Showing papers on "Orbital-free density functional theory published in 2003"
TL;DR: This work constructs a meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters, and describes both molecules and solids with high accuracy, as shown by extensive numerical tests.
Abstract: The electron density, its gradient, and the Kohn-Sham orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The exchange and correlation terms respect two paradigms: one- or two-electron densities and slowly varying densities, and so describe both molecules and solids with high accuracy, as shown by extensive numerical tests. This functional completes the third rung of "Jacob's ladder" of approximations, above the local spin density and GGA rungs.
5,494 citations
TL;DR: In this paper, the electrostatic attraction between the separated charges in long-range excited charge-transfer states originates from the non-local Hartree-Fock exchange potential and is a nonlocal property.
Abstract: The electrostatic attraction between the separated charges in long-range excited charge-transfer states originates from the non-local Hartree-Fock exchange potential and is, thus, a non-local property. Present-day time-dependent density functional theory employing local exchange-correlation functionals does not capture this effect and therefore fails to describe charge-transfer excited states correctly. A hybrid method that is qualitatively correct is described.
1,455 citations
TL;DR: In this paper, a hybrid density functional method for sugar and sugar-like molecules, MPW1S, was presented, which is optimized for sugars and sugarlike molecules using the modified Perdew−Wang density functional.
Abstract: The addition of diffuse functions to a double-ζ basis set is shown to be more important than increasing to a triple-ζ basis when calculating reaction energies, reaction barrier heights, and conformational energies with density functional theory, in particular with the modified Perdew−Wang density functional. It is shown that diffuse basis functions are vital to describe the relative energies between reactants, products, and transition states in isogyric reactions, and they provide enormous improvement in accuracy for conformational equilibria, using 1, 2-ethanediol and butadiene as examples. As a byproduct of the present study, we present a one-parameter hybrid density functional method optimized for sugars and sugar-like molecules; this is called MPW1S.
671 citations
TL;DR: In this article, an extension of density functional theory to situations with significant nondynamical correlation is presented, based on the spin-flip approach which is capable of describing multireference wave functions within a single reference formalism as spin flipping, e.g., α→β, excitations from a high-spin (Ms=1) triplet reference state.
Abstract: An extension of density functional theory to situations with significant nondynamical correlation is presented. The method is based on the spin–flip (SF) approach which is capable of describing multireference wave functions within a single reference formalism as spin–flipping, e.g., α→β, excitations from a high-spin (Ms=1) triplet reference state. An implementation of the spin–flip approach within the Tamm–Dancoff approximation to time-dependent density functional theory (TDDFT) is presented. The new method, SF-TDDFT/TDA or simply SF-DFT, describes target states (i.e., closed- and open-shell singlets, as well as low-spin triplets) by linear response from a reference high-spin triplet (Ms=1) Kohn–Sham state. Contrary to traditional TDDFT, the SF-DFT response equations are solved in a subspace of spin–flipping operators. The method is applied to bond-breaking (ethylene torsional potential), and equilibrium properties of eight diradicals. The results demonstrate significant improvement over traditional Kohn–...
572 citations
TL;DR: In this article, it is argued that the first TDDFT CT excitation energy approximately underestimates the experimental excitation by the average of the integer discontinuities of the donor and acceptor molecules; errors are of the order of several electron volts.
Abstract: Charge-transfer (CT) electronic excitation energies are known to be very poorly predicted by time-dependent density functional theory (TDDFT) using local exchange-correlation functionals. Insight into this observation is provided by a simple analysis of intermolecular CT excitations at infinite separation. It is argued that the first TDDFT CT excitation energy approximately underestimates the experimental excitation by the average of the integer discontinuities of the donor and acceptor molecules; errors are of the order of several electron volts.
532 citations
TL;DR: In this article, a direct optimization method is developed for the computation of the Kohn-Sham kinetic energy density functional Ts from a given electron density and the exchange-correlation potential vxc if this density is from a ground state.
