DOI: 10.1063/1.476976. Why semilocal functionals work: Accuracy of the on-top pair density and importance of system averaging

Why semilocal functionals work: Accuracy of the on-top pair density and importance of system averaging

10.1063/1.476976

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

Gradient-corrected density functionals provide a common tool for electronic structure calculations in quantum chemistry and condensed matter physics. This article explains why local and semilocal approximations work for the exchange-correlation energy. We demonstrate the high accuracy of the local spin-density (LSD) approximation for the on-top pair density, which provides the missing link between real atoms and molecules and the uniform electron gas. Special attention is devoted to the leading correction to exchange in the high-density (or weakly correlated) limit. We give an improved analytic expression for the on-top pair density in the uniform electron gas, calculating its spin-polarization dependence exactly in the high-density limit. We find the exact form of the gradient expansion for the on-top pair density, using Levy’s scaling of the interacting wave function. We also discuss the importance of system averaging, which unweights spatial regions where the density varies most rapidly. We show how the depth of the on-top hole correlates with the degree of locality of the exchange-correlation energy. Finally, we discuss how well fully nonlocal approximations (weighted-density, self-interaction correction, and hybrid-exchange) reproduce the on-top hole.

Bibliography

Burke, K., Perdew, J. P., & Ernzerhof, M. (1998). Why semilocal functionals work: Accuracy of the on-top pair density and importance of system averaging. The Journal of Chemical Physics, 109(10), 3760â3771.

Authors 3

Kieron Burke (first)
John P. Perdew (additional)
Matthias Ernzerhof (additional)

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Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 8:16 a.m.)
Deposited	1 year, 6 months ago (Feb. 5, 2024, 10:05 p.m.)
Indexed	5 months, 1 week ago (March 19, 2025, 8:39 a.m.)
Issued	26 years, 11 months ago (Sept. 8, 1998)
Published	26 years, 11 months ago (Sept. 8, 1998)
Published Print	26 years, 11 months ago (Sept. 8, 1998)

Funders 0

None

BibTeX

@article{Burke_1998, title={Why semilocal functionals work: Accuracy of the on-top pair density and importance of system averaging}, volume={109}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.476976}, DOI={10.1063/1.476976}, number={10}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Burke, Kieron and Perdew, John P. and Ernzerhof, Matthias}, year={1998}, month=sep, pages={3760–3771} }

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