relativistic framework, we propose quantum electrodynamical density-matrix functional theory (QED-DMFT). QED-DMFT gives the energy as a functional of a local one-body $4\\times4$ matrix $Q(x)\\equiv -$, where $\\psi$ and $\\bar{\\psi}$ are 4-component Dirac field and its Dirac conjugate, respectively. We examine some characters of QED-DMFT. After these preparations, by using Q(x), we classify the solutions of QED-DMFT under O(3) rotation, time reversal and spatial inversion. The behavior of Q(x) under nonrelativistic and ultrarelativistic limits are also presented. Finally, we give plans for several extensions and applications of QED-DMFT.
Universality principle and the development of classical density functional theory
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.
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.
Comparison of density estimators. [Estimation of probability density functions
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)
Aharonovich, I.; Horwitz, L. P.
2011-08-01
In previous papers derivations of the Green function have been given for 5D off-shell electrodynamics in the framework of the manifestly covariant relativistic dynamics of Stueckelberg (with invariant evolution parameter τ). In this paper, we reconcile these derivations resulting in different explicit forms, and relate our results to the conventional fundamental solutions of linear 5D wave equations published in the mathematical literature. We give physical arguments for the choice of the Green function retarded in the fifth variable τ.
Real time propagation of the exact two component time-dependent density functional theory
Goings, Joshua J.; Kasper, Joseph M.; Egidi, Franco; Sun, Shichao; Li, Xiaosong
2016-09-01
We report the development of a real time propagation method for solving the time-dependent relativistic exact two-component density functional theory equations (RT-X2C-TDDFT). The method is fundamentally non-perturbative and may be employed to study nonlinear responses for heavy elements which require a relativistic Hamiltonian. We apply the method to several group 12 atoms as well as heavy-element hydrides, comparing with the extensive theoretical and experimental studies on this system, which demonstrates the correctness of our approach. Because the exact two-component Hamiltonian contains spin-orbit operators, the method is able to describe the non-zero transition moment of otherwise spin-forbidden processes in non-relativistic theory. Furthermore, the two-component approach is more cost effective than the full four-component approach, with similar accuracy. The RT-X2C-TDDFT will be useful in future studies of systems containing heavy elements interacting with strong external fields.
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.
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.
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.
Theoretical study of the relativistic molecular rotational g-tensor
Aucar, I. Agustín, E-mail: agustin.aucar@conicet.gov.ar; Gomez, Sergio S., E-mail: ssgomez@exa.unne.edu.ar [Institute for Modeling and Technological Innovation, IMIT (CONICET-UNNE) and Faculty of Exact and Natural Sciences, Northeastern University of Argentina, Avenida Libertad 5400, W3404AAS Corrientes (Argentina); Giribet, Claudia G.; Ruiz de Azúa, Martín C. [Physics Department, Faculty of Exact and Natural Sciences, University of Buenos Aires and IFIBA CONICET, Ciudad Universitaria, Pab. I, 1428 Buenos Aires (Argentina)
2014-11-21
An original formulation of the relativistic molecular rotational g-tensor valid for heavy atom containing compounds is presented. In such formulation, the relevant terms of a molecular Hamiltonian for non-relativistic nuclei and relativistic electrons in the laboratory system are considered. Terms linear and bilinear in the nuclear rotation angular momentum and an external uniform magnetic field are considered within first and second order (relativistic) perturbation theory to obtain the rotational g-tensor. Relativistic effects are further analyzed by carrying out the linear response within the elimination of the small component expansion. Quantitative results for model systems HX (X=F, Cl, Br, I), XF (X=Cl, Br, I), and YH{sup +} (Y=Ne, Ar, Kr, Xe, Rn) are obtained both at the RPA and density functional theory levels of approximation. Relativistic effects are shown to be small for this molecular property. The relation between the rotational g-tensor and susceptibility tensor which is valid in the non-relativistic theory does not hold within the relativistic framework, and differences between both molecular parameters are analyzed for the model systems under study. It is found that the non-relativistic relation remains valid within 2% even for the heavy HI, IF, and XeH{sup +} systems. Only for the sixth-row Rn atom a significant deviation of this relation is found.
Beam transfer functions for relativistic proton bunches with beam–beam interaction
Görgen, P., E-mail: goergen@temf.tu-darmstadt.de [Institut für Theorie Elektromagnetischer Felder (TEMF), Technische Universität Darmstadt, Schloßgartenstr. 8 64289 Darmstadt (Germany); Boine-Frankenheim, O. [Institut für Theorie Elektromagnetischer Felder (TEMF), Technische Universität Darmstadt, Schloßgartenstr. 8 64289 Darmstadt (Germany); Fischer, W. [Brookhaven National Laboratory, Upton, NY 11973 (United States)
2015-03-21
We present a method for the recovery of the transverse tune spread directly from the beam transfer function (BTF). The model is applicable for coasting beams and bunched beams at high energy with a tune spread from transverse nonlinearities induced by the beam–beam effect or by an electron lens. Other sources of tune spread can be added. A method for the recovery of the incoherent tune spread without prior knowledge of the nonlinearity is presented. The approach is based on the analytic model for BTFs of coasting beams, which agrees very well with simulations results for bunched beams at relativistic energies with typically low synchrotron tune. A priori the presented tune spread recovery method is usable only in the absence of coherent modes, but additional simulation data shows its applicability even in the presence of coherent beam–beam modes. Finally agreement of both the analytic and simulation models with measurement data obtained at RHIC is presented. The proposed method successfully recovers the tune spread from analytic, simulated and measured BTF.
Building a Universal Nuclear Energy Density Functional
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
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.
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.
Potential Functions of Al2 by the Relativistic Fock-Space Coupled Cluster Method
Uzi Kaldor
2002-05-01
Full Text Available Abstract: Potential functions of the ground and low excited states of Al2 are calculated by the relativistic Fock-space coupled cluster method in the framework of the projected Dirac-Coulomb Hamiltonian. A moderate-size basis [16s11p3d3f/6s6p3d2f] is used. 3ÃŽÂ u is confirmed as the ground state of the system. Its spin orbit splittings are reproduced well, with the ÃŽÂ› = 1, 2 states lying 32.5 and 66.1 cmÃ¢ÂˆÂ’1, respectively, above the ÃŽÂ› = 0 minimum (experimental values are 30.4 and 63.4 cmÃ¢ÂˆÂ’1. The bond is somewhat too weak, with De 0.14 eV below experiment, Re too high by 0.08 Ã‹ÂšA, and ÃÂ‰e 21 cmÃ¢ÂˆÂ’1 too low. It is speculated that the better agreement obtained in earlier calculations may be due to neglect of basis set superposition errors. The description of bonding in the molecule may be improved by the use of a better basis and the inclusion of more correlation by the intermediate Hamiltonian coupled cluster method, which makes it possible to handle larger P spaces and extend the potential functions to the whole range of internuclear separations.
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
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.
Jiang Chen-Fan-Fu; Zheng Jian; Zhao Bin
2011-01-01
Collective Thomson scattering is theoretically investigated with the inclusion of the relativistic correction of (v/c)2.The correction is rather small for the plasma parameters inferred from the spectra of the thermal electron plasma waves in the plasma. Since the full formula of the corrected result is rather complicated,a simplified one is derived for practical use,which is shown to be in good agreement with the un-simplified one.
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.
Relativistic Quantum Thermodynamics of Ideal Gases in 2 Dimensions
Blas, H.; Pimentel, B. M.; Tomazelli, J. L.
1999-01-01
In this work we study the behavior of relativistic ideal Bose and Fermi gases in two space dimensions. Making use of polylogarithm functions we derive a closed and unified expression for their densities. It is shown that both type of gases are essentially inequivalent, and only in the non-relativistic limit the spinless and equal mass Bose and Fermi gases are equivalent as known in the literature.
Relativistic quantum thermodynamics of ideal gases in two dimensions.
Blas, H; Pimentel, B M; Tomazelli, J L
1999-11-01
In this work we study the behavior of relativistic ideal Bose and Fermi gases in two space dimensions. Making use of polylogarithm functions we derive a closed and unified expression for their densities. It is shown that both type of gases are essentially inequivalent, and only in the non-relativistic limit the spinless and equal mass Bose and Fermi gases are equivalent as known in the literature.
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.
Relativistic magnetohydrodynamics
Hernandez, Juan; Kovtun, Pavel
2017-05-01
We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfvén waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfvén-like waves with a quadratic dispersion relation. We relate the transport coefficients in the "conventional" magnetohydrodynamics (formulated using Maxwell's equations in matter) to those in the "dual" version of magnetohydrodynamics (formulated using the conserved magnetic flux).
Localized form of Fock terms in nuclear covariant density functional theory
Liang, Haozhao; Ring, Peter; Roca-Maza, Xavier; Meng, Jie
2012-01-01
In most of the successful versions of covariant density functional theory in nuclei, the Fock terms are not included explicitly, which leads to local functionals and forms the basis of their widespread applicability at present. However, it has serious consequences for the description of Gamow-Teller resonances (GTR) and spin-dipole resonances (SDR) which can only be cured by adding further phenomenological parameters. Relativistic Hartree-Fock models do not suffer from these problems. They can successfully describe the GTR and SDR as well as the isovector part of the Dirac effective mass without any additional parameters. However, they are non-local and require considerable numerical efforts. By the zero-range reduction and the Fierz transformation, a new method is proposed to take into account the Fock terms in local functionals, which retains the simplicity of conventional models and provides proper descriptions of the spin-isospin channels and the Dirac masses.
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
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...
Bruce, Adam L
2015-01-01
We show the traditional rocket problem, where the ejecta velocity is assumed constant, can be reduced to an integral quadrature of which the completely non-relativistic equation of Tsiolkovsky, as well as the fully relativistic equation derived by Ackeret, are limiting cases. By expanding this quadrature in series, it is shown explicitly how relativistic corrections to the mass ratio equation as the rocket transitions from the Newtonian to the relativistic regime can be represented as products of exponential functions of the rocket velocity, ejecta velocity, and the speed of light. We find that even low order correction products approximate the traditional relativistic equation to a high accuracy in flight regimes up to $0.5c$ while retaining a clear distinction between the non-relativistic base-case and relativistic corrections. We furthermore use the results developed to consider the case where the rocket is not moving relativistically but the ejecta stream is, and where the ejecta stream is massless.
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...
Li, Ming; Kapusta, Joseph I.
2017-01-01
In very high-energy collisions nuclei are practically transparent to each other but produce very hot nearly baryon-free matter in the so-called central rapidity region. The energy in the central rapidity region comes from the kinetic energy of the colliding nuclei. We calculate the energy and rapidity loss of the nuclei using the color glass condensate model. This model also predicts the excitation energy of the nuclear fragments. Using a space-time picture of the collision we calculate the baryon and energy densities of the receding baryonic fireballs. For central collisions of gold nuclei at the highest energy attainable at the Relativistic Heavy-Ion Collider, for example, we find baryon densities more than ten times that of atomic nuclei over a large volume.
Li, Ming
2016-01-01
In very high energy collisions nuclei are practically tranparent to each other but produce very hot, nearly baryon-free, matter in the so-called central rapidity region. The energy in the central rapidity region comes from the kinetic energy of the colliding nuclei. We calculate the energy and rapidity loss of the nuclei using the color glass condensate model. This model also predicts the excitation energy of the nuclear fragments. Using a space-time picture of the collision we calculate the baryon and energy densities of the receding baryonic fireballs. For central collisions of gold nuclei at the highest energy attainable at the Relativistic Heavy Ion Collider, for example, we find baryon densities more than ten times that of atomic nuclei over a large volume.
Bioinorganic Chemistry Modeled with the TPSSh Density Functional
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....
Relativistic electron ring equilibrium with angular momentum spread
Croitoru, M.; Grecu, D. (Institutul de Fizica si Inginerie Nucleara, Bucharest (Romania))
1980-01-01
The equilibrium properties of a relativistic electron ring are determined by solving in a consistent way the Vlasov-Maxwell equations for a distribution function with an angular momentum spread. In the thin ring approximation there have been deduced general formulae for the electron density and the current density. A general theorem concerning the sharp form in space of the electron density is also obtained for the case of a microcanonical distribution function both in energy and angular momentum.
Weibel Instability Growth Rate in Magnetized Plasmas with Quasi-Relativistic Distribution Function
Hosseini, Sayed Ahmad; Mahdavi, Mohammad
2016-12-01
The mechanism of the Weibel instability is investigated for dense magnetized plasmas. As we know, due to the electron velocity distribution, the Coulomb collision effect of electron-ion and the relativistic properties play an important role in such study. In this study an analytical expression for the growth rate and the condition of restricting the Weibel instability are derived for low-frequency limit. These calculations are done for the oscillation frequency dependence on the electron cyclotron frequency. It is shown that, the relativistic properties of the particle lead to increasing the growth rate of the instability. On the other hand the collision effects and background magnetic field try to decrease the growth rate by decreasing the temperature anisotropy and restricting the particles movement.
Peng, Daoling; Weigend, Florian; Reiher, Markus
2013-01-01
We present an efficient algorithm for one- and two-component relativistic exact-decoupling calculations. The spin-orbit coupling was taken into account for the evaluation of relativistically transformed Hamiltonian. The relativistic decoupling transformation has to be evaluated with primitive functions so that the construction of the relativistic one-electron Hamiltonian becomes the bottleneck of the whole calculation for large molecules. We apply our recently developed local DLU scheme [J. Chem. Phys. 136 (2012) 244108] to accelerate this step. With our new implementation two-component relativistic density functional calculations can be performed invoking the resolution-of-identity density-fitting approximation and (Abelian as well as non-Abelian) point group symmetries to accelerate both the exact-decoupling and the two-electron part. The capability of our implementation is illustrated at the example of silver clusters with up to 309 atoms, for which the cohesive energy is calculated and extrapolated to the...
Bodek, K.; Kępka, D.; Rozpędzik, D.; Zejma, J.; Kozela, A.
2017-04-01
A self-calibrating double-Mott polarimeter is proposed for measurement of the spin correlation function of relativistic electron pairs produced in Møller scattering. The polarization of outgoing electrons (appearing when the beam is polarized) is utilized for calibration of effective analyzing powers in the secondary Mott scattering used for spin analysis. The experiment will measure the newly introduced relative spin correlation function. This new observable can be measured with a significantly better accuracy than the regular spin correlation function in a small scale experiment. It is shown that both the spin correlation function and the relative spin correlation function are theoretically equivalent. A specific experimental data analysis scenario is proposed, which effectively eliminates the systematic effects related to the imperfect geometry and detector efficiency.
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)
Karakatsanis, Konstantinos; Lalazissis, G. A.; Ring, Peter; Litvinova, Elena
2017-03-01
Spin-orbit splitting is an essential ingredient for our understanding of the shell structure in nuclei. One of the most important advantages of relativistic mean-field (RMF) models in nuclear physics is the fact that the large spin-orbit (SO) potential emerges automatically from the inclusion of Lorentz-scalar and -vector potentials in the Dirac equation. It is therefore of great importance to compare the results of such models with experimental data. We investigate the size of 2 p and 1 f splittings for the isotone chain 40Ca, 38Ar, 36S, and 34Si in the framework of various relativistic and nonrelativistic density functionals. They are compared with the results of nonrelativistic models and with recent experimental data.
Demianski, Marek
2013-01-01
Relativistic Astrophysics brings together important astronomical discoveries and the significant achievements, as well as the difficulties in the field of relativistic astrophysics. This book is divided into 10 chapters that tackle some aspects of the field, including the gravitational field, stellar equilibrium, black holes, and cosmology. The opening chapters introduce the theories to delineate gravitational field and the elements of relativistic thermodynamics and hydrodynamics. The succeeding chapters deal with the gravitational fields in matter; stellar equilibrium and general relativity
Isolating relativistic effects in large-scale structure
Bonvin, Camille
2014-01-01
We present a fully relativistic calculation of the observed galaxy number counts in the linear regime. We show that besides the density fluctuations and redshift-space distortions, various relativistic effects contribute to observations at large scales. These effects all have the same physical origin: they result from the fact that our coordinate system, namely the galaxy redshift and the incoming photons' direction, is distorted by inhomogeneities in our universe. We then discuss the impact of the relativistic effects on the angular power spectrum and on the two-point correlation function in configuration space. We show that the latter is very well adapted to isolate the relativistic effects since it naturally makes use of the symmetries of the different contributions. In particular, we discuss how the Doppler effect and the gravitational redshift distortions can be isolated by looking for a dipole in the cross-correlation function between a bright and a faint population of galaxies.
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
Lima, Frederico A; Bjornsson, Ragnar; Weyhermüller, Thomas; Chandrasekaran, Perumalreddy; Glatzel, Pieter; Neese, Frank; DeBeer, Serena
2013-12-28
X-ray absorption spectroscopy (XAS) is a widely used experimental technique capable of selectively probing the local structure around an absorbing atomic species in molecules and materials. When applied to heavy elements, however, the quantitative interpretation can be challenging due to the intrinsic spectral broadening arising from the decrease in the core-hole lifetime. In this work we have used high-energy resolution fluorescence detected XAS (HERFD-XAS) to investigate a series of molybdenum complexes. The sharper spectral features obtained by HERFD-XAS measurements enable a clear assignment of the features present in the pre-edge region. Time-dependent density functional theory (TDDFT) has been previously shown to predict K-pre-edge XAS spectra of first row transition metal compounds with a reasonable degree of accuracy. Here we extend this approach to molybdenum K-edge HERFD-XAS and present the necessary calibration. Modern pure and hybrid functionals are utilized and relativistic effects are accounted for using either the Zeroth Order Regular Approximation (ZORA) or the second order Douglas-Kroll-Hess (DKH2) scalar relativistic approximations. We have found that both the predicted energies and intensities are in excellent agreement with experiment, independent of the functional used. The model chosen to account for relativistic effects also has little impact on the calculated spectra. This study provides an important calibration set for future applications of molybdenum HERFD-XAS to complex catalytic systems.
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.
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.
A density functional for sparse matter
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...
A density functional study on the adsorption of hydrogen molecule onto small copper clusters
Xiang-Jun Kuang; Xin-Qiang Wang; Gao-Bin Liu
2011-09-01
An all-electron scalar relativistic calculation on the adsorption of hydrogen molecule onto small copper clusters has been performed by using density functional theory with the generalized gradient approximation (GGA) at PW91 level. Our results reveal that after adsorption of H2 molecule, the Cu-Cu interaction is strengthened and the H-H interaction is weakened, the reactivity enhancement of H2 molecule is obvious. The VIPs, HLGs and VEAs of CuH2 clusters show an obvious odd-even oscillation. It is suggested that the H2 molecule is more favourable to be adsorbed by the even-numbered small copper clusters. Meanwhile, the odd-even alteration of magnetic moments is also observed and may be served as the material with tunable code capacity of `0’ and `1' by adsorbing hydrogen molecule onto odd or even-numbered small copper clusters. Some discrepancies of dissociative adsorption between our work and previous works are found and may be understood in terms of the electron pairing effect and the scalar relativistic effect.
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...
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…
Zare, S.; Yazdani, E.; Rezaee, S.; Anvari, A.; Sadighi-Bonabi, R.
