Relationship between molecular cloud structure and density PDFs
Stanchev, Orlin; Veltchev, Todor V; Shetty, Rahul
2013-01-01
Volume and column density PDFs in molecular clouds are important diagnostics for understanding their general structure. We developed a novel approach to trace the cloud structure by varying the lower PDF cut-off and exploring a suggested mass-density relationship with a power-law index $x^\\prime$. The correspondence of x' as a function of spatial scale to the slope of the high-density PDF tail is studied. To validate the proposed model, we use results from hydrodynamical simulations of a turbulent self-gravitating cloud and recent data on dust continuum emission from the Planck mission.
Nuclear PDFs from neutrino deep inelastic scattering
Energy Technology Data Exchange (ETDEWEB)
I. Schienbein; J. Y. Yu; C. Keppel; J. G. Morfin; F. Olness; J.F. Owens
2007-11-13
We study nuclear effects in charged current deep inelastic neutrino--iron scattering in the framework of a chi^2-analysis of parton distribution functions. We extract a set of iron PDFs and show that under reasonable assumptions it is possible to constrain the valence, light sea and strange quark distributions. We compare our results with nuclear parton distribution functions from the literature and find good agreement. Our iron PDFs are used to compute nuclear correction factors which are required in global analyses of free nucleon PDFs.
Hirai, Masanori
2016-01-01
We discuss consistency of the nuclear effects between the electromagnetic and weak interactions. In order to study a possibility of different nuclear effects in the neutrino DIS process, double differential cross section data are compared with these values obtained by the HKN07 nuclear parton distribution functions (nPDFs). Discrepancies are found in the small and large-$x$ regions, and difference of kinematical value $y$ dependence exists between the $\
Constraining nuclear PDFs with CMS
Chapon, Emilien
2017-01-01
Nuclear parton distribution functions are essential to the understanding of proton-lead collisions. We will review several measurements from CMS that are particularly sensitive to nPDFs. W and Z bosons are medium-blind probes of the initial state of the collisions, and we will present the measurements of their production cross sections in pPb collisions at 5.02 TeV, and as well a asymmetries with an increased sensitivity to nPDFs. We will also report measurements of charmonium production, including the nuclear modification factor of J/psi and psi(2S) in pPb collisions at 5.02 TeV, though other cold nuclear matter effects may also be at play in those processes. At last, we will present measurements of the pseudo-rapidity of dijets in pPb collisions at 5.02 TeV.
Sparse Representation of Photometric Redshift PDFs: Preparing for Petascale Astronomy
Kind, M Carrasco
2014-01-01
One of the consequences of entering the era of precision cosmology is the widespread adoption of photometric redshift probability density functions (PDFs). Both current and future photometric surveys are expected to obtain images of billions of distinct galaxies. As a result, storing and analyzing all of these PDFs will be non-trivial and even more severe if a survey plans to compute and store multiple different PDFs. In this paper we propose the use of a sparse basis representation to fully represent individual photo-$z$ PDFs. By using an Orthogonal Matching Pursuit algorithm and a combination of Gaussian and Voigt basis functions, we demonstrate how our approach is superior to a multi-Gaussian fitting, as we require approximately half of the parameters for the same fitting accuracy with the additional advantage that an entire PDF can be stored by using a 4-byte integer per basis function, and we can achieve better accuracy by increasing the number of bases. By using data from the CFHTLenS, we demonstrate th...
Efficiency issues related to probability density function comparison
Energy Technology Data Exchange (ETDEWEB)
Kelly, P.M.; Cannon, M.; Barros, J.E.
1996-03-01
The CANDID project (Comparison Algorithm for Navigating Digital Image Databases) employs probability density functions (PDFs) of localized feature information to represent the content of an image for search and retrieval purposes. A similarity measure between PDFs is used to identify database images that are similar to a user-provided query image. Unfortunately, signature comparison involving PDFs is a very time-consuming operation. In this paper, we look into some efficiency considerations when working with PDFS. Since PDFs can take on many forms, we look into tradeoffs between accurate representation and efficiency of manipulation for several data sets. In particular, we typically represent each PDF as a Gaussian mixture (e.g. as a weighted sum of Gaussian kernels) in the feature space. We find that by constraining all Gaussian kernels to have principal axes that are aligned to the natural axes of the feature space, computations involving these PDFs are simplified. We can also constrain the Gaussian kernels to be hyperspherical rather than hyperellipsoidal, simplifying computations even further, and yielding an order of magnitude speedup in signature comparison. This paper illustrates the tradeoffs encountered when using these constraints.
Steady-state probability density function in wave turbulence under large volume limit
Institute of Scientific and Technical Information of China (English)
Yeontaek Choia; Sang Gyu Job
2011-01-01
We investigate the possibility for two-mode probability density function (PDF) to have a non-zero flux steady state solution. We take the large volume limit so that the space of modes becomes continuous. It is shown that in this limit all the steady-state two- or higher-mode PDFs are the product of one-mode PDFs. The flux of this steady-state solution turns out to be zero for any finite mode PDF.
Multifractal analysis of the fat-tail PDFs observed in fully developed turbulence
Energy Technology Data Exchange (ETDEWEB)
Arimitsu, T [Graduate School of Pure and Applied Sciences, University of Tsukuba, Ibaraki 305-8571 (Japan); Arimitsu, N [Graduate School of Environment and Information Sciences, Yokohama Nat' l. University, Yokohama 240-8501 (Japan)
2005-01-01
The fundamentals of the multifractal analysis (MFA) is given, which is a unified statistical mechanical theory that treats the systems containing intermittent phenomena and representing fat-tail probability density functions (PDFs) for appropriate observables. MFA utilizes two distinct Tsallis-type MaxEnt distribution functions, one for the tail part of PDF and the other for its center part. It is shown that A and A model within MFA can explain the recently observed PDFs of turbulence in the highest accuracy superior to the analyses based on other multifractal models such as the log-normal model and the p model.
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.
Specialized minimal PDFs for optimized LHC calculations.
Carrazza, Stefano; Forte, Stefano; Kassabov, Zahari; Rojo, Juan
2016-01-01
We present a methodology for the construction of parton distribution functions (PDFs) designed to provide an accurate representation of PDF uncertainties for specific processes or classes of processes with a minimal number of PDF error sets: specialized minimal PDF sets, or SM-PDFs. We construct these SM-PDFs in such a way that sets corresponding to different input processes can be combined without losing information, specifically as regards their correlations, and that they are robust upon smooth variations of the kinematic cuts. The proposed strategy never discards information, so that the SM-PDF sets can be enlarged by the addition of new processes, until the prior PDF set is eventually recovered for a large enough set of processes. We illustrate the method by producing SM-PDFs tailored to Higgs, top-quark pair, and electroweak gauge boson physics, and we determine that, when the PDF4LHC15 combined set is used as the prior, around 11, 4, and 11 Hessian eigenvectors, respectively, are enough to fully describe the corresponding processes.
Specialized minimal PDFs for optimized LHC calculations
Carrazza, Stefano; Kassabov, Zahari; Rojo, Juan
2016-01-01
We present a methodology for the construction of parton distribution functions (PDFs) designed to provide an accurate representation of PDF uncertainties for specific processes or classes of processes with a minimal number of PDF error sets: specialized minimal PDF sets, or SM-PDFs. We construct these SM-PDFs in such a way that sets corresponding to different input processes can be combined without losing information, specifically on their correlations, and that they are robust upon smooth variations of the kinematic cuts. The proposed strategy never discards information, so that the SM-PDF sets can be enlarged by the addition of new processes, until the prior PDF set is eventually recovered for a large enough set of processes. We illustrate the method by producing SM-PDFs tailored to Higgs, top quark pair, and electroweak gauge boson physics, and determine that, when the PDF4LHC15 combined set is used as the prior, around 11, 4 and 11 Hessian eigenvectors respectively are enough to fully describe the corresp...
Bertone, Valerio; Pagani, Davide; Zaro, Marco
2015-01-01
In this paper we discuss the effect of the complete leading-order QED corrections to the DGLAP equations in the perturbative evolution of parton distribution functions (PDFs). This requires the extension of the purely QCD DGLAP evolution, including a PDF for the photons and, consistently, also for the charged leptons $e^{\\pm}$, $\\mu^\\pm$ and $\\tau^\\pm$. We present the implementation of the QED-corrected DGLAP evolution in the presence of photon and lepton PDFs in the APFEL program and, by means of different assumptions for the initial scale PDFs, we produce for the first time PDF sets containing charged lepton distributions. We also present phenomenological studies that aim to assess the impact of the presence of lepton PDFs in the proton for some relevant SM (and BSM) processes at the LHC at 13 TeV and the FCC-hh at 100 TeV. The impact of the photon PDF is also outlined for those processes.
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.
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.
A critical appraisal and evaluation of modern PDFs
Accardi, A.; Alekhin, S.; Blümlein, J.; Garzelli, M. V.; Lipka, K.; Melnitchouk, W.; Moch, S.; Owens, J. F.; Plačakytė, R.; Reya, E.; Sato, N.; Vogt, A.; Zenaiev, O.
2016-08-01
We review the present status of the determination of parton distribution functions (PDFs) in the light of the precision requirements for the LHC in Run 2 and other future hadron colliders. We provide brief reviews of all currently available PDF sets and use them to compute cross sections for a number of benchmark processes, including Higgs boson production in gluon-gluon fusion at the LHC. We show that the differences in the predictions obtained with the various PDFs are due to particular theory assumptions made in the fits of those PDFs. We discuss PDF uncertainties in the kinematic region covered by the LHC and on averaging procedures for PDFs, such as advocated by the PDF4LHC15 sets, and provide recommendations for the usage of PDF sets for theory predictions at the LHC.
A critical appraisal and evaluation of modern PDFs
Energy Technology Data Exchange (ETDEWEB)
Accardi, A. [Hampton University, Hampton, VA (United States); Jefferson Lab, Newport News, VA (United States); Alekhin, S. [Universitaet Hamburg, II. Institut fuer Theoretische Physik, Hamburg (Germany); Institute for High Energy Physics, Protvino, Moscow region (Russian Federation); Bluemlein, J. [Deutsches Elektronensynchrotron DESY, Zeuthen (Germany); Garzelli, M.V.; Moch, S. [Universitaet Hamburg, II. Institut fuer Theoretische Physik, Hamburg (Germany); Lipka, K.; Placakyte, R.; Zenaiev, O. [Deutsches Elektronensynchrotron DESY, Hamburg (Germany); Melnitchouk, W.; Sato, N. [Jefferson Lab, Newport News, VA (United States); Owens, J.F. [Florida State University, Tallahassee, FL (United States); Reya, E. [Technische Universitaet Dortmund, Institut fuer Physik, Dortmund (Germany); Vogt, A. [University of Liverpool, Department of Mathematical Sciences, Liverpool (United Kingdom)
2016-08-15
We review the present status of the determination of parton distribution functions (PDFs) in the light of the precision requirements for the LHC in Run 2 and other future hadron colliders. We provide brief reviews of all currently available PDF sets and use them to compute cross sections for a number of benchmark processes, including Higgs boson production in gluon-gluon fusion at the LHC. We show that the differences in the predictions obtained with the various PDFs are due to particular theory assumptions made in the fits of those PDFs. We discuss PDF uncertainties in the kinematic region covered by the LHC and on averaging procedures for PDFs, such as advocated by the PDF4LHC15 sets, and provide recommendations for the usage of PDF sets for theory predictions at the LHC. (orig.)
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.
Zhao, Zhijun; Liao, Rui
2011-03-01
Free-space optical (FSO) communication systems suffer from average power loss and instantaneous power fading due to the atmospheric turbulence. The channel fading probability density function (pdf) is of critical importance for FSO communication system design and evaluation. The performance and reliability of FSO communication systems can be greatly enhanced if fast-tacking devices are employed at the transmitter in order to compensate laser beam wander at the receiver aperture. The fast-tracking method is especially effective when communication distance is long. This paper studies the fading probability density functions of both fast-tracked and untracked FSO communication channels. Large-scale wave-optics simulations are conducted for both tracked and untracked lasers. In the simulations, the Kolmogorov spectrum is adopted, and it is assumed that the outer scale is infinitely large and the inner scale is negligibly small. The fading pdfs of both fast-tracked and untracked FSO channels are obtained from the simulations. Results show that the fast-tracked channel fading can be accurately modeled as gamma-distributed if receiver aperture size is smaller than the coherence radius. An analytical method is given for calculating the untracked fading pdfs of both point-like and finite-size receiver apertures from the fast-tracked fading pdf. For point-like apertures, the analytical method gives pdfs close to the well-known gamma-gamma pdfs if off-axis effects are omitted in the formulation. When off-axis effects are taken into consideration, the untracked pdfs obtained using the analytical method fit the simulation pdfs better than gamma-gamma distributions for point-like apertures, and closely fit the simulation pdfs for finite-size apertures where gamma-gamma pdfs deviate from those of the simulations significantly.
Leader, Elliot; Stamenov, Dimiter B
2010-01-01
A new combined NLO QCD analysis of the polarized inclusive and semi-inclusive DIS data is presented. In contrast to previous combined analyses, the 1/Q^2 terms (kinematic - target mass corrections, and dynamic - higher twist corrections) in the expression for the nucleon spin structure function g_1 are taken into account. The new COMPASS data are included in the analysis. The impact of the semi-inclusive data on the polarized parton densities (PDFs) and on the higher twist corrections is discussed. The new results for the PDFs are compared to both the LSS'06 PDFs, obtained from the fit to the inclusive DIS data alone, and to those obtained from the DSSV global analysis.
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.
Assumed Probability Density Functions for Shallow and Deep Convection
Directory of Open Access Journals (Sweden)
Steven K Krueger
2010-10-01
Full Text Available The assumed joint probability density function (PDF between vertical velocity and conserved temperature and total water scalars has been suggested to be a relatively computationally inexpensive and unified subgrid-scale (SGS parameterization for boundary layer clouds and turbulent moments. This paper analyzes the performance of five families of PDFs using large-eddy simulations of deep convection, shallow convection, and a transition from stratocumulus to trade wind cumulus. Three of the PDF families are based on the double Gaussian form and the remaining two are the single Gaussian and a Double Delta Function (analogous to a mass flux model. The assumed PDF method is tested for grid sizes as small as 0.4 km to as large as 204.8 km. In addition, studies are performed for PDF sensitivity to errors in the input moments and for how well the PDFs diagnose some higher-order moments. In general, the double Gaussian PDFs more accurately represent SGS cloud structure and turbulence moments in the boundary layer compared to the single Gaussian and Double Delta Function PDFs for the range of grid sizes tested. This is especially true for small SGS cloud fractions. While the most complex PDF, Lewellen-Yoh, better represents shallow convective cloud properties (cloud fraction and liquid water mixing ratio compared to the less complex Analytic Double Gaussian 1 PDF, there appears to be no advantage in implementing Lewellen-Yoh for deep convection. However, the Analytic Double Gaussian 1 PDF better represents the liquid water flux, is less sensitive to errors in the input moments, and diagnoses higher order moments more accurately. Between the Lewellen-Yoh and Analytic Double Gaussian 1 PDFs, it appears that neither family is distinctly better at representing cloudy layers. However, due to the reduced computational cost and fairly robust results, it appears that the Analytic Double Gaussian 1 PDF could be an ideal family for SGS cloud and turbulence
Energy Technology Data Exchange (ETDEWEB)
Alekhin, Sergey [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Institute for High Energy Physics, Protvino (Russian Federation); Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Moch, Sven-Olaf [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Placakyte, Ringaile [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2016-09-15
We present an update of the ABM12 PDF analysis including improved constraints due to the final version of the inclusive DIS HERA data, the Tevatron and LHC data on the W- and Z-production and those on heavy-quark production in the electron- and neutrino-induced DIS at HERA and the fixed-target experiments NOMAD and CHORUS. We also check the impact of the Tevatron and LHC top-quark production data on the PDFs and the strong coupling constant. We obtain α{sub s}(M{sub Z})=0.1145(9) and 0.1147(8) with and without the top-quark data included, respectively.
PDFs, $\\alpha_s$, and quark masses from global fits
Alekhin, S; Moch, S; Placakyte, R
2016-01-01
The strong coupling constant $\\alpha_s$ and the heavy-quark masses, $m_c$, $m_b$, $m_t$ are extracted simultaneosly with the parton distribution functions (PDFs) in the updated ABM12 fit including recent data from CERN-SPS, HERA, Tevatron, and the LHC. The values of \\begin{eqnarray} \
Molini, Annalisa; Katul, Gabriel; Porporato, Amilcare
2010-05-01
Possible linkages between climatic fluctuations in rainfall at low frequencies and local intensity fluctuations within single storms is now receiving significant attention in climate change research. To progress on a narrower scope of this problem, the cross-scale probabilistic structure of rainfall intensity records collected over time scales ranging from hours to decades at sites dominated by either convective or frontal systems is investigated. Across these sites, intermittency buildup from slow to fast time-scales is analyzed in terms of its heavy tailed and asymmetric signatures in the scale-wise evolution of rainfall probability density functions (pdfs). The analysis demonstrates that rainfall records dominated by convective storms develop heavier-tailed power law pdfs across finer scales when compared with their frontal systems counterpart. A concomitant marked asymmetry buildup also emerges across finer time scales necessitating skewed probability laws for quantifying the scale-wise evolution of rainfall pdfs. A scale-dependent probabilistic description of such fat tails, peakedness and asymmetry appearance is proposed and tested by using a modified q-Gaussian model, able to describe the scale wise evolution of rainfall pdfs in terms of the nonextensivity parameter q, a lacunarity (intermittency) correction γ and a tail asymmetry coefficient c, also functions of q.
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.
Parton distributions in the LHC era: MMHT 2014 PDFs.
Harland-Lang, L A; Martin, A D; Motylinski, P; Thorne, R S
We present LO, NLO and NNLO sets of parton distribution functions (PDFs) of the proton determined from global analyses of the available hard scattering data. These MMHT2014 PDFs supersede the 'MSTW2008' parton sets, but they are obtained within the same basic framework. We include a variety of new data sets, from the LHC, updated Tevatron data and the HERA combined H1 and ZEUS data on the total and charm structure functions. We also improve the theoretical framework of the previous analysis. These new PDFs are compared to the 'MSTW2008' parton sets. In most cases the PDFs, and the predictions, are within one standard deviation of those of MSTW2008. The major changes are the [Formula: see text] valence quark difference at small [Formula: see text] due to an improved parameterisation and, to a lesser extent, the strange quark PDF due to the effect of certain LHC data and a better treatment of the [Formula: see text] branching ratio. We compare our MMHT PDF sets with those of other collaborations; in particular with the NNPDF3.0 sets, which are contemporary with the present analysis.
Parton distributions in the LHC era: MMHT 2014 PDFs
Harland-Lang, L A; Motylinski, P; Thorne, R S
2014-01-01
We present LO, NLO and NNLO sets of parton distribution functions (PDFs) of the proton determined from global analyses of the available hard scattering data. These MMHT2014 PDFs supersede the `MSTW2008' parton sets, but are obtained within the same basic framework. We include a variety of new data sets, from the LHC, updated Tevatron data and the HERA combined H1 and ZEUS data on the total and charm structure functions. We also improve the theoretical framework of the previous analysis. These new PDFs are compared to the `MSTW2008' parton sets. Almost always the PDFs, and the predictions, are within one standard deviation of those of MSTW2008. The major changes are the $u-d$ valence quark difference at small $x$ due to an improved parameterisation and, to a lesser extent, the strange quark PDF due to the effect of some LHC data and a better treatment of the $D \\to \\mu$ branching ratio. We compare our MMHT PDF sets with those of other collaborations; in particular with the NNPDF3.0 sets, which are contemporary...
Parton distributions in the LHC era: MMHT 2014 PDFs
Harland-Lang, L. A.; Martin, A. D.; Motylinski, P.; Thorne, R. S.
2015-05-01
We present LO, NLO and NNLO sets of parton distribution functions (PDFs) of the proton determined from global analyses of the available hard scattering data. These MMHT2014 PDFs supersede the `MSTW2008' parton sets, but they are obtained within the same basic framework. We include a variety of new data sets, from the LHC, updated Tevatron data and the HERA combined H1 and ZEUS data on the total and charm structure functions. We also improve the theoretical framework of the previous analysis. These new PDFs are compared to the `MSTW2008' parton sets. In most cases the PDFs, and the predictions, are within one standard deviation of those of MSTW2008. The major changes are the valence quark difference at small due to an improved parameterisation and, to a lesser extent, the strange quark PDF due to the effect of certain LHC data and a better treatment of the branching ratio. We compare our MMHT PDF sets with those of other collaborations; in particular with the NNPDF3.0 sets, which are contemporary with the present analysis.
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...
Ossenkopf, Volker; Schneider, Nicola; Federrath, Christoph; Klessen, Ralf S
2016-01-01
Probability distribution functions (PDFs) of column densities are an established tool to characterize the evolutionary state of interstellar clouds. Using simulations, we show to what degree their determination is affected by noise, line-of-sight contamination, field selection, and the incomplete sampling in interferometric measurements. We solve the integrals that describe the convolution of a cloud PDF with contaminating sources and study the impact of missing information on the measured column density PDF. The effect of observational noise can be easily estimated and corrected for if the root mean square (rms) of the noise is known. For $\\sigma_{noise}$ values below 40\\,\\% of the typical cloud column density, $N_{peak}$, this involves almost no degradation of the accuracy of the PDF parameters. For higher noise levels and narrow cloud PDFs the width of the PDF becomes increasingly uncertain. A contamination by turbulent foreground or background clouds can be removed as a constant shield if the PDF of the c...
Vertical Overlap of Probability Density Functions of Cloud and Precipitation Hydrometeors
Ovchinnikov, M.; Lim, K. S. S.; Larson, V. E.; Wong, M.; Thayer-Calder, K.; Ghan, S. J.
2016-12-01
Coarse-resolution climate models increasingly rely on probability density functions (PDFs) to represent subgrid-scale variability of prognostic variables. While PDFs characterize the horizontal variability, a separate treatment is needed to account for the vertical structure of clouds and precipitation. When sub-columns are drawn from these PDFs for microphysics or radiation parameterizations, appropriate vertical correlations must be enforced via PDF overlap specifications. This study evaluates the representation of PDF overlap in the Subgrid Importance Latin Hypercube Sampler (SILHS) employed in the assumed PDF turbulence and cloud scheme called the Cloud Layers Unified By Binormals (CLUBB). PDF overlap in CLUBB-SILHS simulations of continental and tropical oceanic deep convection is compared with overlap of PDF of various microphysics variables in cloud-resolving model (CRM) simulations of the same cases that explicitly predict the 3D structure of cloud and precipitation fields. CRM results show that PDF overlap varies significantly between different hydrometeor types, as well as between PDFs of mass and number mixing ratios for each species, - a distinction that the current SILHS implementation does not make. Specifically, faster falling species, such as rain and graupel, exhibit significantly higher vertical coherence in their distributions than slow falling cloud liquid and ice. Development of a PDF overlap treatment linked to hydrometeor properties, such as fall speeds, in addition to the currently implemented dependency on the turbulent convective length scale will be discussed.
Energy Technology Data Exchange (ETDEWEB)
Ovchinnikov, Mikhail [Pacific Northwest National Laboratory, Richland Washington USA; Lim, Kyo-Sun Sunny [Pacific Northwest National Laboratory, Richland Washington USA; Korea Atomic Energy Research Institute, Daejeon Republic of Korea; Larson, Vincent E. [Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee Wisconsin USA; Wong, May [Pacific Northwest National Laboratory, Richland Washington USA; National Center for Atmospheric Research, Boulder Colorado USA; Thayer-Calder, Katherine [National Center for Atmospheric Research, Boulder Colorado USA; Ghan, Steven J. [Pacific Northwest National Laboratory, Richland Washington USA
2016-11-05
Coarse-resolution climate models increasingly rely on probability density functions (PDFs) to represent subgrid-scale variability of prognostic variables. While PDFs characterize the horizontal variability, a separate treatment is needed to account for the vertical structure of clouds and precipitation. When sub-columns are drawn from these PDFs for microphysics or radiation parameterizations, appropriate vertical correlations must be enforced via PDF overlap specifications. This study evaluates the representation of PDF overlap in the Subgrid Importance Latin Hypercube Sampler (SILHS) employed in the assumed PDF turbulence and cloud scheme called the Cloud Layers Unified By Binormals (CLUBB). PDF overlap in CLUBB-SILHS simulations of continental and tropical oceanic deep convection is compared with overlap of PDF of various microphysics variables in cloud-resolving model (CRM) simulations of the same cases that explicitly predict the 3D structure of cloud and precipitation fields. CRM results show that PDF overlap varies significantly between different hydrometeor types, as well as between PDFs of mass and number mixing ratios for each species, - a distinction that the current SILHS implementation does not make. In CRM simulations that explicitly resolve cloud and precipitation structures, faster falling species, such as rain and graupel, exhibit significantly higher coherence in their vertical distributions than slow falling cloud liquid and ice. These results suggest that to improve the overlap treatment in the sub-column generator, the PDF correlations need to depend on hydrometeor properties, such as fall speeds, in addition to the currently implemented dependency on the turbulent convective length scale.
The effect of LHC jet data on MSTW PDFs.
Watt, B J A; Motylinski, P; Thorne, R S
We consider the effect on LHC jet cross sections on partons distribution functions (PDFs), in particular the MSTW2008 set of PDFs. We first compare the published inclusive jet data to the predictions using MSTW2008, finding a very good description. We also use the parton distribution reweighting procedure to estimate the impact of these new data on the PDFs, finding that the combined ATLAS 2.76 and 7 TeV data, and CMS 7 TeV data have some significant impact. We then also investigate the impact of ATLAS, CMS and DØ dijet data using the same techniques. In this case we investigate the effect of using different scale choices for the NLO cross section calculation. We find that the dijet data is generally not completely compatible with the corresponding inclusive jet data, often tending to pull PDFs, particularly the gluon distribution, away from the default values. However, the effect depends on the dijet dataset used as well as the scale choice. We also note that conclusions may be affected by limiting the pull on the data luminosity chosen by the best fit, which is sometimes a number of standard deviations. Finally we include the inclusive jet data in a new PDF fit explicitly. This enables us to check the consistency of the exact result with that obtained from the reweighting procedure. There is generally good, but not full quantitative agreement. Hence, the conclusion remains that MSTW2008 PDFs already fit the published jet data well, but the central values and uncertainties are altered and improved, respectively, to a significant, but not dramatic extent by inclusion of these data.
HERAFitter - An Open Source framework to determine PDFs
Camarda, Stefano
2015-01-01
The HERAFitter project provides a framework for the determination of parton distribution functions (PDFs), and tools for assessing the impact of new data on PDFs. In this contribution, HERAFitter is used for a QCD analysis of the legacy measurements of the $W$-boson charge asymmetry and of the $Z$-boson production cross sections, performed at the Tevatron collider in Run II by the D0 and CDF collaborations. The Tevatron measurements are included in a PDF fit performed at next-to-leading order, and compared to the predictions obtained using other PDF sets from different groups. The measurements are in good agreement with NLO QCD theoretical predictions. The Tevatron data provide significant constraints on the $d$-valence quark distribution.
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).
Using Drell-Yan $A_{FB}$ to constrain PDFs
Bodek, A; Khukhunaishvili, A; Sakumoto, W
2015-01-01
We show that measurements of the forward-backward charge asymmetry ($A_{FB}(M,y)$) of Drell-Yan dilepton events produced at hadron colliders provide a new powerful tool to constrain Parton Distribution Functions (PDFs). PDF uncertainties are the dominant source of systematic error in precision measurements at hadron colliders (e.g. $\\chi^2$ values of fits to extract $\\sin^2\\theta_{eff}^{lept}(M_Z)$ from $A_{FB}(M,y)$ with different PDF replicas can be used to place additional constraints on PDFs.In turn, using these constrained PDFs significantly reduces the PDF errors in precision measurements of electroweak parameters. The measurement of the on-shell $\\sin^2\\theta_{W}=1-M_W^2/M_Z^2$ is equivalent to an indirect measurement of the W mass. The errors in this indirect measurement of the W mass are competitive with direct measurements. For example, with 200 fb$^{-1}$ at 13 TeV, the expected error in the indirect measurement of the W mass is $\\pm$9 MeV.
Probability density functions of the average and difference intensities of Friedel opposites.
Shmueli, U; Flack, H D
2010-11-01
Trigonometric series for the average (A) and difference (D) intensities of Friedel opposites were carefully rederived and were normalized to minimize their dependence on sin(theta)/lambda. Probability density functions (hereafter p.d.f.s) of these series were then derived by the Fourier method [Shmueli, Weiss, Kiefer & Wilson (1984). Acta Cryst. A40, 651-660] and their expressions, which admit any chemical composition of the unit-cell contents, were obtained for the space group P1. Histograms of A and D were then calculated for an assumed random-structure model and for 3135 Friedel pairs of a published solved crystal structure, and were compared with the p.d.f.s after the latter were scaled up to the histograms. Good agreement was obtained for the random-structure model and a qualitative one for the published solved structure. The results indicate that the residual discrepancy is mainly due to the presumed statistical independence of the p.d.f.'s characteristic function on the contributions of the interatomic vectors.
Development and evaluation of probability density functions for a set of human exposure factors
Energy Technology Data Exchange (ETDEWEB)
Maddalena, R.L.; McKone, T.E.; Bodnar, A.; Jacobson, J.
1999-06-01
The purpose of this report is to describe efforts carried out during 1998 and 1999 at the Lawrence Berkeley National Laboratory to assist the U.S. EPA in developing and ranking the robustness of a set of default probability distributions for exposure assessment factors. Among the current needs of the exposure-assessment community is the need to provide data for linking exposure, dose, and health information in ways that improve environmental surveillance, improve predictive models, and enhance risk assessment and risk management (NAS, 1994). The U.S. Environmental Protection Agency (EPA) Office of Emergency and Remedial Response (OERR) plays a lead role in developing national guidance and planning future activities that support the EPA Superfund Program. OERR is in the process of updating its 1989 Risk Assessment Guidance for Superfund (RAGS) as part of the EPA Superfund reform activities. Volume III of RAGS, when completed in 1999 will provide guidance for conducting probabilistic risk assessments. This revised document will contain technical information including probability density functions (PDFs) and methods used to develop and evaluate these PDFs. The PDFs provided in this EPA document are limited to those relating to exposure factors.
CTEQ-TEA PDFs and HERA run I+II Combined Data
Hou, Tie-Jiun; Gao, Jun; Guzzi, Marco; Huston, Joey; Nadolsky, Pavel; Pumplin, Jon; Schmidt, Carl; Stump, Daniel; Yuan, C -P
2016-01-01
We analyze the impact of the recent HERA run I+II combination of inclusive deep inelastic scattering cross-section data on the CT14 global analysis of PDFs. New PDFs at NLO and NNLO, called CT14$_{\\textrm{HERA2}}$, are obtained by a refit of the CT14 data ensembles, in which the HERA run I combined measurements are replaced by the new HERA run I+II combination. The CT14 functional parametrization of PDFs is flexible enough to allow good descriptions of different flavor combinations, so we use the same parametrization for CT14$_{\\textrm{HERA2}}$ but with an additional shape parameter for describing the strange quark PDF. We find that the HERA I+II data can be fit reasonably well, and both CT14 and CT14$_{\\textrm{HERA2}}$ PDFs can describe equally well the non-HERA data included in our global analysis. Because the CT14 and CT14$_{\\textrm{HERA2}}$ PDFs agree well within the PDF errors, we continue to recommend CT14 PDFs for the analysis of LHC Run 2 experiments.
Factorization at the LHC: From PDFs to Initial State Jets
Stewart, Iain W; Waalewijn, Wouter J
2009-01-01
We study proton-(anti)proton collisions at the LHC or Tevatron in the presence of experimental restrictions on the hadronic final state and for generic parton momentum fractions. At the scale Q of the hard interaction, factorization does not yield standard parton distribution functions (PDFs) for the initial state. The measurement restricting the hadronic final state introduces a new scale \\mu_B Xl+l- where X is restricted to have no central jets. We comment on the extension to cases where the hadronic final state contains a certain number of isolated central jets.
