Intracule densities in the strong-interaction limit of density functional theory

TL;DR

This paper explores the strong-interaction limit of intracule densities in density functional theory, providing a theoretical framework and calculations that could improve models for electron correlation by using one-electron densities.

Contribution

It develops a new theoretical approach to compute intracule densities in the strong-interaction limit solely from one-electron densities, aiding the construction of better density functional models.

Findings

Strong-interaction intracule densities can be derived from one-electron densities.

Comparison with Kohn-Sham and physical densities offers insights for model development.

The framework simplifies calculations in the strong-interaction limit of DFT.

Abstract

The correlation energy in density functional theory can be expressed exactly in terms of the change in the probability of finding two electrons at a given distance $r_{12}$ (intracule density) when the electron-electron interaction is multiplied by a real parameter $\lambda$ varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the one-electron density is (ideally) kept fixed by a suitable local one-body potential. While an accurate intracule density of the physical system can only be obtained from expensive wavefunction-based calculations, being able to construct good models starting from Kohn-Sham ingredients would highly improve the accuracy of density functional calculations. To this purpose, we investigate the intracule density in the $\lambda\to\infty$ limit of the adiabatic connection. This strong-interaction limit of density functional theory turns out to be, like the opposite non-interacting Kohn-Sham limit, mathematically simple and can be entirely constructed from the knowledge of the one-electron density. We develop here the theoretical framework and, using accurate correlated one-electron densities, we calculate the intracule densities in the strong interaction limit for few atoms. Comparison of our results with the corresponding Kohn-Sham and physical quantities provides useful hints for building approximate intracule densities along the adiabatic connection of density functional theory.