2015-04-01
Propagation of a Gaussian x-ray laser beam has been analyzed in collisionless thermal quantum plasma with considering a ramped density profile. In this density profile due to the increase in the plasma density, an earlier and stronger self-focusing effect is noticed where the beam width oscillates with higher frequency and less amplitude. Moreover, the effect of the density profile slope and the initial plasma density on the laser propagation has been studied. It is found that, by increasing the initial density and the ramp slope, the laser beam focuses faster with less oscillation amplitude, smaller laser spot size and more oscillations. Furthermore, a comparison is made among the laser self-focusing in thermal quantum plasma, cold quantum plasma and classical plasma. It is realized that the laser self-focusing in the quantum plasma becomes stronger in comparison with the classical regime.
Density-functional calculations for rare-earth atoms and ions
Forstreuter, J.; Steinbeck, L.; Richter, M.; Eschrig, H. [Technische Universitaet Dresden, MPG-Arbeitsgruppe Elektronensysteme, D-01062 Dresden (Germany)
1997-04-01
Relativistic local-spin-density (RLSD) and self-interaction-corrected (SIC) RLSD calculations were performed for the whole series of the rare-earth elements. Ionization potentials and radial expectation values with 4f wave functions were calculated. Improvement on nearly all quantities is found for SIC calculations. Comparison with other calculational methods shows that for a description of rare-earth elements SIC-RLSD competes well in accuracy with all of them, including the most accurate quantum-chemical approach. This is important since the SIC calculation has the advantage of being suited for a description of localized f states in solids with a comparatively moderate effort. {copyright} {ital 1997} {ital The American Physical Society}
Time-odd mean fields in covariant density functional theory: Rotating systems
Afanasjev, A V; 10.1103/PhysRev.82.034329
2010-01-01
Time-odd mean fields (nuclear magnetism) and their impact on physical observables in rotating nuclei are studied in the framework of covariant density functional theory (CDFT). It is shown that they have profound effect on the dynamic and kinematic moments of inertia. Particle number, configuration and rotational frequency dependences of their impact on the moments of inertia have been analysed in a systematic way. Nuclear magnetism can also considerably modify the band crossing features such as crossing frequencies and the properties of the kinematic and dynamic moments of inertia in the band crossing region. The impact of time-odd mean fields on the moments of inertia in the regions away from band crossing only weakly depends on the relativistic mean field parametrization, reflecting good localization of the properties of time-odd mean fields in CDFT. The moments of inertia of normal-deformed nuclei considerably deviate from the rigid body value. On the contrary, superdeformed and hyperdeformed nuclei have ...
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.
Relativistic GLONASS and geodesy
Mazurova, E. M.; Kopeikin, S. M.; Karpik, A. P.
2016-12-01
GNSS technology is playing a major role in applications to civil, industrial and scientific areas. Nowadays, there are two fully functional GNSS: American GPS and Russian GLONASS. Their data processing algorithms have been historically based on the Newtonian theory of space and time with only a few relativistic effects taken into account as small corrections preventing the system from degradation on a fairly long time. Continuously growing accuracy of geodetic measurements and atomic clocks suggests reconsidering the overall approach to the GNSS theoretical model based on the Einstein theory of general relativity. This is essentially more challenging but fundamentally consistent theoretical approach to relativistic space geodesy. In this paper, we overview the basic principles of the relativistic GNSS model and explain the advantages of such a system for GLONASS and other positioning systems. Keywords: relativistic GLONASS, Einstein theory of general relativity.
Relativistic (SR-ZORA) quantum theory of atoms in molecules properties.
Anderson, James S M; Rodríguez, Juan I; Ayers, Paul W; Götz, Andreas W
2017-01-15
The Quantum Theory of Atoms in Molecules (QTAIM) is used to elucidate the effects of relativity on chemical systems. To do this, molecules are studied using density-functional theory at both the nonrelativistic level and using the scalar relativistic zeroth-order regular approximation. Relativistic effects on the QTAIM properties and topology of the electron density can be significant for chemical systems with heavy atoms. It is important, therefore, to use the appropriate relativistic treatment of QTAIM (Anderson and Ayers, J. Phys. Chem. 2009, 115, 13001) when treating systems with heavy atoms. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
The benchmark of gutzwiller density functional theory in hydrogen systems
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
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
Numerical Simulations of Driven Supersonic Relativistic MHD Turbulence
Zrake, Jonathan; 10.1063/1.3621748
2011-01-01
Models for GRB outflows invoke turbulence in relativistically hot magnetized fluids. In order to investigate these conditions we have performed high-resolution three-dimensional numerical simulations of relativistic magneto-hydrodynamical (RMHD) turbulence. We find that magnetic energy is amplified to several percent of the total energy density by turbulent twisting and folding of magnetic field lines. Values of epsilon_B near 1% are thus naturally expected. We study the dependence of saturated magnetic field energy fraction as a function of Mach number and relativistic temperature. We then present power spectra of the turbulent kinetic and magnetic energies. We also present solenoidal (curl-like) and dilatational (divergence-like) power spectra of kinetic energy. We propose that relativistic effects introduce novel couplings between these spectral components. The case we explore in most detail is for equal amounts of thermal and rest mass energy, corresponding to conditions after collisions of shells with re...
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.
Meliani, Z.; Keppens, R.; Giacomazzo, B.
2008-01-01
We propose a model that could explain the sudden jet deceleration in active galactic nuclei, thereby invoking density discontinuities. Motivated particularly by recent indications from HYbrid MOrphology Radio Sources (HYMORS) that Fanaroff-Riley classification is induced in some cases by variations in the density of the external medium. We explore how one-sided jet deceleration and a transition to FR I type can occur in HYMORS, which start as FR II (and remain so on the other side). Methods. ...
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.
A Joint Density Function in the Renewal Risk Model
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.
Hilbert Space of Probability Density Functions Based on Aitchison Geometry
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.
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
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
Point form relativistic quantum mechanics and relativistic SU(6)
Klink, W. H.
1993-01-01
The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.
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
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
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.
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.
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
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.
Meliani, Z.; Keppens, R.; Giacomazzo, B.
2008-01-01
Aims. We propose a model that could explain the sudden jet deceleration in active galactic nuclei, thereby invoking density discontinuities. Motivated particularly by recent indications from HYbrid MOrphology Radio Sources (HYMORS) that Fanaroff-Riley classification is induced in some cases by varia
Meliani, Z.; Keppens, R.; Giacomazzo, B.
2008-01-01
Aims. We propose a model that could explain the sudden jet deceleration in active galactic nuclei, thereby invoking density discontinuities. Motivated particularly by recent indications from HYbrid MOrphology Radio Sources (HYMORS) that Fanaroff-Riley classification is induced in some cases by
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.
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.
Generalized quantum similarity in atomic systems: A quantifier of relativistic effects
Martín, A. L.; Angulo, J. C.; Antolín, J.; López-Rosa, S.
2017-02-01
Quantum similarity between Hartree-Fock and Dirac-Fock electron densities reveals the depth of relativistic effects on the core and valence regions in atomic systems. The results emphasize the relevance of differences in the outermost subshells, as pointed out in recent studies by means of Shannon-like functionals. In this work, a generalized similarity functional allows us to go far beyond the Shannon-based analyses. The numerical results for systems throughout the Periodic Table show that discrepancies between the relativistic and non-relativistic descriptions are patently governed by shell-filling patterns.
Linear response of homogeneous nuclear matter with energy density functionals
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
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...
Mattsson, Ann Elisabet
2012-01-01
Density Functional Theory (DFT) based Equation of State (EOS) construction is a prominent part of Sandia's capabilities to support engineering sciences. This capability is based on amending experimental data with information gained from computational investigations, in parts of the phase space where experimental data is hard, dangerous, or expensive to obtain. A prominent materials area where such computational investigations are hard to perform today because of limited accuracy is actinide and lanthanide materials. The Science of Extreme Environment Lab Directed Research and Development project described in this Report has had the aim to cure this accuracy problem. We have focused on the two major factors which would allow for accurate computational investigations of actinide and lanthanide materials: (1) The fully relativistic treatment needed for materials containing heavy atoms, and (2) the needed improved performance of DFT exchange-correlation functionals. We have implemented a fully relativistic treatment based on the Dirac Equation into the LANL code RSPt and we have shown that such a treatment is imperative when calculating properties of materials containing actinides and/or lanthanides. The present standard treatment that only includes some of the relativistic terms is not accurate enough and can even give misleading results. Compared to calculations previously considered state of the art, the Dirac treatment gives a substantial change in equilibrium volume predictions for materials with large spin-orbit coupling. For actinide and lanthanide materials, a Dirac treatment is thus a fundamental requirement in any computational investigation, including those for DFT-based EOS construction. For a full capability, a DFT functional capable of describing strongly correlated systems such as actinide materials need to be developed. Using the previously successful subsystem functional scheme developed by Mattsson et.al., we have created such a functional. In
Mattsson, Ann Elisabet
2012-01-01
Density Functional Theory (DFT) based Equation of State (EOS) construction is a prominent part of Sandia's capabilities to support engineering sciences. This capability is based on amending experimental data with information gained from computational investigations, in parts of the phase space where experimental data is hard, dangerous, or expensive to obtain. A prominent materials area where such computational investigations are hard to perform today because of limited accuracy is actinide and lanthanide materials. The Science of Extreme Environment Lab Directed Research and Development project described in this Report has had the aim to cure this accuracy problem. We have focused on the two major factors which would allow for accurate computational investigations of actinide and lanthanide materials: (1) The fully relativistic treatment needed for materials containing heavy atoms, and (2) the needed improved performance of DFT exchange-correlation functionals. We have implemented a fully relativistic treatment based on the Dirac Equation into the LANL code RSPt and we have shown that such a treatment is imperative when calculating properties of materials containing actinides and/or lanthanides. The present standard treatment that only includes some of the relativistic terms is not accurate enough and can even give misleading results. Compared to calculations previously considered state of the art, the Dirac treatment gives a substantial change in equilibrium volume predictions for materials with large spin-orbit coupling. For actinide and lanthanide materials, a Dirac treatment is thus a fundamental requirement in any computational investigation, including those for DFT-based EOS construction. For a full capability, a DFT functional capable of describing strongly correlated systems such as actinide materials need to be developed. Using the previously successful subsystem functional scheme developed by Mattsson et.al., we have created such a functional. In
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.
Al-Hashimi, M H; Wiese, U -J
2014-01-01
We consider the Schr\\"odinger equation for a relativistic point particle in an external 1-dimensional $\\delta$-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudo-differential operator $H = \\sqrt{p^2 + m^2}$. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infra-red conformal fixed point. Thus it can be used to illustrate non-trivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics.
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.
Nucleation for Lennard-Jones Fluid by Density Functional Theory
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.
Agbemava, S E; Ring, P
2016-01-01
A systematic investigation of octupole deformed nuclei is presented for even-even systems with $Z\\leq 106$ located between the two-proton and two-neutron drip lines. 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. This allows us to assess theoretical uncertainties within the present covariant models for the prediction of physical observables relevant for octupole deformed nuclei. In addition, a detailed comparison with the predictions of non-relativistic models is performed. A new region of octupole deformation, centered around $Z\\sim 98, N\\sim 196$ is predicted for the first time. In terms of its size in the $(Z,N)$ plane and the impact of octupole deformation on binding e...
Relativistic Plasma Polarizer: Impact of Temperature Anisotropy on Relativistic Transparency
Hazeltine, R. D.; Stark, David J.; Bhattacharjee, Chinmoy; Arefiev, Alexey V.; Toncian, Toma; Mahajan, S. M.
2015-11-01
3D particle-in-cell simulations demonstrate that the enhanced transparency of a relativistically hot plasma is sensitive to how the energy is partitioned between different degrees of freedom. We consider here the simplest problem: the propagation of a low amplitude pulse through a preformed relativistically hot anisotropic electron plasma to explore its intrinsic dielectric properties. We find that: 1) the critical density for propagation depends strongly on the pulse polarization, 2) two plasmas with the same density and average energy per electron can exhibit profoundly different responses to electromagnetic pulses, 3) the anisotropy-driven Weibel instability develops as expected; the timescales of the growth and back reaction (on anisotropy), however, are long enough that sufficient anisotropy persists for the entire duration of the simulation. This plasma can then function as a polarizer or a wave plate to dramatically alter the pulse polarization. This work was supported by the U.S. DOE Contract Nos. DE-FG02-04ER54742 and DE-AC05-06OR23100 (D. J. S.) and NNSA Contract No. DE-FC52-08NA28512.
'Antigravity' Propulsion and Relativistic Hyperdrive
Felber, F S
2006-01-01
Exact payload trajectories in the strong gravitational fields of compact masses moving with constant relativistic velocities are calculated. The strong field of a suitable driver mass at relativistic speeds can quickly propel a heavy payload from rest to a speed significantly faster than the driver, a condition called hyperdrive. Hyperdrive thresholds and maxima are calculated as functions of driver mass and velocity.
Specification of Density Functional Approximation by Radial Distribution Function of Bulk Fluid
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.
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.
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.
Higher-accuracy van der Waals density functional
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
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.
Density Functional Theory and Materials Modeling at Atomistic Length Scales
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.
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
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...
Radożycki, Tomasz
2016-11-01
The probability density distributions for the ground states of certain model systems in quantum mechanics and for their classical counterparts are considered. It is shown, that classical distributions are remarkably improved by incorporating into them the Heisenberg uncertainty relation between position and momentum. Even the crude form of this incorporation makes the agreement between classical and quantum distributions unexpectedly good, except for the small area, where classical momenta are large. It is demonstrated that the slight improvement of this form, makes the classical distribution very similar to the quantum one in the whole space. The obtained results are much better than those from the WKB method. The paper is devoted to ground states, but the method applies to excited states too.
Time dependent density functional calculation of plasmon response in clusters
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.
Luciano, Rezzolla
2013-01-01
Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solut...
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.
Global analysis of quadrupole shape invariants based on covariant energy density functionals
Quan, S.; Chen, Q.; Li, Z. P.; Nikšić, T.; Vretenar, D.
2017-05-01
Background: The coexistence of different geometric shapes at low energies presents a universal structure phenomenon that occurs over the entire chart of nuclides. Studies of the shape coexistence are important for understanding the microscopic origin of collectivity and modifications of shell structure in exotic nuclei far from stability. Purpose: The aim of this work is to provide a systematic analysis of characteristic signatures of coexisting nuclear shapes in different mass regions, using a global self-consistent theoretical method based on universal energy density functionals and the quadrupole collective model. Method: The low-energy excitation spectrum and quadrupole shape invariants of the two lowest 0+ states of even-even nuclei are obtained as solutions of a five-dimensional collective Hamiltonian (5DCH) model, with parameters determined by constrained self-consistent mean-field calculations based on the relativistic energy density functional PC-PK1, and a finite-range pairing interaction. Results: The theoretical excitation energies of the states, 21+,41+,02+,22+,23+, as well as the B (E 2 ;01+→21+) values, are in very good agreement with the corresponding experimental values for 621 even-even nuclei. Quadrupole shape invariants have been implemented to investigate shape coexistence, and the distribution of possible shape-coexisting nuclei is consistent with results obtained in recent theoretical studies and available data. Conclusions: The present analysis has shown that, when based on a universal and consistent microscopic framework of nuclear density functionals, shape invariants provide distinct indicators and reliable predictions for the occurrence of low-energy coexisting shapes. This method is particularly useful for studies of shape coexistence in regions far from stability where few data are available.
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.
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.
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
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.
Quantum Geometry: Relativistic energy approach to cooperative electron-nucleary-transition spectrum
Ольга Юрьевна Хецелиус
2014-11-01
Full Text Available An advanced relativistic energy approach is presented and applied to calculating parameters of electron-nuclear 7-transition spectra of nucleus in the atom. The intensities of the spectral satellites are defined in the relativistic version of the energy approach (S-matrix formalism, and gauge-invariant quantum-electrodynamical perturbation theory with the Dirac-Kohn-Sham density-functional zeroth approximation.
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.
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.
Relativistic Quantum Communication
Hosler, Dominic
2013-01-01
In this Ph.D. thesis, I investigate the communication abilities of non-inertial observers and the precision to which they can measure parametrized states. I introduce relativistic quantum field theory with field quantisation, and the definition and transformations of mode functions in Minkowski, Schwarzschild and Rindler spaces. I introduce information theory by discussing the nature of information, defining the entropic information measures, and highlighting the differences between classical and quantum information. I review the field of relativistic quantum information. We investigate the communication abilities of an inertial observer to a relativistic observer hovering above a Schwarzschild black hole, using the Rindler approximation. We compare both classical communication and quantum entanglement generation of the state merging protocol, for both the single and dual rail encodings. We find that while classical communication remains finite right up to the horizon, the quantum entanglement generation tend...
XIAO Hai; LI Jun
2008-01-01
Benchmark calculations on the molar atomization enthalpy, geometry, and vibrational frequencies of uranium hexafluoride (UF6) have been performed by using relativistic density functional theory (DFT) with various levels of relativistic effects, different types of basis sets, and exchange-correlation functionals. Scalar relativistic effects are shown to be critical for the structural properties. The spin-orbit coupling effects are important for the calculated energies, but are much less important for other calculated ground-state properties of closed-shell UF6. We conclude through systematic investigations that ZORA- and RECP-based relativistic DFT methods are both appropriate for incorporating relativistic effects. Comparisons of different types of basis sets (Slater, Gaussian, and plane-wave types) and various levels of theoretical approximation of the exchange-correlation functionals were also made.
Specification of Density Functional Approximation by Radial Distribution Function of Bulk Fluid
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.
Relativistic Kinetic Theory: An Introduction
Sarbach, Olivier
2013-01-01
We present a brief introduction to the relativistic kinetic theory of gases with emphasis on the underlying geometric and Hamiltonian structure of the theory. Our formalism starts with a discussion on the tangent bundle of a Lorentzian manifold of arbitrary dimension. Next, we introduce the Poincare one-form on this bundle, from which the symplectic form and a volume form are constructed. Then, we define an appropriate Hamiltonian on the bundle which, together with the symplectic form yields the Liouville vector field. The corresponding flow, when projected onto the base manifold, generates geodesic motion. Whenever the flow is restricted to energy surfaces corresponding to a negative value of the Hamiltonian, its projection describes a family of future-directed timelike geodesics. A collisionless gas is described by a distribution function on such an energy surface, satisfying the Liouville equation. Fibre integrals of the distribution function determine the particle current density and the stress-energy ten...
Sahoo, Raghunath
2016-01-01
This lecture note covers Relativistic Kinematics, which is very useful for the beginners in the field of high-energy physics. A very practical approach has been taken, which answers "why and how" of the kinematics useful for students working in the related areas.
Dynamics of localized particles from density functional theory
Reinhardt, J.; Brader, J. M.