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.
Importance of Fragmentation Functions in Determining Polarized Parton Densities
Leader, Elliot; Stamenov, Dimiter B
2012-01-01
New fragmentation functions (FFs) are extracted from a NLO QCD fit to the preliminary COMPASS data on pion and kaon multiplicities. It is shown that the new kaon FFs are very different from those of De Florian at al. (DSS) and Hirai et al. (HKNS). The sensitivity of the extracted polarized PDFs to the new FFs is discussed.
SOMz: photometric redshift PDFs with self organizing maps and random atlas
Kind, M Carrasco
2013-01-01
In this paper we explore the applicability of the unsupervised machine learning technique of Self Organizing Maps (SOM) to estimate galaxy photometric redshift probability density functions (PDFs). This technique takes a spectroscopic training set, and maps the photometric attributes, but not the redshifts, to a two dimensional surface by using a process of competitive learning where neurons compete to more closely resemble the training data multidimensional space. The key feature of a SOM is that it retains the topology of the input set, revealing correlations between the attributes that are not easily identified. We test three different 2D topological mapping: rectangular, hexagonal, and spherical, by using data from the DEEP2 survey. We also explore different implementations and boundary conditions on the map and also introduce the idea of a random atlas where a large number of different maps are created and their individual predictions are aggregated to produce a more robust photometric redshift PDF. We a...
Kind, M Carrasco
2013-01-01
With the growth of large photometric surveys, accurately estimating photometric redshifts, preferably as a probability density function (PDF), and fully understanding the implicit systematic uncertainties in this process has become increasingly important. In this paper, we present a new, publicly available, parallel, machine learning algorithm that generates photometric redshift PDFs by using prediction trees and random forest techniques, which we have named TPZ. This new algorithm incorporates measurement errors into the calculation while also dealing efficiently with missing values in the data. In addition, our implementation of this algorithm provides supplementary information regarding the data being analyzed, including unbiased estimates of the accuracy of the technique without resorting to a validation data set, identification of poor photometric redshift areas within the parameter space occupied by the spectroscopic training data, a quantification of the relative importance of the variables used to con...
Institute of Scientific and Technical Information of China (English)
Hong WANG; Hong YUE
2003-01-01
This paper presents a novel approach to detect and diagnose faults in the dynanmic part of a chis of stochastic sys-tems. the Such a group of systems are subjected to a set of crisp inputs but the outputs considered are the measurable probability density functions (PDFs) of the system output, rather than thie system output alone. A new approximation model is developed for the output probability density functions so that the dynamic part of the system is decoupled fron the output probability density functions. A nonlinear adaptive observer is constructed to detect and diagnose the fault in the dynamic part of the system. Convergency analysis is perfomed for the error dynamics raised from the fault detection and diagnosis phase and an applicability study on the detection and diagnosis of the unexpected changes in the 2D grmmage distributions in a paper forming process is included.
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.
Evolving Molecular Cloud Structure and the Column Density Probability Distribution Function
Ward, Rachel L; Sills, Alison
2014-01-01
The structure of molecular clouds can be characterized with the probability distribution function (PDF) of the mass surface density. In particular, the properties of the distribution can reveal the nature of the turbulence and star formation present inside the molecular cloud. In this paper, we explore how these structural characteristics evolve with time and also how they relate to various cloud properties as measured from a sample of synthetic column density maps of molecular clouds. We find that, as a cloud evolves, the peak of its column density PDF will shift to surface densities below the observational threshold for detection, resulting in an underlying lognormal distribution which has been effectively lost at late times. Our results explain why certain observations of actively star-forming, dynamically older clouds, such as the Orion molecular cloud, do not appear to have any evidence of a lognormal distribution in their column density PDFs. We also study the evolution of the slope and deviation point ...
Density Functionals of Chemical Bonding
Directory of Open Access Journals (Sweden)
Mihai V. Putz
2008-06-01
Full Text Available The behavior of electrons in general many-electronic systems throughout the density functionals of energy is reviewed. The basic physico-chemical concepts of density functional theory are employed to highlight the energy role in chemical structure while its extended influence in electronic localization function helps in chemical bonding understanding. In this context the energy functionals accompanied by electronic localization functions may provide a comprehensive description of the global-local levels electronic structures in general and of chemical bonds in special. Becke-Edgecombe and authorÃ¢Â€Â™s Markovian electronic localization functions are discussed at atomic, molecular and solid state levels. Then, the analytical survey of the main workable kinetic, exchange, and correlation density functionals within local and gradient density approximations is undertaken. The hierarchy of various energy functionals is formulated by employing both the parabolic and statistical correlation degree of them with the electronegativity and chemical hardness indices by means of quantitative structure-property relationship (QSPR analysis for basic atomic and molecular systems.
Extended Parameterisations for MSTW PDFs and their effect on Lepton Charge Asymmetry from W Decays
Martin, A D; Stirling, W J; Thorne, R S; Watt, B J A; Watt, G
2012-01-01
We investigate the effect of extending the standard MSTW parameterisation of input parton distribution functions (PDFs) using Chebyshev polynomials. We find evidence that, at most, four powers in the polynomial are sufficient for extremely high precision. Applying this to valence and sea quarks we find an improvement in the global fit, but a significant change only in the small-$x$ valence up-quark PDF, $u_V$. We investigate the effect of also extending, and making more flexible, the `nuclear' correction to deuteron structure functions. The extended `Chebyshev' parameterisation results in an improved stability in the deuteron corrections that are required for the best fit to the `global' data. The resulting PDFs have a significantly, but not dramatically, altered valence down-quark distribution, $d_V$. For the extended set of MSTW PDFs, their uncertainties can be obtained using 23, rather than the usual 20, orthogonal `uncertainty' eigenvectors. Since the dominant effect is on the valence quarks, we present a...
Drell-Yan measurement at COMPASS: a place to test the TMD PDFs universality
Andrieux, Vincent
2017-01-01
For the first time ever, the COMPASS experiment (CERN, SPS) collected in 2015 Drell-Yan (DY) data using a 190 GeV/ c pion beam on a transversely polarized NH3 target. The azimuthal modulations of the DY cross-section give access to the set of transverse momentum dependent (TMD) parton distribution functions (PDFs), which describe the spin structure of the nucleon. Those PDFs were already measured in semi-inclusive deep inelastic scattering (SIDIS) by several experiments and especially COMPASS, which dedicated several campaigns between 2002 and 2010 to measure spin (in)dependent azimuthal asymmetries using a 160 GeV/ c polarized muon beam on a transversely polarized 6LiD or NH3 target. A key interest of extracting those TMD PDFs from different processes is to check the universality and the process-dependent features of TMD PDFs. In this aim, COMPASS is a unique place to test the predicted sign-change of the TMD PDFs using a similar experimental setup and comparable kinematic domain. The main focus of this talk will be set on the physics aspects of the COMPASS polarized Drell-Yan program and related SIDIS results. on behalf of the COMPASS collaboration.
Harland-Lang, L A; Thorne, R S
2016-01-01
We briefly discuss some of the developments since the publication of the MMHT14 parton distributions. In particular we explore the impact of recent LHC data for $W^\\pm,Z$ and $t\\bar{t}$ production, and perform a preliminary new analysis including these data. In this re-fit (which we tentatively call `MMHT16') there are few changes of significance in the central values of the PDFs, but some data reduce the uncertainties, mainly in the strange and valence quark distributions. We find that an extended $\\bar{d}-\\bar{u}$ parametrization only leads to minor changes, with the difference going to zero as $x \\to 0$. We comment on the determination of the photon PDF.
Impact of ATLAS measurements on PDFs
Directory of Open Access Journals (Sweden)
Orlando Nicola
2015-01-01
Full Text Available A review of the ATLAS measurements sensitive to parton distribution functions is presented. The analyses use proton–proton collision data at center–of–mass–energy √s = 7 TeV collected at the Large Hadron Collider between April and November 2011. When included in QCD fits, the ATLAS data allow for improving the experimental constraints on the gluon and strange–quark parton density functions of the proton.
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
Wilson Lines off the Light-cone in TMD PDFs
Mulders, P J
2014-01-01
Transverse Momentum Dependent (TMD) parton distribution functions (PDFs) also take into account the transverse momentum ($p_T$) of the partons. The $p_T$-integrated analogues can be linked directly to quark and gluon matrix elements using the operator product expansion in QCD, involving operators of definite twist. TMDs also involve operators of higher twist, which are not suppressed by powers of the hard scale, however. Taking into account gauge links that no longer are along the light-cone, one finds that new distribution functions arise. They appear at leading order in the description of azimuthal asymmetries in high-energy scattering processes. In analogy to the collinear operator expansion, we define a universal set of TMDs of definite rank and point out the importance for phenomenology.
Nuclear PDFs in the beginning of the LHC era
Paukkunen, Hannu
2014-01-01
The status of the global fits of nuclear parton distributions (nPDFs) is reviewed. In addition to comparing the contemporary analyses of nPDFs, difficulties and controversies posed by the neutrino-nucleus deeply inelastic scattering data is overviewed. At the end, the first dijet data from the LHC proton+lead collisions is briefly discussed.
Nuclear PDFs in the beginning of the LHC era
Energy Technology Data Exchange (ETDEWEB)
Paukkunen, Hannu, E-mail: hannu.paukkunen@jyu.fi [Department of Physics, University of Jyväskylä, P.O. Box 35, FI-40014 (Finland); Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, FI-00014 (Finland)
2014-06-15
The status of the global fits of nuclear parton distributions (nPDFs) is reviewed. In addition to comparing the contemporary analyses of nPDFs, difficulties and controversies posed by the neutrino–nucleus deeply inelastic scattering data is overviewed. At the end, the first dijet data from the LHC proton+lead collisions are briefly discussed.
Robust functional statistics applied to Probability Density Function shape screening of sEMG data.
Boudaoud, S; Rix, H; Al Harrach, M; Marin, F
2014-01-01
Recent studies pointed out possible shape modifications of the Probability Density Function (PDF) of surface electromyographical (sEMG) data according to several contexts like fatigue and muscle force increase. Following this idea, criteria have been proposed to monitor these shape modifications mainly using High Order Statistics (HOS) parameters like skewness and kurtosis. In experimental conditions, these parameters are confronted with small sample size in the estimation process. This small sample size induces errors in the estimated HOS parameters restraining real-time and precise sEMG PDF shape monitoring. Recently, a functional formalism, the Core Shape Model (CSM), has been used to analyse shape modifications of PDF curves. In this work, taking inspiration from CSM method, robust functional statistics are proposed to emulate both skewness and kurtosis behaviors. These functional statistics combine both kernel density estimation and PDF shape distances to evaluate shape modifications even in presence of small sample size. Then, the proposed statistics are tested, using Monte Carlo simulations, on both normal and Log-normal PDFs that mimic observed sEMG PDF shape behavior during muscle contraction. According to the obtained results, the functional statistics seem to be more robust than HOS parameters to small sample size effect and more accurate in sEMG PDF shape screening applications.
Nuclear PDFs at NLO - status report and review of the EPS09 results
Energy Technology Data Exchange (ETDEWEB)
Eskola, K.J. [Department of Physics, P.O. Box 35, FI-40014 University of Jyvaeskylae (Finland); Helsinki Institute of Physics, P.O. Box 64, FI-00014 University of Helsinki (Finland); Paukkunen, H.; Salgado, C.A. [Departamento de Fisica de Particulas and IGFAE, Universidade de Santiago de Compostela (Spain)
2011-04-01
We review the current status of the global DGLAP analysis of nuclear parton distribution functions, nPDFs, focusing on the recent EPS09 analysis [K.J. Eskola, H. Paukkunen, C.A. Salgado, JHEP 0904 (2009) 065. [ (arXiv:0902.4154 [hep-ph])
Nuclear PDFs at NLO - status report and review of the EPS09 results
Eskola, K. J.; Paukkunen, H.; Salgado, C. A.
2011-04-01
We review the current status of the global DGLAP analysis of nuclear parton distribution functions, nPDFs, focusing on the recent EPS09 analysis [K.J. Eskola, H. Paukkunen, C.A. Salgado, JHEP 0904 (2009) 065. [ arXiv:0902.4154 [hep-ph
Lussana, C.
2013-04-01
The presented work focuses on the investigation of gridded daily minimum (TN) and maximum (TX) temperature probability density functions (PDFs) with the intent of both characterising a region and detecting extreme values. The empirical PDFs estimation procedure has been realised using the most recent years of gridded temperature analysis fields available at ARPA Lombardia, in Northern Italy. The spatial interpolation is based on an implementation of Optimal Interpolation using observations from a dense surface network of automated weather stations. An effort has been made to identify both the time period and the spatial areas with a stable data density otherwise the elaboration could be influenced by the unsettled station distribution. The PDF used in this study is based on the Gaussian distribution, nevertheless it is designed to have an asymmetrical (skewed) shape in order to enable distinction between warming and cooling events. Once properly defined the occurrence of extreme events, it is possible to straightforwardly deliver to the users the information on a local-scale in a concise way, such as: TX extremely cold/hot or TN extremely cold/hot.
Density functional theory: Foundations reviewed
Energy Technology Data Exchange (ETDEWEB)
Kryachko, Eugene S., E-mail: eugene.kryachko@ulg.ac.be [Bogolyubov Institute for Theoretical Physics, Kiev, 03680 (Ukraine); Ludeña, Eduardo V., E-mail: popluabe@yahoo.es [Centro de Química, Instituto Venezolano de Investigaciones Científicas, IVIC, Apartado 21827, Caracas 1020-A (Venezuela, Bolivarian Republic of); Prometheus Program, Senescyt (Ecuador); Grupo Ecuatoriano para el Estudio Experimental y Teórico de Nanosistemas, GETNano, USFQ, N104-E, Quito (Ecuador); Escuela Politécnica Superior del Litoral, ESPOL, Guayaquil (Ecuador)
2014-11-10
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
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.
Rebola, João L.; Cartaxo, Adolfo V. T.
The influence of the concatenation of arbitrary optical multiplexers/demultiplexers (MUX/DEMUXs) on the probability density function (PDF) of the output current of a transparent optical network is assessed. All PDF results obtained analytically are compared with estimates from Monte Carlo simulation and an excellent agreement is achieved. The non-Gaussian behavior of the PDFs, previously reported by other authors for square-law detectors, is significantly enhanced with the number of nodes increase due to the noise accumulation along the cascade of MUX/DEMUXs. The increase of the MUX/DEMUXs bandwidth and detuning also enhances the PDFs non-Gaussian behavior. The PDF shape variation with the detuning depends strongly on the number of nodes. Explanations for the Gaussian approximation (GA) accuracy on the assessment of the performance of a concatenation of optical MUX/DEMUXs are also provided. For infinite extinction ratio and tuned MUX/DEMUXs, the GA error probabilities are, in general, pessimistic, due to the inaccurate estimation of the error probability for both bits. For low extinction ratio, the GA is very accurate due to a balance between the error probabilities estimated for the bits "1" and "0." With the detuning increase, the GA estimates can become optimistic.
Filtered density function approach for reactive transport in groundwater
Suciu, Nicolae; Schüler, Lennart; Attinger, Sabine; Knabner, Peter
2016-04-01
Spatial filtering may be used in coarse-grained simulations (CGS) of reactive transport in groundwater, similar to the large eddy simulations (LES) in turbulence. The filtered density function (FDF), stochastically equivalent to a probability density function (PDF), provides a statistical description of the sub-grid, unresolved, variability of the concentration field. Besides closing the chemical source terms in the transport equation for the mean concentration, like in LES-FDF methods, the CGS-FDF approach aims at quantifying the uncertainty over the whole hierarchy of heterogeneity scales exhibited by natural porous media. Practically, that means estimating concentration PDFs on coarse grids, at affordable computational costs. To cope with the high dimensionality of the problem in case of multi-component reactive transport and to reduce the numerical diffusion, FDF equations are solved by particle methods. But, while trajectories of computational particles are modeled as stochastic processes indexed by time, the concentration's heterogeneity is modeled as a random field, with multi-dimensional, spatio-temporal sets of indices. To overcome this conceptual inconsistency, we consider FDFs/PDFs of random species concentrations weighted by conserved scalars and we show that their evolution equations can be formulated as Fokker-Planck equations describing stochastically equivalent processes in concentration-position spaces. Numerical solutions can then be approximated by the density in the concentration-position space of an ensemble of computational particles governed by the associated Itô equations. Instead of sequential particle methods we use a global random walk (GRW) algorithm, which is stable, free of numerical diffusion, and practically insensitive to the increase of the number of particles. We illustrate the general FDF approach and the GRW numerical solution for a reduced complexity problem consisting of the transport of a single scalar in groundwater
Accurate photometric redshift probability density estimation - method comparison and application
Rau, Markus Michael; Brimioulle, Fabrice; Frank, Eibe; Friedrich, Oliver; Gruen, Daniel; Hoyle, Ben
2015-01-01
We introduce an ordinal classification algorithm for photometric redshift estimation, which vastly improves the reconstruction of photometric redshift probability density functions (PDFs) for individual galaxies and galaxy samples. As a use case we apply our method to CFHTLS galaxies. The ordinal classification algorithm treats distinct redshift bins as ordered values, which improves the quality of photometric redshift PDFs, compared with non-ordinal classification architectures. We also propose a new single value point estimate of the galaxy redshift, that can be used to estimate the full redshift PDF of a galaxy sample. This method is competitive in terms of accuracy with contemporary algorithms, which stack the full redshift PDFs of all galaxies in the sample, but requires orders of magnitudes less storage space. The methods described in this paper greatly improve the log-likelihood of individual object redshift PDFs, when compared with a popular Neural Network code (ANNz). In our use case, this improvemen...
Dijets in p+Pb collisions and their quantitative constraints for nuclear PDFs
Paukkunen, Hannu; Salgado, Carlos
2014-01-01
We present a perturbative QCD analysis concerning the production of high-pT dijets in p+Pb collisions at the LHC. The next-to-leading order corrections, scale variations and free-proton PDF uncertainties are found to have only a relatively small influence on the normalized dijet rapidity distributions. Interestingly, however, these novel observables prove to retain substantial sensitivity to the nuclear effects in the PDFs. Especially, they serve as a more robust probe of the nuclear gluon densities at $x>0.01$, than e.g. the inclusive hadron production. We confront our calculations with the recent data by the CMS collaboration. These preliminary data lend striking support to the gluon antishadowing similar to that in the EPS09 nuclear PDFs.
Dijets in p + Pb collisions and their quantitative constraints for nuclear PDFs
Energy Technology Data Exchange (ETDEWEB)
Paukkunen, Hannu, E-mail: hannu.paukkunen@jyu.fi [Department of Physics, University of Jyväskylä, P.O. Box 35, FI-40014 University of Jyväskylä (Finland); Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, FI-00014 (Finland); Eskola, Kari J., E-mail: kari.eskola@jyu.fi [Department of Physics, University of Jyväskylä, P.O. Box 35, FI-40014 University of Jyväskylä (Finland); Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, FI-00014 (Finland); Salgado, Carlos, E-mail: carlos.salgado@usc.es [Departamento de Física de Partículas and IGFAE, Universidade de Santiago de Compostela, E-15782 Galicia (Spain)
2014-11-15
We present a perturbative QCD analysis concerning the production of high-pT dijets in p + Pb collisions at the LHC. The next-to-leading order corrections, scale variations and free-proton PDF uncertainties are found to have only a relatively small influence on the normalized dijet rapidity distributions. Interestingly, however, these novel observables prove to retain substantial sensitivity to the nuclear effects in the PDFs. Especially, they serve as a more robust probe of the nuclear gluon densities at x>0.01, than e.g. the inclusive hadron production. We confront our calculations with the recent data by the CMS Collaboration. These preliminary data lend striking support to the gluon antishadowing similar to that in the EPS09 nuclear PDFs.
Sensitivities to PDFs in parton shower MC generator reweighting and tuning
Buckley, Andy
2016-01-01
Evaluating parton density systematic uncertainties in Monte~Carlo event generator predictions has long been achieved by reweighting between the original and systematic PDFs for the initial state configurations of the individual simulated events. This weighting is now pre-emptively performed in many generators, providing convenient weight factors for PDF and scale systematics -- including for NLO calculations where counterterms make the weight calculation complex. This note attempts a pedagogical discussion and empirical study of the consequences of neglecting the effects of PDF variations on the beyond-fixed-order components of MC models, and the implications for parton shower & MPI tuning strategies. We confirm that the effects are usually small, for well-understood reasons, and discuss the connected issue of consistent treatment of the strong coupling between PDFs and parton showers, where motivations from physical principles and the need for good data-description are not always well-aligned.
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...
Sadeh, Iftach; Lahav, Ofer
2015-01-01
We present ANNz2, a new implementation of the public software for photometric redshift (photo-z) estimation of Collister and Lahav (2004). Large photometric galaxy surveys are important for cosmological studies, and in particular for characterizing the nature of dark energy. The success of such surveys greatly depends on the ability to measure photo-zs, based on limited spectral data. ANNz2 utilizes multiple machine learning methods, such as artificial neural networks, boosted decision/regression trees and k-nearest neighbours. The objective of the algorithm is to dynamically optimize the performance of the photo-z estimation, and to properly derive the associated uncertainties. In addition to single-value solutions, the new code also generates full probability density functions (PDFs) in two different ways. In addition, estimators are incorporated to mitigate possible problems of spectroscopic training samples which are not representative or are incomplete. ANNz2 is also adapted to provide optimized solution...
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
Nuclear PDFs at NLO - status report and review of the EPS09 results
Eskola, K J; Salgado, C A
2010-01-01
We review the current status of the global DGLAP analysis of nuclear parton distribution functions, nPDFs, focusing on the recent EPS09 analysis, whose output, EPS09NLO, is the best-constrained NLO nPDF set on the market. Collinear factorization is found to work very well in the kinematical region studied. With the error sets released in the EPS09 package one can compute how the nPDF-related uncertainties propagate into factorizable nuclear hard-process cross sections. A comparison with the other existing NLO nPDF sets is shown, and the BRAHMS forward-$\\eta$ hadron data from d+Au collisions are discussed in the light of the EPS09 nPDFs and their error sets.
A first unbiased global determination of polarized PDFs and their uncertainties
Nocera, Emanuele R; Forte, Stefano; Ridolfi, Giovanni; Rojo, Juan
2014-01-01
We present a first global determination of spin-dependent parton distribution functions (PDFs) and their uncertainties using the NNPDF methodology: NNPDFpol1.1. Longitudinally polarized deep-inelastic scattering data, already used for the previous NNPDFpol1.0 PDF set, are supplemented with the most recent polarized hadron collider data for inclusive jet and $W$ boson production from the STAR and PHENIX experiments at RHIC, and with open-charm production data from the COMPASS experiment, thereby allowing for a separate determination of the polarized quark and anti-quark PDFs, and an improved determination of the medium- and large-$x$ polarized gluon PDF. We study the phenomenological implications of the NNPDFpol1.1 set, and we provide predictions for the longitudinal double-spin asymmetry for semi-inclusive pion production at RHIC.
Burton, Robin R.
2010-04-01
Three-dimensional (3D) Light Detection And Ranging (LIDAR) systems designed for foliage penetration can produce good bare-earth products in medium to medium-heavy obscuration environments, but product creation becomes increasingly more difficult as the obscuration level increases. A prior knowledge of the obscuration environment over large areas is hard to obtain. The competing factors of area coverage rate and product quality are difficult to balance. Ground-based estimates of obscuration levels are labor intensive and only capture a small portion of the area of interest. Estimates of obscuration levels derived from airborne data require that the area of interest has been collected previously. Recently, there has been a focus on lacunarity (scale dependent measure of translational invariance) to quantify the gap structure of canopies. While this approach is useful, it needs to be evaluated relative to the size of the instantaneous field-of-view (IFOV) of the system under consideration. In this paper, the author reports on initial results to generate not just average obscuration values from overhead canopy photographs, but to generate obscuration probability density functions (PDFs) for both gimbaled linear-mode and geiger-mode airborne LIDAR. In general, gimbaled linear-mode (LM) LIDAR collects data with higher signal-to-noise (SNR), but is limited to smaller areas and cannot collect at higher altitudes. Conversely, geiger-mode (GM) LIDAR has a much lower SNR, but is capable of higher area rates and collecting data at higher altitudes. To date, geiger-mode LIDAR obscurant penetration theory has relied on a single obscuration value, but recent work has extended it to use PDFs1. Whether or not the inclusion of PDFs significantly changes predicted results and more closely matches actual results awaits the generation of PDFs over specific ground truth targets and comparison to actual collections of those ground truth targets. Ideally, examination of individual PDFs
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.
Viironen, K.; Marín-Franch, A.; López-Sanjuan, C.; Varela, J.; Chaves-Montero, J.; Cristóbal-Hornillos, D.; Molino, A.; Fernández-Soto, A.; Vilella-Rojo, G.; Ascaso, B.; Cenarro, A. J.; Cerviño, M.; Cepa, J.; Ederoclite, A.; Márquez, I.; Masegosa, J.; Moles, M.; Oteo, I.; Pović, M.; Aguerri, J. A. L.; Alfaro, E.; Aparicio-Villegas, T.; Benítez, N.; Broadhurst, T.; Cabrera-Caño, J.; Castander, J. F.; Del Olmo, A.; González Delgado, R. M.; Husillos, C.; Infante, L.; Martínez, V. J.; Perea, J.; Prada, F.; Quintana, J. M.
2015-04-01
Context. Most observational results on the high redshift restframe UV-bright galaxies are based on samples pinpointed using the so-called dropout technique or Ly-α selection. However, the availability of multifilter data now allows the dropout selections to be replaced by direct methods based on photometric redshifts. In this paper we present the methodology to select and study the population of high redshift galaxies in the ALHAMBRA survey data. Aims: Our aim is to develop a less biased methodology than the traditional dropout technique to study the high redshift galaxies in ALHAMBRA and other multifilter data. Thanks to the wide area ALHAMBRA covers, we especially aim at contributing to the study of the brightest, least frequent, high redshift galaxies. Methods: The methodology is based on redshift probability distribution functions (zPDFs). It is shown how a clean galaxy sample can be obtained by selecting the galaxies with high integrated probability of being within a given redshift interval. However, reaching both a complete and clean sample with this method is challenging. Hence, a method to derive statistical properties by summing the zPDFs of all the galaxies in the redshift bin of interest is introduced. Results: Using this methodology we derive the galaxy rest frame UV number counts in five redshift bins centred at z = 2.5,3.0,3.5,4.0, and 4.5, being complete up to the limiting magnitude at mUV(AB) = 24, where mUV refers to the first ALHAMBRA filter redwards of the Ly-α line. With the wide field ALHAMBRA data we especially contribute to the study of the brightest ends of these counts, accurately sampling the surface densities down to mUV(AB) = 21-22. Conclusions: We show that using the zPDFs it is easy to select a very clean sample of high redshift galaxies. We also show that it is better to do statistical analysis of the properties of galaxies using a probabilistic approach, which takes into account both the incompleteness and contamination issues in a
Boslough, M.
2011-12-01
Climate-related uncertainty is traditionally presented as an error bar, but it is becoming increasingly common to express it in terms of a probability density function (PDF). PDFs are a necessary component of probabilistic risk assessments, for which simple "best estimate" values are insufficient. Many groups have generated PDFs for climate sensitivity using a variety of methods. These PDFs are broadly consistent, but vary significantly in their details. One axiom of the verification and validation community is, "codes don't make predictions, people make predictions." This is a statement of the fact that subject domain experts generate results using assumptions within a range of epistemic uncertainty and interpret them according to their expert opinion. Different experts with different methods will arrive at different PDFs. For effective decision support, a single consensus PDF would be useful. We suggest that market methods can be used to aggregate an ensemble of opinions into a single distribution that expresses the consensus. Prediction markets have been shown to be highly successful at forecasting the outcome of events ranging from elections to box office returns. In prediction markets, traders can take a position on whether some future event will or will not occur. These positions are expressed as contracts that are traded in a double-action market that aggregates price, which can be interpreted as a consensus probability that the event will take place. Since climate sensitivity cannot directly be measured, it cannot be predicted. However, the changes in global mean surface temperature are a direct consequence of climate sensitivity, changes in forcing, and internal variability. Viable prediction markets require an undisputed event outcome on a specific date. Climate-related markets exist on Intrade.com, an online trading exchange. One such contract is titled "Global Temperature Anomaly for Dec 2011 to be greater than 0.65 Degrees C." Settlement is based
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.
Chowdhury, Snehaunshu
2017-01-23
In this study, we demonstrate the use of a scanning mobility particle sizer (SMPS) as an effective tool to measure the probability density functions (PDFs) of soot nanoparticles in turbulent flames. Time-averaged soot PDFs necessary for validating existing soot models are reported at intervals of ∆x/D∆x/D = 5 along the centerline of turbulent, non-premixed, C2H4/N2 flames. The jet exit Reynolds numbers of the flames investigated were 10,000 and 20,000. A simplified burner geometry based on a published design was chosen to aid modelers. Soot was sampled directly from the flame using a sampling probe with a 0.5-mm diameter orifice and diluted with N2 by a two-stage dilution process. The overall dilution ratio was not evaluated. An SMPS system was used to analyze soot particle concentrations in the diluted samples. Sampling conditions were optimized over a wide range of dilution ratios to eliminate the effect of agglomeration in the sampling probe. Two differential mobility analyzers (DMAs) with different size ranges were used separately in the SMPS measurements to characterize the entire size range of particles. In both flames, the PDFs were found to be mono-modal in nature near the jet exit. Further downstream, the profiles were flatter with a fall-off at larger particle diameters. The geometric mean of the soot size distributions was less than 10 nm for all cases and increased monotonically with axial distance in both flames.
The HI Probability Distribution Function and the Atomic-to-Molecular Transition in Molecular Clouds
Imara, Nia
2016-01-01
We characterize the column density probability distributions functions (PDFs) of the atomic hydrogen gas, HI, associated with seven Galactic molecular clouds (MCs). We use 21 cm observations from the Leiden/Argentine/Bonn Galactic HI Survey to derive column density maps and PDFs. We find that the peaks of the HI PDFs occur at column densities ranging from ~1-2$\\times 10^{21}$ cm$^2$ (equivalently, ~0.5-1 mag). The PDFs are uniformly narrow, with a mean dispersion of $\\sigma_{HI}\\approx 10^{20}$ cm$^2$ (~0.1 mag). We also investigate the HI-to-H$_2$ transition towards the cloud complexes and estimate HI surface densities ranging from 7-16 $M_\\odot$ pc$^{-2}$ at the transition. We propose that the HI PDF is a fitting tool for identifying the HI-to-H$_2$ transition column in Galactic MCs.
The H I Probability Distribution Function and the Atomic-to-molecular Transition in Molecular Clouds
Imara, Nia; Burkhart, Blakesley
2016-10-01
We characterize the column-density probability distribution functions (PDFs) of the atomic hydrogen gas, H i, associated with seven Galactic molecular clouds (MCs). We use 21 cm observations from the Leiden/Argentine/Bonn Galactic H i Survey to derive column-density maps and PDFs. We find that the peaks of the H i PDFs occur at column densities in the range ˜1-2 × 1021 {{cm}}-2 (equivalently, ˜0.5-1 mag). The PDFs are uniformly narrow, with a mean dispersion of {σ }{{H}{{I}}}≈ {10}20 {{cm}}-2 (˜0.1 mag). We also investigate the H i-to-H2 transition toward the cloud complexes and estimate H i surface densities ranging from 7 to 16 {M}⊙ {{pc}}-2 at the transition. We propose that the H i PDF is a fitting tool for identifying the H i-to-H2 transition column in Galactic MCs.