Abstract: A direct optimization method is developed for the computation of the Kohn–Sham kinetic energy density functional Ts from a given electron density and the exchange–correlation potential vxc if this density is from a ground state. The method is based on the construction of a variational functional of the one-electron potential. This functional is derived from the conventional Levy constrained-search formulation and is shown to be closely related to the Lieb functional construction. The one-electron potential is expanded in terms of some fixed terms plus a linear expansion in a basis set. The determination of the Kohn–Sham kinetic energy for an input density is then turned into the maximization of this functional of potential. The analytic first and second derivatives of the variational functional with respect to the linear basis set expansion coefficients and also the nonlinear parameters in the basis set are derived. This enables very efficient iterative optimization of the potential and hence the calculation of Ts and vxc. The efficiency and accuracy of the method is shown in the numerical implementation for atomic and molecular calculations with Gaussian basis set expansions both for molecular orbitals and for one-electron potentials. Finally, this direct optimization method is extended to general density functionals and the analytic derivatives are also developed for use in optimization methods.
283 citations
TL;DR: In this article, the dependency of the semi-empirical fits to a given basis set for a generalized gradient approximation and a hybrid functional is investigated, and the resulting functionals are then tested for other basis sets, evaluating their errors and transferability.
Abstract: 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 generalized gradient approximation and a hybrid functional is investigated. The resulting functionals are then tested for other basis sets, evaluating their errors and transferability.
165 citations
TL;DR: In this paper, the authors give an overview of the fundamental concepts of density functional theory and give a careful discussion of the several density functionals and their differentiability properties, showing that for non-degenerate ground states, the necessary functional derivatives can be calculated by means of linear response theory, but that there are some differentiability problems for degenerate ground state.
Abstract: 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 response theory, but that there are some differentiability problems for degenerate ground states. These problems can be overcome by extending the domains of the functionals. We further show that for every interacting v-representable density we can find a noninteracting v-representable density arbitrarily close and show that this is sufficient to set up a Kohn-Sham scheme. We finally describe two systematic approaches for the construction of density functionals.
111 citations
TL;DR: In this article, the authors review some well-known aspects of density functional theory: the Hohenberg-Kohn theorems, the Kohn-Sham method, the adiabatic connection, and approximations of local nature.
Abstract: Using recent calculations we review some well-known aspects of density functional theory: the Hohenberg-Kohn theorems, the Kohn-Sham method, the adiabatic connection, and the approximations of local nature. Emphasis is put upon using model Hamiltonians, of which the noninteracting or the physical ones are just particular cases. The model Hamiltonians allow us to produce multireference density functional theory and continuously switch to the physical system. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 166 -190, 2003
105 citations
TL;DR: In this article, the authors report the derivation and performance of a spin-restricted density functional formalism for linear time-dependent properties in open-shell molecules, which is based on an exponential parameterization of the density operator with the response functions defined through Ehrenfest's principle.
Abstract: In this paper we report the derivation and the performance of a spin-restricted density functional formalism for linear time-dependent properties in open-shell molecules. The formalism is based on an exponential parameterization of the density operator with the response functions defined through Ehrenfest’s principle. In addition to the derivation of formulas, details of implementation are given as well as a discussion of numerical results for excitation energies and dynamic polarizabilities for a selected set of radicals.
88 citations
TL;DR: In this paper, a method based on an exponential parametrization of the spin-dependent density operator is derived for the evaluation of linear and quadratic response functions for spindependent perturbations.
Abstract: We present density functional response theory generalized to triplet excitations. A method based on an exponential parametrization of the spin-dependent density operator is derived for the evaluation of linear and quadratic response functions for spin-dependent perturbations. The developed methodology is applicable to commonly available functionals, also hybrid functionals including exchange–correlation functionals at the general gradient-approximation level and fractional exact Hartree–Fock exchange. Illustrative calculations are presented for singlet–triplet transition moments and phosphorescence lifetimes, providing numerical data on these quantities for the first time using time-dependent density functional theory.
