Accurate effective potential for density amplitude and the corresponding Kohn-Sham exchange-correlation potential calculated from approximate wavefunctions

TL;DR

This paper explains why wavefunction-based methods yield accurate exchange-correlation potentials in density functional theory, even with approximate wavefunctions, by analyzing the Levy-Perdew-Sahni approach and its effective potential.

Contribution

It demonstrates that the Levy-Perdew-Sahni expression provides accurate potentials from approximate wavefunctions and identifies differences with density inversion methods.

Findings

Wavefunction-based potentials closely match true xc potentials.

LPS effective potential remains accurate with approximate wavefunctions.

Differences between wavefunction and density inversion potentials are clarified.

Abstract

Over the past few years it has been pointed out that direct inversion of accurate but approximate ground state densities leads to Kohn-Sham exchange-correlation (xc) potentials that can differ significantly from the exact xc potential of a given system. On the other hand, the corresponding wavefunction based construction of exchange-correlation potential as done by Baerends et al. and Staroverov et al. obviates such problems and leads to potentials that are very close to the true xc potential. In this paper, we provide an understanding of why the wavefunction based approach gives the exchange-correlation potential accurately. Our understanding is based on the work of Levy, Perdew and Sahni (LPS) who gave an equation for the square root of density (density amplitude) and the expression for the associated effective potential in the terms of the corresponding wavefunction. We show that even with the use of approximate wavefunctions the LPS expression gives accurate effective and exchange-correlation potentials. Based on this we also identify the source of difference between the potentials obtained from a wavefunction and those given by the inversion of the associated density. Finally, we suggest exploring the possibility of obtaining accurate ground-state density from an approximate wavefunction for a system by making use of the LPS effective potential.