A multiconfigurational hybrid density-functional theory
DEFF Research Database (Denmark)
Sharkas, Kamal; Savin, Andreas; Jensen, Hans Jørgen Aagaard
2012-01-01
We propose a multiconfigurational hybrid density-functional theory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the electron-electron interaction. This gives a straightforward extension ...
A multiconfigurational hybrid density-functional theory
DEFF Research Database (Denmark)
Sharkas, Kamal; Savin, Andreas; Jensen, Hans Jørgen Aagaard
2012-01-01
We propose a multiconfigurational hybrid density-functional theory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the electron-electron interaction. This gives a straightforward extension ...
Magnetic fields and density functional theory
Energy Technology Data Exchange (ETDEWEB)
Salsbury Jr., Freddie [Univ. of California, Berkeley, CA (United States)
1999-02-01
A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.
A Tryst With Density: Walter Kohn and Density Functional Theory
Indian Academy of Sciences (India)
Shobhana Narasimhan
2017-08-01
Walter Kohn transformed theoretical chemistry and solid statephysics with his development of density functional theory, forwhich he was awarded the Nobel Prize. This article tries toexplain, in simple terms, why this was an important advancein the field, and to describe precisely what it was that he (togetherwith his collaborators Pierre Hohenberg and Lu JeuSham) achieved.
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.
Implication of CMS data on photon PDFs
Ababekri, Mamut; Isaacson, Joshua; Schmidt, Carl; Yuan, C -P
2016-01-01
Through the use of the CMS measurement of $W$-pair production via photon fusion, constraints on the photon parton distribution function are able to be placed on those from the CTEQ, MRST, and NNPDF collaborations. Furthermore, this data is able to rule out one of the MRST parton distribution sets, and the central prediction from NNPDF. After the announcement of the diphoton excess seen by both ATLAS and CMS, there was a proposal that this excess could be explained by a scalar produced via photon fusion. With the new constraints from the CMS data, the relationship between the total width and the branching ratio for such an object is updated to reflect the newly allowed region.
Unfolding the laws of star formation: the density distribution of molecular clouds.
Kainulainen, Jouni; Federrath, Christoph; Henning, Thomas
2014-04-11
The formation of stars shapes the structure and evolution of entire galaxies. The rate and efficiency of this process are affected substantially by the density structure of the individual molecular clouds in which stars form. The most fundamental measure of this structure is the probability density function of volume densities (ρ-PDF), which determines the star formation rates predicted with analytical models. This function has remained unconstrained by observations. We have developed an approach to quantify ρ-PDFs and establish their relation to star formation. The ρ-PDFs instigate a density threshold of star formation and allow us to quantify the star formation efficiency above it. The ρ-PDFs provide new constraints for star formation theories and correctly predict several key properties of the star-forming interstellar medium.
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.
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.
Relativistic density functional for nuclear structure
2016-01-01
This book aims to provide a detailed introduction to the state-of-the-art covariant density functional theory, which follows the Lorentz invariance from the very beginning and is able to describe nuclear many-body quantum systems microscopically and self-consistently. Covariant density functional theory was introduced in nuclear physics in the 1970s and has since been developed and used to describe the diversity of nuclear properties and phenomena with great success. In order to provide an advanced and updated textbook of covariant density functional theory for graduate students and nuclear physics researchers, this book summarizes the enormous amount of material that has accumulated in the field of covariant density functional theory over the last few decades as well as the latest developments in this area. Moreover, the book contains enough details for readers to follow the formalism and theoretical results, and provides exhaustive references to explore the research literature.
Nuclear Energy Density Functional for KIDS
Gil, Hana; Hyun, Chang Ho; Park, Tae-Sun; Oh, Yongseok
2016-01-01
The density functional theory (DFT) is based on the existence and uniqueness of a universal functional $E[\\rho]$, which determines the dependence of the total energy on single-particle density distributions. However, DFT says nothing about the form of the functional. Our strategy is to first look at what we know, from independent considerations, about the analytical density dependence of the energy of nuclear matter and then, for practical applications, to obtain an appropriate density-dependent effective interaction by reverse engineering. In a previous work on homogeneous matter, we identified the most essential terms to include in our "KIDS" functional, named after the early-stage participating institutes. We now present first results for finite nuclei, namely the energies and radii of $^{16,28}$O, $^{40,60}$Ca.
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.
An unbiased Hessian representation for Monte Carlo PDFs
Energy Technology Data Exchange (ETDEWEB)
Carrazza, Stefano; Forte, Stefano [Universita di Milano, TIF Lab, Dipartimento di Fisica, Milan (Italy); INFN, Sezione di Milano (Italy); Kassabov, Zahari [Universita di Milano, TIF Lab, Dipartimento di Fisica, Milan (Italy); Universita di Torino, Dipartimento di Fisica, Turin (Italy); INFN, Sezione di Torino (Italy); Latorre, Jose Ignacio [Universitat de Barcelona, Departament d' Estructura i Constituents de la Materia, Barcelona (Spain); Rojo, Juan [University of Oxford, Rudolf Peierls Centre for Theoretical Physics, Oxford (United Kingdom)
2015-08-15
We develop a methodology for the construction of a Hessian representation of Monte Carlo sets of parton distributions, based on the use of a subset of the Monte Carlo PDF replicas as an unbiased linear basis, and of a genetic algorithm for the determination of the optimal basis. We validate the methodology by first showing that it faithfully reproduces a native Monte Carlo PDF set (NNPDF3.0), and then, that if applied to Hessian PDF set (MMHT14) which was transformed into a Monte Carlo set, it gives back the starting PDFs with minimal information loss. We then show that, when applied to a large Monte Carlo PDF set obtained as combination of several underlying sets, the methodology leads to a Hessian representation in terms of a rather smaller set of parameters (MC-H PDFs), thereby providing an alternative implementation of the recently suggested Meta-PDF idea and a Hessian version of the recently suggested PDF compression algorithm (CMC-PDFs). The mc2hessian conversion code is made publicly available together with (through LHAPDF6) a Hessian representations of the NNPDF3.0 set, and the MC-H PDF set. (orig.)
An Unbiased Hessian Representation for Monte Carlo PDFs
Carrazza, Stefano; Kassabov, Zahari; Latorre, Jose Ignacio; Rojo, Juan
2015-01-01
We develop a methodology for the construction of a Hessian representation of Monte Carlo sets of parton distributions, based on the use of a subset of the Monte Carlo PDF replicas as an unbiased linear basis, and of a genetic algorithm for the determination of the optimal basis. We validate the methodology by first showing that it faithfully reproduces a native Monte Carlo PDF set (NNPDF3.0), and then, that if applied to Hessian PDF set (MMHT14) which was transformed into a Monte Carlo set, it gives back the starting PDFs with minimal information loss. We then show that, when applied to a large Monte Carlo PDF set obtained as combination of several underlying sets, the methodology leads to a Hessian representation in terms of a rather smaller set of parameters (CMC-H PDFs), thereby providing an alternative implementation of the recently suggested Meta-PDF idea and a Hessian version of the recently suggested PDF compression algorithm (CMC-PDFs). The mc2hessian conversion code is made publicly available togethe...
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.
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.
Versatile Density Functionals for Computational Surface Science
DEFF Research Database (Denmark)
Wellendorff, Jess
Density functional theory (DFT) emerged almost 50 years ago. Since then DFT has established itself as the central electronic structure methodology for simulating atomicscale systems from a few atoms to a few hundred atoms. This success of DFT is due to a very favorable accuracy-to-computational c......Density functional theory (DFT) emerged almost 50 years ago. Since then DFT has established itself as the central electronic structure methodology for simulating atomicscale systems from a few atoms to a few hundred atoms. This success of DFT is due to a very favorable accuracy...... resampling techniques, thereby systematically avoiding problems with overfitting. The first ever density functional presenting both reliable accuracy and convincing error estimation is generated. The methodology is general enough to be applied to more complex functional forms with higher-dimensional fitting...
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.
Density functional theory and multiscale materials modeling
Indian Academy of Sciences (India)
Swapan K Ghosh
2003-01-01
One of the vital ingredients in the theoretical tools useful in materials modeling at all the length scales of interest is the concept of density. In the microscopic length scale, it is the electron density that has played a major role in providing a deeper understanding of chemical binding in atoms, molecules and solids. In the intermediate mesoscopic length scale, an appropriate picture of the equilibrium and dynamical processes has been obtained through the single particle number density of the constituent atoms or molecules. A wide class of problems involving nanomaterials, interfacial science and soft condensed matter has been addressed using the density based theoretical formalism as well as atomistic simulation in this regime. In the macroscopic length scale, however, matter is usually treated as a continuous medium and a description using local mass density, energy density and other related density functions has been found to be quite appropriate. A unique single unified theoretical framework that emerges through the density concept at these diverse length scales and is applicable to both quantum and classical systems is the so called density functional theory (DFT) which essentially provides a vehicle to project the many-particle picture to a single particle one. Thus, the central equation for quantum DFT is a one-particle Schrödinger-like Kohn–Sham equation, while the same for classical DFT consists of Boltzmann type distributions, both corresponding to a system of noninteracting particles in the field of a density-dependent effective potential. Selected illustrative applications of quantum DFT to microscopic modeling of intermolecular interaction and that of classical DFT to a mesoscopic modeling of soft condensed matter systems are presented.
Noncovalent Interactions in Density-Functional Theory
DiLabio, Gino A
2014-01-01
Non-covalent interactions are essential in the description of soft matter, including materials of technological importance and biological molecules. In density-functional theory, common approaches fail to describe dispersion forces, an essential component in noncovalent binding interactions. In the last decade, great progress has been made in the development of accurate and computationally-efficient methods to describe noncovalently bound systems within the framework of density-functional theory. In this review, we give an account of the field from a chemical and didactic perspective, describing different approaches to the calculation of dispersion energies and comparing their accuracy, complexity, popularity, and general availability. This review should be useful to the newcomer who wants to learn more about noncovalent interactions and the different methods available at present to describe them using density-functional theory.
Density Functionals with Broad Applicability in Chemistry
Energy Technology Data Exchange (ETDEWEB)
Zhao, Yan; Truhlar, Donald G.
2008-02-01
The research described in this product was performed in part in the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the Department of Energy's Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. Although density functional theory is widely used in the computational chemistry community, the most popular density functional, B3LYP, has some serious shortcomings: (i) it is better for main-group chemistry than for transition metals; (ii) it systematically underestimates reaction barrier heights; (iii) it is inaccurate for interactions dominated by mediumrange correlation energy, such as van der Waals attraction, aromatic-aromatic stacking, and alkane isomerization energies. We have developed a variety of databases for testing and designing new density functionals. We used these data to design new density functionals, called M06-class (and, earlier, M05-class) functionals, for which we enforced some fundamental exact constraints such as the uniform-electron-gas limit and the absence of self-correlation energy. Our M06-class functionals depend on spin-up and spin-down electron densities (i.e., spin densities), spin density gradients, spin kinetic energy densities, and, for nonlocal (also called hybrid) functionals, Hartree-Fock exchange. We have developed four new functionals that overcome the above-mentioned difficulties: (a) M06, a hybrid meta functional, is a functional with good accuracy “across-theboard” for transition metals, main group thermochemistry, medium-range correlation energy, and barrier heights; (b) M06- 2X, another hybrid meta functional, is not good for transition metals but has excellent performance for main group chemistry, predicts accurate valence and Rydberg electronic excitation energies, and is an excellent functional for aromatic-aromatic stacking interactions; (c) M06-L is not as accurate as M06 for barrier heights but is the most accurate
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
Energy Technology Data Exchange (ETDEWEB)
Koentopp, Max; Chang, Connie [Department of Chemistry and Chemical Biology, Rutgers University, 610 Taylor Road, Piscataway, NJ 08854 (United States); Burke, Kieron [Department of Chemistry, UC Irvine, 1102 Natural Sciences 2, Irvine, CA 92697 (United States); Car, Roberto [Department of Chemistry and Princeton Institute for the Science and Technology of Materials (PRISM), Princeton University, Princeton, NJ 08544 (United States)
2008-02-27
Density functional calculations for the electronic conductance of single molecules are now common. We examine the methodology from a rigorous point of view, discussing where it can be expected to work, and where it should fail. When molecules are weakly coupled to leads, local and gradient-corrected approximations fail, as the Kohn-Sham levels are misaligned. In the weak bias regime, exchange-correlation corrections to the current are missed by the standard methodology. For finite bias, a new methodology for performing calculations can be rigorously derived using an extension of time-dependent current density functional theory from the Schroedinger equation to a master equation. (topical review)
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
DEFF Research Database (Denmark)
Nakamura, A.; Brandbyge, Mads; Hansen, Lars Bruno
1999-01-01
We study the deformation and breaking of an atomic-sized sodium wire using density functional simulations. The wire deforms through sudden atomic rearrangements and smoother atomic displacements. The conductance of the wire exhibits plateaus at integer values in units of 2e(2)/h corresponding...
Density functional and neural network analysis
DEFF Research Database (Denmark)
Jalkanen, K. J.; Bohr, Henrik
1997-01-01
Density functional theory (DFT) calculations have been carried out for hydrated L-alanine, L-alanyl-L-alanine and N-acetyl L-alanine N'-methylamide and examined with respect to the effect of water on the structure, the vibrational frequencies, vibrational absorption (VA) and vibrational circular...
Density functional theory with quantum nuclei
Requist, Ryan
2016-01-01
It is proved that the ground state energy of an electron-nuclear system is a variational functional of the conditional electronic density n_R(r), the nuclear wavefunction \\chi(R) and the quantum geometric tensor of the conditional electronic wavefunction $T_{\\mu\
Current Developments in Nuclear Density Functional Methods
Dobaczewski, J
2010-01-01
Density functional theory (DFT) became a universal approach to compute ground-state and excited configurations of many-electron systems held together by an external one-body potential in condensed-matter, atomic, and molecular physics. At present, the DFT strategy is also intensely studied and applied in the area of nuclear structure. The nuclear DFT, a natural extension of the self-consistent mean-field theory, is a tool of choice for computations of ground-state properties and low-lying excitations of medium-mass and heavy nuclei. Over the past thirty-odd years, a lot of experience was accumulated in implementing, adjusting, and using the density-functional methods in nuclei. This research direction is still extremely actively pursued. In particular, current developments concentrate on (i) attempts to improve the performance and precision delivered by the nuclear density-functional methods, (ii) derivations of density functionals from first principles rooted in the low-energy chromodynamics and effective th...
Density functional theory: Fixing Jacob's ladder
Car, Roberto
2016-09-01
Density functional theory calculations can be carried out with different levels of accuracy, forming a hierarchy that is often represented by the rungs of a ladder. Now a new method has been developed that significantly improves the accuracy of the 'third rung' when calculating the properties of diversely bonded systems.
Exhausting the Information: Novel Bayesian Combination of Photometric Redshift PDFs
Kind, M Carrasco
2014-01-01
The estimation and utilization of photometric redshift (photo-z) PDFs has become increasingly important over the last few years. Primarily this is because of the prominent role photo-z PDFs play in enabling photometric survey data to be used to make cosmological constraints, especially when compared to single estimates. Currently there exist a wide variety of algorithms to compute photo-z's, each with their own strengths and weaknesses. In this paper, we present a novel and efficient Bayesian framework that combines the results from different photo-z techniques into a more powerful and robust estimate by maximizing the information from the photometric data. To demonstrate this we use a supervised machine learning technique based on prediction trees and a random forest, an unsupervised method based on self organizing maps and a random atlas, and a standard template fitting method but can be easily extend to other existing techniques. We use data from the DEEP2 survey and more than $10^6$ galaxies from the SDSS...
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.
Bragg, Andrew D
2016-01-01
In this paper we investigate, using theory and Direct Numerical Simulations (DNS), the Forward In Time (FIT) and Backward In Time (BIT) Probability Density Functions (PDFs) of the separation of inertial particle-pairs in isotropic turbulence. In agreement with our earlier study (Bragg \\emph{et al.}, Phys. Fluids \\textbf{28}, 013305 (2016)), where we compared the FIT and BIT mean-square separations, we find that inertial particles separate much faster BIT than FIT, with the strength of the irreversibility depending upon the final/initial separation of the particle-pair and their Stokes number $St$. However, we also find that the irreversibility shows up in subtle ways in the behavior of the full PDF that it does not in the mean-square separation. In the theory, we derive new predictions, including a prediction for the BIT/FIT PDF for ${St\\geq O(1)}$, and for final/initial separations in the dissipation regime. The prediction shows how caustics in the particle relative velocities in the dissipation range affect...
Adiabatic density-functional perturbation theory
Gonze, Xavier
1995-08-01
The treatment of adiabatic perturbations within density-functional theory is examined, at arbitrary order of the perturbation expansion. Due to the extremal property of the energy functional, standard variation-perturbation theorems can be used. The different methods (Sternheimer equation, extremal principle, Green's function, and sum over state) for obtaining the perturbation expansion of the wave functions are presented. The invariance of the Hilbert space of occupied wave functions with respect to a unitary transformation leads to the definition of a ``parallel-transport-gauge'' and a ``diagonal-gauge'' perturbation expansion. Then, the general expressions are specialized for the second, third, and fourth derivative of the energy, with an example of application of the method up to third order.
Density functional theory 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...
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.
ABM11 PDFs and the cross section benchmarks in NNLO
Alekhin, S; Moch, S -O
2013-01-01
We report an updated version of the ABKM09 NNLO PDF fit, which includes the most recent HERA collider data on the inclusive cross sections and an improved treatment of the heavy-quark contribution to deep-inelastic scattering using advantages of the running-mass definition for the heavy quarks. The ABM11 PDFs obtained from the updated fit are in a good agreement with the recent LHC data on the W- and Z-production within the experimental and PDF uncertainties. We also perform a determination of the strong coupling constant \\alpha_s in a variant of the ABM11 fit insensitive to the influence of the higher twist terms and find the value of \\alpha_s=0.1133(11) which is in good agreement with the nominal ABM11 one and our earlier determination.
Cosmological Density Distribution Function from the Ellipsoidal Collapse Model in Real Space
Ohta, Y; Taruya, A; Ohta, Yasuhiro; Kayo, Issha; Taruya, Atsushi
2004-01-01
We calculate the one-point probability distribution function (PDF) for cosmic density in non-linear regime of the gravitational evolution. Under the local approximation that the evolution of cosmic fluid fields can be characterized by the Lagrangian local dynamics with finite degrees of freedom, the analytic expressions of PDF are derived taking account of the smoothing effect. The validity and the usefulness of the local approximation are then discussed comparing those results with N-body simulations in a Gaussian initial condition. Adopting the ellipsoidal collapse model (ECM) and the spherical collapse model (SCM) as Lagrangian local dynamics, we found that the PDFs from the local approximation excellently match the simulation results in the case of the cold dark matter initial spectrum. As for the scale-free initial spectra given by $P(k)\\propto k^n$, N-body result suffers from spurious numerical effects, which prevent us to give a detailed comparison. Nevertheless, at the quality of N-body data, the mode...
Directory of Open Access Journals (Sweden)
Emilio Gómez-Lázaro
2016-02-01
Full Text Available The Weibull probability distribution has been widely applied to characterize wind speeds for wind energy resources. Wind power generation modeling is different, however, due in particular to power curve limitations, wind turbine control methods, and transmission system operation requirements. These differences are even greater for aggregated wind power generation in power systems with high wind penetration. Consequently, models based on one-Weibull component can provide poor characterizations for aggregated wind power generation. With this aim, the present paper focuses on discussing Weibull mixtures to characterize the probability density function (PDF for aggregated wind power generation. PDFs of wind power data are firstly classified attending to hourly and seasonal patterns. The selection of the number of components in the mixture is analyzed through two well-known different criteria: the Akaike information criterion (AIC and the Bayesian information criterion (BIC. Finally, the optimal number of Weibull components for maximum likelihood is explored for the defined patterns, including the estimated weight, scale, and shape parameters. Results show that multi-Weibull models are more suitable to characterize aggregated wind power data due to the impact of distributed generation, variety of wind speed values and wind power curtailment.
Extended screened exchange functional derived from transcorrelated density functional theory
Umezawa, Naoto
2017-09-01
We propose a new formulation of the correlation energy functional derived from the transcorrelated method in use in density functional theory (TC-DFT). An effective Hamiltonian, HTC, is introduced by a similarity transformation of a many-body Hamiltonian, H , with respect to a complex function F: HTC=1/F H F . It is proved that an expectation value of HTC for a normalized single Slater determinant, Dn, corresponds to the total energy: E [n ] = ⟨Ψn|H |Ψn ⟩ /⟨Ψn|Ψn ⟩ = ⟨Dn|HTC|Dn ⟩ under the two assumptions: (1) The electron density n (r ) associated with a trial wave function Ψn = DnF is v -representable and (2) Ψn and Dn give rise to the same electron density n (r ). This formulation, therefore, provides an alternative expression of the total energy that is useful for the development of novel correlation energy functionals. By substituting a specific function for F, we successfully derived a model correlation energy functional, which resembles the functional form of the screened exchange method. The proposed functional, named the extended screened exchange (ESX) functional, is described within two-body integrals and is parametrized for a numerically exact correlation energy of the homogeneous electron gas. The ESX functional does not contain any ingredients of (semi-)local functionals and thus is totally free from self-interactions. The computational cost for solving the self-consistent-field equation is comparable to that of the Hartree-Fock method. We apply the ESX functional to electronic structure calculations for a solid silicon, H- ion, and small atoms. The results demonstrate that the TC-DFT formulation is promising for the systematic improvement of the correlation energy functional.
Density 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...
Covariant density functional theory for nuclear matter
Energy Technology Data Exchange (ETDEWEB)
Badarch, U.
2007-07-01
The present thesis is organized as follows. In Chapter 2 we study the Nucleon-Nucleon (NN) interaction in Dirac-Brueckner (DB) approach. We start by considering the NN interaction in free-space in terms of the Bethe-Salpeter (BS) equation to the meson exchange potential model. Then we present the DB approach for nuclear matter by extending the BS equation for the in-medium NN interaction. From the solution of the three-dimensional in-medium BS equation, we derive the DB self-energies and total binding energy which are the main results of the DB approach, which we later incorporate in the field theoretical calculation of the nuclear equation of state. In Chapter 3, we introduce the basic concepts of density functional theory in the context of Quantum Hadrodynamics (QHD-I). We reach the main point of this work in Chapter 4 where we introduce the DDRH approach. In the DDRH theory, the medium dependence of the meson-nucleon vertices is expressed as functionals of the baryon field operators. Because of the complexities of the operator-valued functionals we decide to use the mean-field approximation. In Chapter 5, we contrast microscopic and phenomenological approaches to extracting density dependent meson-baryon vertices. Chapter 6 gives the results of our studies of the EOS of infinite nuclear matter in detail. Using formulas derived in Chapters 4 and 5 we calculate the properties of symmetric and asymmetric nuclear matter and pure neutron matter. (orig.)
Density Functional Approach Based on Numerically Obtained Bridge Functional
Institute of Scientific and Technical Information of China (English)
ZHOUShi－Qi
2002-01-01
The ornstein-zenike equation is solved with the Rogers-Young approximation for bulk hard sphere fluid and Lennard-Jones fluid for several state points.Then the resulted bulk fluid radial distribution function combined with the test particle method is employed to determine numerically the function relationship of bridge functional as a function of indirect correlation function.It is found that all of the calculated points from different phase space state points for a same type of fluid collapse onto a same smooth curve.Then the numerically obtained curve is used to substitute the analytic expression of the bridge functional as a function of indirect correlation function required in the methodology [J.Chem.Phys,112(2000)8079] to determine the density distribution of non-uniform hard sphere fluid and Lennard-Jones fluid.The good agreement of theoretical predictions with the computer simulation data is obtained.The present numerical procedure incroporates the knowledge of bulk fluid radial distribution function into the constructing of the density functional approximation and makes the original methodology more accurate and more filexible for various interaction potential fluid.
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
DEFF Research Database (Denmark)
Jalkanen, K. J.; Bohr, Henrik
1997-01-01
Density functional theory (DFT) calculations have been carried out for hydrated L-alanine, L-alanyl-L-alanine and N-acetyl L-alanine N'-methylamide and examined with respect to the effect of water on the structure, the vibrational frequencies, vibrational absorption (VA) and vibrational circular...... dichroism (VCD) intensities. The large changes due to hydration on the structures, relative stability of conformers, and in the VA and VCD spectra observed experimentally are reproduced by the DFT calculations. Furthermore a neural network was constructed for reproducing the inverse scattering data (infer...
Energy Technology Data Exchange (ETDEWEB)
Mattsson, Ann Elisabet; Modine, Normand Arthur; Desjarlais, Michael Paul; Muller, Richard Partain; Sears, Mark P.; Wright, Alan Francis
2006-11-01
A finite temperature version of 'exact-exchange' density functional theory (EXX) has been implemented in Sandia's Socorro code. The method uses the optimized effective potential (OEP) formalism and an efficient gradient-based iterative minimization of the energy. The derivation of the gradient is based on the density matrix, simplifying the extension to finite temperatures. A stand-alone all-electron exact-exchange capability has been developed for testing exact exchange and compatible correlation functionals on small systems. Calculations of eigenvalues for the helium atom, beryllium atom, and the hydrogen molecule are reported, showing excellent agreement with highly converged quantumMonte Carlo calculations. Several approaches to the generation of pseudopotentials for use in EXX calculations have been examined and are discussed. The difficult problem of finding a correlation functional compatible with EXX has been studied and some initial findings are reported.
Progress in the Determination of Polarized PDFs and Higher Twist
Leader, Elliot; Stamenov, Dimiter B
2007-01-01
The impact of the recent very precise CLAS and COMPASS g1/F1 data on polarized parton densities and higher twist effects is discussed. It is demonstrated that the low Q^2 CLAS data improve essentially our knowledge of higher twist corrections to the spin structure function g1, while the large Q^2 COMPASS data influence mainly the strange quark and gluon polarizations. It is also shown that the uncertainties in the determination of the polarized parton densities are significantly reduced. We find also that the present inclusive DIS data cannot rule out a negative polarized and changing in sign gluon densities. The present status of the proton spin sum rule is discussed.
Density Functional Approach Based on Numerically Obtained Bridge Functional
Institute of Scientific and Technical Information of China (English)
ZHOU Shi-Qi
2002-01-01
The Ornstein Zernike equation is solved with the Rogers Young approximation for bulk hard sphere fluidand Lennard-Jones fluid for several state points. Then the resulted bulk fluid radial distribution function combinedwith the test particle method is employed to determine numerically the function relationship of bridge functional as afunction of indirect correlation function. It is found that all of the calculated points from different phase space statepoints for a same type of fluid collapse onto a same smooth curve. Then the numerically obtained curve is used tosubstitute the analytic expression of the bridge functional as a function of indirect correlation function required in themethodology [J. Chem. Phys. 112 (2000) 8079] to deterrnine the density distribution of non-uniform hard spherefluid and Lennard Jones fluid. The good agreement of theoretical predictions with the computer simulation data isobtained. The present numerical procedure incorporates the knowledge of bulk fluid radial distribution function intothe constructing of the density functional approximation and makes the original methodology more accurate and moreflexible for various interaction potential fluid.
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.
Energy Technology Data Exchange (ETDEWEB)
Sahni, Viraht
2016-07-01
This book is on quantal density functional theory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The time-independent QDFT constitutes a special case. The 2{sup nd} edition describes the further development of the theory, and extends it to include the presence of an external magnetostatic field. The theory is based on the 'quantal Newtonian' second and first laws for the individual electron. These laws are in terms of 'classical' fields that pervade all space, and their quantal sources. The fields are separately representative of the electron correlations that must be accounted for in local potential theory. Recent developments show that irrespective of the type of external field the electrons are subject to, the only correlations beyond those due to the Pauli exclusion principle and Coulomb repulsion that need be considered are solely of the correlation-kinetic effects. Foundational to QDFT, the book describes Schroedinger theory from the new perspective of the single electron in terms of the 'quantal Newtonian' laws. Hohenberg-Kohn density functional theory (DFT), new understandings of the theory and its extension to the presence of an external uniform magnetostatic field are described. The physical interpretation via QDFT, in terms of electron correlations, of Kohn-Sham DFT, approximations to it and Slater theory are provided.
Universality principle and the development of classical density functional theory
Institute of Scientific and Technical Information of China (English)
周世琦; 张晓琪
2002-01-01
The universality principle of the free energy density functional and the ‘test particle' trick by Percus are combined to construct the approximate free energy density functional or its functional derivative. Information about the bulk fluid ralial distribution function is integrated into the density functional approximation directly for the first time in the present methodology. The physical foundation of the present methodology also applies to the quantum density functional theory.
Strange Quark PDFs and Implications for Drell-Yan Boson Production at the LHC
Kusina, A; Berge, S; Olness, F I; Schienbein, I; Kovarik, K; Jezo, T; Yu, J Y; Park, K
2012-01-01
Global analyses of Parton Distribution Functions (PDFs) have provided incisive constraints on the up and down quark components of the proton, but constraining the other flavor degrees of freedom is more challenging. Higher-order theory predictions and new data sets have contributed to recent improvements. Despite these efforts, the strange quark PDF has a sizable uncertainty, particularly in the small x region. We examine the constraints from experiment and theory, and investigate the impact of this uncertainty on LHC observables. In particular, we study W/Z production to see how the s-quark uncertainty propagates to these observables, and examine the extent to which precise measurements at the LHC can provide additional information on the proton flavor structure.
PDFs, α{sub s}, and quark masses from global fits
Energy Technology Data Exchange (ETDEWEB)
Alekhin, Sergey [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Institute for High Energy Physics (IHEP), Protvino (Russian Federation); Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Moch, Sven-Olaf [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Placakyte, Ringaile [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2016-09-15
The strong coupling constant α{sub s} and the heavy-quark masses, m{sub c}, m{sub b}, m{sub t} are extracted simultaneously with the parton distribution functions (PDFs) in the updated ABM12 fit including recent data from CERN-SPS, HERA, Tevatron, and the LHC. The values of α{sub s}(M{sub Z})=0.1147±0.0008(exp.), m{sub c}(m{sub c})=1.252±0.018(exp.) GeV, m{sub b}(m{sub b})=3.83±0.12(exp.) GeV, m{sub t}(m{sub t})=160.9±1.1(exp.) GeV are obtained with the MS heavy-quark mass definition being employed throughout the analysis.
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
Energy Technology Data Exchange (ETDEWEB)
Kao, S.; Monahan, J.F.
1977-09-01
Recent work in the field of probability density estimation has included the introduction of some new methods, such as the polynomial and spline methods and the nearest neighbor method, and the study of asymptotic properties in depth. This earlier work is summarized here. In addition, the computational complexity of the various algorithms is analyzed, as are some simulations. The object is to compare the performance of the various methods in small samples and their sensitivity to change in their parameters, and to attempt to discover at what point a sample is so small that density estimation can no longer be worthwhile. (RWR)
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.
Energy Technology Data Exchange (ETDEWEB)
Kapoor, Varun; Brics, Martins; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)
2013-07-01
Autoionizing states are inaccessible to time-dependent density functional theory (TDDFT) using known, adiabatic Kohn-Sham (KS) potentials. We determine the exact KS potential for a numerically exactly solvable model Helium atom interacting with a laser field that is populating an autoionizing state. The exact single-particle density of the population in the autoionizing state corresponds to that of the energetically lowest quasi-stationary state in the exact KS potential. We describe how this exact potential controls the decay by a barrier whose height and width allows for the density to tunnel out and decay with the same rate as in the ab initio time-dependent Schroedinger calculation. However, devising a useful exchange-correlation potential that is capable of governing such a scenario in general and in more complex systems is hopeless. As an improvement over TDDFT, time-dependent reduced density matrix functional theory has been proposed. We are able to obtain for the above described autoionization process the exact time-dependent natural orbitals (i.e., the eigenfunctions of the exact, time-dependent one-body reduced density matrix) and study the potentials that appear in the equations of motion for the natural orbitals and the structure of the two-body density matrix expanded in them.
