Leading correction to the local density approximation for exchange in large-\(Z\) atoms

The large-\(Z\) asymptotic expansion of atomic energies has been useful in determining exact conditions for corrections to the local density approximation in density functional theory. The correction for exchange is fit well with a leading \(Z \ln Z\) term, and we find its coefficient numerically. T...

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Bibliographic Details
Published in:arXiv.org 2023-04
Main Authors: Argaman, Nathan, Redd, Jeremy, Cancio, Antonio C, Burke, Kieron
Format: Article
Language:English
Subjects:
Approximation
Asymptotic series
Density functional theory
Exchanging
Hydrogen atoms
Thermal expansion
Online Access:Get full text
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Summary:The large-\(Z\) asymptotic expansion of atomic energies has been useful in determining exact conditions for corrections to the local density approximation in density functional theory. The correction for exchange is fit well with a leading \(Z \ln Z\) term, and we find its coefficient numerically. The gradient expansion approximation also has such a term, but with a smaller coefficient. Analytic results in the limit of vanishing interaction with hydrogenic orbitals (a Bohr atom) lead to the conjecture that the coefficients are precisely 2.7 times larger than their gradient expansion counterparts, yielding an analytic expression for the exchange-energy correction which is accurate to \(\sim 5\%\) for all \(Z\).
ISSN:2331-8422
DOI:10.48550/arxiv.2204.01030