Constraining density functional approximations to yield self-interaction free potentials

TL;DR

This paper introduces a method to optimize density functional potentials by imposing constraints that eliminate self-interaction errors, leading to more accurate asymptotic behavior and improved one-electron properties.

Contribution

It proposes a novel approach to constrain the effective potential in density functional theory to be free from self-interaction errors, enhancing the accuracy of electronic property predictions.

Findings

Significantly improved asymptotic decay of potentials.

Enhanced accuracy of one-electron properties.

Effective potentials are constrained to be electrostatic of a non-negative density.

Abstract

Self-interactions (SIs) are a major problem in density functional approximations and the source of serious divergence from experimental results. Here, we propose to optimize density functional total energies in terms of the effective local potential, under constraints for the effective potential that guarantee it is free from SI errors and consequently asymptotically correct. More specifically, we constrain the Hartree, exchange and correlation potential to be the electrostatic potential of a non-negative effective repulsive density of $N-1$ electrons. In this way, the optimal effective potentials exhibit the correct asymptotic decay, resulting in significantly improved one-electron properties.