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.
Back in the saddle: Large-deviation statistics of the cosmic log-density field
Uhlemann, Cora; Pichon, Christophe; Bernardeau, Francis; Reimberg, Paulo
2015-01-01
We present a first principle approach to obtain analytical predictions for spherically-averaged cosmic densities in the mildly non-linear regime that go well beyond what is usually achieved by standard perturbation theory. A large deviation principle allows us to compute the leading-order cumulants of average densities in concentric cells. In this symmetry, the spherical collapse model leads to cumulant generating functions that are robust for finite variances and free of critical points when logarithmic density transformations are implemented. They yield in turn accurate density probability distribution functions (PDFs) from a straightforward saddle-point approximation valid for all density values. Based on this easy-to-implement modification, explicit analytic formulas for the evaluation of the one- and two-cell PDF are provided. The theoretical predictions obtained for the PDFs are accurate to a few percent compared to the numerical integration, regardless of the density under consideration and in excellen...
Building a Universal Nuclear Energy Density Functional
Energy Technology Data Exchange (ETDEWEB)
Carlson, Joe A. [Michigan State Univ., East Lansing, MI (United States); Furnstahl, Dick; Horoi, Mihai; Lust, Rusty; Nazaewicc, Witek; Ng, Esmond; Thompson, Ian; Vary, James
2012-12-30
During the period of Dec. 1 2006 – Jun. 30, 2012, the UNEDF collaboration carried out a comprehensive study of all nuclei, based on the most accurate knowledge of the strong nuclear interaction, the most reliable theoretical approaches, the most advanced algorithms, and extensive computational resources, with a view towards scaling to the petaflop platforms and beyond. The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: First, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties; Second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data; Third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory.
Building a Universal Nuclear Energy Density Functional
Energy Technology Data Exchange (ETDEWEB)
Carlson, Joe A. [Michigan State University; Furnstahl, Dick; Horoi, Mihai; Lust, Rusty; Nazaewicc, Witek; Ng, Esmond; Thompson, Ian; Vary, James
2012-12-30
During the period of Dec. 1 2006 – Jun. 30, 2012, the UNEDF collaboration carried out a comprehensive study of all nuclei, based on the most accurate knowledge of the strong nuclear interaction, the most reliable theoretical approaches, the most advanced algorithms, and extensive computational resources, with a view towards scaling to the petaflop platforms and beyond. The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: First, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties; Second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data; Third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory.
The Effect of Final HERA inclusive Cross Section Data on MMHT2014 PDFs
Thorne, R S; Martin, A D; Motylinski, P
2015-01-01
We investigate the effect of including the HERA run I + II combined cross section data on the MMHT2014 PDFs. We present the fit quality within the context of the global fit and when only the HERA data are included. We examine the changes in both the central values and uncertainties in the PDFs. We find that the prediction for the data is good, and only relatively small improvements in $\\chi^2$ and changes in the PDFs are obtained with a refit at both NLO and NNLO. PDF uncertainties are slightly reduced. There is a small dependence of the fit quality on the value of $Q^2_{\\min}$.
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.
Carli, Tancredi; Cooper-Sarkar, Amanda; Gwenlan, Claire; Salam, Gavin P; Siegert, Frank; Starovoitov, Pavel; Sutton, Mark
2010-01-01
A method to facilitate the consistent inclusion of cross-section measurements based on complex final-states from HERA, TEVATRON and the LHC in proton parton density function (PDF) fits has been developed. This can be used to increase the sensitivity of LHC data to deviations from Standard Model predictions. The method stores perturbative coefficients of NLO QCD calculations of final-state observables measured in hadron colliders in look-up tables. This allows the posteriori inclusion of parton density functions (PDFs), and of the strong coupling, as well as the a posteriori variation of the renormalisation and factorisation scales in cross-section calculations. The main novelties in comparison to original work on the subject are the use of higher-order interpolation, which substantially improves the trade-off between accuracy and memory use, and a CPU and computer memory optimised way to construct and store the look-up table using modern software tools. It is demonstrated that a sufficient accuracy on the cro...
Orbital functionals in density-matrix- and current-density-functional theory
Energy Technology Data Exchange (ETDEWEB)
Helbig, N.
2006-05-15
Density-Functional Theory (DFT), although widely used and very successful in the calculation of several observables, fails to correctly describe strongly correlated materials. In the first part of this work we, therefore, introduce reduced-densitymatrix- functional theory (RDMFT) which is one possible way to treat electron correlation beyond DFT. Within this theory the one-body reduced density matrix (1- RDM) is used as the basic variable. Our main interest is the calculation of the fundamental gap which proves very problematic within DFT. In order to calculate the fundamental gap we generalize RDMFT to fractional particle numbers M by describing the system as an ensemble of an N and an N+1 particle system (with N{<=}M{<=}N+1). For each fixed particle number, M, the total energy is minimized with respect to the natural orbitals and their occupation numbers. This leads to the total energy as a function of M. The derivative of this function with respect to the particle number has a discontinuity at integer particle number which is identical to the gap. In addition, we investigate the necessary and sufficient conditions for the 1- RDM of a system with fractional particle number to be N-representable. Numerical results are presented for alkali atoms, small molecules, and periodic systems. Another problem within DFT is the description of non-relativistic many-electron systems in the presence of magnetic fields. It requires the paramagnetic current density and the spin magnetization to be used as basic variables besides the electron density. However, electron-gas-based functionals of current-spin-density-functional Theory (CSDFT) exhibit derivative discontinuities as a function of the magnetic field whenever a new Landau level is occupied, which makes them difficult to use in practice. Since the appearance of Landau levels is, intrinsically, an orbital effect it is appealing to use orbital-dependent functionals. We have developed a CSDFT version of the optimized
Energy Technology Data Exchange (ETDEWEB)
Rullaud, M.
2004-06-01
A new modelization of turbulent combustion is proposed with detailed chemistry and probability density functions (PDFs). The objective is to capture temperature and species concentrations, mainly the CO. The PCM-FTC model, Presumed Conditional Moment - Flame Tabulated Chemistry, is based on the tabulation of laminar premixed and diffusion flames to capture partial pre-mixing present in aeronautical engines. The presumed PDFs is introduced to predict averaged values. The tabulation method is based on the analysis of the chemical structure of laminar premixed and diffusion flames. Hypothesis are presented, tested and validated with Sandia experimental data jet flames. Then, the model is introduced in a turbulent flow simulation software. Three configurations are retained to quantify the level of prediction of this formulation: the D and F-Flames of Sandia and lifted jet flames of methane/air of Stanford. A good agreement is observed between experiments and simulations. The validity of this method is then demonstrated. (author)
Reconstructing parton densities at large fractional momenta
Bacchetta, Alessandro; Pasquini, Barbara; Xiong, Xiaonu
2016-01-01
Parton distribution functions (PDFs) are nonperturbative objects defined by nonlocal light-cone correlations. They cannot be computed directly from Quantum Chromodynamics (QCD). Using a standard lattice QCD approach, it is possible to compute moments of PDFs, which are matrix elements of local operators. Recently, an alternative approach has been proposed, based on the introduction of quasi-parton distribution functions (quasi-PDFs), which are matrix elements of equal-time spatial correlations and hence calculable on lattice. Quasi-PDFs approach standard PDFs in the limit of very large longitudinal proton momenta $P^z$. This limit is not attainable in lattice simulations, and quasi-PDFs fail to reproduce PDFs at high fractional longitudinal momenta. In this paper, we propose a method to improve the reconstruction of PDFs by combining information from quasi-PDFs and from the Mellin moments of regular PDFs. We test our method using the diquark spectator model for up and down valence distributions of both unpola...
Density functional theory in the solid state.
Hasnip, Philip J; Refson, Keith; Probert, Matt I J; Yates, Jonathan R; Clark, Stewart J; Pickard, Chris J
2014-03-13
Density functional theory (DFT) has been used in many fields of the physical sciences, but none so successfully as in the solid state. From its origins in condensed matter physics, it has expanded into materials science, high-pressure physics and mineralogy, solid-state chemistry and more, powering entire computational subdisciplines. Modern DFT simulation codes can calculate a vast range of structural, chemical, optical, spectroscopic, elastic, vibrational and thermodynamic phenomena. The ability to predict structure-property relationships has revolutionized experimental fields, such as vibrational and solid-state NMR spectroscopy, where it is the primary method to analyse and interpret experimental spectra. In semiconductor physics, great progress has been made in the electronic structure of bulk and defect states despite the severe challenges presented by the description of excited states. Studies are no longer restricted to known crystallographic structures. DFT is increasingly used as an exploratory tool for materials discovery and computational experiments, culminating in ex nihilo crystal structure prediction, which addresses the long-standing difficult problem of how to predict crystal structure polymorphs from nothing but a specified chemical composition. We present an overview of the capabilities of solid-state DFT simulations in all of these topics, illustrated with recent examples using the CASTEP computer program.
Combining Molecular Dynamics and Density Functional Theory
Kaxiras, Efthimios
2015-03-01
The time evolution of a system consisting of electrons and ions is often treated in the Born-Oppenheimer approximation, with electrons in their instantaneous ground state. This approach cannot capture many interesting processes that involved excitation of electrons and its effects on the coupled electron-ion dynamics. The time scale needed to accurately resolve the evolution of electron dynamics is atto-seconds. This poses a challenge to the simulation of important chemical processes that typically take place on time scales of pico-seconds and beyond, such as reactions at surfaces and charge transport in macromolecules. We will present a methodology based on time-dependent density functional theory for electrons, and classical (Ehrenfest) dynamics for the ions, that successfully captures such processes. We will give a review of key features of the method and several applications. These illustrate how the atomic and electronic structure evolution unravels the elementary steps that constitute a chemical reaction. In collaboration with: G. Kolesov, D. Vinichenko, G. Tritsaris, C.M. Friend, Departments of Physics and of Chemistry and Chemical Biology.
Bone mineral density, adiposity and cognitive functions
Directory of Open Access Journals (Sweden)
Hamid R Sohrabi
2015-02-01
Full Text Available Cognitive decline and dementia due to Alzheimer’s disease have been associated with genetic, lifestyle, and environmental factors. A number of potentially modifiable risk factors should be taken into account when preventive or ameliorative interventions targeting dementia and its preclinical stages are investigated. Bone mineral density (BMD and body composition are two such potentially modifiable risk factors, and their association with cognitive decline was investigated in this study. 164 participants, aged 34 to 87 years old (62.78±9.27, were recruited for this longitudinal study and underwent cognitive and clinical examinations at baseline and after three years. Blood samples were collected for apolipoprotein E (APOE genotyping and dual energy x-ray absorptiometry (DXA was conducted at the same day as cognitive assessment. Using hierarchical regression analysis, we found that BMD and lean body mass, as measured using DXA were significant predictors of episodic memory. Age, gender, APOE status and premorbid IQ were controlled for. Specifically, the List A learning from California Verbal Learning Test was significantly associated with BMD and lean mass both at baseline and at follow up assessment. Our findings indicate that there is a significant association between BMD and lean body mass and episodic verbal learning. While the involvement of modifiable lifestyle factors in human cognitive function has been examined in different studies, there is a need for further research to understand the potential underlying mechanisms.
Institute of Scientific and Technical Information of China (English)
Zhou Shi-Qi
2007-01-01
A universal theoretical approach is proposed which enables all hard sphere density functional approximations(DFAs) applicable to van der Waals fluids. The resultant DFA obtained by combining the universal theoretical approach with any hard sphere DFAs only needs as input a second-order direct correlation function (DCF) of a coexistence bulk fluid, and is applicable in both supercritical and subcritical temperature regions. The associated effective hard sphere density can be specified by a hard wall sum rule. It is indicated that the value of the effective hard sphere density so determined can be universal, i.e. can be applied to any external potentials different from the single hard wall. As an illustrating example, the universal theoretical approach is combined with a hard sphere bridge DFA to predict the density profile of a hard core attractive Yukawa model fluid influenced by diverse external fields; agreement between the present formalism's predictions and the corresponding simulation data is good or at least comparable to several previous DFT approaches. The primary advantage of the present theoretical approach combined with other hard sphere DFAs is discussed.
A Comparison of new MC-adapted Parton Densities
Kasemets, Tomas
2010-01-01
A selection of the latest and most frequently used parton distribution functions (PDFs) is incorporated in Pythia8, including the Monte Carlo-adapted PDFs from the MSTW and CTEQ collaborations. This article examines the differences in PDFs as well as the effect they have on results of simulations and compare with data collected by the CDF experiment. Monte Carlo-adapted PDFs do a better job than leading- and next-to-leading order PDFs for many observables, but there is room for further improvements.
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.
Ions in solution: density corrected density functional theory (DC-DFT).
Kim, Min-Cheol; Sim, Eunji; Burke, Kieron
2014-05-14
Standard density functional approximations often give questionable results for odd-electron radical complexes, with the error typically attributed to self-interaction. In density corrected density functional theory (DC-DFT), certain classes of density functional theory calculations are significantly improved by using densities more accurate than the self-consistent densities. We discuss how to identify such cases, and how DC-DFT applies more generally. To illustrate, we calculate potential energy surfaces of HO·Cl(-) and HO·H2O complexes using various common approximate functionals, with and without this density correction. Commonly used approximations yield wrongly shaped surfaces and/or incorrect minima when calculated self consistently, while yielding almost identical shapes and minima when density corrected. This improvement is retained even in the presence of implicit solvent.
Ions in solution: Density Corrected Density Functional Theory (DC-DFT)
Kim, Min-Cheol; Burke, Kieron
2014-01-01
Standard density functional approximations often give questionable results for odd-electron radical complexes, with the error typically attributed to self-interaction. In density corrected density functional theory (DC-DFT), certain classes of density functional theory calculations are significantly improved by using densities more accurate than the self-consistent densities. We discuss how to identify such cases, and how DC-DFT applies more generally. To illustrate, we calculate potential energy surfaces of HO$\\cdot$Cl$^-$ and HO$\\cdot$H$_2$O complexes using various common approximate functionals, with and without this density correction. Commonly used approximations yield wrongly shaped surfaces and/or incorrect minima when calculated self consistently, while yielding almost identical shapes and minima when density corrected. This improvement is retained even in the presence of implicit solvent.
Graphene on metals: A van der Waals density functional study
DEFF Research Database (Denmark)
Vanin, Marco; Mortensen, Jens Jørgen; Kelkkanen, Kari André;
2010-01-01
We use density functional theory (DFT) with a recently developed van der Waals density functional (vdW-DF) to study the adsorption of graphene on Co, Ni, Pd, Ag, Au, Cu, Pt, and Al(111) surfaces. In contrast to the local-density approximation (LDA) which predicts relatively strong binding for Ni...
Coclite, A.; Pascazio, G.; De Palma, P.; Cutrone, L.
2016-07-01
Flamelet-Progress-Variable (FPV) combustion models allow the evaluation of all thermochemical quantities in a reacting flow by computing only the mixture fraction Z and a progress variable C. When using such a method to predict turbulent combustion in conjunction with a turbulence model, a probability density function (PDF) is required to evaluate statistical averages (e. g., Favre averages) of chemical quantities. The choice of the PDF is a compromise between computational costs and accuracy level. The aim of this paper is to investigate the influence of the PDF choice and its modeling aspects to predict turbulent combustion. Three different models are considered: the standard one, based on the choice of a β-distribution for Z and a Dirac-distribution for C; a model employing a β-distribution for both Z and C; and the third model obtained using a β-distribution for Z and the statistically most likely distribution (SMLD) for C. The standard model, although widely used, does not take into account the interaction between turbulence and chemical kinetics as well as the dependence of the progress variable not only on its mean but also on its variance. The SMLD approach establishes a systematic framework to incorporate informations from an arbitrary number of moments, thus providing an improvement over conventionally employed presumed PDF closure models. The rational behind the choice of the three PDFs is described in some details and the prediction capability of the corresponding models is tested vs. well-known test cases, namely, the Sandia flames, and H2-air supersonic combustion.
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...
Towards a filtered density function approach for reactive transport in groundwater
Suciu, N.; Schüler, L.; Attinger, S.; Knabner, P.
2016-04-01
Evolution equations for probability density functions (PDFs) and filtered density functions (FDFs) of random species concentrations weighted by conserved scalars are formulated as Fokker-Planck equations describing stochastically equivalent processes in concentration-position spaces. This approach provides consistent numerical PDF/FDF solutions, given by the density in the concentration-position space of an ensemble of computational particles governed by the associated Itô equations. The solutions are obtained by a global random walk (GRW) algorithm, which is stable, free of numerical diffusion, and practically insensitive to the increase of the number of particles. The general FDF approach and the GRW numerical solution are illustrated for a reduced complexity problem consisting of the transport of a single scalar in groundwater. Randomness is induced by the stochastic parameterization of the hydraulic conductivity, characterized by short range correlations and small variance. The objective is to infer the statistics of the random concentration sampled at the plume center of mass, integrated over the transverse dimension of a two-dimensional spatial domain. The PDF/FDF problem can therefore be formulated in a two-dimensional domain as well, a spatial dimension and one in the concentration space. The upscaled drift and diffusion coefficients describing the PDF transport in the physical space are estimated on single-trajectories of diffusion in velocity fields with short-range correlations, owing to their self-averaging property. The mixing coefficients describing the PDF transport in concentration spaces are parameterized by the trend and the noise inferred from the statistical analysis of an ensemble of simulated concentration time series, as well as by classical mixing models. A Gaussian spatial filter applied to a Kraichnan velocity field generator is used to construct coarse-grained simulations (CGS) for FDF problems. The purposes of the CGS simulations are
Bioinorganic Chemistry Modeled with the TPSSh Density Functional
DEFF Research Database (Denmark)
Kepp, Kasper Planeta
2008-01-01
In this work, the TPSSh density functional has been benchmarked against a test set of experimental structures and bond energies for 80 transition-metal-containing diatomics. It is found that the TPSSh functional gives structures of the same quality as other commonly used hybrid and nonhybrid func...... promising density functional for use and further development within the field of bioinorganic chemistry....
Energy Technology Data Exchange (ETDEWEB)
Zobelli, Alberto [Laboratoire de Physique des Solides, Univ. Paris Sud, CNRS UMR, Orsay (France); Ivanovskaya, Viktoria; Wagner, Philipp; Yaya, Abu; Ewels, Chris P. [Institut des Materiaux Jean Rouxel (IMN), CNRS UMR, University of Nantes (France); Suarez-Martinez, Irene [Nanochemistry Research Institute, Curtin University of Technology, Perth, Western Australia (Australia)
2012-02-15
The density functional tight binding approach (DFTB) is well adapted for the study of point and line defects in graphene based systems. After briefly reviewing the use of DFTB in this area, we present a comparative study of defect structures, energies, and dynamics between DFTB results obtained using the dftb+ code, and density functional results using the localized Gaussian orbital code, AIMPRO. DFTB accurately reproduces structures and energies for a range of point defect structures such as vacancies and Stone-Wales defects in graphene, as well as various unfunctionalized and hydroxylated graphene sheet edges. Migration barriers for the vacancy and Stone-Wales defect formation barriers are accurately reproduced using a nudged elastic band approach. Finally we explore the potential for dynamic defect simulations using DFTB, taking as an example electron irradiation damage in graphene. DFTB-MD derived sputtering energy threshold map for a carbon atom in a graphene plane. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
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
Global Analysis of Helicity PDFs: past - present - future
Energy Technology Data Exchange (ETDEWEB)
de Florian, D.; Stratmann, M.; Sassot, R.; Vogelsang, W.
2011-04-11
We discuss the current status of the DSSV global analysis of helicity-dependent parton densities. A comparison with recent semi-inclusive DIS data from COMPASS is presented, and constraints on the polarized strangeness density are examined in some detail.
Generalized Probability Functions
Directory of Open Access Journals (Sweden)
Alexandre Souto Martinez
2009-01-01
Full Text Available From the integration of nonsymmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. Motivated by the mathematical curiosity, we show that these generalized functions are suitable to generalize some probability density functions (pdfs. A very reliable rank distribution can be conveniently described by the generalized exponential function. Finally, we turn the attention to the generalization of one- and two-tail stretched exponential functions. We obtain, as particular cases, the generalized error function, the Zipf-Mandelbrot pdf, the generalized Gaussian and Laplace pdf. Their cumulative functions and moments were also obtained analytically.
Indian Academy of Sciences (India)
Paul W Ayers; Mel Levy
2005-09-01
Using the constrained search and Legendre-transform formalisms, one can derive ``generalized” density-functional theories, in which the fundamental variable is either the electron pair density or the second-order reduced density matrix. In both approaches, the -representability problem is solved by the functional, and the variational principle is with respect to all pair densities (density matrices) that are nonnegative and appropriately normalized. The Legendre-transform formulation provides a lower bound on the constrained-search functional. Noting that experience in density-functional and density-matrix theories suggests that it is easier to approximate functionals than it is to approximate the set of -representable densities sheds some light on the significance of this work.
CT14QED PDFs from Isolated Photon Production in Deep Inelastic Scattering
Schmidt, Carl; Stump, Daniel; Yuan, C -P
2015-01-01
We describe the implementation of Quantum Electrodynamic (QED) evolution at Leading Order (LO) along with Quantum Chromodynamic (QCD) evolution at Next-to-Leading Order (NLO) in the CTEQ-TEA Global analysis package. The photon Parton Distribution Function (PDF) is described by a two-parameter ansatz, coming from radiation off the valence quarks, and based on the CT14 NLO PDFs. Setting the two parameters equal, allows us to completely specify the photon PDF in terms of the momentum fraction carried by the photon, $p_0^\\gamma$, at the initial scale $Q_0=1.295$ GeV. We obtain constraints on the photon PDF by comparing with ZEUS data~\\cite{Chekanov:2009dq} on the production of isolated photons in deep inelastic scattering, $ep\\rightarrow e\\gamma+X$. For this comparison we present a new perturbative calculation of the process that consistently combines the photon-initiated contribution with the quark-initiated contribution. Comparison with the data allows us to put a constraint at the 90% confidence level of $p_0^...
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
DEFF Research Database (Denmark)
Langreth, D.C.; Lundqvist, Bengt; Chakarova-Kack, S.D.;
2009-01-01
forces in molecules, to adsorbed molecules, like benzene, naphthalene, phenol and adenine on graphite, alumina and metals, to polymer and carbon nanotube (CNT) crystals, and hydrogen storage in graphite and metal-organic frameworks (MOFs), and to the structure of DNA and of DNA with intercalators......Sparse matter is abundant and has both strong local bonds and weak nonbonding forces, in particular nonlocal van der Waals (vdW) forces between atoms separated by empty space. It encompasses a broad spectrum of systems, like soft matter, adsorption systems and biostructures. Density...
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…
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.
The impact of the final HERA combined data on PDFs obtained from a global fit
Energy Technology Data Exchange (ETDEWEB)
Harland-Lang, L.A.; Motylinski, P.; Thorne, R.S. [University College London, Department of Physics and Astronomy, London (United Kingdom); Martin, A.D. [Durham University, Institute for Particle Physics Phenomenology, Durham (United Kingdom)
2016-04-15
We investigate the effect of including the HERA run I + II combined cross section data on the MMHT2014 PDFs. We present the fit quality within the context of the global fit and when only the HERA data are included. We examine the changes in both the central values and the uncertainties in the PDFs. We find that the prediction for the data is good, and only relatively small improvements in χ{sup 2} and changes in the PDFs are obtained with a refit at both NLO and NNLO. PDF uncertainties are slightly reduced. There is a small dependence of the fit quality on the value of Q{sup 2}{sub min}. This can be improved by phenomenologically motived corrections to F{sub L}(x, Q{sup 2}) which parametrically are largely in the form of higher-twist type contributions. (orig.)
The impact of the final HERA combined data on PDFs obtained from a global fit
Harland-Lang, L A; Motylinski, P; Thorne, R S
2016-01-01
We investigate the effect of including the HERA run I + II combined cross section data on the MMHT2014 PDFs. We present the fit quality within the context of the global fit and when only the HERA data are included. We examine the changes in both the central values and uncertainties in the PDFs. We find that the prediction for the data is good, and only relatively small improvements in $\\chi^2$ and changes in the PDFs are obtained with a refit at both NLO and NNLO. PDF uncertainties are slightly reduced. There is a small dependence of the fit quality on the value of $Q^2_{\\min}$. This can be improved by phenomenologically motived corrections to $F_L(x,Q^2)$ which parametrically are largely in the form of higher-twist type contributions.
The impact of the final HERA combined data on PDFs obtained from a global fit
Harland-Lang, L. A.; Martin, A. D.; Motylinski, P.; Thorne, R. S.
2016-04-01
We investigate the effect of including the HERA run I + II combined cross section data on the MMHT2014 PDFs. We present the fit quality within the context of the global fit and when only the HERA data are included. We examine the changes in both the central values and the uncertainties in the PDFs. We find that the prediction for the data is good, and only relatively small improvements in χ ^2 and changes in the PDFs are obtained with a refit at both NLO and NNLO. PDF uncertainties are slightly reduced. There is a small dependence of the fit quality on the value of Q^2_{min}. This can be improved by phenomenologically motived corrections to F_L(x,Q^2) which parametrically are largely in the form of higher-twist type contributions.
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.
Schneider, N.; Bontemps, S.; Motte, F.; Ossenkopf, V.; Klessen, R. S.; Simon, R.; Fechtenbaum, S.; Herpin, F.; Tremblin, P.; Csengeri, T.; Myers, P. C.; Hill, T.; Cunningham, M.; Federrath, C.
2016-03-01
The probability distribution function of column density (N-PDF) serves as a powerful tool to characterise the various physical processes that influence the structure of molecular clouds. Studies that use extinction maps or H2 column-density maps (N) that are derived from dust show that star-forming clouds can best be characterised by lognormal PDFs for the lower N range and a power-law tail for higher N, which is commonly attributed to turbulence and self-gravity and/or pressure, respectively. While PDFs from dust cover a large dynamic range (typically N ~ 1020-24 cm-2 or Av~ 0.1-1000), PDFs obtained from molecular lines - converted into H2 column density - potentially trace more selectively different regimes of (column) densities and temperatures. They also enable us to distinguish different clouds along the line of sight through using the velocity information. We report here on PDFs that were obtained from observations of 12CO, 13CO, C18O, CS, and N2H+ in the Cygnus X North region, and make a comparison to a PDF that was derived from dust observations with the Herschel satellite. The PDF of 12CO is lognormal for Av ~ 1-30, but is cut for higher Av because of optical depth effects. The PDFs of C18O and 13CO are mostly lognormal up to Av ~ 1-15, followed by excess up to Av ~ 40. Above that value, all CO PDFs drop, which is most likely due to depletion. The high density tracers CS and N2H+ exhibit only a power law distribution between Av ~ 15 and 400, respectively. The PDF from dust is lognormal for Av ~ 3-15 and has a power-law tail up to Av ~ 500. Absolute values for the molecular line column densities are, however, rather uncertain because of abundance and excitation temperature variations. If we take the dust PDF at face value, we "calibrate" the molecular line PDF of CS to that of the dust and determine an abundance [CS]/[H2] of 10-9. The slopes of the power-law tails of the CS, N2H+, and dust PDFs are -1.6, -1.4, and -2.3, respectively, and are thus consistent
The benchmark of gutzwiller density functional theory in hydrogen systems
Energy Technology Data Exchange (ETDEWEB)
Yao, Y.; Wang, Cai-Zhuang; Ho, Kai-Ming
2012-02-23
We propose an approximate form of the exchange-correlation energy functional for the Gutzwiller density functional theory. It satisfies certain physical constraints in both weak and strong electron correlation limits. We benchmark the Gutzwiller density functional approximation in the hydrogen systems, where the static correlation error is shown to be negligible. The good transferability is demonstrated by applications to the hydrogen molecule and some crystal structures.
The Benchmark of Gutzwiller Density Functional Theory in Hydrogen Systems
Energy Technology Data Exchange (ETDEWEB)
Yao, Yongxin; Wang, Cai-Zhuang; Ho, Kai-Ming
2011-01-13
We propose an approximate form of the exchange-correlation energy functional for the Gutzwiller density functional theory. It satisfies certain physical constraints in both weak and strong electron correlation limits. We benchmark the Gutzwiller density functional approximation in the hydrogen systems, where the static correlation error is shown to be negligible. The good transferability is demonstrated by applications to the hydrogen molecule and some crystal structures. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012
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.
Sheng, Ke; Cai, Jing; Brookeman, James; Molloy, Janelle; Christopher, John; Read, Paul
2006-09-01
Lung tumor motion trajectories measured by four-dimensional CT or dynamic MRI can be converted to a probability density function (PDF), which describes the probability of the tumor at a certain position, for PDF based treatment planning. Using this method in simulated sequential tomotherapy, we study the dose reduction of normal tissues and more important, the effect of PDF reproducibility on the accuracy of dosimetry. For these purposes, realistic PDFs were obtained from two dynamic MRI scans of a healthy volunteer within a 2 week interval. The first PDF was accumulated from a 300 s scan and the second PDF was calculated from variable scan times from 5 s (one breathing cycle) to 300 s. Optimized beam fluences based on the second PDF were delivered to the hypothetical gross target volume (GTV) of a lung phantom that moved following the first PDF The reproducibility between two PDFs varied from low (78%) to high (94.8%) when the second scan time increased from 5 s to 300 s. When a highly reproducible PDF was used in optimization, the dose coverage of GTV was maintained; phantom lung receiving 10%-20% prescription dose was reduced by 40%-50% and the mean phantom lung dose was reduced by 9.6%. However, optimization based on PDF with low reproducibility resulted in a 50% underdosed GTV. The dosimetric error increased nearly exponentially as the PDF error increased. Therefore, although the dose of the tumor surrounding tissue can be theoretically reduced by PDF based treatment planning, the reliability and applicability of this method highly depend on if a reproducible PDF exists and is measurable. By correlating the dosimetric error and PDF error together, a useful guideline for PDF data acquisition and patient qualification for PDF based planning can be derived.
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
Institute of Scientific and Technical Information of China (English)
XU HUAI; TANG LING; Wang De-hui
2013-01-01
In this paper,we consider a general expression for (Φ)(u,x,y),the joint density function of the surplus prior to ruin and the deficit at ruin when the initial surplus is u.In the renewal risk model,this density function is expressed in terms of the corresponding density function when the initial surplus is 0.In the compound Poisson risk process with phase-type claim size,we derive an explicit expression for (Φ)(u,x,y).Finally,we give a numerical example to illustrate the application of these results.
Hilbert Space of Probability Density Functions Based on Aitchison Geometry
Institute of Scientific and Technical Information of China (English)
J. J. EGOZCUE; J. L. D(I)AZ-BARRERO; V. PAWLOWSKY-GLAHN
2006-01-01
The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison's ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.
A molecular density functional theory to study solvation in water
Jeanmairet, Guillaume
2014-01-01
A classical density functional theory is applied to study solvation of solutes in water. An approx- imate form of the excess functional is proposed for water. This functional requires the knowledge of pure solvent direct correlation functions. Those functions can be computed by using molecular simulations such as molecular dynamic or Monte Carlo. It is also possible to use functions that have been determined experimentally. The functional minimization gives access to the solvation free energy and to the equilibrium solvent density. Some correction to the functional are also proposed to get the proper tetrahedral order of solvent molecules around a charged solute and to reproduce the correct long range hydrophobic behavior of big apolar solutes. To proceed the numerical minimization of the functional, the theory has been discretized on two tridimensional grids, one for the space coordinates, the other for the angular coordinates, in a functional minimization code written in modern Fortran, mdft. This program i...