2012-01-01
A fundamental assumption of the dynamical density functional theory (DDFT) of colloidal systems is that a grand-canonical free-energy functional may be employed to generate the thermodynamic driving forces. Using one-dimensional hard rods as a model system, we analyze the validity of this key assumption and show that unphysical self-interactions of the tagged particle density fields, arising from coupling to a particle reservoir, are responsible for the excessively fast relaxation predicted by the theory. Moreover, our findings suggest that even employing a canonical functional would not lead to an improvement for many-particle systems, if only the total density is considered. We present several possible schemes to suppress these effects by incorporating tagged densities. When applied to confined systems, we demonstrate, using a simple example, that DDFT necessarily leads to delocalized tagged particle density distributions, which do not respect the fundamental geometrical constraints apparent in Brownian dynamics simulation data. The implication of these results for possible applications of DDFT to treat the glass transition are discussed.
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.
Benchmark density functional theory calculations for nanoscale conductance
Strange, Mikkel; Bækgaard, Iben Sig Buur; Thygesen, Kristian Sommer;
2008-01-01
We present a set of benchmark calculations for the Kohn-Sham elastic transmission function of five representative single-molecule junctions. The transmission functions are calculated using two different density functional theory methods, namely an ultrasoft pseudopotential plane-wave code...... in combination with maximally localized Wannier functions and the norm-conserving pseudopotential code SIESTA which applies an atomic orbital basis set. All calculations have been converged with respect to the supercell size and the number of k(parallel to) points in the surface plane. For all systems we find...
Benchmarking Density Functionals for Chemical Bonds of Gold
Kepp, Kasper Planeta
2017-01-01
Gold plays a major role in nanochemistry, catalysis, and electrochemistry. Accordingly, hundreds of studies apply density functionals to study chemical bonding with gold, yet there is no systematic attempt to assess the accuracy of these methods applied to gold. This paper reports a benchmark...... against 51 experimental bond enthalpies of AuX systems and seven additional polyatomic and cationic molecules. Twelve density functionals were tested, covering meta functionals, hybrids with variable HF exchange, double-hybrid, dispersion-corrected, and nonhybrid GGA functionals. The defined benchmark...... bonds between gold and noble gases. Zero-point vibrational corrections are relatively small for Au-X bonds, ∼ 11-12 kJ/mol except for Au-H bonds. Dispersion typically provides ∼5 kJ/mol of the total bond enthalpy but grows with system size and is 10 kJ/mol for AuXe and AuKr. HF exchange and LYP...
Density-based mixing parameter for hybrid functionals
Marques, Miguel A. L.; Vidal, Julien; Oliveira, Micael J. T.; Reining, Lucia; Botti, Silvana
2011-01-01
A very popular ab initio scheme to calculate electronic properties in solids is the use of hybrid functionals in density functional theory (DFT) that mixes a portion of the Fock exchange with DFT functionals. In spite of its success, a major problem still remains, related to the use of one single mixing parameter for all materials. Guided by physical arguments that connect the mixing parameter to the dielectric properties of the solid, and ultimately to its band gap, we propose a method to calculate this parameter from the electronic density alone. This approach is able to cut significantly the error of traditional hybrid functionals for large and small gap materials, while retaining a good description of the structural properties. Moreover, its implementation is simple and leads to a negligible increase of the computational time.
Linear density response function in the projector augmented wave method
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...
Efficient Diffuse Basis Sets for Density Functional Theory.
Papajak, Ewa; Truhlar, Donald G
2010-03-09
Eliminating all but the s and p diffuse functions on the non-hydrogenic atoms and all diffuse functions on the hydrogen atoms from the aug-cc-pV(x+d)Z basis sets of Dunning and co-workers, where x = D, T, Q, ..., yields the previously proposed "minimally augmented" basis sets, called maug-cc-pV(x+d)Z. Here, we present extensive and systematic tests of these basis sets for density functional calculations of chemical reaction barrier heights, hydrogen bond energies, electron affinities, ionization potentials, and atomization energies. The tests show that the maug-cc-pV(x+d)Z basis sets are as accurate as the aug-cc-pV(x+d)Z ones for density functional calculations, but the computational cost savings are a factor of about two to seven.
Current Issues in Finite-T Density-Functional Theory and Warm-Correlated Matter †
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
Clustering and pasta phases in nuclear density functional theory
Schuetrumpf, Bastian; Nazarewicz, Witold
2016-01-01
Nuclear density functional theory (DFT) is the tool of choice in describing properties of complex nuclei and intricate phases of bulk nucleonic matter. It is a microscopic approach based on an energy density functional representing the nuclear interaction. An attractive feature of nuclear DFT is that it can be applied to both finite nuclei and pasta phases appearing in the inner crust of neutron stars. While nuclear pasta clusters in a neutron star can be easily characterized through their density distributions, the level of clustering of nucleons in a nucleus can often be difficult to assess. To this end, we use the concept of nucleonic localization. We demonstrate that the localization measure provides us with fingerprints of clusters in light and heavy nuclei, including fissioning systems. Furthermore we investigate the rod-like pasta phase using twist-averaged boundary conditions, which enable calculations in finite volumes accessible by state of the art DFT solvers.
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.
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...
Parker, Edward
2017-08-01
A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can attain speeds arbitrarily close to the speed of light; generalizing the electrostatic and gravitational cases requires special and general relativity, respectively. We find exact closed-form relations between the position, proper time, and coordinate time in both cases, and find that they are no longer harmonic, with oscillation periods that depend on the amplitude. In the highly relativistic limit of both cases, the particle spends almost all of its proper time near the turning points, but almost all of the coordinate time moving through the bulk of the ball. Buchdahl's theorem imposes nontrivial constraints on the general-relativistic case, as a ball of given density can only attain a finite maximum radius before collapsing into a black hole. This article is intended to be pedagogical, and should be accessible to those who have taken an undergraduate course in general relativity.
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.
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.
Effective Maxwell Equations from Time-dependent Density Functional Theory
Weinan E; Jianfeng LU; Xu YANG
2011-01-01
The behavior of interacting electrons in a perfect crystal under macroscopic external electric and magnetic fields is studied. Effective Maxwell equations for the macroscopic electric and magnetic fields are derived starting from time-dependent density functional theory. Effective permittivity and permeability coefficients are obtained.
Density functional theory in surface science and heterogeneous catalysis
Nørskov, Jens Kehlet; Scheffler, M.; Toulhoat, H.
2006-01-01
amount of experimental data gathered during the last decades. This article shows how density functional theory can be used to describe the state of the surface during reactions and the rate of catalytic reactions. It will also show how we are beginning to understand the variation in catalytic activity...
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.
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
Orbital-Free Density Functional Theory for Molecular Structure Calculations
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.
Reproducibility in density functional theory calculations of solids
Lejaeghere, Kurt; Bihlmayer, Gustav; Björkman, Torbjörn
2016-01-01
The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We r...
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.
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.
Density functional theory is straying from the path toward the exact functional.
Medvedev, Michael G; Bushmarinov, Ivan S; Sun, Jianwei; Perdew, John P; Lyssenko, Konstantin A
2017-01-06
The theorems at the core of density functional theory (DFT) state that the energy of a many-electron system in its ground state is fully defined by its electron density distribution. This connection is made via the exact functional for the energy, which minimizes at the exact density. For years, DFT development focused on energies, implicitly assuming that functionals producing better energies become better approximations of the exact functional. We examined the other side of the coin: the energy-minimizing electron densities for atomic species, as produced by 128 historical and modern DFT functionals. We found that these densities became closer to the exact ones, reflecting theoretical advances, until the early 2000s, when this trend was reversed by unconstrained functionals sacrificing physical rigor for the flexibility of empirical fitting. Copyright © 2017, American Association for the Advancement of Science.
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.
Nomura, K.; Rodríguez-Guzmán, R.; Humadi, Y. M.; Robledo, L. M.; Abusara, H.
2017-09-01
The evolution and coexistence of the nuclear shapes as well as the corresponding low-lying collective states and electromagnetic transition rates are investigated along the krypton isotopic chain within the framework of the interacting boson model (IBM). The IBM Hamiltonian is determined through mean-field calculations based on the several parametrizations of the Gogny energy density functional and the relativistic mean-field Lagrangian. The mean-field energy surfaces, as functions of the axial β and triaxial γ quadrupole deformations, are mapped onto the expectation value of the interacting-boson Hamiltonian that explicitly includes the particle-hole excitations. The resulting boson Hamiltonian is then used to compute low-energy excitation spectra as well as E 2 and E 0 transition probabilities for Kr-10070. Our results point to a number of examples of prolate-oblate shape transitions and coexistence both on the neutron-deficient and neutron-rich sides. A reasonable agreement with the available experimental data is obtained for the considered nuclear properties.
Kvaal, Simen; Helgaker, Trygve
2015-11-14
The relationship between the densities of ground-state wave functions (i.e., the minimizers of the Rayleigh-Ritz variation principle) and the ground-state densities in density-functional theory (i.e., the minimizers of the Hohenberg-Kohn variation principle) is studied within the framework of convex conjugation, in a generic setting covering molecular systems, solid-state systems, and more. Having introduced admissible density functionals as functionals that produce the exact ground-state energy for a given external potential by minimizing over densities in the Hohenberg-Kohn variation principle, necessary and sufficient conditions on such functionals are established to ensure that the Rayleigh-Ritz ground-state densities and the Hohenberg-Kohn ground-state densities are identical. We apply the results to molecular systems in the Born-Oppenheimer approximation. For any given potential v ∈ L(3/2)(ℝ(3)) + L(∞)(ℝ(3)), we establish a one-to-one correspondence between the mixed ground-state densities of the Rayleigh-Ritz variation principle and the mixed ground-state densities of the Hohenberg-Kohn variation principle when the Lieb density-matrix constrained-search universal density functional is taken as the admissible functional. A similar one-to-one correspondence is established between the pure ground-state densities of the Rayleigh-Ritz variation principle and the pure ground-state densities obtained using the Hohenberg-Kohn variation principle with the Levy-Lieb pure-state constrained-search functional. In other words, all physical ground-state densities (pure or mixed) are recovered with these functionals and no false densities (i.e., minimizing densities that are not physical) exist. The importance of topology (i.e., choice of Banach space of densities and potentials) is emphasized and illustrated. The relevance of these results for current-density-functional theory is examined.
Equilibrium and non-equilibrium properties of a relativistic gas at the transition temperature
Chacón-Acosta, Guillermo
2016-11-01
The Jüttner distribution function for equilibrium relativistic fluids has two well-known limits, the non-relativistic limit at low temperatures and ultra-relativistic limit for high temperatures. Recently, the description of this transition in velocity space in the system, from a gaussian to a bimodal distribution was made by Mendoza et al. Physically, it is a transition between a regime where the relativistic energy is dominated by kinetic to another where the rest energy dominates. It has been found that the critical temperature at which the relativistic corrections becomes relevant, depends just on the dimension of the system, this allowed a description in terms of the theory of critical points (Montakhab et al.). In this contribution a review of the thermodynamic quantities that are only dependent on the ratio between temperature and critical temperature, and the dimension is made. We will also analyze the effects of critical temperature on dissipative processes in simple special relativistic fluids. Particularly, purely relativistic terms that are usually proportional to the number density gradient are studied. The transport coefficients can be written in terms of the transition temperature, this will allow us to identify the lower order relativistic effects just in terms of the dimension of the system.
Magnetic Dissipation in Relativistic Jets
Yosuke Mizuno
2016-10-01
Full Text Available The most promising mechanisms for producing and accelerating relativistic jets, and maintaining collimated structure of relativistic jets involve magnetohydrodynamical (MHD processes. We have investigated the magnetic dissipation mechanism in relativistic jets via relativistic MHD simulations. We found that the relativistic jets involving a helical magnetic field are unstable for the current-driven kink instability, which leads to helically distorted structure in relativistic jets. We identified the regions of high current density in filamentary current sheets, indicative of magnetic reconnection, which are associated to the kink unstable regions and correlated to the converted regions of magnetic to kinetic energies of the jets. We also found that an over-pressured relativistic jet leads to the generation of a series of stationary recollimation shocks and rarefaction structures by the nonlinear interaction of shocks and rarefaction waves. The differences in the recollimation shock structure due to the difference of the magnetic field topologies and strengths may be observable through mm-VLBI observations and space-VLBI mission.
Balawender, Robert
2009-01-01
The formalism developed in the first paper of the series [arXiv:0901.1060v3] is applied to two thermodynamic systems: (i) of three global observables (the energy, the total electron number and the spin number), (ii) of one global observable (the internal electron energy) and two local (position-dependent) observables (the total electron density and the spin density). The two-component potential of the many-electron system of interest is constructed of a scalar external potential and a collinear magnetic field (coupled only with the spin operator). Various equilibrium characteristics of two systems are defined and investigated. Conditions for the equivalence between two systems (the same equilibrium density matrix demanded) are derived and thoroughly discussed. The applicability of the Hohenberg-Kohn theorem is extended to the thermodynamic spin-density functional theory. Obtained results provide a rigorous mathematical foundation for future derivation of the zero-temperature limit of this theory and determina...
Lei, Youming; Zheng, Fan
2016-12-01
Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.
Lei, Youming; Zheng, Fan
2016-12-01
Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.
Numerical density-to-potential inversions in time-dependent density functional theory.
Jensen, Daniel S; Wasserman, Adam
2016-08-01
We treat the density-to-potential inverse problem of time-dependent density functional theory as an optimization problem with a partial differential equation constraint. The unknown potential is recovered from a target density by applying a multilevel optimization method controlled by error estimates. We employ a classical optimization routine using gradients efficiently computed by the discrete adjoint method. The inverted potential has both a real and imaginary part to reduce reflections at the boundaries and other numerical artifacts. We demonstrate this method on model one-dimensional systems. The method can be straightforwardly extended to a variety of numerical solvers of the time-dependent Kohn-Sham equations and to systems in higher dimensions.
Particle vibrational coupling in covariant density functional theory
Ring, P; 10.1134/S1063778809080055
2009-01-01
A consistent combination of covariant density functional theory (CDFT) and Landau-Migdal Theory of Finite Fermi Systems (TFFS) is presented. Both methods are in principle exact, but Landau-Migdal theory cannot describe ground state properties and density functional theory does not take into account the energy dependence of the self-energy and therefore fails to yield proper single-% particle spectra as well as the coupling to complex configurations in the width of giant resonances. Starting from an energy functional, phonons and their vertices are calculated without any further parameters. They form the basis of particle-vibrational coupling leading to an energy dependence of the self-energy and an induced energy-dependent interaction in the response equation. A subtraction procedure avoids double counting. Applications in doubly magic nuclei and in a chain of superfluid nuclei show excellent agreement with experimental data.
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.
A density functional for liquid [sup 3]He
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.)
Relations among several nuclear and electronic density functional reactivity indexes
Torrent-Sucarrat, Miquel; Luis, Josep M.; Duran, Miquel; Toro-Labbé, Alejandro; Solà, Miquel
2003-11-01
An expansion of the energy functional in terms of the total number of electrons and the normal coordinates within the canonical ensemble is presented. A comparison of this expansion with the expansion of the energy in terms of the total number of electrons and the external potential leads to new relations among common density functional reactivity descriptors. The formulas obtained provide explicit links between important quantities related to the chemical reactivity of a system. In particular, the relation between the nuclear and the electronic Fukui functions is recovered. The connection between the derivatives of the electronic energy and the nuclear repulsion energy with respect to the external potential offers a proof for the "Quantum Chemical le Chatelier Principle." Finally, the nuclear linear response function is defined and the relation of this function with the electronic linear response function is given.
Recent advances in density functional methods, pt. 1-2
Chong, Delano P
1995-01-01
Of all the different areas in computational chemistry, density functional theory (DFT) enjoys the most rapid development. Even at the level of the local density approximation (LDA), which is computationally less demanding, DFT can usually provide better answers than Hartree-Fock formalism for large systems such as clusters and solids. For atoms and molecules, the results from DFT often rival those obtained by ab initio quantum chemistry, partly because larger basis sets can be used. Such encouraging results have in turn stimulated workers to further investigate the formal theory as well as the
Multiphase aluminum equations of state via density functional theory
Sjostrom, Travis; Crockett, Scott; Rudin, Sven
2016-10-01
We have performed density functional theory (DFT) based calculations for aluminum in extreme conditions of both pressure and temperature, up to five times compressed ambient density, and over 1 000 000 K in temperature. In order to cover such a domain, DFT methods including phonon calculations, quantum molecular dynamics, and orbital-free DFT are employed. The results are then used to construct a SESAME equation of state for the aluminum 1100 alloy, encompassing the fcc, hcp, and bcc solid phases as well as the liquid regime. We provide extensive comparison with experiment, and based on this we also provide a slightly modified equation of state for the aluminum 6061 alloy.
Density Functional Theory Studies of Magnetically Confined Fermi Gas
陈宇俊; 马红孺
2001-01-01
A theory is developed for magnetically confined Fermi gas at a low temperature based on the density functional theory. The theory is illustrated by the numerical calculation of the density distributions of Fermi atoms 40K with parameters according to DeMarco and Jin's experiment [Science, 285(1999)1703]. Our results are in close agreement with the experiment. To check the theory, we also performed calculations using our theory at a high temperature, which compared very well to the results of the classical limit.
Perspective: Fundamental aspects of time-dependent density functional theory
Maitra, Neepa T.
2016-06-01
In the thirty-two years since the birth of the foundational theorems, time-dependent density functional theory has had a tremendous impact on calculations of electronic spectra and dynamics in chemistry, biology, solid-state physics, and materials science. Alongside the wide-ranging applications, there has been much progress in understanding fundamental aspects of the functionals and the theory itself. This Perspective looks back to some of these developments, reports on some recent progress and current challenges for functionals, and speculates on future directions to improve the accuracy of approximations used in this relatively young theory.
Density-functional formula for strongly correlated systems
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.
Dispersion corrections to density functionals for water aromatic interactions.
Zimmerli, Urs; Parrinello, Michele; Koumoutsakos, Petros
2004-02-08
We investigate recently published methods for extending density functional theory to the description of long-range dispersive interactions. In all schemes an empirical correction consisting of a C6r(-6) term is introduced that is damped at short range. The coefficient C6 is calculated either from average molecular or atomic polarizabilities. We calculate geometry-dependent interaction energy profiles for the water benzene cluster and compare the results with second-order Møller-Plesset calculations. Our results indicate that the use of the B3LYP functional in combination with an appropriate mixing rule and damping function is recommended for the interaction of water with aromatics.
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.
Spinless relativistic particle in energy-dependent potential and normalization of the wave function
Benchikha, Amar; Chetouani, Lyazid
2014-06-01
The problem of normalization related to a Klein-Gordon particle subjected to vector plus scalar energy-dependent potentials is clarified in the context of the path integral approach. In addition the correction relating to the normalizing constant of wave functions is exactly determined. As examples, the energy dependent linear and Coulomb potentials are considered. The wave functions obtained via spectral decomposition, were found exactly normalized.
