Current-dependent extension of the Perdew-Burke-Ernzerhof exchange-correlation functional

The probability current density is used in addition to the electron density and its gradient as a variable in the construction of an exchange-correlation functional. Starting from the Perdew-Burke-Ernzerhof generalized gradient approximation, we employ exact conditions to build a nonempirical exchange functional. Matching the correlation functional to that for exchange yields a current-dependent approximation for correlation. The resulting functional is given in a simple closed form. Application of this approximation to open shell atoms eliminates the artificial level splitting of formally degenerate states observed with generalized gradient approximations.     

A short-range correlation energy density functional with multi-determinantal reference

We introduce a short-range correlation density functional defined with respect to a multi-determinantal reference which is meant to be used in a multi-determinantal extension of the Kohn–Sham scheme of density functional theory based on a long-range/short-range decomposition of the Coulomb electron–electron interaction. We construct the local density approximation for this functional and discuss its performance on the He atom.     

Intermolecular dispersion energies from time-dependent density functional theory

Non-expanded dispersion energies are calculated from time-dependent coupled-perturbed density functional theory (DFT) employing various non-hybrid and hybrid exchange-correlation potentials and suitable adiabatic local density approximations for the exchange-correlation kernel. Considering the dimer systems He₂, Ne₂, Ar₂, NeAr, NeHF, ArHF, (H₂)₂, (HF)₂, and (H₂O)₂ it is shown that the effects of intramonomer electron correlation on the dispersion energy are accurately reproduced with the PBE0AC exchange-correlation potential. In contrast, the uncoupled sum-over-states approximation yields inacceptable errors. These are mainly due to neglect of the Coulomb and exchange-correlation kernels and therefore, not substantially improved through an asymptotic correction of the exchange-correlation potential.     

Density functionals from many-body perturbation theory: the band gap for semiconductors and insulators

Theoretically the Kohn-Sham band gap differs from the exact quasiparticle energy gap by the derivative discontinuity of the exchange-correlation functional. In practice for semiconductors and insulators the band gap calculated within any local or semilocal density approximations underestimates severely the experimental energy gap. On the other hand, calculations with an "exact" exchange potential derived from many-body perturbation theory via the optimized effective potential suggest that improving the exchange-correlation potential approximation can yield a reasonable agreement between the Kohn-Sham band gap and the experimental gap. The results in this work show that this is not the case. In fact, we add to the exact exchange the correlation that corresponds to the dynamical (random phase approximation) screening in the GW approximation. This accurate exchange-correlation potential provides band structures similar to the local density approximation with the corresponding derivative discontinuity that contributes 30%-50% to the energy gap. Our self-consistent results confirm substantially the results for Si and other semiconductors obtained perturbatively [R. W. Godby et al., Phys. Rev. B 36, 6497 (1987)] and extend the conclusion to LiF and Ar, a wide-gap insulator and a noble-gas solid.     

Generalized-gradient exchange-correlation hole obtained from a correlation factor ansatz

The Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation energy is employed as reference point for the construction of an angle-averaged exchange-correlation hole. First, we develop a new model for the PBE exchange hole. In contrast to the previous model [Ernzerhof and Perdew, J. Chem. Phys. 109, 3313 (1998)], it contains an atomic exchange hole, similar to the Becke-Roussel model [Becke and Roussel, Phys. Rev. A 39, 3761 (1989)]. A correlation factor, i.e., a function multiplying the exchange hole, is proposed that turns the exchange into an exchange-correlation hole. The correlation factor has a simple form and is determined through a number of known conditions that should be satisfied by a generalized-gradient exchange-correlation hole.     