Energy Density Functional for Nuclei and Neutron Stars
Energy Technology Data Exchange (ETDEWEB)
Erler, J. [UTK/ORNL/German Cancer Research Center-Heidelberg; Horowitz, C. J. [UTK/ORNL/Indiana University; Nazarewicz, Witold [UTK/ORNL/University of Warsaw; Rafalski, M. [UTK/ORNL; Reinhard, P.-G. [Universitat Erlangen, Germany
2013-01-01
Background: Recent observational data on neutron star masses and radii provide stringent constraints on the equation of state of neutron rich matter [ Annu. Rev. Nucl. Part. Sci. 62 485 (2012)]. Purpose: We aim to develop a nuclear energy density functional that can be simultaneously applied to finite nuclei and neutron stars. Methods: We use the self-consistent nuclear density functional theory (DFT) with Skyrme energy density functionals and covariance analysis to assess correlations between observables for finite nuclei and neutron stars. In a first step two energy functionals a high density energy functional giving reasonable neutron properties, and a low density functional fitted to nuclear properties are matched. In a second step, we optimize a new functional using exactly the same protocol as in earlier studies pertaining to nuclei but now including neutron star data. This allows direct comparisons of performance of the new functional relative to the standard one. Results: The new functional TOV-min yields results for nuclear bulk properties (energy, rms radius, diffraction radius, and surface thickness) that are of the same quality as those obtained with the established Skyrme functionals, including SV-min. When comparing SV-min and TOV-min, isoscalar nuclear matter indicators vary slightly while isovector properties are changed considerably. We discuss neutron skins, dipole polarizability, separation energies of the heaviest elements, and proton and neutron drip lines. We confirm a correlation between the neutron skin of 208Pb and the neutron star radius. Conclusions: We demonstrate that standard energy density functionals optimized to nuclear data do not carry information on the expected maximum neutron star mass, and that predictions can only be made within an extremely broad uncertainty band. For atomic nuclei, the new functional TOV-min performs at least as well as the standard nuclear functionals, but it also reproduces expected neutron star data
Density functional theory of the crystal field in dioxides
Diviš, M.; Kuriplach, J.; Richter, M.; Steinbeck, L.
1996-04-01
Presented are the results of ab-initio density functional calculations for PrO2 and UO2 using the general potential LAPW and optimized LCAO method in the local density approximation. The crystal field splitting of ionic Pr4+ and U4+ ground states was calculated and compared with predictions of a superposition model.
Charge and spin fluctuations in the density functional theory
Energy Technology Data Exchange (ETDEWEB)
Gyoerffy, B.L.; Barbieri, A. (Bristol Univ. (UK). H.H. Wills Physics Lab.); Staunton, J.B. (Warwick Univ., Coventry (UK). Dept. of Physics); Shelton, W.A.; Stocks, G.M. (Oak Ridge National Lab., TN (USA))
1990-01-01
We introduce a conceptual framework which allow us to treat charge and spin fluctuations about the Local density Approximation (LDA) to the Density Functional Theory (DFT). We illustrate the approach by explicit study of the Disordered Local Moment (DLM) state in Fe above the Curie Temperature {Tc} and the Mott insulating state in MnO. 27 refs., 6 figs.
Excitation Spectra of Nucleobases with Multiconfigurational Density Functional Theory
DEFF Research Database (Denmark)
Hubert, Mickaël; Jensen, Hans Jørgen Aa; Hedegård, Erik D.
2016-01-01
Range-separated hybrid methods between wave function theory and density functional theory (DFT) can provide high-accuracy results, while correcting some of the inherent flaws of both the underlying wave function theory and DFT. We here assess the accuracy for excitation energies of the nucleobases...
Applications and validations of the Minnesota density functionals
Zhao, Yan; Truhlar, Donald G.
2011-01-01
We discuss and review selected recent applications and validations of the Minnesota density functionals, especially the M06 family, emphasizing nanochemistry, organic, inorganic, and biological chemistry, and catalysis and highlighting the broad accuracy of these functionals as compared to previous popular functionals for thermochemistry, kinetics, and noncovalent interactions.
Bayesian reweighting of nuclear PDFs and constraints from proton-lead collisions at the LHC
Armesto, Nestor; Salgado, Carlos A; Zurita, Pia
2013-01-01
New hard-scattering measurements from the LHC proton-lead run have the potential to provide important constraints on the nuclear parton distributions and thus contributing to a better understanding of the initial state in heavy ion collisions. In order to quantify these constraints, as well as to assess the compatibility with available nuclear data from fixed target experiments and from RHIC, the traditional strategy is to perform a global fit of nuclear PDFs. This procedure is however time consuming and technically challenging, and moreover can only be performed by the PDF fitters themselves. In the case of proton PDFs, an alternative approach has been suggested that uses Bayesian inference to propagate the effects of new data into the PDFs without the need of refitting. In this work, we apply this reweighting procedure to study the impact on nuclear PDFs of low-mass Drell-Yan and single-inclusive hadroproduction pseudo-data from proton-lead collisions at the LHC as representative examples. In the hadroprodu...
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
Energy Technology Data Exchange (ETDEWEB)
Kieron Burke
2012-04-30
A huge amount of fundamental research was performed on this grant. Most of it focussed on fundamental issues of electronic structure calculations of transport through single molecules, using density functional theory. Achievements were: (1) First density functional theory with dissipation; (2) Pseudopotential plane wave calculations with master equation; (3) Weak bias limit; (4) Long-chain conductance; and (5) Self-interaction effects in tunneling.
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.
QCD Factorization and PDFs from Lattice QCD Calculation
Ma, Yan-Qing
2014-01-01
In this talk, we review a QCD factorization based approach to extract parton distribution and correlation functions from lattice QCD calculation of single hadron matrix elements of quark-gluon operators. We argue that although the lattice QCD calculations are done in the Euclidean space, the nonperturbative collinear behavior of the matrix elements are the same as that in the Minkowski space, and could be systematically factorized into parton distribution functions with infrared safe matching coefficients. The matching coefficients can be calculated perturbatively by applying the factorization formalism on to asymptotic partonic states.
Linear response of homogeneous nuclear matter with energy density functionals
Energy Technology Data Exchange (ETDEWEB)
Pastore, A. [Institut d’Astronomie et d’Astrophysique, CP 226, Université Libre de Bruxelles, B-1050 Bruxelles (Belgium); Davesne, D., E-mail: davesne@ipnl.in2p3.fr [Institut de Physique Nucléaire de Lyon, CNRS-IN2P3, UMR 5822, Université Lyon 1, F-69622 Villeurbanne (France); Navarro, J. [IFIC (CSIC University of Valencia), Apdo. Postal 22085, E-46071 Valencia (Spain)
2015-03-01
Response functions of infinite nuclear matter with arbitrary isospin asymmetry are studied in the framework of the random phase approximation. The residual interaction is derived from a general nuclear Skyrme energy density functional. Besides the usual central, spin–orbit and tensor terms it could also include other components as new density-dependent terms or three-body terms. Algebraic expressions for the response functions are obtained from the Bethe–Salpeter equation for the particle–hole propagator. Applications to symmetric nuclear matter, pure neutron matter and asymmetric nuclear matter are presented and discussed. Spin–isospin strength functions are analyzed for varying conditions of density, momentum transfer, isospin asymmetry, and temperature for some representative Skyrme functionals. Particular attention is paid to the discussion of instabilities, either real or unphysical, which could manifest in finite nuclei.
Inclusion of Dispersion Effects in Density Functional Theory
DEFF Research Database (Denmark)
Møgelhøj, Andreas
In this thesis, applications and development will be presented within the field of van der Waals interactions in density functional theory. The thesis is based on the three projects: i) van der Waals interactions effect on the structure of liquid water at ambient conditions, ii) development...... and benchmarking of a new van der Waals density functional, and iii) the application of the newly developed functional to CO desorption from Ru(0001). The effect of van der Waals interactions in water was studied by performing ab initio molecular dynamics simulations using PBE and the two recent van der Waals...... density functionals optPBE-vdW and vdW-DF2 with identical computational setup. The two van der Waals functionals have been found to give excellent descriptions of the constituents of water (e.g., water dimers and hexamers). Including van der Waals interactions gives a softer water structure as seen from...
Introduction to Classical Density Functional Theory by Computational Experiment
Jeanmairet, Guillaume; Levesque, Maximilien; Borgis, Daniel
2014-01-01
We present here an introductory practical course to classical density functional theory (cDFT). Density functional theories, whether quantum or classical, rely largely on nonintuitive abstract concepts and applied mathematics. They are nevertheless a powerful tool and an active field of research in physics and chemistry that led to the 1998 Nobel prize in chemistry. We here illustrate the DFT in its most mathematically simple and yet physically relevant form: the classical density functional theory of an ideal fluid in an external field, as applied to the prediction of the structure of liquid neon at the molecular scale. This introductory course is built around the production of a cDFT code written by students using the Mathematica language. In this way, they are brought to deal with (i) the cDFT theory itself, (ii) some basic concepts around the statistical mechanics of simple fluids, (iii) the underlying mathematical and numerical problem of functional minimization, and (iv) a functional programming languag...
Sloppy nuclear energy density functionals: effective model reduction
Niksic, Tamara
2016-01-01
Concepts from information geometry are used to analyse parameter sensitivity for a nuclear energy density functional, representative of a class of semi-empirical functionals that start from a microscopically motivated ansatz for the density dependence of the energy of a system of protons and neutrons. It is shown that such functionals are sloppy, characterized by an exponential range of sensitivity to parameter variations. Responsive to only a few stiff parameter combinations, they exhibit an exponential decrease of sensitivity to variations of the remaining soft parameters. By interpreting the space of model predictions as a manifold embedded in the data space, with the parameters of the functional as coordinates on the manifold, it is also shown that the exponential distribution of model manifold widths corresponds to the distribution of parameter sensitivity. Using the Manifold Boundary Approximation Method, we illustrate how to systematically construct effective nuclear density functionals of successively...
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.
Viironen, K; López-Sanjuan, C; Varela, J; Chaves-Montero, J; Cristóbal-Hornillos, D; Molino, A; Fernández-Soto, A; Ascaso, B; Cenarro, A J; Cerviño, M; Cepa, J; Ederoclite, A; Márquez, I; Masegosa, J; Moles, M; Oteo, I; Pović, M; Aguerri, J A L; Alfaro, E; Aparicio-Villegas, T; Benítez, N; Broadhurst, T; Cabrera-Caño, J; Castander, J F; Del Olmo, A; Delgado, R M González; Husillos, C; Infante, L; Martínez, V J; Perea, J; Prada, F; Quintana, J M
2015-01-01
Context. Most observational results on the high redshift restframe UV-bright galaxies are based on samples pinpointed using the so called dropout technique or Ly-alpha selection. However, the availability of multifilter data allows now replacing the dropout selections by direct methods based on photometric redshifts. In this paper we present the methodology to select and study the population of high redshift galaxies in the ALHAMBRA survey data. Aims. Our aim is to develop a less biased methodology than the traditional dropout technique to study the high redshift galaxies in ALHAMBRA and other multifilter data. Thanks to the wide area ALHAMBRA covers, we especially aim at contributing in the study of the brightest, less frequent, high redshift galaxies. Methods. The methodology is based on redshift probability distribution functions (zPDFs). It is shown how a clean galaxy sample can be obtained by selecting the galaxies with high integrated probability of being within a given redshift interval. However, reach...
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
Institute of Scientific and Technical Information of China (English)
FU Dong
2005-01-01
@@ A non-mean field density functional theory is employed to investigate the vapour-liquid nucleation. The excess Helmholtz free energy functional is formulated in terms of a local density approximation for short ranged repulsion and a density-gradient expansion for long-ranged attractions. An analytical expression for the direct correlation function of a Lennard-Jones fluid is utilized to take into account the effect of long-ranged attractions on intermolecular correlations. With the predicted bulk properties and surface tension as input, the nucleation properties including density profile, work of formation and number of particles at the reduced temperatures T* = 0.694 and 0.741 are inuestigated. The obtained number of particles in the critical nucleus agrees well with the simulation data.
Unbiased polarized PDFs upgraded with new inclusive DIS data
Nocera, Emanuele R
2015-01-01
I present a determination of longitudinally-polarized parton distribution functions of the proton from inclusive deep-inelastic scattering data: NNPDFpol1.0+. This determination, based on the NNPDF methodology, upgrades a previous analysis, NNPDFpol1.0, in two respects: first, it includes all new data sets which have recently become available from the COMPASS experiment at CERN and from the E93-009, EG1-DVCS and E06-014 experiments at JLAB; second, it uses the state-of-the-art unpolarized parton set NNPDF3.0 as a baseline for the reconstruction of fitted observables and for the determination of positivity constraints. I discuss the impact of both these new inputs on the uncertainty of parton distribution functions.
Probability density functions for the variable solar wind near the solar cycle minimum
Vörös,; Leitner, M; Narita, Y; Consolini, G; Kovács, P; Tóth, A; Lichtenberger, J
2015-01-01
Unconditional and conditional statistics is used for studying the histograms of magnetic field multi-scale fluctuations in the solar wind near the solar cycle minimum in 2008. The unconditional statistics involves the magnetic data during the whole year 2008. The conditional statistics involves the magnetic field time series splitted into concatenated subsets of data according to a threshold in dynamic pressure. The threshold separates fast stream leading edge compressional and trailing edge uncompressional fluctuations. The histograms obtained from these data sets are associated with both large-scale (B) and small-scale ({\\delta}B) magnetic fluctuations, the latter corresponding to time-delayed differences. It is shown here that, by keeping flexibility but avoiding the unnecessary redundancy in modeling, the histograms can be effectively described by a limited set of theoretical probability distribution functions (PDFs), such as the normal, log-normal, kappa and logkappa functions. In a statistical sense the...
Specification of Density Functional Approximation by Radial Distribution Function of Bulk Fluid
Institute of Scientific and Technical Information of China (English)
ZHOUShi－Qi
2002-01-01
A systematic methodology is proposed to deal with the weighted density approximation version of classical density functional theory by employing the knowledge of radial distribution function of bulk fluid.The present methodology results from the concept of universality of the free energy density functional combined with the test particle method.It is shown that the new method is very accurate for the predictions of density distribution of a hard sphere fluid at different confining geometries.The physical foundation of the present methodology is also applied to the quantum density functional theory.
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
DEFF Research Database (Denmark)
Lee, Kyuho; Murray, Éamonn D.; Kong, Lingzhu
2010-01-01
We propose a second version of the van der Waals density functional of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)], employing a more accurate semilocal exchange functional and the use of a large-N asymptote gradient correction in determining the vdW kernel. The predicted binding energy...
Wigner Function of Density Operator for Negative Binomial Distribution
Institute of Scientific and Technical Information of China (English)
HE Min-Hua; XU Xing-Lei; ZHANG Duan-Ming; LI Hong-Qi; PAN Gui-Jun; YIN Yan-Ping; CHEN Zhi-Yuan
2008-01-01
By using the technique of integration within an ordered product (IWOP) of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator.
Density-functional perturbation theory goes time-dependent
Gebauer, Ralph; Rocca, Dario; Baroni, Stefano
2009-01-01
The scope of time-dependent density-functional theory (TDDFT) is limited to the lowest portion of the spectrum of rather small systems (a few tens of atoms at most). In the static regime, density-functional perturbation theory (DFPT) allows one to calculate response functions of systems as large as currently dealt with in ground-state simulations. In this paper we present an effective way of combining DFPT with TDDFT. The dynamical polarizability is first expressed as an off-diagonal matrix e...
Density Functional Theory for General Hard-Core Lattice Gases
Lafuente, Luis; Cuesta, José A.
2004-09-01
We put forward a general procedure to obtain an approximate free-energy density functional for any hard-core lattice gas, regardless of the shape of the particles, the underlying lattice, or the dimension of the system. The procedure is conceptually very simple and recovers effortlessly previous results for some particular systems. Also, the obtained density functionals belong to the class of fundamental measure functionals and, therefore, are always consistent through dimensional reduction. We discuss possible extensions of this method to account for attractive lattice models.
Density Functional Theory and Materials Modeling at Atomistic Length Scales
Directory of Open Access Journals (Sweden)
Swapan K. Ghosh
2002-04-01
Full Text Available Abstract: We discuss the basic concepts of density functional theory (DFT as applied to materials modeling in the microscopic, mesoscopic and macroscopic length scales. The picture that emerges is that of a single unified framework for the study of both quantum and classical systems. While for quantum DFT, the central equation is a one-particle Schrodinger-like Kohn-Sham equation, the classical DFT consists of Boltzmann type distributions, both corresponding to a system of noninteracting particles in the field of a density-dependent effective potential, the exact functional form of which is unknown. One therefore approximates the exchange-correlation potential for quantum systems and the excess free energy density functional or the direct correlation functions for classical systems. Illustrative applications of quantum DFT to microscopic modeling of molecular interaction and that of classical DFT to a mesoscopic modeling of soft condensed matter systems are highlighted.
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...
Time dependent density functional calculation of plasmon response in clusters
Institute of Scientific and Technical Information of China (English)
Wang Feng(王锋); Zhang Feng-Shou(张丰收); Eric Suraud
2003-01-01
We have introduced a theoretical scheme for the efficient description of the optical response of a cluster based on the time-dependent density functional theory. The practical implementation is done by means of the fully fledged timedependent local density approximation scheme, which is solved directly in the time domain without any linearization.As an example we consider the simple Na2 cluster and compute its surface plasmon photoabsorption cross section, which is in good agreement with the experiments.
Density functional calculations of spin-wave dispersion curves.
Kleinman, Leonard; Niu, Qian
1998-03-01
Extending the density functional method of Kubler et al( J. Kubler et al, J. Phys. F 18, 469 (1983) and J. Phys. Condens. Matter 1, 8155 (1989). ) for calcuating spin density wave ground states (but not making their atomic sphere approximation which requires a constant spin polarization direction in each WS sphere) we dicuss the calculation of frozen spin-wave eigenfunctions and their total energies. From these and the results of Niu's talk, we describe the calculation of spin-wave frequencies.
New Statistical PDFs: Predictions and Tests up to LHC Energies
Soffer, Jacques
2016-01-01
The quantum statistical parton distributions approach proposed more than one decade ago is revisited by considering a larger set of recent and accurate Deep Inelastic Scattering experimental results. It enables us to improve the description of the data by means of a new determination of the parton distributions. This global next-to-leading order QCD analysis leads to a good description of several structure functions, involving unpolarized parton distributions and helicity distributions, in a broad range of $x$ and $Q^2$ and in terms of a rather small number of free parameters. There are several challenging issues, in particular the behavior of $\\bar d(x) / \\bar u(x)$ at large $x$, a possible large positive gluon helicity distribution, etc.. The predictions of this theoretical approach will be tested for single-jet production and charge asymmetry in $W^{\\pm}$ production in $\\bar p p$ and $p p$ collisions up to LHC energies, using recent data and also for forthcoming experimental results.
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.
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.
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.
Institute of Scientific and Technical Information of China (English)
周世琦
2002-01-01
In this Letter, we truncate the functional expansion of the non-uniform first-order direct correlation function (DCF) around the bulk density at the lowest order. But the truncation is performed formally and exactly by making use of functional counterpart of the Lagrangian theorem of differential calculus. Consequently the expansion coefficient, i.e. the uniform second-order DCF, is replaced by its non-uniform counterpart whose density argument is an appropriate mixture of calculated density distribution and the bulk density with a mixing parameter determined by a hard-wall sum rule. The non-uniform second-order DCF is then approximated by the uniform second-order DCF with an appropriate weighted density as its density argument. The present formally exact truncated functional expansion predicts the density distribution in good agreement with simulation data for hard sphere and Lennard-Jones fluid exerted by an external field.
Specification of Density Functional Approximation by Radial Distribution Function of Bulk Fluid
Institute of Scientific and Technical Information of China (English)
ZHOU Shi-Qi
2002-01-01
A systematic methodology is proposed to deal with the weighted density approximation version of clas-sical density functional theory by employing the knowledge of radial distribution function of bulk fluid. The presentmethodology results from the concept of universality of the free energy density functional combined with the test particlemethod. It is shown that the new method is very accurate for the predictions of density distribution ofa hard sphere fluidat different confining geometries. The physical foundation of the present methodology is also applied to the quantumdensity functional theory.
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
DEFF Research Database (Denmark)
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...
Jian, Y; Yao, R; Mulnix, T; Jin, X; Carson, R E
2015-01-07
Resolution degradation in PET image reconstruction can be caused by inaccurate modeling of the physical factors in the acquisition process. Resolution modeling (RM) is a common technique that takes into account the resolution degrading factors in the system matrix. Our previous work has introduced a probability density function (PDF) method of deriving the resolution kernels from Monte Carlo simulation and parameterizing the LORs to reduce the number of kernels needed for image reconstruction. In addition, LOR-PDF allows different PDFs to be applied to LORs from different crystal layer pairs of the HRRT. In this study, a thorough test was performed with this new model (LOR-PDF) applied to two PET scanners-the HRRT and Focus-220. A more uniform resolution distribution was observed in point source reconstructions by replacing the spatially-invariant kernels with the spatially-variant LOR-PDF. Specifically, from the center to the edge of radial field of view (FOV) of the HRRT, the measured in-plane FWHMs of point sources in a warm background varied slightly from 1.7 mm to 1.9 mm in LOR-PDF reconstructions. In Minihot and contrast phantom reconstructions, LOR-PDF resulted in up to 9% higher contrast at any given noise level than image-space resolution model. LOR-PDF also has the advantage in performing crystal-layer-dependent resolution modeling. The contrast improvement by using LOR-PDF was verified statistically by replicate reconstructions. In addition, [(11)C]AFM rats imaged on the HRRT and [(11)C]PHNO rats imaged on the Focus-220 were utilized to demonstrated the advantage of the new model. Higher contrast between high-uptake regions of only a few millimeter diameter and the background was observed in LOR-PDF reconstruction than in other methods.
Benchmarking Density Functionals for Chemical Bonds of Gold
DEFF Research Database (Denmark)
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
DEFF Research Database (Denmark)
Yan, Jun; Mortensen, Jens Jørgen; Jacobsen, Karsten Wedel;
2011-01-01
We present an implementation of the linear density response function within the projector-augmented wave method with applications to the linear optical and dielectric properties of both solids, surfaces, and interfaces. The response function is represented in plane waves while the single......-particle eigenstates can be expanded on a real space grid or in atomic-orbital basis for increased efficiency. The exchange-correlation kernel is treated at the level of the adiabatic local density approximation (ALDA) and crystal local field effects are included. The calculated static and dynamical dielectric...... functions of Si, C, SiC, AlP, and GaAs compare well with previous calculations. While optical properties of semiconductors, in particular excitonic effects, are generally not well described by ALDA, we obtain excellent agreement with experiments for the surface loss function of graphene and the Mg(0001...
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.
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.
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.
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...
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
Institute of Scientific and Technical Information of China (English)
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
DEFF Research Database (Denmark)
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
Institute of Scientific and Technical Information of China (English)
Huajie Chen; Aihui Zhou
2008-01-01
We give here an overview of the orbital-free density functional theory that is used for modeling atoms and molecules. We review typical approximations to the kinetic energy, exchange-correlation corrections to the kinetic and Hartree energies, and constructions of the pseudopotentials. We discuss numerical discretizations for the orbital-free methods and include several numerical results for illustrations.
Exact ensemble density-functional theory for excited states
Yang, Zeng-hui; Pribram-Jones, Aurora; Burke, Kieron; Needs, Richard J; Ullrich, Carsten A
2014-01-01
We construct exact Kohn-Sham potentials for the ensemble density-functional theory (EDFT) of excited states from the ground and excited states of helium. The exchange-correlation potential is compared with current approximations, which miss prominent features. The ensemble derivative discontinuity is tested, and the virial theorem is proven and illustrated.
Reproducibility in density functional theory calculations of solids
DEFF Research Database (Denmark)
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.
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.
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...
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
Energy Technology Data Exchange (ETDEWEB)
Barranco, M. (Dept. de Estructura y Constituyentes de la Materia, Barcelona Univ. (Spain)); Jezek, D.M. (Dept. de Estructura y Constituyentes de la Materia, Barcelona Univ. (Spain)); Hernandez, E.S. (Dept. de Fisica, Univ. de Buenos Aires (Argentina)); Navarro, J. (Dept. de Fisica Atomica, Molecular y Nuclear, Valencia Univ. (Spain)); Serra, Ll. (Dipt. di Fisica, Milan Univ. (Italy))
1993-11-01
We present a density functional for the description of liquid [sup 3]He properties at zero temperture in a mean field approximation. Its basic ingredients are a zero-range, particle- and spin-density dependent effective interaction of Skyrme type, and a long-range effective interaction of Lennard-Jones type supplemented with a weighted density approximation similar to the one used in the study of classical fluids, to phenomenologically account for short range correlations. After fixing the value of its parameters, the functional yields a good desription of the equation of state and Landau parameters (spin symmetric and spin antisymmetric as well) from saturation to solidification densities. The zero sound propagation at finite momentum transfer is quantitatively reproduced up to the Fermi momentum, and qualitatively above it. The surface tension is in agreement with experiment, which makes the functional well suited for [sup 3]He drop calculations. We describe the structure of drops made of up to 516 atoms. As a novel application, we discuss the possible appearance of triplet pairing in a nl-shell of a drop applying the formalism to the 1j-shell holding up to 30 atoms from N=169 to 198. (orig.)
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
Institute of Scientific and Technical Information of China (English)
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
Institute of Scientific and Technical Information of China (English)
WANG Huaiyu; HAN Rushan; CHEN Nanxian
2005-01-01
Density functional method is applied for strongly correlated systems. Based on the assumption that the systems are composed of electrons in singly-occupied orbitals and those in doubly-occupied orbitals, a set of self-consistent equations are obtained by standard variation procedure. The equations consist of two parts. One part is to solve the wave functions of the electrons in singly-occupied orbitals and the other is to solve the wave functions of the electrons in doubly-occupied orbitals. The physical meanings of the terms appearing in the equations are discussed.
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.
Reduced density matrix functional theory at finite temperature
Energy Technology Data Exchange (ETDEWEB)
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.
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
Energy Technology Data Exchange (ETDEWEB)
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.
Time-dependent density-functional theory for extended systems
Energy Technology Data Exchange (ETDEWEB)
Botti, Silvana [European Theoretical Spectroscopy Facility (ETSF) (Country Unknown); Schindlmayr, Arno [European Theoretical Spectroscopy Facility (ETSF) (Country Unknown); Del Sole, Rodolfo [European Theoretical Spectroscopy Facility (ETSF) (Country Unknown); Reining, Lucia [European Theoretical Spectroscopy Facility (ETSF) (Country Unknown)
2007-03-15
For the calculation of neutral excitations, time-dependent density functional theory (TDDFT) is an exact reformulation of the many-body time-dependent Schroedinger equation, based on knowledge of the density instead of the many-body wavefunction. The density can be determined in an efficient scheme by solving one-particle non-interacting Schroedinger equations-the Kohn-Sham equations. The complication of the problem is hidden in the-unknown-time-dependent exchange and correlation potential that appears in the Kohn-Sham equations and for which it is essential to find good approximations. Many approximations have been suggested and tested for finite systems, where even the very simple adiabatic local-density approximation (ALDA) has often proved to be successful. In the case of solids, ALDA fails to reproduce optical absorption spectra, which are instead well described by solving the Bethe-Salpeter equation of many-body perturbation theory (MBPT). On the other hand, ALDA can lead to excellent results for loss functions (at vanishing and finite momentum transfer). In view of this and thanks to recent successful developments of improved linear-response kernels derived from MBPT, TDDFT is today considered a promising alternative to MBPT for the calculation of electronic spectra, even for solids. After reviewing the fundamentals of TDDFT within linear response, we discuss different approaches and a variety of applications to extended systems.
Covariant density functional theory: Reexamining the structure of superheavy nuclei
Agbemava, S E; Nakatsukasa, T; Ring, P
2015-01-01
A systematic investigation of even-even superheavy elements in the region of proton numbers $100 \\leq Z \\leq 130$ and in the region of neutron numbers from the proton-drip line up to neutron number $N=196$ is presented. For this study we use five most up-to-date covariant energy density functionals of different types, with a non-linear meson coupling, with density dependent meson couplings, and with density-dependent zero-range interactions. Pairing correlations are treated within relativistic Hartree-Bogoliubov (RHB) theory based on an effective separable particle-particle interaction of finite range and deformation effects are taken into account. This allows us to assess the spread of theoretical predictions within the present covariant models for the binding energies, deformation parameters, shell structures and $\\alpha$-decay half-lives. Contrary to the previous studies in covariant density functional theory, it was found that the impact of $N=172$ spherical shell gap on the structure of superheavy elemen...
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
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
Directory of Open Access Journals (Sweden)
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
Energy Technology Data Exchange (ETDEWEB)
Pribram-Jones, Aurora; Burke, Kieron [Department of Chemistry, University of California-Irvine, Irvine, California 92697 (United States); Yang, Zeng-hui; Ullrich, Carsten A. [Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211 (United States); Trail, John R.; Needs, Richard J. [Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE (United Kingdom)
2014-05-14
A new method for extracting ensemble Kohn-Sham potentials from accurate excited state densities is applied to a variety of two-electron systems, exploring the behavior of exact ensemble density functional theory. The issue of separating the Hartree energy and the choice of degenerate eigenstates is explored. A new approximation, spin eigenstate Hartree-exchange, is derived. Exact conditions that are proven include the signs of the correlation energy components and the asymptotic behavior of the potential for small weights of the excited states. Many energy components are given as a function of the weights for two electrons in a one-dimensional flat box, in a box with a large barrier to create charge transfer excitations, in a three-dimensional harmonic well (Hooke's atom), and for the He atom singlet-triplet ensemble, singlet-triplet-singlet ensemble, and triplet bi-ensemble.
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.
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...
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.
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
Energy Technology Data Exchange (ETDEWEB)
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
DEFF Research Database (Denmark)
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
DEFF Research Database (Denmark)
Mortensen, Jens Jørgen; Kaasbjerg, Kristen; Frederiksen, Søren Lund
2005-01-01
We present a practical scheme for performing error estimates for density-functional theory calculations. The approach, which is based on ideas from Bayesian statistics, involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies...... for molecules and solids. Fluctuations within the ensemble can then be used to estimate errors relative to experiment on calculated quantities such as binding energies, bond lengths, and vibrational frequencies. It is demonstrated that the error bars on energy differences may vary by orders of magnitude...
Formation energies of rutile metal dioxides using density functional theory
DEFF Research Database (Denmark)
Martinez, Jose Ignacio; Hansen, Heine Anton; Rossmeisl, Jan
2009-01-01
We apply standard density functional theory at the generalized gradient approximation (GGA) level to study the stability of rutile metal oxides. It is well known that standard GGA exchange and correlation in some cases is not sufficient to address reduction and oxidation reactions. Especially...... and due to a more accurate description of exchange for this particular GGA functional compared to PBE. Furthermore, we would expect the self-interaction problem to be largest for the most localized d orbitals; that means the late 3d metals and since Co, Fe, Ni, and Cu do not form rutile oxides...
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
Time-dependent density functional theory: Causality and other problems
Energy Technology Data Exchange (ETDEWEB)
Ruggenthaler, Michael; Bauer, Dieter [Max-Planck-Inst. fuer Kernphysik, Heidelberg (Germany)
2007-07-01
Time-dependent density functional theory (TDDFT) is a reformulation of the time dependent many-body problem in quantum mechanics which is capable of reducing the computational cost to calculate, e.g., strongly driven many-electron systems enormously. Recent developments were able to overcome fundamental problems associated with ionization processes. Still vital issues have to be clarified. Besides the construction of the underlying functionals we investigate the causality problem of TDDFT by general considerations and by studying a exactly solvable system of two correlated electrons in an intense laser-pulse. For the latter system, the two alternative approaches to the construction of the action functional or a constrained functional derivative by van Leeuwen and Gal, respectively, are explored.
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.
Energy Technology Data Exchange (ETDEWEB)
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
Energy Technology Data Exchange (ETDEWEB)
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.
