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arXiv · 2303.14149

Two-term asymptotics of the exchange energy of the electron gas on symmetric polytopes in the high-density limit

Thiago Carvalho Corso
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Abstract

We derive a two-term asymptotic expansion for the exchange energy of the free electron gas on strictly tessellating polytopes and fundamental domains of lattices in the thermodynamic limit. This expansion comprises a bulk (volume-dependent) term, the celebrated Dirac exchange, and a novel surface correction stemming from a boundary layer and finite-size effects. Furthermore, we derive analogous two-term asymptotic expansions for semi-local density functionals. By matching the coefficients of these asymptotic expansions, we obtain an integral constraint for semi-local approximations of the exchange energy used in density functional theory.

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Thiago Carvalho Corso. 2023-03-24. Two-term asymptotics of the exchange energy of the electron gas on symmetric polytopes in the high-density limit. https://doi.org/10.1007/s11040-024-09485-w

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