Kim, Inkoo; Lee, Yoon Sup, E-mail: yslee@kaist.edu [Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701 (Korea, Republic of)
2014-10-28
We report the formulation and implementation of KRCASPT2, a two-component multi-configurational second-order perturbation theory based on Kramers restricted complete active space self-consistent field (KRCASSCF) reference function, in the framework of the spin-orbit relativistic effective core potential. The zeroth-order Hamiltonian is defined as the sum of nondiagonal one-electron operators with generalized two-component Fock matrix elements as scalar factors. The Kramers symmetry within the zeroth-order Hamiltonian is maintained via the use of a state-averaged density, allowing a consistent treatment of degenerate states. The explicit expressions are derived for the matrix elements of the zeroth-order Hamiltonian as well as for the perturbation vector. The use of a fully variational reference function and nondiagonal operators in relativistic multi-configurational perturbation theory is reported for the first time. A series of initial calculations are performed on the ionization potential and excitation energies of the atoms of the 6p-block; the results display a significant improvement over those from KRCASSCF, showing a closer agreement with experimental results. Accurate atomic properties of the superheavy elements of the 7p-block are also presented, and the electronic structures of the low-lying excited states are compared with those of their lighter homologues.
Kim, Inkoo; Lee, Yoon Sup
2014-10-28
We report the formulation and implementation of KRCASPT2, a two-component multi-configurational second-order perturbation theory based on Kramers restricted complete active space self-consistent field (KRCASSCF) reference function, in the framework of the spin-orbit relativistic effective core potential. The zeroth-order Hamiltonian is defined as the sum of nondiagonal one-electron operators with generalized two-component Fock matrix elements as scalar factors. The Kramers symmetry within the zeroth-order Hamiltonian is maintained via the use of a state-averaged density, allowing a consistent treatment of degenerate states. The explicit expressions are derived for the matrix elements of the zeroth-order Hamiltonian as well as for the perturbation vector. The use of a fully variational reference function and nondiagonal operators in relativistic multi-configurational perturbation theory is reported for the first time. A series of initial calculations are performed on the ionization potential and excitation energies of the atoms of the 6p-block; the results display a significant improvement over those from KRCASSCF, showing a closer agreement with experimental results. Accurate atomic properties of the superheavy elements of the 7p-block are also presented, and the electronic structures of the low-lying excited states are compared with those of their lighter homologues.
Reduced density matrix functional theory at finite temperature
Baldsiefen, Tim
2012-10-15
Density functional theory (DFT) is highly successful in many fields of research. There are, however, areas in which its performance is rather limited. An important example is the description of thermodynamical variables of a quantum system in thermodynamical equilibrium. Although the finite-temperature version of DFT (FT-DFT) rests on a firm theoretical basis and is only one year younger than its brother, groundstate DFT, it has been successfully applied to only a few problems. Because FT-DFT, like DFT, is in principle exact, these shortcomings can be attributed to the difficulties of deriving valuable functionals for FT-DFT. In this thesis, we are going to present an alternative theoretical description of quantum systems in thermal equilibrium. It is based on the 1-reduced density matrix (1RDM) of the system, rather than on its density and will rather cumbersomly be called finite-temperature reduced density matrix functional theory (FT-RDMFT). Its zero-temperature counterpart (RDMFT) proved to be successful in several fields, formerly difficult to address via DFT. These fields include, for example, the calculation of dissociation energies or the calculation of the fundamental gap, also for Mott insulators. This success is mainly due to the fact that the 1RDM carries more directly accessible ''manybody'' information than the density alone, leading for example to an exact description of the kinetic energy functional. This sparks the hope that a description of thermodynamical systems employing the 1RDM via FT-RDMFT can yield an improvement over FT-DFT. Giving a short review of RDMFT and pointing out difficulties when describing spin-polarized systems initiates our work. We then lay the theoretical framework for FT-RDMFT by proving the required Hohenberg-Kohn-like theorems, investigating and determining the domain of FT-RDMFT functionals and by deriving several properties of the exact functional. Subsequently, we present a perturbative method to
Szirmai, Jen\\Ho
2011-01-01
The aim of this paper to determine the locally densest horoball packing arrangements and their densities with respect to fully asymptotic tetrahedra with at least one plane of symmetry in hyperbolic 3-space $\\bar{\\mathbf{H}}^3$ extended with its absolute figure, where the ideal centers of horoballs give rise to vertices of a fully asymptotic tetrahedron. We allow horoballs of different types at the various vertices. Moreover, we generalize the notion of the simplicial density function in the extended hyperbolic space $\\bar{\\mathbf{H}}^n, ~(n \\ge 2)$, and prove that, in this sense, {\\it the well known B\\"or\\"oczky--Florian density upper bound for "congruent horoball" packings of $\\bar{\\mathbf{H}}^3$ does not remain valid to the fully asymptotic tetrahedra.} The density of this locally densest packing is $\\approx 0.874994$, may be surprisingly larger than the B\\"or\\"oczky--Florian density upper bound $\\approx 0.853276$ but our local ball arrangement seems not to have extension to the whole hyperbolic space.
Velders, G.J.M.; Feil, D.
1989-01-01
Quantum-chemical density-functional theory (DFT) calculations, using the local-density approximation (LDA), have been performed for hydrogen-bounded silicon clusters to determine the electron density distribution of the Si-Si bond. The density distribution in the bonding region is compared with calc
The force distribution probability function for simple fluids by density functional theory.
Rickayzen, G; Heyes, D M
2013-02-28
Classical density functional theory (DFT) is used to derive a formula for the probability density distribution function, P(F), and probability distribution function, W(F), for simple fluids, where F is the net force on a particle. The final formula for P(F) ∝ exp(-AF(2)), where A depends on the fluid density, the temperature, and the Fourier transform of the pair potential. The form of the DFT theory used is only applicable to bounded potential fluids. When combined with the hypernetted chain closure of the Ornstein-Zernike equation, the DFT theory for W(F) agrees with molecular dynamics computer simulations for the Gaussian and bounded soft sphere at high density. The Gaussian form for P(F) is still accurate at lower densities (but not too low density) for the two potentials, but with a smaller value for the constant, A, than that predicted by the DFT theory.
A search for X-ray reprocessing echoes in the power spectral density functions of AGN
Emmanoulopoulos, D.; Papadakis, I. E.; Epitropakis, A.; Pecháček, T.; Dovčiak, M.; McHardy, I. M.
2016-09-01
We present the results of a detailed study of the X-ray power spectral density (PSD) functions of 12 X-ray bright AGN, using almost all the archival XMM-Newton data. The total net exposure of the EPIC-pn light curves is larger than 350 ks in all cases (and exceeds 1 Ms in the case of 1H 0707-497). In a physical scenario in which X-ray reflection occurs in the inner part of the accretion disc of AGN, the X-ray reflection component should be a filtered echo of the X-ray continuum signal and should be equal to the convolution of the primary emission with the response function of the disc. Our primary objective is to search for these reflection features in the 5-7 keV (iron line) and 0.5-1 keV (soft) bands, where the X-ray reflection fraction is expected to be dominant. We fit to the observed periodograms two models: a simple bending power-law model (BPL) and a BPL model convolved with the transfer function of the accretion disc assuming the lamp-post geometry and X-ray reflection from a homogeneous disc. We do not find any significant features in the best-fitting BPL model residuals either in individual PSDs in the iron band, soft and full band (0.3-10 keV) or in the average PSD residuals of the brightest and more variable sources (with similar black hole mass estimates). The typical amplitude of the soft and full-band residuals is around 3-5 per cent. It is possible that the expected general relativistic effects are not detected because they are intrinsically lower than the uncertainty of the current PSDs, even in the strong relativistic case in which X-ray reflection occurs on a disc around a fast rotating black hole having an X-ray source very close above it. However, we could place strong constrains to the X-ray reflection geometry with the current data sets if we knew in advance the intrinsic shape of the X-ray PSDs, particularly its high-frequency slope.
Hakim, Rémi
1994-01-01
Il existe à l'heure actuelle un certain nombre de théories relativistes de la gravitation compatibles avec l'expérience et l'observation. Toutefois, la relativité générale d'Einstein fut historiquement la première à fournir des résultats théoriques corrects en accord précis avec les faits.
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.
SURFACE SYMMETRY ENERGY OF NUCLEAR ENERGY DENSITY FUNCTIONALS
Nikolov, N; Schunck, N; Nazarewicz, W; Bender, M; Pei, J
2010-12-20
We study the bulk deformation properties of the Skyrme nuclear energy density functionals. Following simple arguments based on the leptodermous expansion and liquid drop model, we apply the nuclear density functional theory to assess the role of the surface symmetry energy in nuclei. To this end, we validate the commonly used functional parametrizations against the data on excitation energies of superdeformed band-heads in Hg and Pb isotopes, and fission isomers in actinide nuclei. After subtracting shell effects, the results of our self-consistent calculations are consistent with macroscopic arguments and indicate that experimental data on strongly deformed configurations in neutron-rich nuclei are essential for optimizing future nuclear energy density functionals. The resulting survey provides a useful benchmark for further theoretical improvements. Unlike in nuclei close to the stability valley, whose macroscopic deformability hangs on the balance of surface and Coulomb terms, the deformability of neutron-rich nuclei strongly depends on the surface-symmetry energy; hence, its proper determination is crucial for the stability of deformed phases of the neutron-rich matter and description of fission rates for r-process nucleosynthesis.
Differentiable but exact formulation of density-functional theory
Kvaal, Simen; Teale, Andrew M; Helgaker, Trygve
2013-01-01
The universal density functional $F$ of density-functional theory is a complicated and ill-behaved function of the density--in particular, $F$ is not differentiable, making many formal manipulations more complicated. Whilst $F$ has been well characterized in terms of convex analysis as forming a conjugate pair $(F,E)$ with the ground-state energy $E$ via the Hohenberg-Kohn and Lieb variation principles, $F$ is only subdifferentiable on a small (but dense) set of its domain. In this article, we apply a tool from convex analysis, Moreau-Yosida regularization, to construct, for any $\\epsilon>0$, pairs of conjugate functionals $({}^\\epsilon\\!E,{}^\\epsilon\\! F)$ that converge to $(E,F)$ pointwise everywhere as $\\epsilon\\rightarrow 0^+$, and such that ${}^\\epsilon\\!F$ is (Fr\\'echet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box, which does not change the physics. It is noteworthy that no information is lost in the Moreau-Yosida regularization...
Differentiable but exact formulation of density-functional theory.
Kvaal, Simen; Ekström, Ulf; Teale, Andrew M; Helgaker, Trygve
2014-05-14
The universal density functional F of density-functional theory is a complicated and ill-behaved function of the density-in particular, F is not differentiable, making many formal manipulations more complicated. While F has been well characterized in terms of convex analysis as forming a conjugate pair (E, F) with the ground-state energy E via the Hohenberg-Kohn and Lieb variation principles, F is nondifferentiable and subdifferentiable only on a small (but dense) subset of its domain. In this article, we apply a tool from convex analysis, Moreau-Yosida regularization, to construct, for any ε > 0, pairs of conjugate functionals ((ε)E, (ε)F) that converge to (E, F) pointwise everywhere as ε → 0(+), and such that (ε)F is (Fréchet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box. It is noteworthy that no information is lost in the Moreau-Yosida regularization: the physical ground-state energy E(v) is exactly recoverable from the regularized ground-state energy (ε)E(v) in a simple way. All concepts and results pertaining to the original (E, F) pair have direct counterparts in results for ((ε)E, (ε)F). The Moreau-Yosida regularization therefore allows for an exact, differentiable formulation of density-functional theory. In particular, taking advantage of the differentiability of (ε)F, a rigorous formulation of Kohn-Sham theory is presented that does not suffer from the noninteracting representability problem in standard Kohn-Sham theory.
Jones, Bernard J. T.; Markovic, Dragoljub
1997-06-01
Preface; Prologue: Conference overview Bernard Carr; Part I. The Universe At Large and Very Large Redshifts: 2. The size and age of the Universe Gustav A. Tammann; 3. Active galaxies at large redshifts Malcolm S. Longair; 4. Observational cosmology with the cosmic microwave background George F. Smoot; 5. Future prospects in measuring the CMB power spectrum Philip M. Lubin; 6. Inflationary cosmology Michael S. Turner; 7. The signature of the Universe Bernard J. T. Jones; 8. Theory of large-scale structure Sergei F. Shandarin; 9. The origin of matter in the universe Lev A. Kofman; 10. New guises for cold-dark matter suspects Edward W. Kolb; Part II. Physics and Astrophysics Of Relativistic Compact Objects: 11. On the unification of gravitational and inertial forces Donald Lynden-Bell; 12. Internal structure of astrophysical black holes Werner Israel; 13. Black hole entropy: external facade and internal reality Valery Frolov; 14. Accretion disks around black holes Marek A. Abramowicz; 15. Black hole X-ray transients J. Craig Wheeler; 16. X-rays and gamma rays from active galactic nuclei Roland Svensson; 17. Gamma-ray bursts: a challenge to relativistic astrophysics Martin Rees; 18. Probing black holes and other exotic objects with gravitational waves Kip Thorne; Epilogue: the past and future of relativistic astrophysics Igor D. Novikov; I. D. Novikov's scientific papers and books.
Time-dependent density-functional theory for extended systems
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.
Open-system Kohn-Sham density functional theory.
Zhou, Yongxi; Ernzerhof, Matthias
2012-03-07
A simple model for electron transport through molecules is provided by the source-sink potential (SSP) method [F. Goyer, M. Ernzerhof, and M. Zhuang, J. Chem. Phys. 126, 144104 (2007)]. In SSP, the boundary conditions of having an incoming and outgoing electron current are enforced through complex potentials that are added to the Hamiltonian. Depending on the sign of the imaginary part of the potentials, current density is generated or absorbed. In this way, a finite system can be used to model infinite molecular electronic devices. The SSP has originally been developed for the Hückel method and subsequently it has been extended [F. Goyer and M. Ernzerhof, J. Chem. Phys. 134, 174101 (2011)] to the Hubbard model. Here we present a step towards its generalization for first-principles electronic structure theory methods. In particular, drawing on our earlier work, we discuss a new generalized density functional theory for complex non-Hermitian Hamiltonians. This theory enables us to combine SSP and Kohn-Sham theory to obtain a method for the description of open systems that exchange current density with their environment. Similarly, the Hartree-Fock method is extended to the realm of non-Hermitian, SSP containing Hamiltonians. As a proof of principle, we present the first applications of complex-density functional theory (CODFT) as well as non-Hermitian Hartree-Fock theory to electron transport through molecules. © 2012 American Institute of Physics
Generalized One-Dimensional Point Interaction in Relativistic and Non-relativistic Quantum Mechanics
Shigehara, T; Mishima, T; Cheon, T; Cheon, Taksu
1999-01-01
We first give the solution for the local approximation of a four parameter family of generalized one-dimensional point interactions within the framework of non-relativistic model with three neighboring $\\delta$ functions. We also discuss the problem within relativistic (Dirac) framework and give the solution for a three parameter family. It gives a physical interpretation for so-called high energy substantially differ between non-relativistic and relativistic cases.
On the description of subsystems in relativistic hypersurface Bohmian mechanics.
Dürr, Detlef; Lienert, Matthias
2014-09-08
A candidate for a realistic relativistic quantum theory is the hypersurface Bohm-Dirac model. Its formulation uses a foliation of space-time into space-like hypersurfaces. In order to apply the theory and to make contact with the usual quantum formalism, one needs a framework for the description of subsystems. The presence of spin together with the foliation renders the subsystem description more complicated than in the non-relativistic case with spin. In this paper, we provide such a framework in terms of an appropriate conditional density matrix and an effective wave function as well as clarify their relation, thereby generalizing previous subsystem descriptions in the non-relativistic case.
A relativistic spin zero particle in a spherical cavity
Gouveia, Tomé M.; Fiolhais, Miguel C. N.; Birman, Joseph L.
2015-09-01
The problem of a relativistic massive scalar particle trapped in an infinite potential spherical well is pedagogically addressed in this paper. The wave function solutions and probability density of the Klein-Gordon equation in spherical coordinates are derived, as well as the energy levels. The results are compared with the non-relativistic solutions of the Schrödinger equation for different values of the particle’s mass. As expected, for very large masses the non-relativistic results are recovered. For illustration, these results are discussed in the specific case of the standard model Higgs field constrained inside a proton, in the quadratic approximation of the Higgs potential around the expectation value.
What Density Functional Theory could do for Quantum Information
Mattsson, Ann
2015-03-01
The Hohenberg-Kohn theorem of Density Functional Theory (DFT), and extensions thereof, tells us that all properties of a system of electrons can be determined through their density, which uniquely determines the many-body wave-function. Given access to the appropriate, universal, functionals of the density we would, in theory, be able to determine all observables of any electronic system, without explicit reference to the wave-function. On the other hand, the wave-function is at the core of Quantum Information (QI), with the wave-function of a set of qubits being the central computational resource in a quantum computer. While there is seemingly little overlap between DFT and QI, reliance upon observables form a key connection. Though the time-evolution of the wave-function and associated phase information is fundamental to quantum computation, the initial and final states of a quantum computer are characterized by observables of the system. While observables can be extracted directly from a system's wave-function, DFT tells us that we may be able to intuit a method for extracting them from its density. In this talk, I will review the fundamentals of DFT and how these principles connect to the world of QI. This will range from DFT's utility in the engineering of physical qubits, to the possibility of using it to efficiently (but approximately) simulate Hamiltonians at the logical level. The apparent paradox of describing algorithms based on the quantum mechanical many-body wave-function with a DFT-like theory based on observables will remain a focus throughout. The ultimate goal of this talk is to initiate a dialog about what DFT could do for QI, in theory and in practice. 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.
Resveratrol preserves cerebrovascular density and cognitive function in aging mice
Charlotte A Oomen
2009-12-01
Full Text Available Resveratrol, a natural polyphenol abundant in grapes and red wine, has been reported to exert numerous beneficial health effects. Among others, acute neuroprotective effects of resveratrol have been reported in several models of neurodegeneration, both in vitro and in vivo. In the present study we examined the neuroprotective effects of long term dietary supplementation with resveratrol in mice on behavioral, neurochemical and cerebrovascular level. We report a preserved cognitive function in resveratrol treated aging mice, as shown by an enhanced acquisition of a spatial Y-maze task. This was paralleled by a higher microvascular density and a lower number of microvascular abnormalities in comparison to aging non-treated control animals. We found no effects of resveratrol supplementation on cholinergic cell number or fiber density. The present findings support the hypothesis that resveratrol exerts beneficial effects on the brain by maintaining cerebrovascular health. Via this mechanism resveratrol can contribute to the preservation of cognitive function during aging.
The neutron polaron as a constraint on nuclear density functionals
Forbes, M M; Hebeler, K; Lesinski, T; Schwenk, A
2013-01-01
We study the energy of an impurity that interacts strongly in a sea of fermions when the effective range of the impurity-fermion interaction becomes important. This directly maps the Fermi polaron of condensed matter physics and ultracold atoms to strongly interacting neutrons. We present first Quantum Monte Carlo results for the neutron polaron and compare these with calculations based on effective field theory that also include contributions beyond effective-range effects. We show that predictions of state-of-the-art nuclear density functionals vary substantially and generally underestimate the neutron polaron energy. Our results thus provide a novel constraint for nuclear density functionals, in particular for the time-odd components.
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.
Excitations and benchmark ensemble density functional theory for two electrons
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.
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.
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...
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.
