The correlation potential in density functional theory at the GW-level: spherical atoms

TL;DR

This paper develops a new numerical method to compute the exchange-correlation potential in density functional theory at the GW level for spherical atoms, improving accuracy and physical realism over previous approaches.

Contribution

A novel cubic spline-based numerical method for deriving the XC potential at the GW level, addressing the inverse engineering problem in DFT.

Findings

Potentials lack unphysical ripples and have correct asymptotic tails.

Improved excitation energy predictions compared to LDA, GGA, and MP2-based potentials.

Method performs well for spherical atoms, enhancing DFT accuracy.

Abstract

As part of a project to obtain better optical response functions for nano materials and other systems with strong excitonic effects we here calculate the exchange-correlation (XC) potential of density-functional theory (DFT) at a level of approximation which corresponds to the dynamically- screened-exchange or GW approximation. In this process we have designed a new numerical method based on cubic splines which appears to be superior to other techniques previously applied to the "inverse engineering problem" of DFT, i.e., the problem of finding an XC potential from a known particle density. The potentials we obtain do not suffer from unphysical ripple and have, to within a reasonable accuracy, the correct asymptotic tails outside localized systems. The XC potential is an important ingredient in finding the particle-conserving excitation energies in atoms and molecules and our potentials perform better in this regard as compared to the LDA potential, potentials from GGA:s, and a DFT potential based on MP2 theory.