TL;DR: In this article, the response of an extended periodic system to a homogeneous field (of wave-vector $q = 0) cannot be obtained from a time-dependent density functional theory (TDDFT) calculation, because the Runge-Gross theorem does not apply.
Abstract: The response of an extended periodic system to a homogeneous field (of wave-vector $q=0)$ cannot be obtained from a $q=0$ time-dependent density functional theory (TDDFT) calculation, because the Runge-Gross theorem does not apply. Time-dependent current--density functional theory is needed and demonstrates that one key ingredient missing from TDDFT is the macroscopic current. In the low-frequency limit, in certain cases, density polarization functional theory is recovered and a formally exact expression for the polarization functional is given.
01 Jan 2003
TL;DR: In this paper, the basic idea of orbital-dependent xc-functionals is illustrated by the simplest and, at the same time, most important functional of this type, the exact exchange of density functional theory (DFT).
Abstract: This chapter is devoted to orbital-dependent exchange-correlation (xc) functionals, a concept that has attracted more and more attention during the last ten years. After a few preliminary remarks, which clarify the scope of this review and introduce the basic notation, some motivation will be given why such implicit density functionals are of definite interest, in spite of the fact that one has to cope with additional complications (compared to the standard xc-functionals). The basic idea of orbital-dependent xc-functionals is then illustrated by the simplest and, at the same time, most important functional of this type, the exact exchange of density functional theory (DFT - for a review see e.g. [1], or the chapter by J. Perdew and S. Kurth in this volume).
TL;DR: In this paper, a density functional theory for the effect of fluid-fluid and fluid-surface attractive interactions on the structure of polymers at surfaces is presented, which treats the ideal gas free-energy functional exactly and uses a weighted density approximation for the hard chain contribution to the excess free energy functional.
Abstract: A density functional theory is presented for the effect of fluid–fluid and fluid–surface attractive interactions on the structure of polymers at surfaces. The theory treats the ideal gas free-energy functional exactly and uses a weighted density approximation for the hard chain contribution to the excess free-energy functional. The attractive interactions are calculated using the bulk fluid direct correlation function obtained from the polymer reference interaction site model theory. The predictions of the theory are in good agreement with computer simulation results for the density profiles of freely rotating fused-sphere chains at surfaces for a wide range of densities and temperatures. The results emphasize the importance of using different approximations for the hard sphere and attractive interactions in density functional theories for polymers.
TL;DR: In this article, it is shown that half of the parallel-spin eigenvalues of the reconstructed two-electron density matrix are necessarily negative, and that these spurious negative eigen values lower the electronic energy substantially.
Abstract: Several “reconstructive” proposals for density matrix functional theory are investigated, each of which expresses the two-electron density matrix, and therefore the electronic energy, as a functional of the natural orbitals and their occupation numbers. It is shown that for each of these functionals, half of the parallel-spin eigenvalues of the reconstructed two-electron density matrix are necessarily negative. Illustrative all-electron calculations for Be and LiH, in a variety of Gaussian basis sets, demonstrate that these spurious negative eigenvalues lower the electronic energy substantially. In spite of this, there is no indication that the variationally optimized energy diverges as the basis set approaches completeness, as has been suggested based on calculations with a small number of active orbitals. The apparent variational instability reported previously is attributed to qualitative differences between the minimal-basis and extended-basis potential curves, for certain functionals. However, we ide...
TL;DR: A new simple scheme for self‐interaction correction of exchange functionals in the density functional theory that reproduces a transition state that is not given by pure functionals and provides a clear improvement in cases where the barriers are underestimated by conventional “pure” functionals.
Abstract: We propose a new simple scheme for self-interaction correction (SIC) of exchange functionals in the density functional theory. In the new scheme, exchange energies are corrected by substituting exchange self-interactions for exchange functionals in regions of self-interaction. To classify the regions of self-interaction, we take advantage of the property of the total kinetic energy density approaching the Weizsacker density in the case of electrons in isolated orbitals. The scheme differs from conventional SIC methods in that it produces optimized molecular structures. Applying the scheme to the calculation of reaction energy barriers showed that it provides a clear improvement in cases where the barriers are underestimated by conventional "pure" functionals. In particular, we found that this scheme even reproduces a transition state that is not given by pure functionals.