Time-dependent exchange-correlation current density functionals with memory

Most present applications of time-dependent density functional theory use adiabatic functionals, i.e., the effective potential at time t is determined solely by the density at the same time. This paper discusses a method that aims to go beyond this approximation, by incorporating "memory" effects: the derived exchange-correlation potential will depend not only on present densities but also on the past. In order to ensure the potentials are causal, we formulate the action on the Keldysh contour for electrons in electromagnetic fields, from which we derive suitable Kohn-Sham equations. The exchange-correlation action is now a functional of the electron density and velocity field. A specific action functional is constructed which is Galilean invariant and yields a causal exchange-correlation vector potential for the Kohn-Sham equations incorporating memory effects. We show explicitly that the net exchange-correlation Lorentz force is zero. The potential is consistent with known dynamical properties of the homogeneous electron gas (in the linear response limit).     

Communication: A global hybrid generalized gradient approximation to the exchange-correlation functional that satisfies the second-order density-gradient constraint and has broad applicability in chemistry

We extend our recent SOGGA11 approximation to the exchange-correlation functional to include a percentage of Hartree-Fock exchange. The new functional, called SOGGA11-X, has better overall performance for a broad chemical database than any previously available global hybrid generalized gradient approximation, and in addition it satisfies an extra physical constraint in that it is correct to second order in the density-gradient.     

Electrostatic exchange-correlation charge density in Be and Ne: quantal density functional theoretic analysis

Using classical electrostatics, the total effective integrated charge-density function is calculated for Be and Ne using the multiplicative potentials derived from (1) Hartree and (2) Hartree–Fock approximation to quantal density functional theory (3)exchange-only optimized effective potential and (4) Kohn–Sham exchange-correlation potential using the quantum Monte Carlo density. The evolution of effective integrated charge-density function for these atoms is examined as the electron correlation is built up stepwise from its absence to the stage of its near complete presence. These results provide a deeper understanding of the Kohn–Sham exchange-correlation potential in terms the correspondingly defined integrated charge-density functions based on the Poisson equation. This paper is dedicated to Professor Karl Jug on the occasion of his 65th Birthday     

Linearity condition for orbital energies in density functional theory: construction of orbital-specific hybrid functional

This study proposes a novel approach to construct the orbital-specific (OS) hybrid exchange-correlation functional by imposing the linearity condition: ?(2)E/?f(i)(2)|(0≤f(i)≤1) = ??(i)/?f(i)|(0≤f(i)≤1) = 0, where E, ε(i), and f(i) represent the total energy, orbital energy, and occupation number of the ith orbital. The OS hybrid exchange-correlation functional, of which the OS Hartree-Fock exchange (HFx) portion is determined by the linearity condition, reasonably reproduces the ionization potentials not only from valence orbitals but also from core ones in a sense of Koopmans' theorem. The obtained short-range HFx portions are consistent with the parameters empirically determined in core-valence-Rydberg-Becke-3-parameter-Lee-Yang-Parr hybrid functional [Nakata et al., J. Chem. Phys., 124, 094105 (2006); ibid, 125, 064109 (2006)].     

Two-component density functional theory of positron binding to negative ions

The problem of binding in positron-negative ion systems has been addressed via two-component density functional theory. Calculations have been performed within the local density approximation for electron exchange-correlation as well as for the electron-positron correlation potential using a self-interaction corrected version of the density functional equations. Our results indicate that a positron forms a stable bound state with the negative ions Li⁻,B⁻,C⁻,O⁻,F⁻ and Cl⁻ with respect to dissociation into a negative ion and a positron or a neutral atom and positronium. Inclusion of electron-positron correlation deepens the positron bound state and stabilizes the system compared to earlier exchange-only calculations.     

The importance of electronic exchange-correlation in non-self-consistent frozen density approximation

The effects of different treatments for the exchange-correlation energy on the accuracy of non-self-consistent frozen density approximation (FDA) are discussed. Local spin density approximation (LSDA) and non-local spin density approximation (NLSDA) are employed, respectively. Corresponding results obtained by using full-self-consistent density functional theory (DFT) are also given for the purpose of comparison. Explicit calculations for hydrogen bonds, covalent bonds and ionic bonds indicate that, comparing with LSDA, NLSDA can improve the accuracy of FDA as well as that of DFT. This improvement attributed to the refinements in the treatment for the electronic exchange-correlation energy may help to extend the application of FDA.     