Viscosity spectral function of a scale invariant non-relativistic fluid from holography
Schaefer, Thomas
2014-01-01
We study the viscosity spectral function of a holographic 2+1 dimensional fluid with Schroedinger symmetry. The model is based on a twisted compactification of $Ads_5\\times S_5$. We numerically compute the spectral function of the stress tensor correlator for all frequencies, and analytically study the limits of high and low frequency. We compute the shear viscosity, the viscous relaxation time, and the quasi-normal mode spectrum in the shear channel. We find a number of unexpected results: The high frequency behavior is governed by a fractional 1/3 power law, the viscous relaxation time is negative, and the quasi-normal mode spectrum in the shear channel is not doubled.
Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory
Lin, Lin; Shao, Sihong; E, Weinan
2012-11-06
We present for the first time an efficient iterative method to directly solve the four-component Dirac-Kohn-Sham (DKS) density functional theory. Due to the existence of the negative energy continuum in the DKS operator, the existing iterative techniques for solving the Kohn-Sham systems cannot be efficiently applied to solve the DKS systems. The key component of our method is a novel filtering step (F) which acts as a preconditioner in the framework of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The resulting method, dubbed the LOBPCG-F method, is able to compute the desired eigenvalues and eigenvectors in the positive energy band without computing any state in the negative energy band. The LOBPCG-F method introduces mild extra cost compared to the standard LOBPCG method and can be easily implemented. We demonstrate our method in the pseudopotential framework with a planewave basis set which naturally satisfies the kinetic balance prescription. Numerical results for Pt$_{2}$, Au$_{2}$, TlF, and Bi$_{2}$Se$_{3}$ indicate that the LOBPCG-F method is a robust and efficient method for investigating the relativistic effect in systems containing heavy elements.
Guasp, J.; Pastor, I.; Álvarez-Estrada, R. F.; Castejón, F.
2015-02-01
Analytical results obtained recently of the ab-initio classical incoherent Thomson Scattering (TS) spectrum from a single-electron (Alvarez-Estrada et al 2012 Phys. Plasmas 19 062302) have been numerically implemented in a paralelized code to efficiently compute the TS emission from a given electron distribution function, irrespective of its characteristics and/or the intensity of the incoming radiation. These analytical results display certain differences, when compared with other authors, in the general case of incoming linearly and circularly polarized radiation and electrons with arbitrary initial directions. We regard such discrepancies and the ubiquitous interest in TS as motivations for this work. Here, we implement some analytical advances (like generalized Bessel functions for incoming linearly polarized radiation) in TS. The bulk of this work reports on the efficient computation of TS spectra (based upon our analytical approach), for an electron population having an essentially arbitrary distribution function and for both incoming linearly and circularly polarized radiation. A detailed comparison between the present approach and a previous Monte Carlo one (Pastor et al 2011 Nuclear Fusion 51 043011), dealing with the ab-initio computation of TS spectra, is reported. Both approaches are shown to fully agree with each other. As key computational improvements, the analytical technique yields a × 30 to × 100 gain in computation time and is a very flexible tool to compute the scattered spectrum and eventually the scattered electromagnetic fields in the time domain. The latter are computed explicitly here for the first time, as far as we know. Scaling laws for the power integrated over frequency versus initial kinetic energy are studied for the case of isotropic and monoenergetic electron distribution functions and their potential application as diagnostic tools for high-energy populations is briefly discussed. Finally, we discuss the application of these
Density functional theory across chemistry, physics and biology.
van Mourik, Tanja; Bühl, Michael; Gaigeot, Marie-Pierre
2014-03-13
The past decades have seen density functional theory (DFT) evolve from a rising star in computational quantum chemistry to one of its major players. This Theme Issue, which comes half a century after the publication of the Hohenberg-Kohn theorems that laid the foundations of modern DFT, reviews progress and challenges in present-day DFT research. Rather than trying to be comprehensive, this Theme Issue attempts to give a flavour of selected aspects of DFT.
Green's function based density estimation
Kovesarki, Peter; Brock, Ian C.; Nuncio Quiroz, Adriana Elizabeth [Physikalisches Institut, Universitaet Bonn (Germany)
2012-07-01
A method was developed based on Green's function identities to estimate probability densities. This can be used for likelihood estimations and for binary classifications. It offers several advantages over neural networks, boosted decision trees and other, regression based classifiers. For example, it is less prone to overtraining, and it is much easier to combine several samples. Some capabilities are demonstrated using ATLAS data.
Buckled graphene: A model study based on density functional theory
Khan, Mohammad A.
2010-09-01
We make use of ab initio calculations within density functional theory to investigate the influence of buckling on the electronic structure of single layer graphene. Our systematic study addresses a wide range of bond length and bond angle variations in order to obtain insights into the energy scale associated with the formation of ripples in a graphene sheet. © 2010 Elsevier B.V. All rights reserved.
Probability density function modeling for sub-powered interconnects
Pater, Flavius; Amaricǎi, Alexandru
2016-06-01
This paper proposes three mathematical models for reliability probability density function modeling the interconnect supplied at sub-threshold voltages: spline curve approximations, Gaussian models,and sine interpolation. The proposed analysis aims at determining the most appropriate fitting for the switching delay - probability of correct switching for sub-powered interconnects. We compare the three mathematical models with the Monte-Carlo simulations of interconnects for 45 nm CMOS technology supplied at 0.25V.
Reproducibility in density functional theory calculations of solids
2016-01-01
This is the author accepted manuscript.The final version is available from the American Association for the Advancement of Science via http://dx.doi.org/10.1126/science.aad3000 The widespread popularity of density-functional theory has given rise to a vast range of dedicated codes to predict molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions on the reproducibility of such predictions. We report the results of a community-...
Density functional theory studies of transition metal nanoparticles in catalysis
Greeley, Jeffrey Philip; Rankin, Rees; Zeng, Zhenhua
2013-01-01
Periodic Density Functional Theory calculations are capable of providing powerful insights into the structural, energetics, and electronic phenomena that underlie heterogeneous catalysis on transition metal nanoparticles. Such calculations are now routinely applied to single crystal metal surfaces...... and to subnanometer metal clusters. Descriptions of catalysis on truly nanosized structures, however, are generally not as well developed. In this talk, I will illustrate different approaches to analyzing nanocatalytic phenomena with DFT calculations. I will describe case studies from heterogeneous catalysis...
Density functional theory study on the molecular structure of loganin
Pandey, Anoop Kumar; Siddiqui, Shamoon Ahmad; Dwivedi, Apoorva; Raj, Kanwal; Misra, Neeraj
2011-01-01
The computational Quantum Chemistry (QC) has been used for different types of problems, for example: structural biology, surface phenomena and liquid phase. In this paper we have employed the density functional method for the study of molecular structure of loganin. The equilibrium geometry, harmonic vibrational frequencies and infrared intensities were calculated by B3LYP/6-311G (d, p) method and basis set combinations. It was found that the optimized parameters obtained by the DFT/B3LYP met...
Chemical reactivity in the framework of pair density functional theories.
Otero, Nicolás; Mandado, Marcos
2012-05-15
Chemical reactivity descriptors are derived within the framework of the pair density functional theory. These indices provide valuable information about bonding rearrangements and activating mechanisms upon electrophilic or nucleophilic reactions. Indices derived and tested in this work represent nonlocal counterparts of the local reactivity indices derived in the context of conceptual density functional theory (CDFT) and frequently used in reactivity studies; the Fukui function, the local softness and the dual descriptor. In this work, we show how these nonlocal indices provide a quantum chemical basis to explain the success of qualitative resonance models in chemical reactivity predictions. Also, local information is implicitly contained as CDFT indices are obtained by simple integration. As illustrative examples, we have considered in this work the Markovnikov's rule, the reactivity of enolate anion, the nucleophilic conjugate addition to α,β-unsaturated compounds and the electrophilic aromatic substitution of benzene derivatives. The densities used in this work were obtained with Hartree-Fock, Kohn-Sham DFT, and singles and doubles configuration interaction (CISD) approaches. Copyright © 2012 Wiley Periodicals, Inc.
Linear Scaling Density Functional Calculations with Gaussian Orbitals
Scuseria, Gustavo E.
1999-01-01
Recent advances in linear scaling algorithms that circumvent the computational bottlenecks of large-scale electronic structure simulations make it possible to carry out density functional calculations with Gaussian orbitals on molecules containing more than 1000 atoms and 15000 basis functions using current workstations and personal computers. This paper discusses the recent theoretical developments that have led to these advances and demonstrates in a series of benchmark calculations the present capabilities of state-of-the-art computational quantum chemistry programs for the prediction of molecular structure and properties.
Bayesian error estimation in density-functional theory
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
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...
Atomistic force field for alumina fit to density functional theory.
Sarsam, Joanne; Finnis, Michael W; Tangney, Paul
2013-11-28
We present a force field for bulk alumina (Al2O3), which has been parametrized by fitting the energies, forces, and stresses of a large database of reference configurations to those calculated with density functional theory (DFT). We use a functional form that is simpler and computationally more efficient than some existing models of alumina parametrized by a similar technique. Nevertheless, we demonstrate an accuracy of our potential that is comparable to those existing models and to DFT. We present calculations of crystal structures and energies, elastic constants, phonon spectra, thermal expansion, and point defect formation energies.
Time-dependent density-functional theory concepts and applications
Ullrich, Carsten A
2011-01-01
Time-dependent density-functional theory (TDDFT) describes the quantum dynamics of interacting electronic many-body systems formally exactly and in a practical and efficient manner. TDDFT has become the leading method for calculating excitation energies and optical properties of large molecules, with accuracies that rival traditional wave-function based methods, but at a fraction of the computational cost.This book is the first graduate-level text on the concepts and applications of TDDFT, including many examples and exercises, and extensive coverage of the literature. The book begins with a s
Nechaev, I. A.; Krasovskii, E. E.
2016-11-01
We present a method to microscopically derive a small-size k .p Hamiltonian in a Hilbert space spanned by physically chosen ab initio spinor wave functions. Without imposing any complementary symmetry constraints, our formalism equally treats three- and two-dimensional systems and simultaneously yields the Hamiltonian parameters and the true Z2 topological invariant. We consider bulk crystals and thin films of Bi2Se3 , Bi2Te3 , and Sb2Te3 . It turns out that the effective continuous k .p models with open boundary conditions often incorrectly predict the topological character of thin films.
Huhn, William P.; Blum, Volker
2017-08-01
We quantify the accuracy of different non-self-consistent and self-consistent spin-orbit coupling (SOC) treatments in Kohn-Sham and hybrid density functional theory by providing a band-structure benchmark set for the valence and low-lying conduction energy bands of 103 inorganic compounds, covering chemical elements up to polonium. Reference energy band structures for the PBE density functional are obtained using the full-potential (linearized) augmented plane wave code wien2k, employing its self-consistent treatment of SOC including Dirac-type p1 /2 orbitals in the basis set. We use this benchmark set to benchmark a computationally simpler, non-self-consistent all-electron treatment of SOC based on scalar-relativistic orbitals and numeric atom-centered orbital basis functions. For elements up to Z ≈50 , both treatments agree virtually exactly. For the heaviest elements considered (Tl, Pb, Bi, Po), the band-structure changes due to SOC are captured with a relative deviation of 11% or less. For different density functionals (PBE versus the hybrid HSE06), we show that the effect of spin-orbit coupling is usually similar but can be dissimilar if the qualitative features of the predicted underlying scalar-relativistic band structures do not agree. All band structures considered in this work are available online via the NOMAD repository to aid in future benchmark studies and methods development.
Time-dependent density functional theory: Causality and other problems
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.
Franco-Pérez, Marco; Ayers, Paul W; Gázquez, José L; Vela, Alberto
2015-12-28
We explore the local and nonlocal response functions of the grand canonical potential density functional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the density functional theory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model.
Franco-Pérez, Marco, E-mail: francopj@mcmaster.ca, E-mail: ayers@mcmaster.ca, E-mail: jlgm@xanum.uam.mx, E-mail: avela@cinvestav.mx [Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1 (Canada); Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México, D.F. 09340 (Mexico); Ayers, Paul W., E-mail: francopj@mcmaster.ca, E-mail: ayers@mcmaster.ca, E-mail: jlgm@xanum.uam.mx, E-mail: avela@cinvestav.mx [Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1 (Canada); Gázquez, José L., E-mail: francopj@mcmaster.ca, E-mail: ayers@mcmaster.ca, E-mail: jlgm@xanum.uam.mx, E-mail: avela@cinvestav.mx [Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México, D.F. 09340 (Mexico); Vela, Alberto, E-mail: francopj@mcmaster.ca, E-mail: ayers@mcmaster.ca, E-mail: jlgm@xanum.uam.mx, E-mail: avela@cinvestav.mx [Departamento de Química, Centro de Investigación y de Estudios Avanzados (Cinvestav), Av. Instituto Politécnico Nacional 2508, México, D.F. 07360 (Mexico)
2015-12-28
We explore the local and nonlocal response functions of the grand canonical potential density functional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the density functional theory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model.
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.
Orbital nodal surfaces: Topological challenges for density functionals
Aschebrock, Thilo; Armiento, Rickard; Kümmel, Stephan
2017-06-01
Nodal surfaces of orbitals, in particular of the highest occupied one, play a special role in Kohn-Sham density-functional theory. The exact Kohn-Sham exchange potential, for example, shows a protruding ridge along such nodal surfaces, leading to the counterintuitive feature of a potential that goes to different asymptotic limits in different directions. We show here that nodal surfaces can heavily affect the potential of semilocal density-functional approximations. For the functional derivatives of the Armiento-Kümmel (AK13) [Phys. Rev. Lett. 111, 036402 (2013), 10.1103/PhysRevLett.111.036402] and Becke88 [Phys. Rev. A 38, 3098 (1988), 10.1103/PhysRevA.38.3098] energy functionals, i.e., the corresponding semilocal exchange potentials, as well as the Becke-Johnson [J. Chem. Phys. 124, 221101 (2006), 10.1063/1.2213970] and van Leeuwen-Baerends (LB94) [Phys. Rev. A 49, 2421 (1994), 10.1103/PhysRevA.49.2421] model potentials, we explicitly demonstrate exponential divergences in the vicinity of nodal surfaces. We further point out that many other semilocal potentials have similar features. Such divergences pose a challenge for the convergence of numerical solutions of the Kohn-Sham equations. We prove that for exchange functionals of the generalized gradient approximation (GGA) form, enforcing correct asymptotic behavior of the potential or energy density necessarily leads to irregular behavior on or near orbital nodal surfaces. We formulate constraints on the GGA exchange enhancement factor for avoiding such divergences.
Differentiable but exact formulation of density-functional theory
Kvaal, Simen, E-mail: simen.kvaal@kjemi.uio.no; Ekström, Ulf; Helgaker, Trygve [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo (Norway); Teale, Andrew M. [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo (Norway); School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)
2014-05-14
The universal density functional F of density-functional theory is a complicated and ill-behaved function of the density—in particular, F is not differentiable, making many formal manipulations more complicated. While F has been well characterized in terms of convex analysis as forming a conjugate pair (E, F) with the ground-state energy E via the Hohenberg–Kohn and Lieb variation principles, F is nondifferentiable and subdifferentiable only on a small (but dense) subset of its domain. In this article, we apply a tool from convex analysis, Moreau–Yosida regularization, to construct, for any ε > 0, pairs of conjugate functionals ({sup ε}E, {sup ε}F) that converge to (E, F) pointwise everywhere as ε → 0{sup +}, and such that {sup ε}F is (Fréchet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box. It is noteworthy that no information is lost in the Moreau–Yosida regularization: the physical ground-state energy E(v) is exactly recoverable from the regularized ground-state energy {sup ε}E(v) in a simple way. All concepts and results pertaining to the original (E, F) pair have direct counterparts in results for ({sup ε}E, {sup ε}F). The Moreau–Yosida regularization therefore allows for an exact, differentiable formulation of density-functional theory. In particular, taking advantage of the differentiability of {sup ε}F, a rigorous formulation of Kohn–Sham theory is presented that does not suffer from the noninteracting representability problem in standard Kohn–Sham theory.
Ma, Li; Ray, Asok K.
2010-03-01
As a continuation of our studies of pure actinide metals using hybrid density functional theory,footnotetextR. Atta-Fynn and A. K. Ray, Europhysics Letters, 85, 27008-p1- p6 (2009); Chemical Physics Letters, 482, 223-227 (2009). we present here a systematic study of the electronic and geometric structure properties of mixed actinide dioxides, U0.5Pu0.5O2, U0.5Am0.5O2, Pu0.5Am0.5 O2 and U0.8Pu0.2O2. The fraction of exact Hartree-Fock exchange used was 40%. To investigate the effect of spin-orbit coupling on the ground state electronic and geometric structure properties, computations have been carried out at two theoretical levels, one at the scalar-relativistic level with no spin-orbit coupling and one at the fully relativistic level with spin-orbit coupling. Thermodynamic properties have been calculated by a coupling of first-principles calculation and lattice dynamics.
Kullie, Ossama [University of Kassel, Department of Natural Science, Institute of Physics (Germany)
2008-07-01
Using two spinor minimax method combined with finite element methods accompanied with extrapolation and counterpoise techniques enable us to obtain relativistic highly accurate results for two atomic molecules. Like in our previous work for the (Hartree-) Dirac-Fock-Slater (DFS) functional approximation, we investigate in this work the density functional approximations of the relativistic and nonrelativistic local-density functional, presenting highly accurate benchmark results of chemical properties on the dimers of the group 11(Ib) of the periodic table of elements. The comparison with DFS, with experimental and literature's results shows that DFS is better behaved than the other two local functionals.
Density-functional perturbation theory goes time-dependent
Gebauer, Ralph
2008-05-01
Full Text Available 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 element of the resolvent of the Kohn-Sham Liouvillian super-operator. A DFPT representation of response functions allows one to avoid the calculation of unoccupied Kohn-Sham orbitals. The resolvent of the Liouvillian is finally conveniently evaluated using a newly developed non-symmetric Lanczos technique, which allows for the calculation of the entire spectrum with a single Lanczos recursion chain. Each step of the chain essentially requires twice as many operations as a single step of the iterative diagonalization of the unperturbed Kohn-Sham Hamiltonian or, for that matter, as a single time step of a Car-Parrinello molecular dynamics run. The method will be illustrated with a few case molecular applications.
Density-dependence of functional spiking networks in vitro
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.
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%.
Stochastic Time-Dependent Current-Density Functional Theory
D'Agosta, Roberto
2008-03-01
Static and dynamical density functional methods have been applied with a certain degree of success to a variety of closed quantum mechanical systems, i.e., systems that can be described via a Hamiltonian dynamics. However, the relevance of open quantum systems - those coupled to external environments, e.g., baths or reservoirs - cannot be overestimated. To investigate open quantum systems with DFT methods we have introduced a new theory, we have named Stochastic Time-Dependent Current Density Functional theory (S-TDCDFT) [1]: starting from a suitable description of the system dynamics via a stochastic Schrödinger equation [2], we have proven that given an initial quantum state and the coupling between the system and the environment, there is a one-to-one correspondence between the ensemble-averaged current density and the external vector potential applied to the system.In this talk, I will introduce the stochastic formalism needed for the description of open quantum systems, discuss in details the theorem of Stochastic TD-CDFT, and provide few examples of its applicability like the dissipative dynamics of excited systems, quantum-measurement theory and other applications relevant to charge and energy transport in nanoscale systems.[1] M. Di Ventra and R. D'Agosta, Physical Review Letters 98, 226403 (2007)[2] N.G. van Kampen, Stochastic processes in Physics and Chemistry, (North Holland, 2001), 2nd ed.