01 Jan 2003
TL;DR: The goal of this chapter is to supply the beginner with a brief pedagogical overview of DFT, combining the technical aspects of the numerical implementations, and to hope that the beginner obtains a general impression of the capabilities and limitations of D FT.
Abstract: The success of density functional theory (DFT) is clearly demonstrated by the overwhelming amount of research articles describing results obtained within DFT that were published in the last decades. There is also a fair number of books reviewing the basics of the theory and its extensions (e.g., the present volume, [1] and [2]). These works fall mainly into three classes: those dealing with the theory (proposing extensions, new functionals, etc.), those concerned with the technical aspects of the numerical implementations, and others - the vast majority - presenting results. In our opinion, any scientist working in the field should have a sound knowledge of the three classes. For example, a theorist developing a new functional should be aware of the difficulties in implementing it. Or the applied scientist, performing calculations on specific systems, should know the limitations of the theory and of the numerical implementation she/he is using. The goal of this chapter is to supply the beginner with a brief pedagogical overview of DFT, combining the abovementioned aspects. However, we will not review its foundations - we redirect the reader to the chapter of J. Perdew and S. Kurth that opens this book. Obviously, we will not be able to provide many details, but we hope that the beginner obtains a general impression of the capabilities and limitations of DFT.
TL;DR: In this article, the authors used density functional theory in an orbital-free implementation to calculate the properties of pure fcc Al, hcp and bcc Mg, and the meta-stable alloy phase β'' (Al3Mg).
Abstract: We have used density functional theory in an orbital-free, implementation to calculate the properties of pure fcc Al, hcp and bcc Mg, and the meta-stable alloy phase β'' (Al3Mg). Five linear-response-based kinetic energy density functionals have been used, one of which has a density-dependent (DD) response kernel. We demonstrate that orbital-free density functional theory (OF-DFT) can produce physically accurate properties for Al–Mg alloys, if the kinetic energy density functional employed has a DD-kernel.
TL;DR: In this paper, a simple, self-consistent method to correct the self-interaction error in density functional theory approaches is presented, which is based on an average density selfinteraction correction.
TL;DR: In this article, a new method for defining an energy density for the noninteracting kinetic energy of density functional theory is given, which is a density functional determined completely by the kinetic energy functional itself.
Abstract: A new method for defining an energy density for the noninteracting kinetic energy of density functional theory is given. The resulting energy density is a density functional determined completely by the kinetic energy functional itself. Although this method is not constructive, it allows for a direct comparison between exact and approximate functionals pointwise in space. For simple systems, the new energy density is calculated exactly, and compared with traditional choices, on both formal and physical grounds. Finally, the energy densities of both the gradient expansion and the von Weizsacker approximation are calculated, and compared with the exact quantity. The errors in the von Weizsacker approximation are identified.
TL;DR: The present partitioned density functional theory performs much better than several previous density functional perturbation theory approaches and a recently proposed bridge density functional approximation.
Abstract: The existing classical density functional approach for nonuniform Lennard-Jones fluid, which is based on dividing the Lennard-Jones interaction potential into a short-range, repulsive part, and a smoothly varying, long-range, attractive tail, was improved by dividing the bulk second-order direct correlation function into strongly density-depending short-range part and weakly density-depending long-range part. The latter is treated by functional perturbation expansion truncated at the lowest order whose accuracy depends on how weakly the long-range part depends on the bulk density. The former is treated by the truncated functional perturbation expansion which is rewritten in the form of the simple weighted density approximation and incorporates the omitted higher-order terms by applying Lagrangian theorem of differential calculus to the reformulated form. The two approximations are put into the density profile equation of the density functional theory formalism to predict the density distribution for Lennard-Jones fluid in contact with a hard wall or between two hard walls within the whole density range for reduced temperature ${T}^{*}=1.35$ and a density point for reduced temperature ${T}^{*}=1.$ The present partitioned density functional theory performs much better than several previous density functional perturbation theory approaches and a recently proposed bridge density functional approximation.