Double-hybrid density-functional theory made rigorous

We provide a rigorous derivation of a class of double-hybrid approximations, combining Hartree-Fock exchange and second-order M?ller-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 a 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.     

Communication: rationale for a new class of double-hybrid approximations in density-functional theory

We provide a rationale for a new class of double-hybrid approximations introduced by Bre?mond and Adamo [J. Chem. Phys. 135, 024106 (2011)] which combine an exchange-correlation density functional with Hartree-Fock exchange weighted by λ and second-order M?ller-Plesset (MP2) correlation weighted by λ(3). We show that this double-hybrid model can be understood in the context of the density-scaled double-hybrid model proposed by Sharkas et al. [J. Chem. Phys. 134, 064113 (2011)], as approximating the density-scaled correlation functional E(c)[n(1/λ)] by a linear function of λ, interpolating between MP2 at λ = 0 and a density-functional approximation at λ = 1. Numerical results obtained with the Perdew-Burke-Ernzerhof density functional confirms the relevance of this double-hybrid model.     

Does the gradient-regulated connection improve the description of correlated metal bond properties?

Gradient-regulated connection (GRAC) is a generalized gradient approximation exchange density functional designed by combining the revPBE and PW91 exchange functionals to impose their behaviors in the slowly- and fast-varying density regions, respectively. Such a construction allows one single density functional to accurately estimate both covalent and weak interactions occurring in main-group-based molecular systems. For the first time, the assessment of the performance of the GRAC exchange functional is extended to the modeling of various metal bond energy and structure properties. This assessment shows that when GRAC is coupled with the Perdew, Burke, Ernzerhof (PBE) correlation, the resulting exchange-correlation density functional is an excellent alternative to global hybrids to model bond dissociation energy, atomic electronic excitation energy, and bond length structure properties of single-reference metal bonds. It also shows that coupling with the Tognetti, Cortona, Adamo (TCA) correlation constitutes a robust approach to tackle energy bond properties of organometallic complexes with multi-reference character.     

Random-phase-approximation-based correlation energy functionals: benchmark results for atoms

The random phase approximation for the correlation energy functional of the density functional theory has recently attracted renewed interest. Formulated in terms of the Kohn-Sham orbitals and eigenvalues, it promises to resolve some of the fundamental limitations of the local density and generalized gradient approximations, as, for instance, their inability to account for dispersion forces. First results for atoms, however, indicate that the random phase approximation overestimates correlation effects as much as the orbital-dependent functional obtained by a second order perturbation expansion on the basis of the Kohn-Sham Hamiltonian. In this contribution, three simple extensions of the random phase approximation are examined; (a) its augmentation by a local density approximation for short-range correlation, (b) its combination with the second order exchange term, and (c) its combination with a partial resummation of the perturbation series including the second order exchange. It is found that the ground state and correlation energies as well as the ionization potentials resulting from the extensions (a) and (c) for closed subshell atoms are clearly superior to those obtained with the unmodified random phase approximation. Quite some effort is made to ensure highly converged data, so that the results may serve as benchmark data. The numerical techniques developed in this context, in particular, for the inherent frequency integration, should also be useful for applications of random phase approximation-type functionals to more complex systems.     

The importance of Colle–Salvetti for computational density functional theory

The purpose of this presentation is to show the importance of the Colle–Salvetti (Theor Chim Acta 37:329, 1975) paper in the development of modern computational density functional theory. To do this we cover the following topics (1) the Bright Wilson understanding (2) the Kohn–Sham equations (3) local density exchange (4) the exchange-hole (5) generalised gradient approximation for exchange (Becke and Cohen) (6) left–right correlation and dynamic correlation (7) the development of the Lee–Yang–Parr dynamic correlation functional from the Colle–Salvetti paper (8) the early success of GGA DFT. Finally we observe that the the BLYP and OLYP exchange-correlation functionals are not semi-empirical; this may explain their great success.