Silva-Junior, Mario R.; Schreiber, Marko; Sauer, Stephan P. A.;
2008-01-01
Time-dependent density functional theory (TD-DFT) and DFT-based multireference configuration interaction (DFT/MRCI) calculations are reported for a recently proposed benchmark set of 28 medium-sized organic molecules. Vertical excitation energies, oscillator strengths, and excited-state dipole...... moments are computed using the same geometries (MP2/6-31G*) and basis set (TZVP) as in our previous ab initio benchmark study on electronically excited states. The results from TD-DFT (with the functionals BP86, B3LYP, and BHLYP) and from DFT/MRCI are compared against the previous high-level ab initio...
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.
Diez, Reinaldo Pis [CEQUINOR, Centro de Quimica Inorganica (CONICET, UNLP), Departamento de Quimica, Facultad de Ciencias Exactas, UNLP CC 962, B1900AVV La Plata (Argentina); Karasiev, Valentin V [Centro de Qimica, Instituto Venezolano de Investigaciones Cientificas, IVIC, Apartado 21827, Caracas 1020-A (Venezuela)
2003-07-14
A relationship between the auxiliary density, {rho}(r), defined within the framework of the weighted density approximation and the kinetic energy modulating factor, A{sub N}([{rho}(r)]; r), which appears in the local-scaling transformation version of density functional theory is presented. This relationship imposes the condition of positiveness on the kinetic energy modulating factor and this, in turn, leads to an important mathematical condition on any approximate kinetic energy density functional. It is shown that two well-known approximate kinetic energy density functionals do not satisfy the above relationship at distances very close to the nucleus. By forcing a given approximate kinetic energy density functional to obey the above condition, both the kinetic and exchange energies can be obtained within a framework similar to that of the weighted density approximation. Results on some closed-shell atomic systems provide support for those ideas.
Mean Spherical Approximation-Based Partitioned Density Functional Theory
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
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.
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.
Revisiting the Fermi Surface in Density Functional Theory
Das, Mukunda P.; Green, Frederick
2016-06-01
The Fermi surface is an abstract object in the reciprocal space of a crystal lattice, enclosing the set of all those electronic band states that are filled according to the Pauli principle. Its topology is dictated by the underlying lattice structure and its volume is the carrier density in the material. The Fermi surface is central to predictions of thermal, electrical, magnetic, optical and superconducting properties in metallic systems. Density functional theory is a first-principles method used to estimate the occupied-band energies and, in particular, the isoenergetic Fermi surface. In this review we survey several key facts about Fermi surfaces in complex systems, where a proper theoretical understanding is still lacking. We address some critical difficulties.
Study of Magnesium Diboride Clusters Using Hybrid Density Functional Theory
D. Rodríguez
2007-12-01
Full Text Available Using hybrid density functional theory and a relatively large basis set, the lowest energy equilibrium structure, vibrational spectrum, and natural orbital analysis were obtained for magnesium diboride clusters [(MgB2x for x=1,2, and 3]. For comparison, boron clusters [BxÃ‚Â forÃ‚Â x=2,4,Ã‚Â andÃ‚Â 6] were also considered. The MgB2 and (MgB22 showed equilibrium structures with the boron atoms in arrangements similar to what was obtained for pure boron atoms, whereas, for (MgB23 a different arrangement of boron was obtained. From the population analysis, large electron density in the boron atoms forming the clusters was observed.
Dynamic density functional theory of solid tumor growth: Preliminary models
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.
Density functional study of ferromagnetism in alkali metal thin films
Prasenjit Sen
2010-04-01
Electronic and magnetic structures of (1 0 0) films of K and Cs, having thicknesses of one to seven layers, are calculated within the plane-wave projector augmented wave (PAW) formalism of the density functional theory (DFT), using both local spin density approximation (LSDA) and the PW91 generalized gradient approximation (GGA). Only a six-layer Cs film is found to have a ferromagnetic (FM) state which is degenerate with a paramagnetic (PM) state within the accuracy of these calculations. These results are compared with those obtained from calculations on a finite-thickness uniform jellium model (UJM), and it is argued that within LSDA or GGA, alkali metal thin films cannot be claimed to have an FM ground state. Relevance of these results to the experiments on transition metal-doped alkali metal thin films and bulk hosts are also discussed.
Applications of large-scale density functional theory in biology
Cole, Daniel J.; Hine, Nicholas D. M.
2016-10-01
Density functional theory (DFT) has become a routine tool for the computation of electronic structure in the physics, materials and chemistry fields. Yet the application of traditional DFT to problems in the biological sciences is hindered, to a large extent, by the unfavourable scaling of the computational effort with system size. Here, we review some of the major software and functionality advances that enable insightful electronic structure calculations to be performed on systems comprising many thousands of atoms. We describe some of the early applications of large-scale DFT to the computation of the electronic properties and structure of biomolecules, as well as to paradigmatic problems in enzymology, metalloproteins, photosynthesis and computer-aided drug design. With this review, we hope to demonstrate that first principles modelling of biological structure-function relationships are approaching a reality.
Characterizing the Spatial Density Functions of Neural Arbors
Teeter, Corinne Michelle
Recently, it has been proposed that a universal function describes the way in which all arbors (axons and dendrites) spread their branches over space. Data from fish retinal ganglion cells as well as cortical and hippocampal arbors from mouse, rat, cat, monkey and human provide evidence that all arbor density functions (adf) can be described by a Gaussian function truncated at approximately two standard deviations. A Gaussian density function implies that there is a minimal set of parameters needed to describe an adf: two or three standard deviations (depending on the dimensionality of the arbor) and an amplitude. However, the parameters needed to completely describe an adf could be further constrained by a scaling law found between the product of the standard deviations and the amplitude of the function. In the following document, I examine the scaling law relationship in order to determine the minimal set of parameters needed to describe an adf. First, I find that the at, two-dimensional arbors of fish retinal ganglion cells require only two out of the three fundamental parameters to completely describe their density functions. Second, the three-dimensional, volume filling, cortical arbors require four fundamental parameters: three standard deviations and the total length of an arbor (which corresponds to the amplitude of the function). Next, I characterize the shape of arbors in the context of the fundamental parameters. I show that the parameter distributions of the fish retinal ganglion cells are largely homogenous. In general, axons are bigger and less dense than dendrites; however, they are similarly shaped. The parameter distributions of these two arbor types overlap and, therefore, can only be differentiated from one another probabilistically based on their adfs. Despite artifacts in the cortical arbor data, different types of arbors (apical dendrites, non-apical dendrites, and axons) can generally be differentiated based on their adfs. In addition, within
INTERACTIVE VISUALIZATION OF PROBABILITY AND CUMULATIVE DENSITY FUNCTIONS
Potter, Kristin
2012-01-01
The probability density function (PDF), and its corresponding cumulative density function (CDF), provide direct statistical insight into the characterization of a random process or field. Typically displayed as a histogram, one can infer probabilities of the occurrence of particular events. When examining a field over some two-dimensional domain in which at each point a PDF of the function values is available, it is challenging to assess the global (stochastic) features present within the field. In this paper, we present a visualization system that allows the user to examine two-dimensional data sets in which PDF (or CDF) information is available at any position within the domain. The tool provides a contour display showing the normed difference between the PDFs and an ansatz PDF selected by the user and, furthermore, allows the user to interactively examine the PDF at any particular position. Canonical examples of the tool are provided to help guide the reader into the mapping of stochastic information to visual cues along with a description of the use of the tool for examining data generated from an uncertainty quantification exercise accomplished within the field of electrophysiology.
Dynamic density functional theory with hydrodynamic interactions and fluctuations
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.
Graphene oxide and adsorption of chloroform: a density functional study
Kuisma, Elena; Lindberg, Th Benjamin; Gillberg, Christoffer A; Idh, Sebastian; Schroder, Elsebeth
2016-01-01
Chlorinated hydrocarbon compounds are of environmental concerns, since they are toxic to humans and other mammals, are widespread, and exposure is hard to avoid. Understanding and improving methods to reduce the amount of the substances is important. We present an atomic-scale calculational study of the adsorption of chlorine-based substance chloroform (CHCl3) on graphene oxide, as a step in estimating the capacity of graphene oxide for filtering out such substances, e.g., from drinking water. The calculations are based on density functional theory (DFT), and the recently developed consistent-exchange functional for the van der Waals density-functional method (vdW-DF-cx) is employed. We obtain values of the chloroform adsorption energy varying from roughly 0.2 to 0.4 eV per molecule. This is comparable to previously found results for chloroform adsorbed directly on clean graphene, using similar calculations. In a wet environment, like filters for drinking water, the graphene will not stay clean and will likel...
Relativistic and non-relativistic geodesic equations
Giambo' , R.; Mangiarotti, L.; Sardanashvily, G. [Camerino Univ., Camerino, MC (Italy). Dipt. di Matematica e Fisica
1999-07-01
It is shown that any dynamic equation on a configuration space of non-relativistic time-dependent mechanics is associated with connections on its tangent bundle. As a consequence, every non-relativistic dynamic equation can be seen as a geodesic equation with respect to a (non-linear) connection on this tangent bundle. Using this fact, the relationships between relativistic and non-relativistic equations of motion is studied.
Application of Density Functional Theory to Systems Containing Metal Atoms
Bauschlicher, Charles W., Jr.
2006-01-01
The accuracy of density functional theory (DFT) for problems involving metal atoms is considered. The DFT results are compared with experiment as well as results obtained using the coupled cluster approach. The comparisons include geometries, frequencies, and bond energies. The systems considered include MO2, M(OH)+n, MNO+, and MCO+2. The DFT works well for frequencies and geometries, even in case with symmetry breaking; however, some examples have been found where the symmetry breaking is quite severe and the DFT methods do not work well. The calculation of bond energies is more difficult and examples of successes as well as failures of DFT will be given.
Nuclear clustering in the energy density functional approach
Ebran, J.-P., E-mail: jean-paul.ebran@cea.fr [CEA,DAM,DIF, F-91297 Arpajon (France); Khan, E. [Institut de Physique Nucléaire, Université Paris-Sud CEA, IN2P3 CNRS, F-91406 Orsay Cedex (France); Nikšić, T.; Vretenar, D. [Physics Department, Faculty of Science, University of Zagreb, 10000 Zagreb (Croatia)
2015-10-15
Nuclear Energy Density Functionals (EDFs) are a microscopic tool of choice extensively used over the whole chart to successfully describe the properties of atomic nuclei ensuing from their quantum liquid nature. In the last decade, they also have proved their ability to deal with the cluster phenomenon, shedding a new light on its fundamental understanding by treating on an equal footing both quantum liquid and cluster aspects of nuclei. Such a unified microscopic description based on nucleonic degrees of freedom enables to tackle the question pertaining to the origin of the cluster phenomenon and emphasizes intrinsic mechanisms leading to the emergence of clusters in nuclei.
Continuation of probability density functions using a generalized Lyapunov approach
Baars, S., E-mail: s.baars@rug.nl [Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK Groningen (Netherlands); Viebahn, J.P., E-mail: viebahn@cwi.nl [Centrum Wiskunde & Informatica (CWI), P.O. Box 94079, 1090 GB, Amsterdam (Netherlands); Mulder, T.E., E-mail: t.e.mulder@uu.nl [Institute for Marine and Atmospheric research Utrecht, Department of Physics and Astronomy, Utrecht University, Princetonplein 5, 3584 CC Utrecht (Netherlands); Kuehn, C., E-mail: ckuehn@ma.tum.de [Technical University of Munich, Faculty of Mathematics, Boltzmannstr. 3, 85748 Garching bei München (Germany); Wubs, F.W., E-mail: f.w.wubs@rug.nl [Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK Groningen (Netherlands); Dijkstra, H.A., E-mail: h.a.dijkstra@uu.nl [Institute for Marine and Atmospheric research Utrecht, Department of Physics and Astronomy, Utrecht University, Princetonplein 5, 3584 CC Utrecht (Netherlands); School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY (United States)
2017-05-01
Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability density functions of systems of stochastic partial differential equations near fixed points, under a small noise approximation. Key innovation is the efficient solution of a generalized Lyapunov equation using an iterative method involving low-rank approximations. We apply and illustrate the capabilities of the method using a problem in physical oceanography, i.e. the occurrence of multiple steady states of the Atlantic Ocean circulation.
Density Functional Modelling of Elastic Properties of Elemental Semiconductors
M. Verma
2011-01-01
Full Text Available The expressions for bulk modulus, its first and second pressure derivatives for elemental semiconductors are derived using the ab initio pseudopotential approach to the total crystal energy within the framework of local Density Functional formalism. The expression for the second pressure derivative of the bulk modulus for four-fold crystal structures are derived for the first time within the pseudopotential framework. The computed results for the semiconductors under study are very close to the available experimental data and will be useful in the study of equation of states.
Determining Ionospheric Irregularity Spectral Density Function from Japan GEONET
Lay, E. H.; Light, M. E.; Parker, P. A.; Carrano, C. S.; Haaser, R. A.
2015-12-01
Japan's GEONET GPS network is the densest GPS monitoring network in the world, with 1200+ receivers over the area of Japan. Measuring and calibrating the integrated total electron content (TEC) from each station has been done in many cases to provide detailed maps of ionospheric disturbances over Japan. We use TEC measurements from Japan's GEONET array to determine an empirically derived description of the 2-dimensional scale sizes of spatial irregularities above Japan. The contributions from various scale sizes will be included in a statistical description for the irregularity spectral density (ISD) function. We will compare the statistics of the spatial irregularities between calm and moderately scintillated conditions.
Density functional theory studies of doping in Titania
2010-01-01
The structural and electronic properties of rutile and anatase, and the influence of both mono- and co-doping, have been studied using Density Functional Theory. Ge-doped anatase and rutile exhibit different band gap-narrowing mechanisms; in particular, host Ti 3d states move to lower energy regions in anatase and Ge 4s impurities states locate below the conduction band of rutile. For S-doping, S 3p states locate above the top of the valence band and mix with O 2p states, leading to band gap ...
Use of density functional theory in drug metabolism studies
Rydberg, Patrik; Jørgensen, Flemming Steen; Olsen, Lars
2014-01-01
INTRODUCTION: The cytochrome P450 enzymes (CYPs) metabolize many drug compounds. They catalyze a wide variety of reactions, and potentially, a large number of different metabolites can be generated. Density functional theory (DFT) has, over the past decade, been shown to be a powerful tool...... isoforms. This is probably due to the fact that the binding of the substrates is not the major determinant. When binding of the substrate plays a significant role, the well-known issue of determining the free energy of binding is the challenge. How approaches taking the protein environment into account...
Dynamical density functional theory with hydrodynamic interactions in confined geometries
Goddard, B. D.; Nold, A.; Kalliadasis, S.
2016-12-01
We study the dynamics of colloidal fluids in both unconfined geometries and when confined by a hard wall. Under minimal assumptions, we derive a dynamical density functional theory (DDFT) which includes hydrodynamic interactions (HI; bath-mediated forces). By using an efficient numerical scheme based on pseudospectral methods for integro-differential equations, we demonstrate its excellent agreement with the full underlying Langevin equations for systems of hard disks in partial confinement. We further use the derived DDFT formalism to elucidate the crucial effects of HI in confined systems.
Atomic volumes and polarizabilities in density-functional theory.
Kannemann, Felix O; Becke, Axel D
2012-01-21
Becke and Johnson introduced an ad hoc definition of atomic volume [J. Chem. Phys. 124, 014204 (2006)] in order to obtain atom-in-molecule polarizabilities from free-atom polarizabilities in their nonempirical exchange-hole dipole moment model of dispersion interactions. Here we explore the dependence of Becke-Johnson atomic volumes on basis sets and density-functional approximations and provide reference data for all atoms H-Lr. A persuasive theoretical foundation for the Becke-Johnson definition is also provided.
Energy Continuity in Degenerate Density Functional Perturbation Theory
Palenik, Mark C
2016-01-01
Fractional occupation numbers can produce open-shell degeneracy in density functional theory. We develop the corresponding perturbation theory by requiring that a differentiable map connects the initial and perturbed states. The degenerate state connects to a single perturbed state which extremizes, but does not necessarily minimize or maximize, the energy with respect to occupation numbers. Using a system of three electrons in a harmonic oscillator potential, we relate the counterintuitive sign of first-order occupation numbers to eigenvalues of the electron-electron interaction Hessian.
Augmented Lagrangian Method for Constrained Nuclear Density Functional Theory
Staszczak, A; Baran, A; Nazarewicz, W
2010-01-01
The augmented Lagrangiam method (ALM), widely used in quantum chemistry constrained optimization problems, is applied in the context of the nuclear Density Functional Theory (DFT) in the self-consistent constrained Skyrme Hartree-Fock-Bogoliubov (CHFB) variant. The ALM allows precise calculations of multidimensional energy surfaces in the space of collective coordinates that are needed to, e.g., determine fission pathways and saddle points; it improves accuracy of computed derivatives with respect to collective variables that are used to determine collective inertia; and is well adapted to supercomputer applications.
Quantification of Uncertainties in Nuclear Density Functional theory
Schunck, N; Higdon, D; Sarich, J; Wild, S
2014-01-01
Reliable predictions of nuclear properties are needed as much to answer fundamental science questions as in applications such as reactor physics or data evaluation. Nuclear density functional theory is currently the only microscopic, global approach to nuclear structure that is applicable throughout the nuclear chart. In the past few years, a lot of effort has been devoted to setting up a general methodology to assess theoretical uncertainties in nuclear DFT calculations. In this paper, we summarize some of the recent progress in this direction. Most of the new material discussed here will be be published in separate articles.
Visualization techniques for spatial probability density function data
Udeepta D Bordoloi
2006-01-01
Full Text Available Novel visualization methods are presented for spatial probability density function data. These are spatial datasets, where each pixel is a random variable, and has multiple samples which are the results of experiments on that random variable. We use clustering as a means to reduce the information contained in these datasets; and present two different ways of interpreting and clustering the data. The clustering methods are used on two datasets, and the results are discussed with the help of visualization techniques designed for the spatial probability data.