Density-functional perturbation theory goes time-dependent
Directory of Open Access Journals (Sweden)
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
Energy Technology Data Exchange (ETDEWEB)
Ham, Michael I [Los Alamos National Laboratory; Gintautuas, Vadas [Los Alamos National Laboratory; Rodriguez, Marko A [Los Alamos National Laboratory; Bettencourt, Luis M A [Los Alamos National Laboratory; Bennett, Ryan [UNIV OF NORTH TEXAS; Santa Maria, Cara L [UNIV OF NORTH TEXAS
2008-01-01
During development, the mammalian brain differentiates into specialized regions with unique functional abilities. While many factors contribute to this functional specialization, we explore the effect neuronal density can have on neuronal interactions. Two types of networks, dense (50,000 neurons and glia support cells) and sparse (12,000 neurons and glia support cells), are studied. A competitive first response model is applied to construct activation graphs that represent pairwise neuronal interactions. By observing the evolution of these graphs during development in vitro we observe that dense networks form activation connections earlier than sparse networks, and that link-!llltropy analysis of the resulting dense activation graphs reveals that balanced directional connections dominate. Information theoretic measures reveal in addition that early functional information interactions (of order 3) are synergetic in both dense and sparse networks. However, during development in vitro, such interactions become redundant in dense, but not sparse networks. Large values of activation graph link-entropy correlate strongly with redundant ensembles observed in the dense networks. Results demonstrate differences between dense and sparse networks in terms of informational groups, pairwise relationships, and activation graphs. These differences suggest that variations in cell density may result in different functional specialization of nervous system tissue also in vivo.
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.
DEFF Research Database (Denmark)
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.
Energy Technology Data Exchange (ETDEWEB)
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
Institute of Scientific and Technical Information of China (English)
ZHOU Shi-Qi
2003-01-01
Previous literature claims that the density functional theory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0(3)(r1, r2, r3) =ζ∫ dr4a(r4 - r1)a(r4 - r2)a(r4 - r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ζ and the short range of the a kernel function.Improvement over the previous theories is proposed and tested.
Mean Spherical Approximation-Based Partitioned Density Functional Theory
Institute of Scientific and Technical Information of China (English)
ZHOUShi-Qi
2003-01-01
Previous literature claims that the density functional theory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C0(3)(r1, r2, r3) =(∫dr4a(r4-r1)a(r4-r2)a(r4-r3) as the uniform third order direct correlation function (DCF) for the tail part,here kernel function a(r) = (6/πσ3)Heaviside(σ/2 - r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ξ and the short range of the a kernel function.Improvement over the previous theories is proposed and tested.
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
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
Arnaud Chauviere
2012-03-01
Full Text Available Cancer is a disease that can be seen as a complex system whose dynamics and growth result from nonlinear processes coupled across wide ranges of spatio-temporal scales. The current mathematical modeling literature addresses issues at various scales but the development of theoretical methodologies capable of bridging gaps across scales needs further study. We present a new theoretical framework based on Dynamic Density Functional Theory (DDFT extended, for the first time, to the dynamics of living tissues by accounting for cell density correlations, different cell types, phenotypes and cell birth/death processes, in order to provide a biophysically consistent description of processes across the scales. We present an application of this approach to tumor growth.
Equation of State in a Generalized Relativistic Density Functional Approach
Typel, Stefan
2015-01-01
The basic concepts of a generalized relativistic density functional approach to the equation of state of dense matter are presented. The model is an extension of relativistic mean-field models with density-dependent couplings. It includes explicit cluster degrees of freedom. The formation and dissolution of nuclei is described with the help of mass shifts. The model can be adapted to the description of finite nuclei in order to study the effect of $\\alpha$-particle correlations at the nuclear surface on the neutron skin thickness of heavy nuclei. Further extensions of the model to include quark degrees of freedom or an energy dependence of the nucleon self-energies are outlined.
Density functional study of ferromagnetism in alkali metal thin films
Indian Academy of Sciences (India)
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
Dynamic density functional theory with hydrodynamic interactions and fluctuations
Energy Technology Data Exchange (ETDEWEB)
Donev, Aleksandar, E-mail: donev@courant.nyu.edu; Vanden-Eijnden, Eric, E-mail: eve2@courant.nyu.edu [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
2014-06-21
We derive a closed equation for the empirical concentration of colloidal particles in the presence of both hydrodynamic and direct interactions. The ensemble average of our functional Langevin equation reproduces known deterministic Dynamic Density Functional Theory (DDFT) [M. Rex and H. Löwen, “Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps,” Phys. Rev. Lett. 101(14), 148302 (2008)], and, at the same time, it also describes the microscopic fluctuations around the mean behavior. We suggest separating the ideal (non-interacting) contribution from additional corrections due to pairwise interactions. We find that, for an incompressible fluid and in the absence of direct interactions, the mean concentration follows Fick's law just as for uncorrelated walkers. At the same time, the nature of the stochastic terms in fluctuating DDFT is shown to be distinctly different for hydrodynamically-correlated and uncorrelated walkers. This leads to striking differences in the behavior of the fluctuations around Fick's law, even in the absence of pairwise interactions. We connect our own prior work [A. Donev, T. G. Fai, and E. Vanden-Eijnden, “A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law,” J. Stat. Mech.: Theory Exp. (2014) P04004] on fluctuating hydrodynamics of diffusion in liquids to the DDFT literature, and demonstrate that the fluid cannot easily be eliminated from consideration if one wants to describe the collective diffusion in colloidal suspensions.
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...
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
Energy Technology Data Exchange (ETDEWEB)
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
Energy Technology Data Exchange (ETDEWEB)
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
Directory of Open Access Journals (Sweden)
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
DEFF Research Database (Denmark)
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
Directory of Open Access Journals (Sweden)
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.
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...
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.
Polymer density functional approach to efficient evaluation of path integrals
DEFF Research Database (Denmark)
Brukhno, Andrey; Vorontsov-Velyaminov, Pavel N.; Bohr, Henrik
2005-01-01
A polymer density functional theory (P-DFT) has been extended to the case of quantum statistics within the framework of Feynman path integrals. We start with the exact P-DFT formalism for an ideal open chain and adapt its efficient numerical solution to the case of a ring. We show that, similarly......, the path integral problem can, in principle, be solved exactly by making use of the two-particle pair correlation function (2p-PCF) for the ends of an open polymer, half of the original. This way the exact data for one-dimensional quantum harmonic oscillator are reproduced in a wide range of temperatures......-consistent iteration so as to correctly account for the interparticle interactions. The algorithm is speeded up by taking convolutions with the aid of fast Fourier transforms. We apply this approximate path integral DFT (PI-DFT) method to systems within spherical symmetry: 3D harmonic oscillator, atoms of hydrogen...
Energetics of cyclohexane isomers: a density-functional study
Lee, C Y
1999-01-01
The binding energies and the geometric structures of conformational isomers of cyclohexane (C sub 6 H sub 1 sub 2) are determined from the density-functional theory combined with ultrasoft pseudopotentials and gradient-corrected nonlocal exchange-correlation functionals. The ground-state chair conformation is found to have a binding energy of 99.457 eV, and the metastable twist-boat conformation has 99.161 eV. The chair conformation converts to another conformation via a half-chair conformation with an energy barrier of 0.507 eV whereas the twist-boat conformation converts to another twist-boat conformation via a boat conformation with a much smaller energy barrier of 0.015 eV.
Uncertainty Quantification and Propagation in Nuclear Density Functional Theory
Energy Technology Data Exchange (ETDEWEB)
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)
Energy Technology Data Exchange (ETDEWEB)
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
Energy Technology Data Exchange (ETDEWEB)
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
Institute of Scientific and Technical Information of China (English)
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...
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.
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.
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.
Daubechies wavelets for linear scaling density functional theory
Energy Technology Data Exchange (ETDEWEB)
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
Energy Technology Data Exchange (ETDEWEB)
Lafuente, Luis; Cuesta, Jose A [Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matematicas, Universidad Carlos III de Madrid, 28911 Leganes, Madrid (Spain)
2005-08-26
Rosenfeld's fundamental-measure theory for lattice models is given a rigorous formulation in terms of the theory of Moebius functions of partially ordered sets. The free-energy density functional is expressed as an expansion in a finite set of lattice clusters. This set is endowed with a partial order, so that the coefficients of the cluster expansion are connected to its Moebius function. Because of this, it is rigorously proven that a unique such expansion exists for any lattice model. The low-density analysis of the free-energy functional motivates a redefinition of the basic clusters (zero-dimensional cavities) which guarantees a correct zero-density limit of the pair and triplet direct correlation functions. This new definition extends Rosenfeld's theory to lattice models with any kind of short-range interaction (repulsive or attractive, hard or soft, one or multicomponent ...). Finally, a proof is given that these functionals have a consistent dimensional reduction, i.e. the functional for dimension d' can be obtained from that for dimension d (d' < d) if the latter is evaluated at a density profile confined to a d'-dimensional subset.
Burkhart, Blakesley; Collins, David
2016-01-01
We derive an analytic expression for the transitional column density value ($s_t$) between the lognormal and power-law form of the probability distribution function (PDF) in star-forming molecular clouds. Our expression for $s_t$ depends on the mean column density, the variance of the lognormal portion of the PDF, and the slope of the power-law portion of the PDF. We show that $s_t$ can be related to physical quantities such as the sonic Mach number of the flow and the power-law index for a self-gravitating isothermal sphere. This implies that the transition point between the lognormal and power-law density/column density PDF represents the critical density where turbulent and thermal pressure balance, the so-called "post-shock density." We test our analytic prediction for the transition column density using dust PDF observations reported in the literature as well as numerical MHD simulations of self-gravitating supersonic turbulence with the Enzo code. We find excellent agreement between the analytic $s_t$ a...
A density functional for liquid {sup 4}He including the pair distribution function
Energy Technology Data Exchange (ETDEWEB)
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
Energy Technology Data Exchange (ETDEWEB)
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
Directory of Open Access Journals (Sweden)
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)
Energy Technology Data Exchange (ETDEWEB)
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.
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
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
Institute of Scientific and Technical Information of China (English)
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
Directory of Open Access Journals (Sweden)
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
Institute of Scientific and Technical Information of China (English)
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
Energy Technology Data Exchange (ETDEWEB)
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
Institute of Scientific and Technical Information of China (English)
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
Energy Technology Data Exchange (ETDEWEB)
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
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
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.
Scalable Nuclear Density Functional Theory with Sky3D
Afibuzzaman, Md; Aktulga, Hasan Metin
2016-01-01
In nuclear astro-physics, the quantum simulation of large inhomogenous dense systems as present in the crusts of neutron stars presents big challenges. The feasible number of particles in a simulation box with periodic boundary conditions is strongly limited due to the immense computational cost of the quantum methods. In this paper, we describe the techniques used to parallelize Sky3D, a nuclear density functional theory code that operates on an equidistant grid, and optimize its performance on distributed memory architectures. We also describe cache blocking techniques to accelerate the compute-intensive matrix calculation part in Sky3D. Presented techniques allow Sky3D to achieve good scaling and high performance on a large number of cores, as demonstrated through detailed performance analysis on Edison, a Cray XC30 supercomputer.
Periodic Density Functional Theory Solver using Multiresolution Analysis with MADNESS
Harrison, Robert; Thornton, William
2011-03-01
We describe the first implementation of the all-electron Kohn-Sham density functional periodic solver (DFT) using multi-wavelets and fast integral equations using MADNESS (multiresolution adaptive numerical environment for scientific simulation; http://code.google.com/p/m-a-d-n-e-s-s). The multiresolution nature of a multi-wavelet basis allows for fast computation with guaranteed precision. By reformulating the Kohn-Sham eigenvalue equation into the Lippmann-Schwinger equation, we can avoid using the derivative operator which allows better control of overall precision for the all-electron problem. Other highlights include the development of periodic integral operators with low-rank separation, an adaptable model potential for nuclear potential, and an implementation for Hartree Fock exchange. This work was supported by NSF project OCI-0904972 and made use of resources at the Center for Computational Sciences at Oak Ridge National Laboratory under contract DE-AC05-00OR22725.
Density Functional Theory using Multiresolution Analysis with MADNESS
Thornton, Scott; Harrison, Robert
2012-02-01
We describe the first implementation of the all-electron Kohn-Sham density functional periodic solver (DFT) using multi-wavelets and fast integral equations using MADNESS (multiresolution adaptive numerical environment for scientific simulation; http://code.google.com/p/m-a-d-n-e-s-s). The multiresolution nature of a multi-wavelet basis allows for fast computation with guaranteed precision. By reformulating the Kohn-Sham eigenvalue equation into the Lippmann-Schwinger equation, we can avoid using the derivative operator which allows better control of overall precision for the all-electron problem. Other highlights include the development of periodic integral operators with low-rank separation, an adaptable model potential for the nuclear potential, and an implementation for Hartree-Fock exchange.
Dipole polarizability of 120Sn and nuclear energy density functionals
Hashimoto, T; Reinhard, P -G; Tamii, A; von Neumann-Cosel, P; Adachi, T; Aoi, N; Bertulani, C A; Fujita, H; Fujita, Y; Ganioǧlu, E; Hatanaka, K; Iwamoto, C; Kawabata, T; Khai, N T; Krugmann, A; Martin, D; Matsubara, H; Miki, K; Neveling, R; Okamura, H; Ong, H J; Poltoratska, I; Ponomarev, V Yu; Richter, A; Sakaguchi, H; Shimbara, Y; Shimizu, Y; Simonis, J; Smit, F D; Süsoy, G; Thies, J H; Suzuki, T; Yosoi, M; Zenihiro, J
2015-01-01
The electric dipole strength distribution in 120Sn between 5 and 22 MeV has been determined at RCNP Osaka from a polarization transfer analysis of proton inelastic scattering at E_0 = 295 MeV and forward angles including 0{\\deg}. Combined with photoabsorption data an electric dipole polarizability alpha_D(120Sn) = 8.93(36) fm^3 is extracted. The correlation of this value with alpha_D for 208Pb serves as a test of energy density functionals (EDFs). The majority of models based on Skyrme interactions can describe the data while relativistic approaches fail. The accuracy of the experimental results provides important constraints on the static isovector properties of EDFs used to predict symmetry energy parameters and the neutron skin thickness of nuclei.
Band Anticrossing in Dilute Germanium Carbides Using Hybrid Density Functionals
Stephenson, Chad A.; O'brien, William A.; Qi, Meng; Penninger, Michael; Schneider, William F.; Wistey, Mark A.
2016-04-01
Dilute germanium carbides (Ge1- x C x ) offer a direct bandgap for compact silicon photonics, but widely varying properties have been reported. This work reports improved band structure calculations for Ge1- x C x using ab initio simulations that employ the HSE06 exchange-correlation density functional. Contrary to Vegard's law, the conduction band minimum at Γ is consistently found to decrease with increasing C content, while L and X valleys change much more slowly. The calculated Ge bandgap is within 11% of experimental values. A decrease in energy at the Γ conduction band valley of (170 meV ± 50)/%C is predicted, leading to a direct bandgap for x > 0.008. These results indicate a promising material for Group IV lasers.
Experimental assessment of presumed filtered density function models
Stetsyuk, V.; Soulopoulos, N.; Hardalupas, Y.; Taylor, A. M. K. P.
2015-06-01
Measured filtered density functions (FDFs) as well as assumed beta distribution model of mixture fraction and "subgrid" scale (SGS) scalar variance z '' 2 ¯ , used typically in large eddy simulations, were studied by analysing experimental data, obtained from two-dimensional planar, laser induced fluorescence measurements in isothermal swirling turbulent flows at a constant Reynolds number of 29 000 for different swirl numbers (0.3, 0.58, and 1.07). Two-dimensional spatial filtering, by using a box filter, was performed in order to obtain the filtered variables, namely, resolved mean and "subgrid" scale scalar variance. These were used as inputs for assumed beta distribution of mixture fraction and top-hat FDF shape estimates. The presumed beta distribution model, top-hat FDF, and the measured filtered density functions were used to integrate a laminar flamelet solution in order to calculate the corresponding resolved temperature. The experimentally measured FDFs varied with the flow swirl number and both axial and radial positions in the flow. The FDFs were unimodal at flow regions with low SGS scalar variance, z '' 2 ¯ 0.02. Bimodal FDF could be observed for a filter size of approximately 1.5-2 times the Batchelor scale. Unimodal FDF could be observed for a filter size as large as four times the Batchelor scale under well-mixed conditions. In addition, two common computational models (a gradient assumption and a scale similarity model) for the SGS scalar variance were used with the aim to evaluate their validity through comparison with the experimental data. It was found that the gradient assumption model performed generally better than the scale similarity one.
Thyroid function and bone mineral density among Indian subjects
Directory of Open Access Journals (Sweden)
Raman K Marwaha
2012-01-01
Full Text Available Background : Thyroid hormones affect bone remodeling in patients with thyroid disease by acting directly or indirectly on bone cells. In view of limited information on correlation of thyroid function with bone mineral density (BMD in euthyroid subjects, we undertook this study to evaluate the correlation between thyroid function with BMD in subjects with normal thyroid function and subclinical hypothyroidism. Material and Methods : A total of 1290 subjects included in this cross sectional study, were divided in Group-1 with normal thyroid function and Group-2 with subclinical hypothyroidism. Fasting blood samples were drawn for the estimation of serum 25(OHD, intact parathyroid hormone, total and ionized calcium, inorganic phosphorus, and alkaline phosphatase. BMD at lumbar spine, femur, and forearm was measured. Results : BMD at all sites (radius, femur, and spine were comparable in both groups. There was no difference in BMD when subjects were divided in tertiles of TSH in either group. In group-1, FT4 and TSH were positively associated with BMD at 33% radius whereas FT3 was negatively associated with BMD at femoral neck in multiple regression analysis after adjustment for age, sex, BMI, 25(OHD and PTH levels. In group-2, there was no association observed between TSH and BMD at any site. Amongst all study subjects FT4 and FT3 were positively correlated with BMD at lumbar spine and radius respectively among all subjects. Conclusion: TSH does not affect BMD in euthyroid subjects and subjects with subclinical hypothyroidism. Thyroid hormones appear to have more pronounced positive effect on cortical than trabecular bone in euthyroid subjects.
Current Density Functional Theory Using Meta-Generalized Gradient Exchange-Correlation Functionals.
Furness, James W; Verbeke, Joachim; Tellgren, Erik I; Stopkowicz, Stella; Ekström, Ulf; Helgaker, Trygve; Teale, Andrew M
2015-09-08
We present the self-consistent implementation of current-dependent (hybrid) meta-generalized gradient approximation (mGGA) density functionals using London atomic orbitals. A previously proposed generalized kinetic energy density is utilized to implement mGGAs in the framework of Kohn-Sham current density functional theory (KS-CDFT). A unique feature of the nonperturbative implementation of these functionals is the ability to seamlessly explore a wide range of magnetic fields up to 1 au (∼235 kT) in strength. CDFT functionals based on the TPSS and B98 forms are investigated, and their performance is assessed by comparison with accurate coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) data. In the weak field regime, magnetic properties such as magnetizabilities and nuclear magnetic resonance shielding constants show modest but systematic improvements over generalized gradient approximations (GGA). However, in the strong field regime, the mGGA-based forms lead to a significantly improved description of the recently proposed perpendicular paramagnetic bonding mechanism, comparing well with CCSD(T) data. In contrast to functionals based on the vorticity, these forms are found to be numerically stable, and their accuracy at high field suggests that the extension of mGGAs to CDFT via the generalized kinetic energy density should provide a useful starting point for further development of CDFT approximations.
Yang, Yang; Brorsen, Kurt R.; Culpitt, Tanner; Pak, Michael V.; Hammes-Schiffer, Sharon
2017-09-01
Multicomponent density functional theory (DFT) enables the consistent quantum mechanical treatment of both electrons and protons. A major challenge has been the design of electron-proton correlation (epc) functionals that produce even qualitatively accurate proton densities. Herein an electron-proton correlation functional, epc17, is derived analogously to the Colle-Salvetti formalism for electron correlation and is implemented within the nuclear-electronic orbital (NEO) framework. The NEO-DFT/epc17 method produces accurate proton densities efficiently and is promising for diverse applications.
Hoyer, Chad E; Gagliardi, Laura; Truhlar, Donald G
2015-11-05
Time-dependent Kohn-Sham density functional theory (TD-KS-DFT) is useful for calculating electronic excitation spectra of large systems, but the low-energy spectra are often complicated by artificially lowered higher-energy states. This affects even the lowest energy excited states. Here, by calculating the lowest energy spin-conserving excited state for atoms from H to K and for formaldehyde, we show that this problem does not occur in multiconfiguration pair-density functional theory (MC-PDFT). We use the tPBE on-top density functional, which is a translation of the PBE exchange-correlation functional. We compare to a robust multireference method, namely, complete active space second-order perturbation theory (CASPT2), and to TD-KS-DFT with two popular exchange-correlation functionals, PBE and PBE0. We find for atoms that the mean unsigned error (MUE) of MC-PDFT with the tPBE functional improves from 0.42 to 0.40 eV with a double set of diffuse functions, whereas the MUEs for PBE and PBE0 drastically increase from 0.74 to 2.49 eV and from 0.45 to 1.47 eV, respectively.
Hybrid density functional theory band structure engineering in hematite.
Pozun, Zachary D; Henkelman, Graeme
2011-06-14
We present a hybrid density functional theory (DFT) study of doping effects in α-Fe(2)O(3), hematite. Standard DFT underestimates the band gap by roughly 75% and incorrectly identifies hematite as a Mott-Hubbard insulator. Hybrid DFT accurately predicts the proper structural, magnetic, and electronic properties of hematite and, unlike the DFT+U method, does not contain d-electron specific empirical parameters. We find that using a screened functional that smoothly transitions from 12% exact exchange at short ranges to standard DFT at long range accurately reproduces the experimental band gap and other material properties. We then show that the antiferromagnetic symmetry in the pure α-Fe(2)O(3) crystal is broken by all dopants and that the ligand field theory correctly predicts local magnetic moments on the dopants. We characterize the resulting band gaps for hematite doped by transition metals and the p-block post-transition metals. The specific case of Pd doping is investigated in order to correlate calculated doping energies and optical properties with experimentally observed photocatalytic behavior.
Antisites in III-V semiconductors: Density functional theory calculations
Chroneos, A.
2014-07-14
Density functional based simulation, corrected for finite size effects, is used to investigate systematically the formation of antisite defects in III-V semiconductors (III=Al, Ga, and In and V=P, As, and Sb). Different charge states are modelled as a function of the Fermi level and under different growth conditions. The formation energies of group III antisites (III V q) decrease with increasing covalent radius of the group V atom though not group III radius, whereas group V antisites (V I I I q) show a consistent decrease in formation energies with increase in group III and group V covalent radii. In general, III V q defects dominate under III-rich conditions and V I I I q under V-rich conditions. Comparison with equivalent vacancy formation energy simulations shows that while antisite concentrations are always dominant under stoichiometric conditions, modest variation in growth or doping conditions can lead to a significantly higher concentration of vacancies. © 2014 AIP Publishing LLC.
Acrolein impairs the cholesterol transport functions of high density lipoproteins.
Chadwick, Alexandra C; Holme, Rebecca L; Chen, Yiliang; Thomas, Michael J; Sorci-Thomas, Mary G; Silverstein, Roy L; Pritchard, Kirkwood A; Sahoo, Daisy
2015-01-01
High density lipoproteins (HDL) are considered athero-protective, primarily due to their role in reverse cholesterol transport, where they transport cholesterol from peripheral tissues to the liver for excretion. The current study was designed to determine the impact of HDL modification by acrolein, a highly reactive aldehyde found in high abundance in cigarette smoke, on the cholesterol transport functions of HDL. HDL was chemically-modified with acrolein and immunoblot and mass spectrometry analyses confirmed apolipoprotein crosslinking, as well as acrolein adducts on apolipoproteins A-I and A-II. The ability of acrolein-modified HDL (acro-HDL) to serve as an acceptor of free cholesterol (FC) from COS-7 cells transiently expressing SR-BI was significantly decreased. Further, in contrast to native HDL, acro-HDL promotes higher neutral lipid accumulation in murine macrophages as judged by Oil Red O staining. The ability of acro-HDL to mediate efficient selective uptake of HDL-cholesteryl esters (CE) into SR-BI-expressing cells was reduced compared to native HDL. Together, the findings from our studies suggest that acrolein modification of HDL produces a dysfunctional particle that may ultimately promote atherogenesis by impairing functions that are critical in the reverse cholesterol transport pathway.
Assessment of density functional methods with correct asymptotic behavior
Tsai, Chen-Wei; Li, Guan-De; Chai, Jeng-Da
2012-01-01
Long-range corrected (LC) hybrid functionals and asymptotically corrected (AC) model potentials are two distinct density functional methods with correct asymptotic behavior. They are known to be accurate for properties that are sensitive to the asymptote of the exchange-correlation potential, such as the highest occupied molecular orbital energies and Rydberg excitation energies of molecules. To provide a comprehensive comparison, we investigate the performance of the two schemes and others on a very wide range of applications, including the asymptote problems, self-interaction-error problems, energy-gap problems, charge-transfer problems, and many others. The LC hybrid scheme is shown to consistently outperform the AC model potential scheme. In addition, to be consistent with the molecules collected in the IP131 database [Y.-S. Lin, C.-W. Tsai, G.-D. Li, and J.-D. Chai, J. Chem. Phys. 136, 154109 (2012)], we expand the EA115 and FG115 databases to include, respectively, the vertical electron affinities and f...
Hardness of FeB4: density functional theory investigation.
Zhang, Miao; Lu, Mingchun; Du, Yonghui; Gao, Lili; Lu, Cheng; Liu, Hanyu
2014-05-07
A recent experimental study reported the successful synthesis of an orthorhombic FeB4 with a high hardness of 62(5) GPa [H. Gou et al., Phys. Rev. Lett. 111, 157002 (2013)], which has reignited extensive interests on whether transition-metal borides compounds will become superhard materials. However, it is contradicted with some theoretical studies suggesting transition-metal boron compounds are unlikely to become superhard materials. Here, we examined structural and electronic properties of FeB4 using density functional theory. The electronic calculations show the good metallicity and covalent Fe-B bonding. Meanwhile, we extensively investigated stress-strain relations of FeB4 under various tensile and shear loading directions. The calculated weakest tensile and shear stresses are 40 GPa and 25 GPa, respectively. Further simulations (e.g., electron localization function and bond length along the weakest loading direction) on FeB4 show the weak Fe-B bonding is responsible for this low hardness. Moreover, these results are consistent with the value of Vickers hardness (11.7-32.3 GPa) by employing different empirical hardness models and below the superhardness threshold of 40 GPa. Our current results suggest FeB4 is a hard material and unlikely to become superhard (>40 GPa).
Solvation of complex surfaces via molecular density functional theory.
Levesque, Maximilien; Marry, Virginie; Rotenberg, Benjamin; Jeanmairet, Guillaume; Vuilleumier, Rodolphe; Borgis, Daniel
2012-12-14
We show that classical molecular density functional theory, 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 Clay Force Field (CLAYFF). Solvent energetics and structure are found to depend weakly upon the atomic charges distribution of the clay surface, even for a rather polar solvent. We conclude on the consequences of such findings for force-field development.
Antisites in III-V semiconductors: Density functional theory calculations
Energy Technology Data Exchange (ETDEWEB)
Chroneos, A., E-mail: alex.chroneos@open.ac.uk [Engineering and Innovation, The Open University, Milton Keynes MK7 6AA (United Kingdom); Tahini, H. A. [Department of Materials, Imperial College London, London SW7 2AZ (United Kingdom); PSE Division, KAUST, Thuwal 23955-6900 (Saudi Arabia); Schwingenschlögl, U., E-mail: udo.schwingenschlogl@kaust.edu.sa [PSE Division, KAUST, Thuwal 23955-6900 (Saudi Arabia); Grimes, R. W., E-mail: r.grimes@imperial.ac.uk [Department of Materials, Imperial College London, London SW7 2AZ (United Kingdom)
2014-07-14
Density functional based simulation, corrected for finite size effects, is used to investigate systematically the formation of antisite defects in III-V semiconductors (III = Al, Ga, and In and V = P, As, and Sb). Different charge states are modelled as a function of the Fermi level and under different growth conditions. The formation energies of group III antisites (III{sub V}{sup q}) decrease with increasing covalent radius of the group V atom though not group III radius, whereas group V antisites (V{sub III}{sup q}) show a consistent decrease in formation energies with increase in group III and group V covalent radii. In general, III{sub V}{sup q} defects dominate under III-rich conditions and V{sub III}{sup q} under V-rich conditions. Comparison with equivalent vacancy formation energy simulations shows that while antisite concentrations are always dominant under stoichiometric conditions, modest variation in growth or doping conditions can lead to a significantly higher concentration of vacancies.
Lovett, Ronald
1988-06-01
All predictive theories for the spatial variation of the density in an inhomogeneous system can be constructed by approximating exact, nonlinear integral equations which relate the density and pair correlation functions of the system. It is shown that the set of correct kernels in the exact integral equations for the density is on the boundary between the set of kernels for which the integral equations have no solution for the density and the set for which the integral equations have a multiplicity of solutions. Thus arbitrarily small deviations from the correct kernel can make these integral equations insoluble. A heuristic model equation is used to illustrate how the density functional problem can be so sensitive to the approximation made to the correlation function kernel and it is then shown explicitly that this behavior is realized in the relation between the density and the direct correlation function and in the lowest order BGYB equation. Functional equations are identified for the kernels in these equations which are satisified by the correct kernels, which guarantee a unique solution to the integral equations, and which provide a natural constraint on approximations which can be used in density functional theory. It is also shown that this sensitive behavior is a general property of density functional problems and that the methodology for constructing the constraints is equally general. A variety of applications of density functional theory are reviewed to illustrate practical consequences of this sensitivity.
Density-functional study of U-Mo alloys
Landa, Alexander; Soderlind, Per; Turchi, Patrice E. A.
2011-03-01
The U-Mo and U-Zr alloys proved to be very promising fuels for advanced fast nuclear reactors. According to numerous experiments, the main advantages of U-Mo fuels over U-Zr fuels lies in a much lower constituent redistribution due to the existence a single γ -U-Mo phase with body-centered cubic structure over typical fuel operation temperatures. Density-functional theory (EMTO-CPA technique) previously used to describe phase equilibria in U-Zr alloys [A. Landa, P. Söderlind, P. E. A. Turchi, Journal of Alloys and Compounds, 478 (2009) 103] is extended to investigate the ground-state properties of U-Mo solid solutions. Calculated heats of formation of bcc U-Zr and U-Mo alloys are compared with CALPHAD assessments. We discuss how the heat of formation in both alloys correlates with the charge transfer between the alloy components, and how the specific behavior of the density of states in the vicinity of the Fermi level promotes the stabilization of the U2 Mo compound. Our calculations prove that, due to the existence of a single γ -phase over the typical fuel operation temperatures, γ -U-Mo alloys should indeed have much lower constituent redistribution than γ -U-Zr alloys for which binodal decomposition causes a high degree of constituent redistribution. This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Transport through correlated systems with density functional theory
Kurth, S.; Stefanucci, G.
2017-10-01
We present recent advances in density functional theory (DFT) for applications in the field of quantum transport, with particular emphasis on transport through strongly correlated systems. We review the foundations of the popular Landauer–Büttiker(LB) + DFT approach. This formalism, when using approximations to the exchange-correlation (xc) potential with steps at integer occupation, correctly captures the Kondo plateau in the zero bias conductance at zero temperature but completely fails to capture the transition to the Coulomb blockade (CB) regime as the temperature increases. To overcome the limitations of LB + DFT, the quantum transport problem is treated from a time-dependent (TD) perspective using TDDFT, an exact framework to deal with nonequilibrium situations. The steady-state limit of TDDFT shows that in addition to an xc potential in the junction, there also exists an xc correction to the applied bias. Open shell molecules in the CB regime provide the most striking examples of the importance of the xc bias correction. Using the Anderson model as guidance we estimate these corrections in the limit of zero bias. For the general case we put forward a steady-state DFT which is based on one-to-one correspondence between the pair of basic variables, steady density on and steady current across the junction and the pair local potential on and bias across the junction. Like TDDFT, this framework also leads to both an xc potential in the junction and an xc correction to the bias. Unlike TDDFT, these potentials are independent of history. We highlight the universal features of both xc potential and xc bias corrections for junctions in the CB regime and provide an accurate parametrization for the Anderson model at arbitrary temperatures and interaction strengths, thus providing a unified DFT description for both Kondo and CB regimes and the transition between them.
