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

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.

28 pages, 2 figures

References in corpus (3)

• 100 years of Weyl's law
• Next-order correction to the Dirac exchange energy of the free electron gas in the thermodynamic limit and generalized gradient approximations
• Crystallographic groups, strictly tessellating polytopes, and analytic eigenfunctions