Li, Ji-Lai; Mata, Ricardo A; Ryde, Ulf
2013-03-12
The oxygen-atom transfer reaction catalyzed by the mononuclear molybdenum enzyme dimethyl sulfoxide reductase (DMSOR) has attracted considerable attention through both experimental and theoretical studies. We show here that this reaction is more sensitive to details of quantum mechanical calculations than what has previously been appreciated. Basis sets of at least triple-ζ quality are needed to obtain qualitatively correct results. Dispersion has an appreciable effect on the reaction, in particular the binding of the substrate or the dissociation of the product (up to 34 kJ/mol). Polar and nonpolar solvation effects are also significant, especially if the enzyme can avoid cavitation effects by using a preformed active-site cavity. Relativistic effects are considerable (up to 22 kJ/mol), but they are reasonably well treated by a relativistic effective core potential. Various density-functional methods give widely different results for the activation and reaction energy (differences of over 100 kJ/mol), mainly reflecting the amount of exact exchange in the functional, owing to the oxidation of Mo from +IV to +VI. By calibration toward local CCSD(T0) calculations, we show that none of eight tested functionals (TPSS, BP86, BLYP, B97-D, TPSSH, B3LYP, PBE0, and BHLYP) give accurate energies for all states in the reaction. Instead, B3LYP gives the best activation barrier, whereas pure functionals give more accurate energies for the other states. Our best results indicate that the enzyme follows a two-step associative reaction mechanism with an overall activation enthalpy of 63 kJ/mol, which is in excellent agreement with the experimental results.
Relativistic heat conduction and thermoelectric properties of nonuniform plasmas
Honda, M
2003-01-01
Relativistic heat transport in electron-two-temperature plasmas with density gradients has been investigated. The Legendre expansion analysis of relativistically modified kinetic equations shows that strong inhibition of heat flux appears in relativistic temperature regimes, suppressing the classical Spitzer-H{\\"a}rm conduction. The Seebeck coefficient, the Wiedemann-Franz law, and the thermoelectric figure of merit are derived in the relativistic regimes.
Ab initio molecular dynamics using hybrid density functionals
Guidon, Manuel; Schiffmann, Florian; Hutter, Jürg; Vandevondele, Joost
2008-06-01
Ab initio molecular dynamics simulations with hybrid density functionals have so far found little application due to their computational cost. In this work, an implementation of the Hartree-Fock exchange is presented that is specifically targeted at ab initio molecular dynamics simulations of medium sized systems. We demonstrate that our implementation, which is available as part of the CP2K/Quickstep program, is robust and efficient. Several prescreening techniques lead to a linear scaling cost for integral evaluation and storage. Integral compression techniques allow for in-core calculations on systems containing several thousand basis functions. The massively parallel implementation respects integral symmetry and scales up to hundreds of CPUs using a dynamic load balancing scheme. A time-reversible multiple time step scheme, exploiting the difference in computational efficiency between hybrid and local functionals, brings further time savings. With extensive simulations of liquid water, we demonstrate the ability to perform, for several tens of picoseconds, ab initio molecular dynamics based on hybrid functionals of systems in the condensed phase containing a few thousand Gaussian basis functions.
Galilean relativistic fluid mechanics
Ván, Péter
2015-01-01
Single component Galilean-relativistic (nonrelativistic) fluids are treated independently of reference frames. The basic fields are given, their balances, thermodynamic relations and the entropy production is calculated. The usual relative basic fields, the mass, momentum and energy densities, the diffusion current density, the pressure tensor and the heat flux are the time- and spacelike components of the third order mass-momentum-energy density tensor according to a velocity field. The transformation rules of the basic fields are derived and prove that the non-equilibrium thermodynamic background theory, that is the Gibbs relation, extensivity condition and the entropy production is absolute, that is independent of the reference frame and also of the fluid velocity. --- Az egykomponensu Galilei-relativisztikus (azaz nemrelativisztikus) disszipativ folyadekokat vonatkoztatasi rendszertol fuggetlenul targyaljuk. Megadjuk az alapmennyisegeket, ezek merlegeit, a termodinamikai osszefuggeseket es kiszamoljuk az ...
Polymer density functional approach to efficient evaluation of path integrals
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.
Uncertainty Quantification and Propagation in Nuclear Density Functional Theory
Schunck, N; McDonnell, J D; Higdon, D; Sarich, J; Wild, S M
2015-03-17
Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going eff orts seek to better root nuclear DFT in the theory of nuclear forces, energy functionals remain semi-phenomenological constructions that depend on a set of parameters adjusted to experimental data in fi nite nuclei. In this paper, we review recent eff orts to quantify the related uncertainties, and propagate them to model predictions. In particular, we cover the topics of parameter estimation for inverse problems, statistical analysis of model uncertainties and Bayesian inference methods. Illustrative examples are taken from the literature.
BUILDING A UNIVERSAL NUCLEAR ENERGY DENSITY FUNCTIONAL (UNEDF)
Nazarewicz, Witold
2012-07-01
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.
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.
Solvation of complex surfaces via molecular density functional theory
Levesque, Maximilien; Rotenberg, Benjamin; Jeanmairet, Guillaume; Vuilleumier, Rodolphe; Borgis, Daniel
2012-01-01
We show that classical molecular density functional theory (MDFT), here in the homogeneous reference fluid approximation in which the functional is inferred from the properties of the bulk solvent, is a powerful new tool to study, at a fully molecular level, the solvation of complex surfaces and interfaces by polar solvents. This implicit solvent method allows for the determination of structural, orientational and energetic solvation properties that are on a par with all-atom molecular simulations performed for the same system, while reducing the computer time by two orders of magnitude. This is illustrated by the study of an atomistically-resolved clay surface composed of over a thousand atoms wetted by a molecular dipolar solvent. The high numerical efficiency of the method is exploited to carry a systematic analysis of the electrostatic and non-electrostatic components of the surface-solvent interaction within the popular CLAYFF force field. Solvent energetics and structure are found to depend weakly upon ...
Electronic properties of graphene nanoribbons: A density functional investigation
Kumar, Sandeep, E-mail: skumar198712@gmail.com; Sharma, Hitesh, E-mail: dr.hitesh.phys@gmail.com [Department of Physics, Punjab Technical University Kapurthala, Punjab-144601 (India)
2015-05-15
Density functional theory calculations have been performed on graphene nano ribbons (GNRs) to investigate the electronic properties as a function of chirality, size and hydrogenation on the edges. The calculations were performed on GNRs with armchair and zigzag configurations with 28, 34, 36, 40, 50, 56, 62, 66 carbon atoms. The structural stability of AGNR and ZGNR increases with the size of nanoribbon where as hydrogenation of GNR tends to lowers their structural stability. All GNRs considered have shown semiconducting behavior with HOMO-LUMO gap decreasing with the increase in the GNR size. The hydrogenation of GNR decreases its HOMO-LUMO gap significantly. The results are in agreement with the available experimental and theoretical results.
A numerical efficient way to minimize classical density functional theory.
Edelmann, Markus; Roth, Roland
2016-02-21
The minimization of the functional of the grand potential within the framework of classical density functional theory in three spatial dimensions can be numerically very demanding. The Picard iteration, that is often employed, is very simple and robust but can be rather slow. While a number of different algorithms for optimization problems have been suggested, there is still great need for additional strategies. Here, we present an approach based on the limited memory Broyden algorithm that is efficient and relatively simple to implement. We demonstrate the performance of this algorithm with the minimization of an inhomogeneous bulk structure of a fluid with competing interactions. For the problems we studied, we find that the presented algorithm improves performance by roughly a factor of three.
Calculations of Optical Rotation from Density Functional Theory
António Canal Neto; Francisco Elias Jorge
2007-01-01
Density function theory calculations of frequency-dependent optical rotations [α]ω for three rigid chiral molecules are reported. Calculations have been carried out at the sodium D line frequency, using the ADZP basis set and a wide variety of functionals. Gauge-invariant atomic orbitals are used to guarantee origin-independent values of [α]D. In addition, study of geometry dependence of [α]D. Is reported. Using the geometries optimized at the B3LYP/ADZP level, the mean absolute deviation of B3LYP/ADZP and experimental [α]D values yields 60.1°/(dm g/cm3). According to our knowledge, this value has not been achieved until now with any other model.
Ho, Gregory S.; Lignères, Vincent L.; Carter, Emily A.
2008-07-01
We derive an analytic form of the Wang-Govind-Carter (WGC) [Wang , Phys. Rev. B 60, 16350 (1999)] kinetic energy density functional (KEDF) with the density-dependent response kernel. A real-space aperiodic implementation of the WGC KEDF is then described and used in linear scaling orbital-free density functional theory (OF-DFT) calculations.
PEXSI-$\\Sigma$: A Green's function embedding method for Kohn-Sham density functional theory
Li, Xiantao; Lu, Jianfeng
2016-01-01
As Kohn-Sham density functional theory (KSDFT) being applied to increasingly more complex materials, the periodic boundary condition associated with supercell approaches also becomes unsuitable for a number of important scenarios. Green's function embedding methods allow a more versatile treatment of complex boundary conditions, and hence provide an attractive alternative to describe complex systems that cannot be easily treated in supercell approaches. In this paper, we first revisit the literature of Green's function embedding methods from a numerical linear algebra perspective. We then propose a new Green's function embedding method called PEXSI-$\\Sigma$. The PEXSI-$\\Sigma$ method approximates the density matrix using a set of nearly optimally chosen Green's functions evaluated at complex frequencies. For each Green's function, the complex boundary conditions are described by a self energy matrix $\\Sigma$ constructed from a physical reference Green's function, which can be computed relatively easily. In th...
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.
General relativistic Boltzmann equation, I: Covariant treatment
Debbasch, F.; van Leeuwen, W.A.
2009-01-01
This series of two articles aims at dissipating the rather dense haze existing in the present literature around the General Relativistic Boltzmann equation. In this first article, the general relativistic one-particle distribution function in phase space is defined as an average of delta functions.
Wang, Ziyue; Zhuang, Pengfei
2017-07-01
The pion superfluid and the corresponding Goldstone and soft modes are investigated in a two-flavor quark-meson model with a functional renormalization group. By solving the flow equations for the effective potential and the meson two-point functions at finite temperature and isospin density, the critical temperature for the superfluid increases sizeably in comparison with solving the flow equation for the potential only. The spectral function for the soft mode shows clearly a transition from meson gas to quark gas with increasing temperature and a crossover from Bose-Einstein condensation to Bardeen-Cooper-Schrieffer pairing of quarks with increasing isospin density.
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.
Leardini, Fabrice
2013-01-01
This manuscript presents a problem on special relativity theory (SRT) which embodies an apparent paradox relying on the concept of simultaneity. The problem is represented in the framework of Greek epic poetry and structured in a didactic way. Owing to the characteristic properties of Lorenz transformations, three events which are simultaneous in a given inertial reference system, occur at different times in the other two reference frames. In contrast to the famous twin paradox, in the present case there are three, not two, different inertial observers. This feature provides a better framework to expose some of the main characteristics of SRT, in particular, the concept of velocity and the relativistic rule of addition of velocities.
Scattering in Relativistic Particle Mechanics.
de Bievre, Stephan
The problem of direct interaction in relativistic particle mechanics has been extensively studied and a variety of models has been proposed avoiding the conclusions of the so-called no-interaction theorems. In this thesis we study scattering in the relativistic two-body problem. We use our results to analyse gauge invariance in Hamiltonian constraint models and the uniqueness of the symplectic structure in manifestly covariant relativistic particle mechanics. We first present a general geometric framework that underlies approaches to relativistic particle mechanics. This permits a model-independent and geometric definition of the notions of asymptotic completeness and of Moller and scattering operators. Subsequent analysis of these concepts divides into two parts. First, we study the kinematic properties of the scattering transformation, i.e. those properties that arise solely from the invariance of the theory under the Poincare group. We classify all canonical (symplectic) scattering transformations on the relativistic phase space for two free particles in terms of a single function of the two invariants of the theory. We show how this function is determined by the center of mass time delay and scattering angle and vice versa. The second part of our analysis of the relativistic two-body scattering problem is devoted to the dynamical properties of the scattering process. Hence, we turn to two approaches to relativistic particle mechanics: the Hamiltonian constraint models and the manifestly covariant formalism. Using general geometric arguments, we prove "gauge invariance" of the scattering transformation in the Todorov -Komar Hamiltonian constraint model. We conclude that the scattering cross sections of the Todorov-Komar models have the same angular dependence as their non-relativistic counterpart, irrespective of a choice of gauge. This limits the physical relevance of those models. We present a physically non -trivial Hamiltonian constraint model, starting from
Daubechies wavelets for linear scaling density functional theory
Mohr, Stephan [Institut für Physik, Universität Basel, Klingelbergstr. 82, 4056 Basel (Switzerland); Univ. Grenoble Alpes, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble (France); Ratcliff, Laura E.; Genovese, Luigi; Caliste, Damien; Deutsch, Thierry [Univ. Grenoble Alpes, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble (France); Boulanger, Paul [Univ. Grenoble Alpes, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble (France); Institut Néel, CNRS and Université Joseph Fourier, B.P. 166, 38042 Grenoble Cedex 09 (France); Goedecker, Stefan [Institut für Physik, Universität Basel, Klingelbergstr. 82, 4056 Basel (Switzerland)
2014-05-28
We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10 000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.
García-Aldea, David; Alvarellos, J. E.
2009-03-01
We present several nonlocal exchange energy density functionals that reproduce the linear response function of the free electron gas. These nonlocal functionals are constructed following a similar procedure used previously for nonlocal kinetic energy density functionals by Chac'on-Alvarellos-Tarazona, Garc'ia-Gonz'alez et al., Wang-Govind-Carter and Garc'ia-Aldea-Alvarellos. The exchange response function is not known but we have used the approximate response function developed by Utsumi and Ichimaru, even we must remark that the same ansatz can be used to reproduce any other response function with the same scaling properties. We have developed two families of new nonlocal functionals: one is constructed with a mathematical structure based on the LDA approximation -- the Dirac functional for the exchange - and for the second one the structure of the second order gradient expansion approximation is took as a model. The functionals are constructed is such a way that they can be used in localized systems (using real space calculations) and in extended systems (using the momentum space, and achieving a quasilinear scaling with the system size if a constant reference electron density is defined).
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
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.
Multifragmentation calculated with relativistic forces
Feldmeier, H; Papp, G
1995-01-01
A saturating hamiltonian is presented in a relativistically covariant formalism. The interaction is described by scalar and vector mesons, with coupling strengths adjusted to the nuclear matter. No explicit density depe ndence is assumed. The hamiltonian is applied in a QMD calculation to determine the fragment distribution in O + Br collision at different energies (50 -- 200 MeV/u) to test the applicability of the model at low energies. The results are compared with experiment and with previous non-relativistic calculations. PACS: 25.70Mn, 25.75.+r
Buehring, W.
1983-03-01
Non-relativistic scattering phase shifts, bound state energies, and wave function normalization factors for a screened Coulomb potential of the Hulthen type are presented in the form of relatively simple analytic expressions. These formulae have been obtained by a suitable renormalization procedure applied to the quantities derived from an approximate Schroedinger equation which contains the exact Hulthen potential together with an approximate angular momentum term. When the screening exponent vanishes, our formulae reduce to the exact Coulomb expresions. The interrelation between our formulae and Pratt's analytic perturbation theory for screened Coulomb potentials' is discussed.
A density functional for liquid {sup 4}He including the pair distribution function
Szybisz, Leszek [Laboratorio TANDAR, Departamento de Fisica, Comision Nacional de Energia Atomica, Av. del Libertador 8250, RA-1429 Buenos Aires (Argentina) and Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, RA-1428 Buenos Aires (Argentina) and Consejo Nacional de Investigaciones Cientificas y Tecnicas, Av. Rivadavia 1917, RA-1033 Buenos Aires (Argentina)]. E-mail: szybisz@tandar.cnea.gov.ar; Urrutia, Ignacio [Laboratorio TANDAR, Departamento de Fisica, Comision Nacional de Energia Atomica, Av. del Libertador 8250, RA-1429 Buenos Aires (Argentina) and Comision de Investigaciones Cientificas de la Prov. de Buenos Aires, Calle 526 entre 10 y 11, RA-1900 La Plata (Argentina)]. E-mail: iurrutia@cnea.gov.ar
2005-04-25
A new semi-microscopic functional for studying adsorption of {sup 4}He on solid surfaces is presented. In this proposal the helium-helium interaction is screened at small distances by the pair distribution function g(r) and, in addition, the contribution which plays an important role in the interpretation of the experimental static response function is written in terms of the gradient of g(r). This functional reproduces the usual test properties. Moreover, a detailed comparison with results of the Orsay-Trento density functional is performed.
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...
Accurate ionization potential of semiconductors from efficient density functional calculations
Ye, Lin-Hui
2016-07-01
Despite its huge successes in total-energy-related applications, the Kohn-Sham scheme of density functional theory cannot get reliable single-particle excitation energies for solids. In particular, it has not been able to calculate the ionization potential (IP), one of the most important material parameters, for semiconductors. We illustrate that an approximate exact-exchange optimized effective potential (EXX-OEP), the Becke-Johnson exchange, can be used to largely solve this long-standing problem. For a group of 17 semiconductors, we have obtained the IPs to an accuracy similar to that of the much more sophisticated G W approximation (GWA), with the computational cost of only local-density approximation/generalized gradient approximation. The EXX-OEP, therefore, is likely as useful for solids as for finite systems. For solid surfaces, the asymptotic behavior of the vx c has effects similar to those of finite systems which, when neglected, typically cause the semiconductor IPs to be underestimated. This may partially explain why standard GWA systematically underestimates the IPs and why using the same GWA procedures has not been able to get an accurate IP and band gap at the same time.
Density functional theory based generalized effective fragment potential method
Nguyen, Kiet A., E-mail: kiet.nguyen@wpafb.af.mil, E-mail: ruth.pachter@wpafb.af.mil [Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433 (United States); UES, Inc., Dayton, Ohio 45432 (United States); Pachter, Ruth, E-mail: kiet.nguyen@wpafb.af.mil, E-mail: ruth.pachter@wpafb.af.mil [Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433 (United States); Day, Paul N. [Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433 (United States); General Dynamics Information Technology, Inc., Dayton, Ohio 45431 (United States)
2014-06-28
We present a generalized Kohn-Sham (KS) density functional theory (DFT) based effective fragment potential (EFP2-DFT) method for the treatment of solvent effects. Similar to the original Hartree-Fock (HF) based potential with fitted parameters for water (EFP1) and the generalized HF based potential (EFP2-HF), EFP2-DFT includes electrostatic, exchange-repulsion, polarization, and dispersion potentials, which are generated for a chosen DFT functional for a given isolated molecule. The method does not have fitted parameters, except for implicit parameters within a chosen functional and the dispersion correction to the potential. The electrostatic potential is modeled with a multipolar expansion at each atomic center and bond midpoint using Stone's distributed multipolar analysis. The exchange-repulsion potential between two fragments is composed of the overlap and kinetic energy integrals and the nondiagonal KS matrices in the localized molecular orbital basis. The polarization potential is derived from the static molecular polarizability. The dispersion potential includes the intermolecular D3 dispersion correction of Grimme et al. [J. Chem. Phys. 132, 154104 (2010)]. The potential generated from the CAMB3LYP functional has mean unsigned errors (MUEs) with respect to results from coupled cluster singles, doubles, and perturbative triples with a complete basis set limit (CCSD(T)/CBS) extrapolation, of 1.7, 2.2, 2.0, and 0.5 kcal/mol, for the S22, water-benzene clusters, water clusters, and n-alkane dimers benchmark sets, respectively. The corresponding EFP2-HF errors for the respective benchmarks are 2.41, 3.1, 1.8, and 2.5 kcal/mol. Thus, the new EFP2-DFT-D3 method with the CAMB3LYP functional provides comparable or improved results at lower computational cost and, therefore, extends the range of applicability of EFP2 to larger system sizes.
