Exchange-correlation functionals via local interpolation along the adiabatic connection

TL;DR

This paper develops local interpolation models along the adiabatic connection to improve density-functional approximations, emphasizing the role of the strong coupling limit and demonstrating their effectiveness on atomic and molecular systems.

Contribution

It introduces a local modeling approach for the adiabatic connection in density functional theory, enhancing size-consistency and treatment of strong correlation effects.

Findings

Local models outperform global ones in accuracy.

Inclusion of SCE functional improves strong correlation treatment.

Analytic model for initial slope aids in functional development.

Abstract

The construction of density-functional approximations is explored by modeling the adiabatic connection em locally, using energy densities defined in terms of the electrostatic potential of the exchange-correlation hole. These local models are more amenable to the construction of size-consistent approximations than their global counterparts. In this work we use accurate input local ingredients to assess the accuracy of range of local interpolation models against accurate exchange-correlation energy densities. The importance of the strictly-correlated electrons (SCE) functional describing the strong coupling limit is emphasized, enabling the corresponding interpolated functionals to treat strong correlation effects. In addition to exploring the performance of such models numerically for the helium and beryllium isoelectronic series and the dissociation of the hydrogen molecule, an approximate analytic model is presented for the initial slope of the local adiabatic connection. Comparisons are made with approaches based on global models and prospects for future approximations based on the local adiabatic connection are discussed.