DEFF Research Database (Denmark)
Sharma, S.; Pittalis, S.; Kurth, S.;
2007-01-01
The relative merits of current-spin-density- and spin-density-functional theory are investigated for solids treated within the exact-exchange-only approximation. Spin-orbit splittings and orbital magnetic moments are determined at zero external magnetic field. We find that for magnetic (Fe, Co...
Comment on "Density functional theory is straying from the path toward the exact functional"
DEFF Research Database (Denmark)
Kepp, Kasper Planeta
2017-01-01
Medvedev et al (Reports, 6 January 2017, p. 49) argue that recent density functionals stray from the path toward exactness. This conclusion rests on very compact 1s2 and 1s22s2 systems favored by the Hartree-Fock picture. Comparison to actual energies for the same systems indicates that the "stra...
DEFF Research Database (Denmark)
Vallejo, Federico Calle; Martinez, Jose Ignacio; Rossmeisl, Jan
2011-01-01
) at the cathode. In this contribution, on the basis of Density Functional Theory (DFT) calculations, we show that graphitic materials with active sites composed of 4 nitrogen atoms and transition metal atoms belonging to groups 7 to 9 in the periodic table are active towards ORR, and also towards Oxygen Evolution...
Current Density-Functional Theory using meta-Generalized Gradient Exchange--Correlation Functionals
Furness, James W; Tellgren, Erik I; Stopkowicz, Stella; Ekström, Ulf; Helgaker, Trygve; Teale, Andrew M
2015-01-01
We present the self-consistent implementation of current-dependent (hybrid) meta generalized gradient approximation (mGGA) density functionals using London atomic orbitals. A previously proposed generalized kinetic energy density is utilized to implement mGGAs in the framework of Kohn--Sham current density-functional theory (KS-CDFT). A unique feature of the non-perturbative implementation of these functionals is the ability to seamlessly explore a wide range of magnetic fields up to 1 a.u. ($\\sim 235000$T) in strength. CDFT functionals based on the TPSS and B98 forms are investigated and their performance is assessed by comparison with accurate CCSD(T) data. In the weak field regime magnetic properties such as magnetizabilities and NMR shielding constants show modest but systematic improvements over GGA functionals. However, in strong field regime the mGGA based forms lead to a significantly improved description of the recently proposed perpendicular paramagnetic bonding mechanism, comparing well with CCSD(T...
Xia, Junchao; Carter, Emily
2014-03-01
We propose a density decomposition scheme using a Wang-Govind-Carter (WGC)-based kinetic energy density functional (KEDF) to accurately and efficiently simulate covalent systems within orbital-free (OF) density functional theory (DFT). By using a local, density-dependent scale function, the total density is decomposed into a localized density within covalent bond regions and a flattened delocalized density, with the former described by semilocal KEDFs and the latter treated by the WGC KEDF. The new model predicts reasonable equilibrium volumes, bulk moduli, and phase ordering energies for various semiconductors compared to Kohn-Sham (KS) DFT benchmarks. The surface energy of Si(100) also agrees well with KSDFT. We further apply the model to study mechanical properties of Li-Si alloys, which have been recently recognized as a promising candidate for next-generation anodes of Li-ion batteries with outstanding capacity. We study multiple crystalline Li-Si alloys. The WGCD KEDF predicts accurate cell lattice vectors, equilibrium volumes, elastic moduli, electron densities, alloy formation and Li adsorption energies. Because of its quasilinear scaling, coupled with the level of accuracy shown here, OFDFT appears quite promising for large-scale simulation of such materials phenomena. Office of Naval Research, National Science Foundation, Tigress High Performance Computing Center.
Global and local curvature in density functional theory
Zhao, Qing; Ioannidis, Efthymios I.; Kulik, Heather J.
2016-08-01
Piecewise linearity of the energy with respect to fractional electron removal or addition is a requirement of an electronic structure method that necessitates the presence of a derivative discontinuity at integer electron occupation. Semi-local exchange-correlation (xc) approximations within density functional theory (DFT) fail to reproduce this behavior, giving rise to deviations from linearity with a convex global curvature that is evidence of many-electron, self-interaction error and electron delocalization. Popular functional tuning strategies focus on reproducing piecewise linearity, especially to improve predictions of optical properties. In a divergent approach, Hubbard U-augmented DFT (i.e., DFT+U) treats self-interaction errors by reducing the local curvature of the energy with respect to electron removal or addition from one localized subshell to the surrounding system. Although it has been suggested that DFT+U should simultaneously alleviate global and local curvature in the atomic limit, no detailed study on real systems has been carried out to probe the validity of this statement. In this work, we show when DFT+U should minimize deviations from linearity and demonstrate that a "+U" correction will never worsen the deviation from linearity of the underlying xc approximation. However, we explain varying degrees of efficiency of the approach over 27 octahedral transition metal complexes with respect to transition metal (Sc-Cu) and ligand strength (CO, NH3, and H2O) and investigate select pathological cases where the delocalization error is invisible to DFT+U within an atomic projection framework. Finally, we demonstrate that the global and local curvatures represent different quantities that show opposing behavior with increasing ligand field strength, and we identify where these two may still coincide.
Numerical methods for high-dimensional probability density function equations
Cho, H.; Venturi, D.; Karniadakis, G. E.
2016-01-01
In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker-Planck and Dostupov-Pugachev equations), random wave theory (Malakhov-Saichev equations) and coarse-grained stochastic systems (Mori-Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.
Parameterizing deep convection using the assumed probability density function method
Directory of Open Access Journals (Sweden)
R. L. Storer
2014-06-01
Full Text Available Due to their coarse horizontal resolution, present-day climate models must parameterize deep convection. This paper presents single-column simulations of deep convection using a probability density function (PDF parameterization. The PDF parameterization predicts the PDF of subgrid variability of turbulence, clouds, and hydrometeors. That variability is interfaced to a prognostic microphysics scheme using a Monte Carlo sampling method. The PDF parameterization is used to simulate tropical deep convection, the transition from shallow to deep convection over land, and mid-latitude deep convection. These parameterized single-column simulations are compared with 3-D reference simulations. The agreement is satisfactory except when the convective forcing is weak. The same PDF parameterization is also used to simulate shallow cumulus and stratocumulus layers. The PDF method is sufficiently general to adequately simulate these five deep, shallow, and stratiform cloud cases with a single equation set. This raises hopes that it may be possible in the future, with further refinements at coarse time step and grid spacing, to parameterize all cloud types in a large-scale model in a unified way.
A Density Functional Study of Bare and Hydrogenated Platinum Clusters
Sebetci, A
2006-01-01
We perform density functional theory calculations using Gaussian atomic-orbital methods within the generalized gradient approximation for the exchange and correlation to study the interactions in the bare and hydrogenated platinum clusters. The minimum-energy structures, binding energies, relative stabilities, vibrational frequencies and the highest occupied and lowest unoccupied molecular-orbital gaps of Pt_nH_m (n=1-5, m=0-2) clusters are calculated and compared with previously studied pure platinum and hydrogenated platinum clusters. We investigate any magic behavior in hydrogenated platinum clusters and find that Pt_4H_2 is more stable than its neighboring sizes. Our results do not agree with a previous conclusion that 3D geometries of Pt tetramer and pentamer are unfavored. On the contrary, the lowest energy structure of Pt_4 is found to be a distorted tetrahedron and that of Pt_5 is found to be a bridge site capped tetrahedron which is a new global minimum for Pt_5 cluster. The successive addition of H ...
Density Functional Theory for Phase-Ordering Transitions
Energy Technology Data Exchange (ETDEWEB)
Wu, Jianzhong [Univ. of California, Riverside, CA (United States)
2016-03-30
Colloids display astonishing structural and dynamic properties that can be dramatically altered by modest changes in the solution condition or an external field. This complex behavior stems from a subtle balance of colloidal forces and intriguing mesoscopic and macroscopic phase transitions that are sensitive to the processing conditions and the dispersing environment. Whereas the knowledge on the microscopic structure and phase behavior of colloidal systems at equilibrium is now well-advanced, quantitative predictions of the dynamic properties and the kinetics of phase-ordering transitions in colloids are not always realized. Many important mesoscopic and off-equilibrium colloidal states remain poorly understood. The proposed research aims to develop a new, unifying approach to describe colloidal dynamics and the kinetics of phase-ordering transitions based on accomplishments from previous work for the equilibrium properties of both uniform and inhomogeneous systems and on novel concepts from the state-of-the-art dynamic density functional theory. In addition to theoretical developments, computational research is designed to address a number of fundamental questions on phase-ordering transitions in colloids, in particular those pertinent to a competition of the dynamic pathways leading to various mesoscopic structures, off-equilibrium states, and crystalline phases. By providing a generic theoretical framework to describe equilibrium, metastable as well as non-ergodic phase transitions concurrent with the colloidal self-assembly processes, accomplishments from this work will have major impacts on both fundamental research and technological applications.
Numerical methods for high-dimensional probability density function equations
Energy Technology Data Exchange (ETDEWEB)
Cho, H. [Department of Mathematics, University of Maryland College Park, College Park, MD 20742 (United States); Venturi, D. [Department of Applied Mathematics and Statistics, University of California Santa Cruz, Santa Cruz, CA 95064 (United States); Karniadakis, G.E., E-mail: gk@dam.brown.edu [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States)
2016-01-15
In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker–Planck and Dostupov–Pugachev equations), random wave theory (Malakhov–Saichev equations) and coarse-grained stochastic systems (Mori–Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.
Density functional theory study of phase IV of solid hydrogen
Pickard, Chris J.; Martinez-Canales, Miguel; Needs, Richard J.
2012-06-01
We have studied solid hydrogen up to pressures of 300 GPa and temperatures of 350 K using density functional theory methods and have found “mixed structures” that are more stable than those predicted earlier. Mixed structures consist of alternate layers of strongly bonded molecules and weakly bonded graphene-like sheets. Quasiharmonic vibrational calculations show that mixed structures are the most stable at room temperature over the pressure range 250-295 GPa. These structures are stabilized with respect to strongly bonded molecular phases at room temperature by the presence of lower frequency vibrational modes arising from the graphene-like sheets. Our results for the mixed structures are consistent with the experimental Raman data [M. I. Eremets and I. A. Troyan, Nat. Mater.1476-112210.1038/nmat3175 10, 927 (2011) and R. T. Howie , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.108.125501 108, 125501 (2012)]. We find that mixed phases are reasonable structural models for phase IV of hydrogen.
Applications of density functional theory in materials science and engineering
Alvarado, Manuel, Jr.
Density Functional Theory (DFT) is a powerful tool that can be used to model various systems in materials science. Our research applies DFT to two problems of interest. First, an organic/inorganic complex dye system known as a Mayan pigment is modeled to determine chemical binding sites, verifying each model with physical data such as UV/Vis spectra. Preliminary studies on palygorskite-based mayan pigments (mayacrom blue, mayacrom purple) show excellent agreement with experimental studies when using a dimer dye geometry binding with tetrahedrally-coordinated aluminum impurity sites in palygorksite. This approach is applied to a sepiolite-based organic/inorganic dye system using thioindigo attached to a tetrahedral aluminum impurity site with an additional aluminum impurity site in close proximity to the binding site. As a second application of DFT, various grain orientations in beta-Sn are modeled under imposed strains in order to calculate elastic properties of this system. These calculations are intended to clarify discrepancies in published, experimental crystal compliance values.
Density-functional study of plutonium monoxide monohydride
Qiu, Ruizhi; Lu, Haiyan; Ao, Bingyun; Tang, Tao; Chen, Piheng
2017-03-01
The structural, electronic, mechanical, optical, thermodynamic properties of plutonium monoxide monohydride (PuOH) are studied by density-functional calculations within the framework of LDA/GGA and LDA/GGA+U. From the total energy calculation, the lowest-energy crystal structure of PuOH is predicted to have space group F 4 bar 3 m (No. 216). Within the LDA+U framework, the calculated lattice parameter of F 4 bar 3 m -PuOH is in good agreement with the experimental value and the corresponding ground state is predicted to be an antiferromagnetic charge-transfer insulator. Furthermore, we investigate the bonding character of PuOH by analyzing the electron structure and find that there are a stronger Pu-O bond and a weaker Pu-H bond. The mechanical properties including the elastic constants, elastic moduli and Debye's temperature, and the optical properties including the reflectivity and absorption coefficient are also calculated. We then compute the phonon spectrum which verified the dynamical stability of F 4 bar 3 m -PuOH. Some thermodynamic quantities such as the specific heat are evaluated. Finally we calculate the formation energy of PuOH, and the reaction energies for the oxidation of PuOH and PuOH-coated Pu, which are in reasonable agreement with the experimental values.
Chiroptical Properties of Amino Acids: A Density Functional Theory Study
Directory of Open Access Journals (Sweden)
Martine Adrian-Scotto
2010-04-01
Full Text Available Amino acids are involved in many scientific theories elucidating possible origins of life on Earth. One of the challenges when discussing the evolutionary origin of biopolymers such as proteins and oligonucleotides in living organisms is the phenomenon that these polymers implement monomers of exclusively one handedness, a feature called biomolecular homochirality. Many attempts have been made to understand this process of racemic symmetry breaking. Assuming an extraterrestrial origin of the molecular building blocks of living organisms, their susceptibility to asymmetric photolysis by the absorption of circularly polarized electromagnetic radiation in interstellar space was proposed. In order to predict whether the interaction of circularly polarized light with various racemic amino acids can induce an enantiomeric excess, we investigated the electronic and chiroptical properties of the amino acids valine and isovaline by a molecular modelling approach based on quantum chemistry (Density Functional Theory. The average spectra of both L-valine and L-isovaline have been produced on the basis of Boltzmann population analysis using computed spectra for the various conformations of each amino acid.
Density functional studies of methanol decomposition on subnanometer Pd clusters.
Energy Technology Data Exchange (ETDEWEB)
Mehmood, F.; Greeley, J.; Curtiss, L. A.
2009-12-31
A density functional theory study of the decomposition of methanol on subnanometer palladium clusters (primarily Pd{sub 4}) is presented. Methanol dehydrogenation through C-H bond breaking to form hydroxymethyl (CH{sub 2}OH) 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 (CH{sub 3}O) and formaldehyde (CH{sub 2}O), 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 (CH{sub 3}OCH{sub 3}) 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.
Embedding germanium in graphene: A density functional theory study
Xu, Zhuo; Li, Yangping; Tan, Tingting; Liu, Zhengtang
2017-03-01
Based on the density functional theory, we investigate the structural, electronic, and magnetic properties of graphene sheet with substitutional Ge atoms in both single and double vacancies, and graphene sheet with Ge-chain impurity. We find the substitutional Ge is chemically bonded to graphene, and is more stable in the double vacancy site. The electronic properties indicate that metallic and semiconductor states with a range of band gaps from 0 to 0.87 eV could be obtained depending on different substitution sites, concentrations, and vacancy types. Magnetic moment is observed in graphene with single vacancy. Tunable electronic behaviors are also observed in graphene sheet with Ge-chain impurity, and a magnetic moment of 2.9 μB is observed in single Ge-chain incorporated 4 × 4 graphene supercell. From these investigations, we conclude that by doping of Ge in vacancy-contained graphene, it could provide great advantages for its application in future nanoscale devices.
Density Functional Theory Study of Spirodienone Stereoisomers in Lignin
Energy Technology Data Exchange (ETDEWEB)
Elder, Thomas [USDA-Forest; Berstis, Laura [National; Biosciences; Beckham, Gregg T. [National; Crowley, Michael F. [National; Biosciences
2017-07-10
The spirodienone structure in lignin is a relatively recent discovery, and it has been found to occur in lignin of various plant species at concentrations of ~3%, which is sufficiently high to be important for better understanding of its properties and reactivity. The cyclic structure, with a ..beta..-1 bond, has been proposed to be a precursor for acyclic ..beta..-1 linkages in lignin. Previous analytical work has revealed the presence, but not the absolute configuration, of two stereoisomeric forms of spirodienone. The objective of the current work was to determine if there are thermodynamic differences that could help identify the experimentally observed stereoisomers. Results from density functional theory calculations reveal the presence of clusters of stereoisomers with varying stability that may be of use in narrowing the list of possible structures. Furthermore, the bond dissociation enthalpy of the cyclic ring exhibited a particularly high value for the C-O cleavage reaction relative to more conventional ether bonds in lignin, perhaps due to limited electron delocalization possibilities.
Density functional theory study of BnC clusters.
Liu, Chunhui; Han, Peilin; Tang, Mingsheng
2011-05-15
B(n)C clusters (n = 3-10) were studied at the density functional theory (DFT) (B3LYP)/6-311G** level of theory. The calculations predicted that the most stable configurations of the B(n) C clusters are the (n + 1)-membered cyclic structures. For boron-carbon clusters, the configurations containing greater numbers of three-membered boron rings are more favorable, except for the B(7)C and B(9)C clusters. Through molecular orbital analysis of these B(n)C clusters, we have concluded that π-electron delocalization plays a crucial role in the stability of n + 1-membered cyclic structures. In this paper, the relative stability of each cluster is discussed based on their single atomic-binding energies. The capability of clusters to obtain or lose an electron was also discussed, based on their vertical electron detachment energies (VDEs), adiabatic electron detachment energies (ADEs), vertical electron affinities (VEAs) and adiabatic electron affinities (AEAs). Copyright © 2011 John Wiley & Sons, Ltd.
Metal catalyzed ethylene epoxidation: A comparative density functional theory study
Institute of Scientific and Technical Information of China (English)
Ruipeng Ren; Yongkang Lü; Xianyong Pang; Guichang Wang
2011-01-01
Ethylene epoxidation on Ag(111), Pt(111), Rh(111) and Mo(100) has been studied by density functional theory (DFT) calculations. The results show that the adsorption energies of possible adsorbed species involved in the ethylene epoxidation increase in the order: Ag＜Pt＜Rh＜Mo, and the activation energies of the formation of epoxide (EtO) and acetaldehyde (Ac) follow the same order. Moreover, it is found that the smallest difference in the activation energies between EtO formation and Ac formation is shown on Ag. These results indicate that the metallic Ag shows the highest between activity and selectivity for ethylene epoxidation among the studied metal surfaces. Perhaps, the stability of OMME intermediate is the crucial factor in controlling the activity and selectivity. And the stronger the binding of OMME, the lower the activity and selectivity are. In addition, the relationships between the reaction enthalpy and activation energy on these four metal surfaces are investigated,and it is found that such a correlation is only applied for OMME(a) → EtO(a) and OMME(a) → Ac(a), while invalid for the case of C2H4(a) +O(a) → OMME(a).
Simple preconditioning for time-dependent density functional perturbation theory
Lehtovaara, Lauri; Marques, Miguel A. L.
2011-07-01
By far, the most common use of time-dependent density functional theory is in the linear-reponse regime, where it provides information about electronic excitations. Ideally, the linear-response equations should be solved by a method that avoids the use of the unoccupied Kohn-Sham states — such as the Sternheimer method — as this reduces the complexity and increases the precision of the calculation. However, the Sternheimer equation becomes ill-conditioned near and indefinite above the first resonant frequency, seriously hindering the use of efficient iterative solution methods. To overcome this serious limitation, and to improve the general convergence properties of the iterative techniques, we propose a simple preconditioning strategy. In our method, the Sternheimer equation is solved directly as a linear equation using an iterative Krylov subspace method, i.e., no self-consistent cycle is required. Furthermore, the preconditioner uses the information of just a few unoccupied states and requires simple and minimal modifications to existing implementations. In this way, convergence can be reached faster and in a considerably wider frequency range than the traditional approach.
Calaminici, Patrizia; Janetzko, Florian; Köster, Andreas M; Mejia-Olvera, Roberto; Zuniga-Gutierrez, Bernardo
2007-01-28
Density functional theory optimized basis sets for gradient corrected functionals for 3d transition metal atoms are presented. Double zeta valence polarization and triple zeta valence polarization basis sets are optimized with the PW86 functional. The performance of the newly optimized basis sets is tested in atomic and molecular calculations. Excitation energies of 3d transition metal atoms, as well as electronic configurations, structural parameters, dissociation energies, and harmonic vibrational frequencies of a large number of molecules containing 3d transition metal elements, are presented. The obtained results are compared with available experimental data as well as with other theoretical data from the literature.
Cantero, J; The ATLAS collaboration
2014-01-01
Measurement of the inclusive photon production performed by the ATLAS collaboration using 4.6 fb-1 of sqrt(s)=7 TeV collision data is reported. Comparisons to the data of nextto-leading order QCD calculations MCFM and JetPhox with different PDFs are presented. The theoretical uncertainties, including scale, strong coupling, and PDF uncertainties are evaluated. The compatibility between data and theory is assessed by q2 evaluation, taking into account the correlations between systematic uncertainties. The cross sections for photons produced in association with jets are also measured by the ATLAS collaboration at sqrt(s)=7 TeV as functions of photon and jet kinematics and are compared to next-to-leading-order QCD calculations.
Quantum Drude friction for time-dependent density functional theory
Neuhauser, Daniel; Lopata, Kenneth
2008-10-01
way to very simple finite grid description of scattering and multistage conductance using time-dependent density functional theory away from the linear regime, just as absorbing potentials and self-energies are useful for noninteracting systems and leads.
SUePDF: a program to obtain quantitative pair distribution functions from electron diffraction data
Tran, Dung Trung; Svensson, Gunnar; Tai, Cheuk-Wai
2017-01-01
SUePDF is a graphical user interface program written in MATLAB to achieve quantitative pair distribution functions (PDFs) from electron diffraction data. The program facilitates structural studies of amorphous materials and small nanoparticles using electron diffraction data from transmission electron microscopes. It is based on the physics of electron scattering as well as the total scattering methodology. A method of background modeling is introduced to treat the intensity tail of the direct beam, inelastic scattering and incoherent multiple scattering. Kinematical electron scattering intensity is scaled using the electron scattering factors. The PDFs obtained after Fourier transforms are normalized with respect to number density, nanoparticle form factor and the non-negativity of probability density. SUePDF is distributed as free software for academic users. PMID:28190994
Litchford, Ron J.; Jeng, San-Mou
1992-01-01
The performance of a recently introduced statistical transport model for turbulent particle dispersion is studied here for rigid particles injected into a round turbulent jet. Both uniform and isosceles triangle pdfs are used. The statistical sensitivity to parcel pdf shape is demonstrated.
What determines the density structure of molecular clouds ? A case study of Orion B with Herschel
Schneider, N; Konyves, V; Bontemps, S; Motte, F; Federrath, C; Ward-Thompson, D; Arzoumanian, D; Benedettini, M; Bressert, E; Didelon, P; Di Francesco, J; Griffin, M; Hennemann, M; Hill, T; Palmeirim, P; Pezzuto, S; Peretto, N; Roy, A; Rygl, K L J; Spinoglio, L; White, G; 10.1088/2041-8205/766/2/L17
2013-01-01
A key parameter to the description of all star formation processes is the density structure of the gas. In this letter, we make use of probability distribution functions (PDFs) of Herschel column density maps of Orion B, Aquila, and Polaris, obtained with the Herschel Gould Belt survey (HGBS). We aim to understand which physical processes influence the PDF shape, and with which signatures. The PDFs of Orion B (Aquila) show a lognormal distribution for low column densities until Av 3 (6), and a power-law tail for high column densities, consistent with a rho r^-2 profile for the equivalent spherical density distribution. The PDF of Orion B is broadened by external compression due to the nearby OB stellar aggregates. The PDF of a quiescent subregion of the non-star-forming Polaris cloud is nearly lognormal, indicating that supersonic turbulence governs the density distribution. But we also observe a deviation from the lognormal shape at Av>1 for a subregion in Polaris that includes a prominent filament. We concl...
Scalar filtered mass density functions in nonpremixed turbulent jet flames
Energy Technology Data Exchange (ETDEWEB)
Drozda, Tomasz G.; Wang, Guanghua; Sankaran, Vaidyanathan; Mayo, Jackson R.; Oefelein, Joseph C.; Barlow, Robert S. [Combustion Research Facility, Sandia National Laboratories, P.O. Box 969, MS 9051, Livermore, CA 94551 (United States)
2008-10-15
Filtered mass density functions (FMDFs) of mixture fraction and temperature are studied by analyzing experimental data obtained from one-dimensional Raman/Rayleigh/LIF measurements of nonpremixed CH{sub 4}/H{sub 2}/N{sub 2} turbulent jet flames at Reynolds numbers of 15,200 and 22,800 (DLR-A and -B). The experimentally determined FMDFs are conditioned on the Favre filtered values of the mixture fraction and its variance. Filter widths are selected as fixed multiples of the experimentally determined dissipation length scale at each measurement location. One-dimensional filtering using a top-hat filter is performed to obtain the filtered variables used for conditioning. The FMDFs are obtained by binning the mass and filter kernel weighted samples. Emphasis is placed on the shapes of the FMDFs in the fuel-rich, fuel-lean, and stoichiometric intervals for the Favre filtered mixture fraction, and low, medium, and high values for the Favre filtered mixture fraction variance. It is found that the FMDFs of mixture fraction are unimodal in samples with low mixture fraction variance and bimodal in samples with high variance. However, the FMDFs of mixture fraction at the smallest filter size studied are unimodal for all values of the variance. The FMDFs of temperature are unimodal in samples with low mixture fraction variance, and either unimodal or bimodal, depending on the mixture fraction mean, in samples with high variance. The influence of the filter size and the jet Reynolds number on the FMDFs is also considered. (author)
Density functional theory study of neutral and oxidized thiophene oligomers
Energy Technology Data Exchange (ETDEWEB)
Dai, Yafei; Wei, Chengwei [School of Physics Science and Technology and Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210023 (China); Blaisten-Barojas, Estela, E-mail: blaisten@gmu.edu [Computational Materials Science Center and School of Physics, Astronomy and Computational Sciences, George Mason University, Fairfax, Virginia 22030 (United States)
2013-11-14
The effect of oxidation on the energetics and structure of thiophene (Th) oligomers is studied with density functional theory at the B3PW91/6-311++G(d,p) level. Neutral n-Th oligomers (2 < n < 13) are gently curved planar chains. Ionization potential and electron affinity results show that n-Th oligomers are easier to be oxidized as their chain length increases. Oxidation states +2, +4, +6, and +8 are energetically stable in 12-Th. Upon oxidation the conjugated backbone of 12-Th switches from extended benzenoid phase to quinoid phase localized on groups of monomers regularly spaced along the chain. Oxidized states +2, +4, +6, and +8 of 12-Th display two +1e localized at the ends of their chains only because of the finite size of the chains. In 12-Th this end-effect extends over the two terminal monomers forming a positive-negative charge duet. This peculiar charge localization makes n-Th oligomers different from other conducting polymers with similar structure, such as polypyrrole. The spectrum of single-electron molecular states of oxidized 12-Th displays two localized single-electron states in the HOMO-LUMO energy gap per +2 oxidation state. Oligothiophene 12-Th doped with F atoms at 1:2 concentration presents a charge transfer of 3.4 e from oligomer to dopants that increases to 4.8 e in the presence of solvent. The charge distribution in these F-doped oligomers is similar to the +4 oxidation state of 12-Th. It is predicted that dopants produce an enhanced charge transfer localized in the proximity of their locations enhancing the formation of bipolarons in the central part of the oligomer chain.
Informing saccharide structural NMR studies with density functional theory calculations.
Klepach, Thomas; Zhao, Hongqiu; Hu, Xiaosong; Zhang, Wenhui; Stenutz, Roland; Hadad, Matthew J; Carmichael, Ian; Serianni, Anthony S
2015-01-01
Density functional theory (DFT) is a powerful computational tool to enable structural interpretations of NMR spin-spin coupling constants ( J-couplings) in saccharides, including the abundant (1)H-(1)H ( JHH), (13)C-(1)H ( JCH), and (13)C-(13)C ( JCC) values that exist for coupling pathways comprised of 1-4 bonds. The multiple hydroxyl groups in saccharides, with their attendant lone-pair orbitals, exert significant effects on J-couplings that can be difficult to decipher and quantify without input from theory. Oxygen substituent effects are configurational and conformational in origin (e.g., axial/equatorial orientation of an OH group in an aldopyranosyl ring; C-O bond conformation involving an exocyclic OH group). DFT studies shed light on these effects, and if conducted properly, yield quantitative relationships between a specific J-coupling and one or more conformational elements in the target molecule. These relationships assist studies of saccharide structure and conformation in solution, which are often challenged by the presence of conformational averaging. Redundant J-couplings, defined as an ensemble of J-couplings sensitive to the same conformational element, are particularly helpful when the element is flexible in solution (i.e., samples multiple conformational states on the NMR time scale), provided that algorithms are available to convert redundant J-values into meaningful conformational models. If the latter conversion is achievable, the data can serve as a means of testing, validating, and refining theoretical methods like molecular dynamics (MD) simulations, which are currently relied upon heavily to assign conformational models of saccharides in solution despite a paucity of experimental data needed to independently validate the method.
Energy Technology Data Exchange (ETDEWEB)
Fattebert, J
2008-07-29
We describe an iterative algorithm to solve electronic structure problems in Density Functional Theory. The approach is presented as a Subspace Accelerated Inexact Newton (SAIN) solver for the non-linear Kohn-Sham equations. It is related to a class of iterative algorithms known as RMM-DIIS in the electronic structure community. The method is illustrated with examples of real applications using a finite difference discretization and multigrid preconditioning.
TMD PDFs in Drell-Yan lepton pair production at LHC
Energy Technology Data Exchange (ETDEWEB)
Baranov, S.P. [Lebedev Institute of Physics, 119991 Moscow (Russian Federation); Lipatov, A.V. [SINP, Lomonosov Moscow State University, 119991 Moscow, Russia Joint Institute of Nuclear Physics, 141980 Dubna, Moscow Region (Russian Federation); Zotov, N.P. [SINP, Lomonosov Moscow State University, 119991 Moscow (Russian Federation)
2015-04-10
We consider the transverse momentum dependent (TMD) quark densities of the proton which are very important ingredients for unpolarized Drell-Yan (DY) lepton pair production. We calculate the TMD sea quark density as a convolution of the Catani-Ciafaloni-Fiorani-Marchesini (CCFM)-evolved gluon distribution and the TMD gluon-to-quark splitting function. Based on the O(α{sup 2}) production amplitude q{sup *}+(q-bar){sup *} →Z/γ{sup *}→l{sup +}+l{sup −}, calculated by taking into account the effective q{sup *}(q-bar){sup *}Z/γ{sup *} - vertex, we analyze the distributions on the dilepton invariant mass, transverse momentum and rapidity and specific angular correlations between the produced leptons as measured by the CMS, ATLAS and LHCb collaborations. We briefly duscuss also the process of assiciated lepton pair and jet production in pp collisions at the LHC.
TMD PDFs in Drell-Yan lepton pair production at LHC
Baranov, S P; Zotov, N P
2014-01-01
We consider the transverse momentum dependent (TMD) quark densities of the proton which are very important ingredients for unpolarized Drell-Yan (DY) lepton pair production. We calculate the TMD sea quark density as a convolution of the Catani-Ciafaloni-Fiorani-Marchesini (CCFM)-evolved gluon distribution and the TMD gluon-to-quark splitting function. Based on the ${\\cal O}(\\alpha^2)$ production amplitude $q^* + \\bar q^* \\to Z/\\gamma^* \\to l^+ + l^-$, calculated by taking into account the effective $q^*\\bar q^* Z/\\gamma^*$ - vertex, we analyze the distributions on the dilepton invariant mass, transverse momentum and rapidity and specific angular correlations between the produced leptons as measured by the CMS, ATLAS and LHCb collaborations. We briefly duscuss also the process of assiciated lepton pair and jet production in $pp$ collisions at the LHC.