Density functional theory predictions of isotropic hyperfine coupling constants.
Hermosilla, L; Calle, P; García de la Vega, J M; Sieiro, C
2005-02-17
The reliability of density functional theory (DFT) in the determination of the isotropic hyperfine coupling constants (hfccs) of the ground electronic states of organic and inorganic radicals is examined. Predictions using several DFT methods and 6-31G, TZVP, EPR-III and cc-pVQZ basis sets are made and compared to experimental values. The set of 75 radicals here studied was selected using a wide range of criteria. The systems studied are neutral, cationic, anionic; doublet, triplet, quartet; localized, and conjugated radicals, containing 1H, 9Be, 11B, 13C, 14N, 17O, 19F, 23Na, 25Mg, 27Al, 29Si, 31P, 33S, and 35Cl nuclei. The considered radicals provide 241 theoretical hfcc values, which are compared with 174 available experimental ones. The geometries of the studied systems are obtained by theoretical optimization using the same functional and basis set with which the hfccs were calculated. Regression analysis is used as a basic and appropriate methodology for this kind of comparative study. From this analysis, we conclude that DFT predictions of the hfccs are reliable for B3LYP/TZVP and B3LYP/EPR-III combinations. Both functional/basis set scheme are the more useful theoretical tools for predicting hfccs if compared to other much more expensive methods.
Probucol alleviates atherosclerosis and improves high density lipoprotein function
Zhong Jian-Kai
2011-11-01
Full Text Available Abstract Background Probucol is a unique hypolipidemic agent that decreases high density lipoprotein cholesterol (HDL-C. However, it is not definite that whether probucol hinders the progression of atherosclerosis by improving HDL function. Methods Eighteen New Zealand White rabbits were randomly divided into the control, atherosclerosis and probucol groups. Control group were fed a regular diet; the atherosclerosis group received a high fat diet, and the probucol group received the high fat diet plus probucol. Hepatocytes and peritoneal macrophages were isolated for [3H] labeled cholesterol efflux rates and expression of ABCA1 and SR-B1 at gene and protein levels; venous blood was collected for serum paraoxonase 1, myeloperoxidase activity and lipid analysis. Aorta were prepared for morphologic and immunohistochemical analysis after 12 weeks. Results Compared to the atherosclerosis group, the paraoxonase 1 activity, cholesterol efflux rates, expression of ABCA1 and SR-BI in hepatocytes and peritoneal macrophages, and the level of ABCA1 and SR-BI in aortic lesions were remarkably improved in the probucol group, But the serum HDL cholesterol concentration, myeloperoxidase activity, the IMT and the percentage plaque area of aorta were significantly decreased. Conclusion Probucol alleviated atherosclerosis by improving HDL function. The mechanisms include accelerating the process of reverse cholesterol transport, improving the anti-inflammatory and anti-oxidant functions.
Building A Universal Nuclear Energy Density Functional (UNEDF)
Carlson, Joe [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Furnstahl, Dick [The Ohio State Univ., Columbus, OH (United States); Horoi, Mihai [Central Michigan Univ., Mount Pleasant, MI (United States); Lusk, Rusty [Argonne National Lab. (ANL), Argonne, IL (United States); Nazarewicz, Witek [Univ. of Tennessee, Knoxville, TN (United States); Ng, Esmond [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Thompson, Ian [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Vary, James [Iowa State Univ., Ames, IA (United States)
2012-09-30
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. The main physics areas of UNEDF, defined at the beginning of the project, were: ab initio structure; ab initio functionals; DFT applications; DFT extensions; reactions.
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.
Interactive design of probability density functions for shape grammars
Dang, Minh
2015-11-02
A shape grammar defines a procedural shape space containing a variety of models of the same class, e.g. buildings, trees, furniture, airplanes, bikes, etc. We present a framework that enables a user to interactively design a probability density function (pdf) over such a shape space and to sample models according to the designed pdf. First, we propose a user interface that enables a user to quickly provide preference scores for selected shapes and suggest sampling strategies to decide which models to present to the user to evaluate. Second, we propose a novel kernel function to encode the similarity between two procedural models. Third, we propose a framework to interpolate user preference scores by combining multiple techniques: function factorization, Gaussian process regression, autorelevance detection, and l1 regularization. Fourth, we modify the original grammars to generate models with a pdf proportional to the user preference scores. Finally, we provide evaluations of our user interface and framework parameters and a comparison to other exploratory modeling techniques using modeling tasks in five example shape spaces: furniture, low-rise buildings, skyscrapers, airplanes, and vegetation.
Insights into phase transitions and entanglement from density functional theory
Wei, Bo-Bo
2016-11-01
Density functional theory (DFT) has met great success in solid state physics, quantum chemistry and in computational material sciences. In this work we show that DFT could shed light on phase transitions and entanglement at finite temperatures. Specifically, we show that the equilibrium state of an interacting quantum many-body system which is in thermal equilibrium with a heat bath at a fixed temperature is a universal functional of the first derivatives of the free energy with respect to temperature and other control parameters respectively. This insight from DFT enables us to express the average value of any physical observable and any entanglement measure as a universal functional of the first derivatives of the free energy with respect to temperature and other control parameters. Since phase transitions are marked by the nonanalytic behavior of free energy with respect to control parameters, the physical quantities and entanglement measures may present nonanalytic behavior at critical point inherited from their dependence on the first derivative of free energy. We use two solvable models to demonstrate these ideas. These results give new insights for phase transitions and provide new profound connections between entanglement and phase transitions in interacting quantum many-body physics.
Mohazzabi, Pirooz
2017-09-01
Using molecular dynamics simulations, binary collision density in a dense non-ideal gas with Lennard-Jones interactions is investigated. It is shown that the functional form of the dependence of collision density on particle density and collision diameter remains the same as that for an ideal gas. The temperature dependence of the collision density, however, has a very different form at low temperatures, where it decreases as temperature increases. But at higher temperatures the functional form becomes the same as that for an ideal gas.
Zheng, Xiao; Yam, ChiYung; Wang, Fan; Chen, GuanHua
2011-08-28
We present the time-dependent holographic electron density theorem (TD-HEDT), which lays the foundation of time-dependent density-functional theory (TDDFT) for open electronic systems. For any finite electronic system, the TD-HEDT formally establishes a one-to-one correspondence between the electron density inside any finite subsystem and the time-dependent external potential. As a result, any electronic property of an open system in principle can be determined uniquely by the electron density function inside the open region. Implications of the TD-HEDT on the practicality of TDDFT are also discussed.
Direct recursive identification of the Preisach hysteresis density function
Ruderman, Michael
2013-12-01
In this paper, a novel direct method of recursive identification of the Preisach hysteresis density function is proposed. Using the discrete dynamic Preisach model, which is a state-space realization of the classical scalar Preisach model, the method is designed based on the output increment error. After giving the general formulation, the identification scheme implemented for a discretized Preisach plane is introduced and evaluated through the use of numerical simulations. Two cases of Gaussian mixtures are considered for mapping the hysteresis system to be identified. The parameter convergence is shown for a low-pass filtered white-noise input. Further, the proposed identification method is applied to a magnetism-related application example, where the flux linkage hysteresis of a proportional solenoid is assumed from the measurements, and then the inverse of a standard demagnetization procedure is utilized as the identification sequence.
Density Function Theory Studies on Reaction of HCS with OH
PEI Ke-Mei; LI Yi-Min; LI Hai-Yang
2003-01-01
The exothermic reaction of HCS with OH on the single-state potential energy surface was explored by means of Density Function Theory(DFT). The equilibrium structural parameters, the harmonic vibrational frequencies, the total energies and the zero point energies(ZPE) of all the species in the reaction were computed. Six intermediates and seven transition states were located, three exothermic channels were found. The frequency analysis and the Intrinsic Reaction Coordinate(IRC) calculation confirm that the transitions are truthful. The results indicate that there are three exothermic channels and their corresponding products are: P1(H2O+CS), P2(H2S+CO), P3(OCS+H2), and P1 has a larger branch ratio.
Density functional theory studies of HCOOH decomposition on Pd(111)
Scaranto, Jessica; Mavrikakis, Manos
2016-08-01
The investigation of formic acid (HCOOH) decomposition on transition metal surfaces is important to derive useful insights for vapor phase catalysis involving HCOOH and for the development of direct HCOOH fuel cells (DFAFC). Here we present the results obtained from periodic, self-consistent, density functional theory (DFT-GGA) calculations for the elementary steps involved in the gas-phase decomposition of HCOOH on Pd(111). Accordingly, we analyzed the minimum energy paths for HCOOH dehydrogenation to CO2 + H2 and dehydration to CO + H2O through the carboxyl (COOH) and formate (HCOO) intermediates. Our results suggest that HCOO formation is easier than COOH formation, but HCOO decomposition is more difficult than COOH decomposition, in particular in the presence of co-adsorbed O and OH species. Therefore, both paths may contribute to HCOOH decomposition. CO formation goes mainly through COOH decomposition.
Study of spontaneous fission lifetimes using nuclear density functional theory
Sadhukhan Jhilam
2013-12-01
Full Text Available The spontaneous fission lifetimes have been studied microscopically by minimizing the collective action integral in a two-dimensional collective space of quadrupole moments (Q20, Q22 representing elongation and triaxiality. The microscopic collective potential and inertia tensor are obtained by solving the self-consistent Hartree-Fock-Bogoliubov (HFB equations with the Skyrme energy density functional and mixed pairing interaction. The mass tensor is computed within the perturbative Adiabatic Time-Dependent HFB (ATDHFB approach in the cranking approximation. The dynamic fission trajectories have been obtained by minimizing the collective action using two different numerical techniques. The values of spontaneous fission lifetimes obtained in this way are compared with the static results.
Pairing Nambu-Goldstone modes within nuclear density functional theory
Hinohara, Nobuo
2016-01-01
We show that the Nambu-Goldstone formalism of the broken gauge symmetry in the presence of the $T=1$ pairing condensate offers a quantitative description of the binding energy differences of open-shell superfluid nuclei. We conclude that the pairing rotational moments of inertia are excellent pairing indicators, which are free from ambiguities attributed to odd-mass systems. We offer a new, unified interpretation of the binding-energy differences traditionally viewed in the shell model picture as signatures of the valence nucleon properties. We present the first systematic analysis of the off-diagonal pairing rotational moments of inertia, and demonstrate the mixing of the neutron and proton pairing rotational modes in the ground states of even-even nuclei. Finally, we discuss the importance of mass measurements of neutron-rich nuclei for constraining the pairing energy density functional.
Oxygen adsorption on pyrite (100) surface by density functional theory
孙伟; 胡岳华; 邱冠周; 覃文庆
2004-01-01
Pyrite (FeS2) bulk and (100) surface properties and the oxygen adsorption on the surface were studied by using density functional theory methods. The results show that in the formation of FeS2 (100) surface, there exists a process of electron transfer from Fe dangling bond to S dangling bond. In this situation, surface Fe and S atoms have more ionic properties. Both Fe2+ and S2- have high electrochemistry reduction activity, which is the base for oxygen adsorption. From the viewpoint of adsorption energy, the parallel form oxygen adsorption is in preference.The result also shows that the state of oxygen absorbed on FeS2 surface acts as peroxides rather than O2.
Descriptions of carbon isotopes within the energy density functional theory
Ismail, Atef [Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia and Department of Physics, Al-Azhar University, 71524 Assiut (Egypt); Cheong, Lee Yen; Yahya, Noorhana [Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak (Malaysia); Tammam, M. [Department of Physics, Al-Azhar University, 71524 Assiut (Egypt)
2014-10-24
Within the energy density functional (EDF) theory, the structure properties of Carbon isotopes are systematically studied. The shell model calculations are done for both even-A and odd-A nuclei, to study the structure of rich-neutron Carbon isotopes. The EDF theory indicates the single-neutron halo structures in {sup 15}C, {sup 17}C and {sup 19}C, and the two-neutron halo structures in {sup 16}C and {sup 22}C nuclei. It is also found that close to the neutron drip-line, there exist amazing increase in the neutron radii and decrease on the binding energies BE, which are tightly related with the blocking effect and correspondingly the blocking effect plays a significant role in the shell model configurations.
Electrostatic potential of several small molecules from density functional theory
无
2006-01-01
A number of density functional theory (DFT) methods were used to calculate the electrostatic potential for the series of molecules N2, F2, NH3, H2O, CHF3, CHCl3, C6H6, TiF4, CO(NH2)2 and C4H5N3O compared with QCISD (quadratic configuration interaction method including single and double substitutions) results. Comparisons were made between the DFT computed results and the QCISD ab initio ones and MP2 ab initio ones, compared with the root-mean-square deviation and electrostatic potential difference contours figures. It was found that the hybrid DFT method B3LYP, yields electrostatic potential in good agreement with the QCISD results. It is suggest this is a useful approach, especially for large molecules that are difficult to study by ab initio methods.
Superconductivity in layered binary silicides: A density functional theory study
Flores-Livas, José A.; Debord, Régis; Botti, Silvana; San Miguel, Alfonso; Pailhès, Stéphane; Marques, Miguel A. L.
2011-11-01
A class of metal disilicides (of the form XSi2, where X is a divalent metal) crystallizes in the EuGe2 structure, formed by hexagonal corrugated silicon planes intercalated with metal atoms. These compounds are superconducting like other layered superconductors, such as MgB2. Moreover, their properties can be easily tuned either by external pressure or by negative chemical pressure (i.e., by changing the metal), which makes disilicides an ideal testbed to study superconductivity in layered systems. In view of this, we present an extensive density functional theory study of the electronic and phonon band structures as well as the electron-phonon interaction of metal disilicides. Our results explain the variation of the superconducting transition temperature with pressure and the species of the intercalating atom, and allow us to predict superconductivity for compounds not yet synthesized belonging to this family.
Density Functional Studies of Methanol Decomposition on Subnanometer Pd Clusters
Mehmood, Faisal; Greeley, Jeffrey P.; Curtiss, Larry A.
2009-12-31
A density functional theory study of the decomposition of methanol on subnanometer palladium clusters (primarily Pd4) is presented. Methanol dehydrogenation through C-H bond breaking to form hydroxymethyl (CH2OH) as the initial step, followed by steps involving formation of hydroxymethylene (CHOH), formyl (CHO), and carbon monoxide (CO), is found to be the most favorable reaction pathway. A competing dehydrogenation pathway with O-H bond breaking as the first step, followed by formation of methoxy (CH3O) and formaldehyde (CH2O), is slightly less favorable. In contrast, pathways involving C-O bond cleavage are much less energetically favorable, and no feasible pathways involving C-O bond formation to yield dimethyl ether (CH3OCH3) are found. Comparisons of the results are made with methanol decomposition products adsorbed on more extended Pd surfaces; all reaction intermediates are found to bind slightly more strongly to the clusters than to the surfaces.
Density Functional Theory of Polymer Structure and Conformations
Zhaoyang Wei
2016-04-01
Full Text Available We present a density functional approach to quantitatively evaluate the microscopic conformations of polymer chains with consideration of the effects of chain stiffness, polymer concentration, and short chain molecules. For polystyrene (PS, poly(ethylene oxide (PEO, and poly(methyl methacrylate (PMMA melts with low-polymerization degree, as chain length increases, they display different stretching ratios and show non-universal scaling exponents due to their different chain stiffnesses. In good solvent, increase of PS concentration induces the decline of gyration radius. For PS blends containing short (m1 = 1 − 100 and long (m = 100 chains, the expansion of long chains becomes unobvious once m 1 is larger than 40, which is also different to the scaling properties of ideal chain blends.
Time-dependent density functional theory for quantum transport.
Zheng, Xiao; Chen, GuanHua; Mo, Yan; Koo, SiuKong; Tian, Heng; Yam, ChiYung; Yan, YiJing
2010-09-21
Based on our earlier works [X. Zheng et al., Phys. Rev. B 75, 195127 (2007); J. S. Jin et al., J. Chem. Phys. 128, 234703 (2008)], we propose a rigorous and numerically convenient approach to simulate time-dependent quantum transport from first-principles. The proposed approach combines time-dependent density functional theory with quantum dissipation theory, and results in a useful tool for studying transient dynamics of electronic systems. Within the proposed exact theoretical framework, we construct a number of practical schemes for simulating realistic systems such as nanoscopic electronic devices. Computational cost of each scheme is analyzed, with the expected level of accuracy discussed. As a demonstration, a simulation based on the adiabatic wide-band limit approximation scheme is carried out to characterize the transient current response of a carbon nanotube based electronic device under time-dependent external voltages.
Zeolite-Catalyzed Hydrocarbon Formation from Methanol: Density Functional Simulations
George Fitzgerald
2002-04-01
Full Text Available Abstract: We report detailed density functional theory (DFT calculations of important mechanisms in the methanol to gasoline (MTG process in a zeolite catalyst. Various reaction paths and energy barriers involving C-O bond cleavage and the first C-C bond formation are investigated in detail using all-electron periodic supercell calculations and recently developed geometry optimization and transition state search algorithms. We have further investigated the formation of ethanol and have identified a different mechanism than previously reported [1], a reaction where water does not play any visible role. Contrary to recent cluster calculations, we were not able to find a stable surface ylide structure. However, a stable ylide structure built into the zeolite framework was found to be possible, albeit a very high reaction barrier.
Machine-learned approximations to Density Functional Theory Hamiltonians
Hegde, Ganesh; Bowen, R. Chris
2017-01-01
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest. PMID:28198471
Machine-learned approximations to Density Functional Theory Hamiltonians
Hegde, Ganesh; Bowen, R. Chris
2017-02-01
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus ab initio DFT, creating such approximations involves significant manual intervention and is highly inefficient for high-throughput electronic structure screening calculations. In this letter, we propose the use of machine-learning for prediction of DFT Hamiltonians. Using suitable representations of atomic neighborhoods and Kernel Ridge Regression, we show that an accurate and transferable prediction of DFT Hamiltonians for a variety of material environments can be achieved. Electronic structure properties such as ballistic transmission and band structure computed using predicted Hamiltonians compare accurately with their DFT counterparts. The method is independent of the specifics of the DFT basis or material system used and can easily be automated and scaled for predicting Hamiltonians of any material system of interest.
Density functional theory for inhomogeneous associating chain fluids.
Bryk, P; Sokołowski, S; Pizio, O
2006-07-14
We propose a nonlocal density functional theory for associating chain molecules. The chains are modeled as tangent spheres, which interact via Lennard-Jones (12,6) attractive interactions. A selected segment contains additional, short-ranged, highly directional interaction sites. The theory incorporates an accurate treatment of the chain molecules via the intramolecular potential formalism and should accurately describe systems with strongly varying external fields, e.g., attractive walls. Within our approach we investigate the structure of the liquid-vapor interface and capillary condensation of a simple model of associating chains with only one associating site placed on the first segment. In general, the properties of inhomogeneous associating chains depend on the association energy. Similar to the bulk systems we find the behavior of associating chains of a given length to be in between that for the nonassociating chains of the same length and that for the nonassociating chains twice as large.