Accurate all-electron correlation energies for the closed-shell atoms from Ar to Rn and their relationship to the corresponding MP2 correlation energies

McCarthy, Shane P.; Thakkar, Ajit J.

doi:10.1063/1.3547262

Cited by 37 publications

(33 citation statements)

References 53 publications

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“…Their energies are −1/2n 2 , where n is the principal quantum number. Via the virial theorem, T S = −E, and accounting for double occupation of the orbitals, in fact T S (N ) = 1 2 S N/2 (28) where S N is the partial sum from the introduction. Thus our purely mathematical example is in fact a relevant example.…”

Section: Illustration: Hydrogenic Atomsmentioning

confidence: 99%

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Locality of correlation in density functional theory

Burke

Cancio

Gould

et al. 2016

The Journal of Chemical Physics

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The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi 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 supports the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around 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 E C → −A C Z ln Z + B C Z as Z → ∞, where Z is the atomic number, A C is known, and we estimate B C to be about 37 millihartrees. The local density approximation yields A C exactly, but a very incorrect value for B C , showing that the local approximation is less relevant for 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 B C a functional of the TF density for the system. The implications for construction of approximate density functionals are discussed.

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Section: Illustration: Hydrogenic Atomsmentioning

confidence: 99%

“…We cannot hope to answer this question in general at present, but we can try to answer this question in the one case where we have sufficient data: atoms. By very carefully analyzing accurate correlation energies 28 for a sequence of non-relativistic atoms up to Z = 86, we find they can be fitted to the following form:…”

Section: Introductionmentioning

confidence: 99%

Locality of correlation in density functional theory

Burke

Cancio

Gould

et al. 2016

The Journal of Chemical Physics

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“…Atomic correlation energies are accurately known up to Ar [75][76][77] and are known with reasonable accuracy beyond. 78 My philosophy of DFA design, and that of many others, is that atoms are the logical calibration targets. This philosophy is often labeled "empirical."…”

Section: Gradient Approximations: the Ascendency Of Dftmentioning

confidence: 99%

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

Becke

2014

The Journal of Chemical Physics

1,322

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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“…[28][29][30] for 2 Z 18, which are also included in Fig. 2 (Cha1996), (2) the results [41,42] tabulated in [38] (Bue2007-08), and (7) results from Ref. [43] for 2 Z 18 (Mos1997).…”

Section: Testing the Relation For Other Calculationsmentioning

confidence: 99%

Scaling in the correlation energies of atomic ions

2014

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We show through numerical investigations that the ground-state correlation energies of atomic ions follow an unexpectedly simple scaling relation, E c ≈ Z 4/3 f c (Z/N), where N is the number of electrons, Z is the atomic number, and f c is a universal function, for which an analytic expression with a one-parameter fit can be provided. The relation agrees well with several sets of correlation energies obtained from different methods for atomic ions with N = 2, . . . ,18 and Z = 2, . . . ,28. Moreover, our relation gives a good agreement with neutral atoms up to N ≈ 90. Our main result is readily applicable to estimating correlation energies of heavy elements, for which there are no available data in the literature. The simplicity of the relation may also have implications in the development of correlation functionals within density-functional theory.

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Accurate all-electron correlation energies for the closed-shell atoms from Ar to Rn and their relationship to the corresponding MP2 correlation energies

Cited by 37 publications

References 53 publications

Locality of correlation in density functional theory

Locality of correlation in density functional theory

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

Scaling in the correlation energies of atomic ions

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