TMD PDFs in Drell-Yan lepton pair production at LHC
Baranov, S. P.; Lipatov, A. V.; Zotov, N. P.
2015-04-01
We consider the transverse momentum dependent (TMD) quark densities of the proton which are very important ingredients for unpolarized Drell-Yan (DY) lepton pair production. We calculate the TMD sea quark density as a convolution of the Catani-Ciafaloni-Fiorani-Marchesini (CCFM)-evolved gluon distribution and the TMD gluon-to-quark splitting function. Based on the 𝒪(α2) production amplitude q*+q¯*→Z /γ*→l++l- calculated by taking into account the effective q*q¯*Z /γ* - vertex, we analyze the distributions on the dilepton invariant mass, transverse momentum and rapidity and specific angular correlations between the produced leptons as measured by the CMS, ATLAS and LHCb collaborations. We briefly duscuss also the process of assiciated lepton pair and jet production in pp collisions at the LHC.
Ronca, Enrico; Angeli, Celestino; Belpassi, Leonardo; De Angelis, Filippo; Tarantelli, Francesco; Pastore, Mariachiara
2014-09-09
Making use of the recently developed excited state charge displacement analysis [E. Ronca et al., J. Chem. Phys. 140, 054110 (2014)], suited to quantitatively characterize the charge fluxes coming along an electronic excitation, we investigate the role of the density relaxation effects in the overall description of electronically excited states of different nature, namely, valence, ionic, and charge transfer (CT), considering a large set of prototypical small and medium-sized molecular systems. By comparing the response densities provided by time-dependent density functional theory (TDDFT) and the corresponding relaxed densities obtained by applying the Z-vector postlinear-response approach [N. C. Handy and H. F. Schaefer, J. Chem. Phys. 81, 5031 (1984)] with those obtained by highly correlated state-of-the-art wave function calculations, we show that the inclusion of the relaxation effects is imperative to get an accurate description of the considered excited states. We also examine what happens at the quality of the response function when an increasing amount of Hartree-Fock (HF) exchange is included in the functional, showing that the usually improved excitation energies in the case of CT states are not always the consequence of an improved description of their overall properties. Remarkably, we find that the relaxation of the response densities is always able to reproduce, independently of the extent of HF exchange in the functional, the benchmark wave function densities. Finally, we propose a novel and computationally convenient strategy, based on the use of the natural orbitals derived from the relaxed TDDFT density to build zero-order wave function for multireference perturbation theory calculations. For a significant set of different excited states, the proposed approach provided accurate excitation energies, comparable to those obtained by computationally demanding ab initio calculations.
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.
Calculate Electric Field Gradient of TiO2 Within Density Functional Theory
Institute of Scientific and Technical Information of China (English)
2008-01-01
<正>TiO2 electric field gradient has been calculated utilizing WIEN2K program, which is ab initio based on density function theory (DFT). DFT uses the charge density as a variable instead of electronic wave
Tellgren, E I; Teale, A M; Furness, J W; Lange, K K; Ekström, U; Helgaker, T
2014-01-21
We present a novel implementation of Kohn-Sham density-functional theory utilizing London atomic orbitals as basis functions. External magnetic fields are treated non-perturbatively, which enable the study of both magnetic response properties and the effects of strong fields, using either standard density functionals or current-density functionals-the implementation is the first fully self-consistent implementation of the latter for molecules. Pilot applications are presented for the finite-field calculation of molecular magnetizabilities, hypermagnetizabilities, and nuclear magnetic resonance shielding constants, focusing on the impact of current-density functionals on the accuracy of the results. Existing current-density functionals based on the gauge-invariant vorticity are tested and found to be sensitive to numerical details of their implementation. Furthermore, when appropriately regularized, the resulting magnetic properties show no improvement over standard density-functional results. An advantage of the present implementation is the ability to apply density-functional theory to molecules in very strong magnetic fields, where the perturbative approach breaks down. Comparison with high accuracy full-configuration-interaction results show that the inadequacies of current-density approximations are exacerbated with increasing magnetic field strength. Standard density-functionals remain well behaved but fail to deliver high accuracy. The need for improved current-dependent density-functionals, and how they may be tested using the presented implementation, is discussed in light of our findings.
Ghosh, Soumen; Sonnenberger, Andrew L; Hoyer, Chad E; Truhlar, Donald G; Gagliardi, Laura
2015-08-11
The correct description of charge transfer in ground and excited states is very important for molecular interactions, photochemistry, electrochemistry, and charge transport, but it is very challenging for Kohn-Sham (KS) density functional theory (DFT). KS-DFT exchange-correlation functionals without nonlocal exchange fail to describe both ground- and excited-state charge transfer properly. We have recently proposed a theory called multiconfiguration pair-density functional theory (MC-PDFT), which is based on a combination of multiconfiguration wave function theory with a new type of density functional called an on-top density functional. Here we have used MC-PDFT to study challenging ground- and excited-state charge-transfer processes by using on-top density functionals obtained by translating KS exchange-correlation functionals. For ground-state charge transfer, MC-PDFT performs better than either the PBE exchange-correlation functional or CASPT2 wave function theory. For excited-state charge transfer, MC-PDFT (unlike KS-DFT) shows qualitatively correct behavior at long-range with great improvement in predicted excitation energies.
Density functional theory study of the oligomerization of carboxylic acids.
Di Tommaso, Devis; Watson, Ken L
2014-11-20
We present a density functional theory [M06-2X/6-31+G(d,p)] study of the structures and free energies of formation of oligomers of four carboxylic acids (formic acid, acetic acid, tetrolic acid, and benzoic acid) in water, chloroform, and carbon tetrachloride. Solvation effects were treated using the SMD continuum solvation model. The low-lying energy structures of molecular complexes were located by adopting an efficient search procedure to probe the potential energy surfaces of the oligomers of carboxylic acids (CA)n (n = 2-6). The free energies of the isomers of (CA)n in solution were determined as the sum of the electronic energy, vibrational-rotational-translational gas-phase contribution, and solvation free energy. The assessment of the computational protocol adopted in this study with respect to the dimerization of acetic acid, (AA)2, and formic acid, (FA)2, located new isomers of (AA)2 and (FA)2 and gave dimerization constants in good agreement with the experimental values. The calculation of the self-association of acetic acid, tetrolic acid, and benzoic acid shows the following: (i) Classic carboxylic dimers are the most stable isomer of (CA)2 in both the gas phase and solution. (ii) Trimers of carboxylic acid are stable in apolar aprotic solvents. (iii) Molecular clusters consisting of two interacting classic carboxylic dimers (CA)4,(D+D) are the most stable type of tetramers, but their formation from the self-association of classic carboxylic dimers is highly unfavorable. (iv) For acetic acid and tetrolic acid the reactions (CA)2 + 2CA → (CA)4,(D+D) and (CA)3 + CA → (CA)4,(D+D) are exoergonic, but these aggregation pathways go through unstable clusters that could hinder the formation of tetrameric species. (v) For tetrolic acid the prenucleation species that are more likely to form in solution are dimeric and trimeric structures that have encoded structural motifs resembling the α and β solid forms of tetrolic acid. (vi) Stable tetramers of
Lymphatic vessel density and function in experimental bladder cancer
Directory of Open Access Journals (Sweden)
Maier Julie
2007-11-01
Full Text Available Abstract Background The lymphatics form a second circulatory system that drains the extracellular fluid and proteins from the tumor microenvironment, and provides an exclusive environment in which immune cells interact and respond to foreign antigen. Both cancer and inflammation are known to induce lymphangiogenesis. However, little is known about bladder lymphatic vessels and their involvement in cancer formation and progression. Methods A double transgenic mouse model was generated by crossing a bladder cancer-induced transgenic, in which SV40 large T antigen was under the control of uroplakin II promoter, with another transgenic mouse harboring a lacZ reporter gene under the control of an NF-κB-responsive promoter (κB-lacZ exhibiting constitutive activity of β-galactosidase in lymphatic endothelial cells. In this new mouse model (SV40-lacZ, we examined the lymphatic vessel density (LVD and function (LVF during bladder cancer progression. LVD was performed in bladder whole mounts and cross-sections by fluorescent immunohistochemistry (IHC using LYVE-1 antibody. LVF was assessed by real-time in vivo imaging techniques using a contrast agent (biotin-BSA-Gd-DTPA-Cy5.5; Gd-Cy5.5 suitable for both magnetic resonance imaging (MRI and near infrared fluorescence (NIRF. In addition, IHC of Cy5.5 was used for time-course analysis of co-localization of Gd-Cy5.5 with LYVE-1-positive lymphatics and CD31-positive blood vessels. Results SV40-lacZ mice develop bladder cancer and permitted visualization of lymphatics. A significant increase in LVD was found concomitantly with bladder cancer progression. Double labeling of the bladder cross-sections with LYVE-1 and Ki-67 antibodies indicated cancer-induced lymphangiogenesis. MRI detected mouse bladder cancer, as early as 4 months, and permitted to follow tumor sizes during cancer progression. Using Gd-Cy5.5 as a contrast agent for MRI-guided lymphangiography, we determined a possible reduction of lymphatic
Zinc surface complexes on birnessite: A density functional theory study
Energy Technology Data Exchange (ETDEWEB)
Kwon, Kideok D.; Refson, Keith; Sposito, Garrison
2009-01-05
Biogeochemical cycling of zinc is strongly influenced by sorption on birnessite minerals (layer-type MnO2), which are found in diverse terrestrial and aquatic environments. Zinc has been observed to form both tetrahedral (Zn{sup IV}) and octahedral (Zn{sup VI}) triple-corner-sharing surface complexes (TCS) at Mn(IV) vacancy sites in hexagonal birnessite. The octahedral complex is expected to be similar to that of Zn in the Mn oxide mineral, chalcophanite (ZnMn{sub 3}O{sub 7} {center_dot} 3H{sub 2}O), but the reason for the occurrence of the four-coordinate Zn surface species remains unclear. We address this issue computationally using spin-polarized Density Functional Theory (DFT) to examine the Zn{sub IV}-TCS and Zn{sup VI}-TCS species. Structural parameters obtained by DFT geometry optimization were in excellent agreement with available experimental data on Zn-birnessites. Total energy, magnetic moments, and electron-overlap populations obtained by DFT for isolated Zn{sup IV}-TCS revealed that this species is stable in birnessite without a need for Mn(III) substitution in the octahedral sheet and that it is more effective in reducing undersaturation of surface O at a Mn vacancy than is Zn{sub VI}-TCS. Comparison between geometry-optimized ZnMn{sub 3}O{sub 7} {center_dot} 3H{sub 2}O (chalcophanite) and the hypothetical monohydrate mineral, ZnMn{sub 3}O{sub 7} {center_dot} H{sub 2}O, which contains only tetrahedral Zn, showed that the hydration state of Zn significantly affects birnessite structural stability. Finally, our study also revealed that, relative to their positions in an ideal vacancy-free MnO{sub 2}, Mn nearest to Zn in a TCS surface complex move toward the vacancy by 0.08-0.11 {angstrom}, while surface O bordering the vacancy move away from it by 0.16-0.21 {angstrom}, in agreement with recent X-ray absorption spectroscopic analyses.
Molecular density functional theory of water including density–polarization coupling
Jeanmairet, Guillaume; Levy, Nicolas; Levesque, Maximilien; Borgis, Daniel
2016-01-01
International audience; We present a three-dimensional molecular density functional theory of water derived fromfirst-principles that relies on the particle’s density and multipolar polarization density andincludes the density–polarization coupling. This brings two main benefits: (i) scalar densityand vectorial multipolar polarization density fields are much more tractable and give morephysical insight than the full position and orientation densities, and (ii) it includes the fulldensity–pola...
Error estimates for density-functional theory predictions of surface energy and work function
De Waele, Sam; Lejaeghere, Kurt; Sluydts, Michael; Cottenier, Stefaan
2016-12-01
Density-functional theory (DFT) predictions of materials properties are becoming ever more widespread. With increased use comes the demand for estimates of the accuracy of DFT results. In view of the importance of reliable surface properties, this work calculates surface energies and work functions for a large and diverse test set of crystalline solids. They are compared to experimental values by performing a linear regression, which results in a measure of the predictable and material-specific error of the theoretical result. Two of the most prevalent functionals, the local density approximation (LDA) and the Perdew-Burke-Ernzerhof parametrization of the generalized gradient approximation (PBE-GGA), are evaluated and compared. Both LDA and GGA-PBE are found to yield accurate work functions with error bars below 0.3 eV, rivaling the experimental precision. LDA also provides satisfactory estimates for the surface energy with error bars smaller than 10%, but GGA-PBE significantly underestimates the surface energy for materials with a large correlation energy.
Exact density functional and wave function embedding schemes based on orbital localization
Hégely, Bence; Nagy, Péter R.; Ferenczy, György G.; Kállay, Mihály
2016-08-01
Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.
Energy Technology Data Exchange (ETDEWEB)
Tellgren, E. I., E-mail: erik.tellgren@kjemi.uio.no; Lange, K. K.; Ekström, U.; Helgaker, T. [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo (Norway); Teale, A. M., E-mail: andrew.teale@nottingham.ac.uk [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); Furness, J. W. [School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)
2014-01-21
We present a novel implementation of Kohn–Sham density-functional theory utilizing London atomic orbitals as basis functions. External magnetic fields are treated non-perturbatively, which enable the study of both magnetic response properties and the effects of strong fields, using either standard density functionals or current-density functionals—the implementation is the first fully self-consistent implementation of the latter for molecules. Pilot applications are presented for the finite-field calculation of molecular magnetizabilities, hypermagnetizabilities, and nuclear magnetic resonance shielding constants, focusing on the impact of current-density functionals on the accuracy of the results. Existing current-density functionals based on the gauge-invariant vorticity are tested and found to be sensitive to numerical details of their implementation. Furthermore, when appropriately regularized, the resulting magnetic properties show no improvement over standard density-functional results. An advantage of the present implementation is the ability to apply density-functional theory to molecules in very strong magnetic fields, where the perturbative approach breaks down. Comparison with high accuracy full-configuration-interaction results show that the inadequacies of current-density approximations are exacerbated with increasing magnetic field strength. Standard density-functionals remain well behaved but fail to deliver high accuracy. The need for improved current-dependent density-functionals, and how they may be tested using the presented implementation, is discussed in light of our findings.
Energy Technology Data Exchange (ETDEWEB)
Kantar, Yeliz Mert; Usta, Ilhan [Department of Statistics, Anadolu University, Eskisehir 26470 (Turkey)
2008-05-15
In this study, the minimum cross entropy (MinxEnt) principle is applied for the first time to the wind energy field. This principle allows the inclusion of previous information of a wind speed distribution and covers the maximum entropy (MaxEnt) principle, which is also discussed by Li and Li and Ramirez as special cases in their wind power study. The MinxEnt probability density function (pdf) derived from the MinxEnt principle are used to determine the diurnal, monthly, seasonal and annual wind speed distributions. A comparison between MinxEnt pdfs defined on the basis of the MinxEnt principle and the Weibull pdf on wind speed data, which are taken from different sources and measured in various regions, is conducted. The wind power densities of the considered regions obtained from Weibull and MinxEnt pdfs are also compared. The results indicate that the pdfs derived from the MinxEnt principle fit better to a variety of measured wind speed data than the conventionally applied empirical Weibull pdf. Therefore, it is shown that the MinxEnt principle can be used as an alternative method to estimate both wind distribution and wind power accurately. (author)
Kusina, A; Clark, D B; Godat, E; Jezo, T; Kovarik, K; Olness, F I; Schienbein, I; Yu, J Y
2016-01-01
We provide a comprehensive comparison of W/Z vector boson production data in proton-lead and lead-lead collisions at the LHC with predictions obtained using the nCTEQ15 PDFs. We identify the measurements which have the largest potential impact on the PDFs, and estimate the effect of including these data using a Monte Carlo reweighting method. We find this data set can provide information about both the nuclear corrections and the heavy flavor (strange) PDF components. As the proton flavor determination is dependent on nuclear corrections (from heavy target DIS, for example), this information can also help improve the proton PDFs.
Robledo, L. M.
2010-06-01
I discuss the inadequacy of the 'projected density' prescription to be used in density-dependent forces/functionals when calculations beyond mean field are pursued. The case of calculations aimed at the symmetry restoration of mean fields obtained with effective realistic forces of the Skyrme or Gogny type is considered in detail. It is shown that, at least for the restoration of spatial symmetries like rotations, translations or parity, the above prescription yields catastrophic results for the energy that drive the intrinsic wave-function to configurations with infinite deformation, thereby preventing its use both in projection after and before variation.
Robledo, L M
2010-01-01
I discuss the inadequacy of the "projected density" prescription to be used in density dependent forces/functionals when calculations beyond mean field are pursued. The case of calculations aimed at the symmetry restoration of mean fields obtained with effective realistic forces of the Skyrme or Gogny type is considered in detail. It is shown that at least for the restoration of spatial symmetries like rotations, translations or parity the above prescription yields catastrophic results for the energy that drive the intrinsic wave function to configurations with infinite deformation, preventing thereby its use both in projection after and before variation.
DEFF Research Database (Denmark)
Bast, Radovan; Jensen, Hans Jørgen Aagaard; Saue, Trond
2009-01-01
We report an implementation of adiabatic time-dependent density functional theory based on the 4-component relativistic Dirac-Coulomb Hamiltonian and a closed-shell reference. The implementation includes noncollinear spin magnetization and full derivatives of functionals, including hybrid...... and time reversal symmetry on trial vectors to obtain even better reductions in terms of memory and run time, and without invoking approximations. Further reductions are obtained by exploiting point group symmetries for D2h and subgroups in a symmetry scheme where symmetry reductions translate...... into reduction of algebra from quaternion to complex or real. For hybrid GGAs with noncollinear spin magnetization we derive a new computationally advantageous equation for the full second variational derivatives of such exchange-correlation functionals. We apply our implementation to calculations on the ns2...
A Density Functional Study of Atomic Carbon Adsorption on δ-Pu(111)Surface
Institute of Scientific and Technical Information of China (English)
WEI Hong-Yuan; XIONG Xiao-Ling; SONG Hong-Tao; LUO Shun-Zhong
2010-01-01
@@ Adsorption of atomic carbon on δ-Pu(111)surface is investigated systematically using density functional theory with RPBE functional.The adsorption energies,adsorption structures,Mulliken population,work functions,layer and projected density of states are calculated in wide ranges of coverage,which have never been studied before as far as we know.
The functional response to prey density in an acarine system
Fransz, H.G.
1974-01-01
Predacious mites are considered to be important natural enemies of phytophagous mites. Their efficiency in the natural control of prey populations depends on the relationships of the number of prey killed per predator per time unit and the oviposition rate on the one hand and prey density on the
Patching the Exchange-Correlation Potential in Density Functional Theory.
Huang, Chen
2016-05-10
A method for directly patching exchange-correlation (XC) potentials in materials is derived. The electron density of a system is partitioned into subsystem densities by dividing its Kohn-Sham (KS) potential among the subsystems. Inside each subsystem, its projected KS potential is required to become the total system's KS potential. This requirement, together with the nearsightedness principle of electronic matters, ensures that the electronic structures inside subsystems can be good approximations to the total system's electronic structure. The nearsightedness principle also ensures that subsystem densities could be well localized in their regions, making it possible to use high-level methods to invert the XC potentials for subsystem densities. Two XC patching methods are developed. In the local XC patching method, the total system's XC potential is improved in the cluster region. We show that the coupling between a cluster and its environment is important for achieving a fast convergence of the electronic structure in the cluster region. In the global XC patching method, we discuss how to patch the subsystem XC potentials to construct the XC potential in the total system, aiming to scale up high-level quantum mechanics simulations of materials. Proof-of-principle examples are given.
Stretched hydrogen molecule from a constrained-search density-functional perspective
Energy Technology Data Exchange (ETDEWEB)
Valone, Steven M [Los Alamos National Laboratory; Levy, Mel [DIKE UNIV.
2009-01-01
Constrained-search density functional theory gives valuable insights into the fundamentals of density functional theory. It provides exact results and bounds on the ground- and excited-state density functionals. An important advantage of the theory is that it gives guidance in the construction of functionals. Here they engage constrained search theory to explore issues associated with the functional behavior of 'stretched bonds' in molecular hydrogen. A constrained search is performed with familiar valence bond wavefunctions ordinarily used to describe molecular hydrogen. The effective, one-electron hamiltonian is computed and compared to the corresponding uncorrelated, Hartree-Fock effective hamiltonian. Analysis of the functional suggests the need to construct different functionals for the same density and to allow a competition among these functions. As a result the correlation energy functional is composed explicitly of energy gaps from the different functionals.
Ruggenthaler, Michael; Penz, Markus; van Leeuwen, Robert
2015-05-27
In this work we review the mapping from densities to potentials in quantum mechanics, which is the basic building block of time-dependent density-functional theory and the Kohn-Sham construction. We first present detailed conditions such that a mapping from potentials to densities is defined by solving the time-dependent Schrödinger equation. We specifically discuss intricacies connected with the unboundedness of the Hamiltonian and derive the local-force equation. This equation is then used to set up an iterative sequence that determines a potential that generates a specified density via time propagation of an initial state. This fixed-point procedure needs the invertibility of a certain Sturm-Liouville problem, which we discuss for different situations. Based on these considerations we then present a discussion of the famous Runge-Gross theorem which provides a density-potential mapping for time-analytic potentials. Further we give conditions such that the general fixed-point approach is well-defined and converges under certain assumptions. Then the application of such a fixed-point procedure to lattice Hamiltonians is discussed and the numerical realization of the density-potential mapping is shown. We conclude by presenting an extension of the density-potential mapping to include vector-potentials and photons.
Particle number and probability density functional theory and A-representability.
Pan, Xiao-Yin; Sahni, Viraht
2010-04-28
In Hohenberg-Kohn density functional theory, the energy E is expressed as a unique functional of the ground state density rho(r): E = E[rho] with the internal energy component F(HK)[rho] being universal. Knowledge of the functional F(HK)[rho] by itself, however, is insufficient to obtain the energy: the particle number N is primary. By emphasizing this primacy, the energy E is written as a nonuniversal functional of N and probability density p(r): E = E[N,p]. The set of functions p(r) satisfies the constraints of normalization to unity and non-negativity, exists for each N; N = 1, ..., infinity, and defines the probability density or p-space. A particle number N and probability density p(r) functional theory is constructed. Two examples for which the exact energy functionals E[N,p] are known are provided. The concept of A-representability is introduced, by which it is meant the set of functions Psi(p) that leads to probability densities p(r) obtained as the quantum-mechanical expectation of the probability density operator, and which satisfies the above constraints. We show that the set of functions p(r) of p-space is equivalent to the A-representable probability density set. We also show via the Harriman and Gilbert constructions that the A-representable and N-representable probability density p(r) sets are equivalent.
Fromager, Emmanuel
2014-01-01
The exact formulation of multi-configuration density-functional theory (DFT) is discussed in this work. As an alternative to range-separated methods, where electron correlation effects are split in the coordinate space, the combination of Configuration Interaction methods with orbital occupation functionals is explored at the formal level through the separation of correlation effects in the orbital space. When applied to model Hamiltonians, this approach leads to an exact Site-Occupation Embedding Theory (SOET). An adiabatic connection expression is derived for the complementary bath functional and a comparison with Density Matrix Embedding Theory (DMET) is made. Illustrative results are given for the simple two-site Hubbard model. SOET is then applied to a quantum chemical Hamiltonian, thus leading to an exact Complete Active Space Site-Occupation Functional Theory (CASSOFT) where active electrons are correlated explicitly within the CAS and the remaining contributions to the correlation energy are described...
Sundararaman, Ravishankar
2014-01-01
Classical density-functional theory provides an efficient alternative to molecular dynamics simulations for understanding the equilibrium properties of inhomogeneous fluids. However, application of density-functional theory to multi-site molecular fluids has so far been limited by complications due to the implicit molecular geometry constraints on the site densities, whose resolution typically requires expensive Monte Carlo methods. Here, we present a general scheme of circumventing this so-called inversion problem: compressed representations of the orientation density. This approach allows us to combine the superior iterative convergence properties of multipole representations of the fluid configuration with the improved accuracy of site-density functionals. Next, from a computational perspective, we show how to extend the DFT++ algebraic formulation of electronic density-functional theory to the classical fluid case and present a basis-independent discretization of our formulation for molecular classical de...
Local thermodynamic mapping for effective liquid density-functional theory
Kyrlidis, Agathagelos; Brown, Robert A.
1992-01-01
The structural-mapping approximation introduced by Lutsko and Baus (1990) in the generalized effective-liquid approximation is extended to include a local thermodynamic mapping based on a spatially dependent effective density for approximating the solid phase in terms of the uniform liquid. This latter approximation, called the local generalized effective-liquid approximation (LGELA) yields excellent predictions for the free energy of hard-sphere solids and for the conditions of coexistence of a hard-sphere fcc solid with a liquid. Moreover, the predicted free energy remains single valued for calculations with more loosely packed crystalline structures, such as the diamond lattice. The spatial dependence of the weighted density makes the LGELA useful in the study of inhomogeneous solids.
HI column density distribution function at z=0 : Connection to damped Ly alpha statistics
Zwaan, Martin; Verheijen, MAW; Briggs, FH
We present a measurement of the HI column density distribution function f(N-HI) at the present epoch for column densities > 10(20) cm(-2). These high column densities compare to those measured in damped Ly alpha lines seen in absorption against background quasars. Although observationally rare, it
HI column density distribution function at z=0 : Connection to damped Ly alpha statistics
Zwaan, Martin; Verheijen, MAW; Briggs, FH
1999-01-01
We present a measurement of the HI column density distribution function f(N-HI) at the present epoch for column densities > 10(20) cm(-2). These high column densities compare to those measured in damped Ly alpha lines seen in absorption against background quasars. Although observationally rare, it a
Wave-function inspired density functional applied to the H$_2$/H$_2^+$ challenge
Zhang, Igor Ying; Scheffler, Matthias
2016-01-01
We start from the Bethe-Goldstone equation (BGE) to derive a simple orbital-dependent correlation functional -- BGE2 -- which terminates the BGE expansion at the second-order, but retains the self-consistent coupling of electron-pair orrelations. We demonstrate that BGE2 is size consistent and one-electron "self-correlation" free. The electron-pair correlation coupling ensures the correct H$_2$ dissociation limit and gives a finite correlation energy for any system even if it has a no energy gap. BGE2 provides a good description of both H$_2$ and H$_2^+$ dissociation, which is regarded as a great challenge in density functional theory (DFT). We illustrate the behavior of BGE2 analytically by considering H$_2$ in a minimal basis. Our analysis shows that BGE2 captures essential features of the adiabatic connection path that current state-of-the-art DFT approximations do not.
Energy Technology Data Exchange (ETDEWEB)
Solovyeva, Alisa [Gorlaeus Laboratories, Leiden Institute of Chemistry, Leiden University, P.O. Box 9502, 2300 RA Leiden (Netherlands); Technical University Braunschweig, Institute for Physical and Theoretical Chemistry, Hans-Sommer-Str. 10, 38106 Braunschweig (Germany); Pavanello, Michele [Gorlaeus Laboratories, Leiden Institute of Chemistry, Leiden University, P.O. Box 9502, 2300 RA Leiden (Netherlands); Neugebauer, Johannes [Technical University Braunschweig, Institute for Physical and Theoretical Chemistry, Hans-Sommer-Str. 10, 38106 Braunschweig (Germany)
2012-05-21
Subsystem density-functional theory (DFT) is a powerful and efficient alternative to Kohn-Sham DFT for large systems composed of several weakly interacting subunits. Here, we provide a systematic investigation of the spin-density distributions obtained in subsystem DFT calculations for radicals in explicit environments. This includes a small radical in a solvent shell, a {pi}-stacked guanine-thymine radical cation, and a benchmark application to a model for the special pair radical cation, which is a dimer of bacteriochlorophyll pigments, from the photosynthetic reaction center of purple bacteria. We investigate the differences in the spin densities resulting from subsystem DFT and Kohn-Sham DFT calculations. In these comparisons, we focus on the problem of overdelocalization of spin densities due to the self-interaction error in DFT. It is demonstrated that subsystem DFT can reduce this problem, while it still allows to describe spin-polarization effects crossing the boundaries of the subsystems. In practical calculations of spin densities for radicals in a given environment, it may thus be a pragmatic alternative to Kohn-Sham DFT calculations. In our calculation on the special pair radical cation, we show that the coordinating histidine residues reduce the spin-density asymmetry between the two halves of this system, while inclusion of a larger binding pocket model increases this asymmetry. The unidirectional energy transfer in photosynthetic reaction centers is related to the asymmetry introduced by the protein environment.
Constrained Parmeterization of Reduced Density Approximation of Kinetic Energy Functionals
Chakraborty, Debajit; Trickey, Samuel; Karasiev, Valentin
2014-03-01
Evaluation of forces in ab initio MD is greatly accelerated by orbital-free DFT, especially at finite temperature. The recent achievement of a fully non-empirical constraint-based generalized gradient (GGA) functional for the Kohn-Sham KE Ts [ n ] brings to light the inherent limitations of GGAs. This motivates inclusion of higher-order derivatives in the form of reduced derivative approximation (RDA) functionals. That, in turn, requires new functional forms and design criteria. RDA functionals are constrained further to produce a positive-definite, non-singular Pauli potential. We focus on designing a non-empirical constraint-based meta-GGA functional with certain combinations of higher-order derivatives which avoid nuclear-site singularities to a specified order of gradient expansion. Here we report progress on this agenda. Work supported by U.S. Dept. of Energy, grant DE-SC0002139.
Łazarski, Roman; Burow, Asbjörn Manfred; Grajciar, Lukáš; Sierka, Marek
2016-10-30
A full implementation of analytical energy gradients for molecular and periodic systems is reported in the TURBOMOLE program package within the framework of Kohn-Sham density functional theory using Gaussian-type orbitals as basis functions. Its key component is a combination of density fitting (DF) approximation and continuous fast multipole method (CFMM) that allows for an efficient calculation of the Coulomb energy gradient. For exchange-correlation part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097) is extended to energy gradients. Computational efficiency and asymptotic O(N) scaling behavior of the implementation is demonstrated for various molecular and periodic model systems, with the largest unit cell of hematite containing 640 atoms and 19,072 basis functions. The overall computational effort of energy gradient is comparable to that of the Kohn-Sham matrix formation. © 2016 Wiley Periodicals, Inc.
Nakatsukasa, Takashi
2012-01-01
We present the basic concepts and our recent developments in the density functional approaches with the Skyrme functionals for describing nuclear dynamics at low energy. The time-dependent density-functional theory (TDDFT) is utilized for the exact linear response with an external perturbation. For description of collective dynamics beyond the perturbative regime, we present a theory of a decoupled collective submanifold to describe for a slow motion based on the TDDFT. Selected applications are shown to demonstrate the quality of their performance and feasibility. Advantages and disadvantages in the numerical aspects are also discussed.
Novel blind source separation algorithm using Gaussian mixture density function
Institute of Scientific and Technical Information of China (English)
孔薇; 杨杰; 周越
2004-01-01
The blind source separation (BSS) is an important task for numerous applications in signal processing, communications and array processing. But for many complex sources blind separation algorithms are not efficient because the probability distribution of the sources cannot be estimated accurately. So in this paper, to justify the ME(maximum enteropy) approach, the relation between the ME and the MMI(minimum mutual information) is elucidated first. Then a novel algorithm that uses Gaussian mixture density to approximate the probability distribution of the sources is presented based on the ME approach. The experiment of the BSS of ship-radiated noise demonstrates that the proposed algorithm is valid and efficient.