Improved Statistical Exchange Approximation for Inhomogeneous Many-Electron Systems

Herman, Frank; Dyke, J. P. Van; Ortenburger, Irene B.

doi:10.1103/physrevlett.22.807

Cited by 380 publications

(89 citation statements)

References 14 publications

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“…However, it is, at variance with eq. [13], not positive for all s (17d), as shown in the Ar atom in Fig. 7.…”

Section: Expansion Of the Spherically Averaged Fermi-holementioning

confidence: 99%

“…The functions p z y , and as a consequence, EY, ' are in the HFS and the LSD methods represented simply as local functions of the electron density, and most attempts to improve upon the two methods have involved the inclusion of correction terms depending on derivatives of the electron density in the representation of ETY. However, in earlier investigations (13) the forms chosen for such correction terms were based on dimensional arguments rather than on an analysis of the functions p?'. Also, the expression for ET' in terms of electron-density derivatives, known as the gradient expansion of E y or the non-local representation of Ez', has met with considerable criticism (7), and it has been claimed that the gradient expansion of Ez' in fact is divergent.…”

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confidence: 99%

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On the shape of spherically averaged Fermi-hole correlation functions in density functional theory. 1. Atomic systems

Tschinke¹,

Ziegler²

1989

Can. J. Chem.

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We have compared, for atomic systems, the spherically averaged Fermi-hole correlation function p ! ( r l , s ) in the Hartree-Fock theory with the corresponding function p;i",r,, s ) employed in local density functional theory. It is shown that, in contrast to pQ,U(rl, s ) , the function pg", rl , s ) behaves qualitatively incorrectly at positions r l of the reference electron far from the nucleus. Furthermore, we have shown that the qualitatively incorrect behaviour of p;2E(rl, s ) can be remedied by an approximate expansion of p","(r I , s ) in powers of s , where s is the inter-electronic distance. However, such an expansion must be conducted in two regions due to the discontinuity of p",(rl, s ) as a function of s at the atomic nucleus. Based on the two-region expansion of p","(r,, s ) , we have developed an alternative approximate density functional expansionPQp&(rl, S) for the spherically averaged Fermi-hole correlation function. The corresponding exchange energy density functional yields values for the exchange energies of atoms in good agreement with Hartree-Fock results.Key words: atomic exchange energy, density functional theory, Fermi hole. I. Introduction Hohenberg and Kohn (1) demonstrated in 1964 that the ground-state energy of an electronic system is an unique (albeit unknown) functional of the electron density. This remarkable theorem gave credence to previous work by Slater (2) and others (3), and initiated an extensive study (4, 5) into the relation between electronic energy and electron density, a field that now has become known as (energy) density functional theory.In the last 15 years, due to a number of innovative implementations (6), it has become possible to carry out calculations based on approximate density functionals. Of the various approximate density functional methods, the HartreeFock-Slater (or X a ) scheme (7) is by far the most commonly used in chemistry. The accumulated experience with the HFS method seems to indicate that geometrical parameters (8), force constants (9), and spectroscopic energy differences (Sp, 10) (ionization potentials and excitation energies) are in good to fair agreement with experiment. However, bond energies (80-b, 1 l a ) are not in general well represented by the HFS method as indicated in Table 1, where several of the theoretical values obtained from HFS calculations typically are too high in comparison with experiment.The slightly more elaborate Local Spin Density method (LSD) (5p) provides geometrical parameters comparable to those obtained from ~l % calculations @a), whereas-ionization potentials and excitation energies from LSD calculations (12) compare somewhat better with experiment than the corresponding HFS results. However, the LSD method does not uniformly

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“…However, it is, at variance with eq. [13], not positive for all s (17d), as shown in the Ar atom in Fig. 7.…”

Section: Expansion Of the Spherically Averaged Fermi-holementioning

confidence: 99%

mentioning

confidence: 99%

On the shape of spherically averaged Fermi-hole correlation functions in density functional theory. 1. Atomic systems

Tschinke¹,

Ziegler²

1989

Can. J. Chem.

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“…The functional derivative (i.e., the KS potential) of the gradient term diverges in the exponential tails of finite systems. 50 This is not just a computational nuisance. It reflects a fundamental failure of the LGC functional form.…”

Section: Gradient Approximations: the Ascendency Of Dftmentioning

confidence: 99%

“…In the 1970s and 80s, at least three different theoretical values [46][47][48][49] were published. Earlier, in 1969, the pragmatic approach of fitting β to atomic exchange energies had been taken by Herman et al 50,51 The Herman value,…”

Section: Gradient Approximations: the Ascendency Of Dftmentioning

confidence: 99%

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Perspective: Fifty years of density-functional theory in chemical physics

Becke

2014

The Journal of Chemical Physics

1,326

964

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Since its formal inception in 1964-1965, Kohn-Sham density-functional theory (KS-DFT) has become the most popular electronic structure method in computational physics and chemistry. Its popularity stems from its beautifully simple conceptual framework and computational elegance. The rise of KS-DFT in chemical physics began in earnest in the mid 1980s, when crucial developments in its exchange-correlation term gave the theory predictive power competitive with welldeveloped wave-function methods. Today KS-DFT finds itself under increasing pressure to deliver higher and higher accuracy and to adapt to ever more challenging problems. If we are not mindful, however, these pressures may submerge the theory in the wave-function sea. KS-DFT might be lost. I am hopeful the Kohn-Sham philosophical, theoretical, and computational framework can be preserved. This Perspective outlines the history, basic concepts, and present status of KS-DFT in chemical physics, and offers suggestions for its future development. © 2014 AIP Publishing LLC.

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From explicit to implicit density functionals

1999

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The concept of orbital-and eigenvalue-dependent exchange-Ž . correlation xc energy functionals is reviewed. We show how such functionals can be derived in a systematic fashion via a perturbation expansion, utilizing the Kohn᎐Sham system as a noninteracting reference system. We demonstrate that the second-order contribution to this expansion of the xc-energy functional includes the leading term of the van der Waals interaction. The optimized-Ž . potential method OPM , which allows the calculation of the multiplicative xc-potential corresponding to an orbital-and eigenvalue-dependent xc-energy functional via an integral equation, is discussed in detail. We examine an approximate analytical solution of the OPM integral equation, pointing out that, for eigenvalue-dependent functionals, the three paths used in the literature for the derivation of this approximation yield different results. Finally, a number of illustrative results, both for the exchange-only limit and for the combination of the exact exchange with various correlation functionals, are given.

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Improved Statistical Exchange Approximation for Inhomogeneous Many-Electron Systems

Cited by 380 publications

References 14 publications

On the shape of spherically averaged Fermi-hole correlation functions in density functional theory. 1. Atomic systems

On the shape of spherically averaged Fermi-hole correlation functions in density functional theory. 1. Atomic systems

Perspective: Fifty years of density-functional theory in chemical physics

From explicit to implicit density functionals

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