TL;DR: In this article, a new natural orbital functional is obtained based on the analysis of the general properties for the one and two-particle reduced density matrices, and the spin structure of the correction term from the improved Bardeen-Cooper-Schrieffer theory is considered.
Abstract: Based on the analysis of the general properties for the one- and two-particle reduced density matrices, a new natural orbital functional is obtained. It is shown that by partitioning the two-particle reduced density matrix in an antisymmeterized product of one-particle reduced density matrices and a correction Γc we can derive a corrected Hartree–Fock theory. The spin structure of the correction term from the improved Bardeen–Cooper–Schrieffer theory is considered to take into account the correlation between pairs of electrons with antiparallel spins. The analysis affords a nonidempotent condition for the one-particle reduced density matrix. Test calculations of the correlation energy and the dipole moment of several molecules in the ground state demonstrate the reliability of the formalism. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 317–323, 2003
TL;DR: In this paper, a generalization of the density functional theory was proposed, which leads to single-particle equations of motion with a quasilocal mean-field operator, which contains the quasiparticle position-dependent effective mass and a spin-orbit potential.
Abstract: In this paper we propose a generalization of the density functional theory. The theory leads to single-particle equations of motion with a quasilocal mean-field operator, which contains a quasiparticle position-dependent effective mass and a spin-orbit potential. The energy density functional is constructed using the extended Thomas-Fermi approximation and the ground-state properties of doubly magic nuclei are considered within the framework of this approach. Calculations were performed using the finite-range Gogny D1S forces and the results are compared with the exact Hartree-Fock calculations.
TL;DR: In this paper, a refined formulation of an existing polymer density functional theory is presented, wherein an intrachain stiffness is introduced via a bending potential, which leads to a considerable improvement of the predicted density profile for a hard sphere polymer melt, at low density.
Abstract: A refined formulation of an existing polymer density functional theory is presented, wherein an intrachain stiffness is introduced via a bending potential. Comparisons with Metropolis Monte Carlo simulations in a slit geometry shows that this leads to a considerable improvement of the predicted density profile for a hard sphere polymer melt, at low density. We also show how the corresponding surface interactions are affected by the inclusion of this intramolecular correlation. We expect that the improvement obtained will be even more important in the description of, for example, polyelectrolytes, although such comparisons are not made in this preliminary study.
TL;DR: The quantal theory of both ground and excited degenerate states is described and a rigorous physical interpretation of the corresponding Kohn-Sham energy functionals of the density, ensemble density, bidensity and ensemble bidensity, and of their respective functional derivatives is provided.
Abstract: The treatment of degenerate states within Kohn-Sham density functional theory is a problem of long-standing and current interest. We propose a solution to this mapping from the interacting degenerate system to that of the noninteracting fermion model whereby the equivalent density and energy are obtained via the unifying physical framework of quantal density functional theory. We describe the quantal theory of both ground and excited degenerate states, and for the cases of both pure state and ensemble v-representable densities. The quantal description further provides a rigorous physical interpretation of the corresponding Kohn-Sham energy functionals of the density, ensemble density, bidensity and ensemble bidensity, and of their respective functional derivatives. We conclude with examples of the mappings within the quantal theory.
TL;DR: In this article, the second-order correlation potential was shown to be equivalent to the high-density scaling limit of the exact correlation potential, and thus provided the first self-consistent finite-basis-set implementation of a Kohn-Sham (KS) potential correct through secondorder.
Abstract: Formal connections between the high-density scaling limit of the correlation energy functional Ec[n] in density functional theory and second-order energy expressions from different perturbation theory formulations are presented. It is demonstrated that the second-order correlation potential considered by Grabowski et al. [J. Chem. Phys. 116, 4415 (2002)] is equivalent to the high-density limit of the exact correlation potential, and thus provides the first self-consistent finite-basis-set implementation of a Kohn–Sham (KS) potential correct through second-order. A different second-order correlation functional based on the exchange-only KS approach is introduced. It is shown that this second-order correlation functional leads to the same self-consistent KS realization as the one derived from the second-order component of Ec[n].
