Reduction of Electronic Wavefunctions to Kohn-Sham Effective Potentials

TL;DR

This paper introduces a new method to derive the Kohn-Sham exchange-correlation potential directly from electronic wavefunctions, enabling better testing and development of density functional approximations.

Contribution

A novel approach to compute $v_{XC}( extbf{r})$ from wavefunctions using density matrices, avoiding numerical and basis-set issues of traditional methods.

Findings

Method is free from basis-set artifacts.

Allows direct probing of the exchange-correlation functional derivative.

Simplifies the calculation compared to many-body techniques.

Abstract

A method for calculating the Kohn--Sham exchange-correlation potential, $v_\text{XC}(\mathbf{r})$, from a given electronic wavefunction is devised and implemented. It requires on input one- and two-electron density matrices and involves construction of the generalized Fock matrix. The method is free from numerical limitations and basis-set artifacts of conventional schemes for constructing $v_\text{XC}(\mathbf{r})$ in which the potential is recovered from a given electron density, and is simpler than various many-body techniques. The chief significance of this development is that it allows one to directly probe the functional derivative of the true exchange-correlation energy functional and to rigorously test and improve various density-functional approximations.