TL;DR: In this article, a simple formalism for the calculation of the derivatives of the electronic density matrix at any order, within density functional theory, is presented, contrary to previous ones, is not based on the perturbative expansion of the Kohn-Sham wavefunctions.
Abstract: We present a simple formalism for the calculation of the derivatives of the electronic density matrix at any order, within density functional theory. Our approach, contrary to previous ones, is not based on the perturbative expansion of the Kohn-Sham wavefunctions. It has the following advantages: (i) it allows a simple derivation for the expression for the high order derivatives of the density matrix; (ii) in extended insulators, the treatment of uniform-electric-field perturbations and of the polarization derivatives is straightforward.
TL;DR: It is shown how the use of the spin current density as a basic variable solves this problem, and an explicit local expression for the exchange-correlation fields as functionals of thespin currents is provided.
Abstract: It has been known for some time that the exchange-correlation potential in time-dependent density-functional theory is an intrinsically nonlocal functional of the density as soon as one goes beyond the adiabatic approximation. In this paper we show that a much more severe nonlocality problem, with a completely different physical origin, plagues the exchange-correlation potentials in time-dependent spin-density functional theory. We show how the use of the spin current density as a basic variable solves this problem, and we provide an explicit local expression for the exchange-correlation fields as functionals of the spin currents.
TL;DR: In this article, a variational quantum Monte Carlo realization of the adiabatic connection technique is used to calculate the most relevant quantities in Hohenberg-Kohn-Sham density functional theory for several strongly inhomogeneous electron-gas systems.
Abstract: We use a variational quantum Monte Carlo realization of the adiabatic connection technique to calculate the most relevant quantities in Hohenberg-Kohn-Sham density functional theory for several strongly inhomogeneous electron-gas systems. Results for the coupling-constant dependence of the exchange-correlation energy, the pair-correlation function, the exchange-correlation hole, and the exchange and correlation energy densities are presented. Comparisons are made with the interaction strength interpolation ~ISI! approximation, the local density approximation ~LDA!, the gradient expansion approximation ~GEA!, the generalized gradient approximation ~GGA!, and the weighted density approximation ~WDA!. The coupling-constant dependence of the exchange-correlation energy is accurately described by an ISI model that incorporates information on the strong-interaction limit. Unlike either the LDA or GEA, the WDA is successful in describing the nonlocal structure of the exchange-correlation hole. The LDA errors in the exchange-correlation energy density show a remarkable correlation with the Laplacian of the density. The GGA worsens the error in the integrated exchange-correlation energy as the inhomogeneity of the systems increases. This failure is shared by current meta-GGA functionals and is shown to be caused by the inability of these functionals to describe the LDA overestimation ~in absolute value! of the exchange energy density around density maxima. It is suggested that this effect could be taken into account by including Laplacian terms in semilocal density functionals.
TL;DR: In this paper, the authors compared the results of the restricted open-shell Kohn-Sham and wave-function-based methods with time-dependent density functional theory and wave function based methods.
Abstract: Singlet excited state geometries of a set of medium sized molecules with different characteristic lowest excitations are studied. Geometry optimizations of excited states are performed with two closely related restricted open-shell Kohn–Sham methods and within linear response to time-dependent density functional theory. The results are compared to wave-function based methods. Excitation energies (vertical and adiabatic) calculated from the open-shell methods show systematic errors depending on the type of excitation. However, for all states accessible by the restricted methods a good agreement for the geometries with time-dependent density functional theory and wave-function based methods is found. An analysis of the energy with respect to the mixing angle for the singly occupied orbitals reveals that some states (mostly [ n → π ∗ ] ) are stable when symmetry constraints are relaxed and others (mostly [ π → π ∗ ] ) are instable. This has major implications on the applicability of the restricted open-shell methods in molecular dynamics simulations.