Prediction of the derivative discontinuity in density functional theory from an electrostatic description of the exchange and correlation potential

TL;DR

This paper introduces an electrostatic-based method to improve exchange-correlation potentials in density functional theory, accurately capturing the derivative discontinuity and predicting the fundamental gap.

Contribution

It presents a novel electrostatic approach to approximate the XC functional and corrects the asymptotic behavior, enabling direct prediction of the derivative discontinuity.

Findings

Corrects asymptotic behavior of XC potentials

Predicts the derivative discontinuity directly

Improves fundamental gap estimation

Abstract

We propose a new approach to approximate the exchange and correlation (XC) functional in density functional theory. The XC potential is considered as an electrostatic potential, generated by a fictitious XC density, which is in turn a functional of the electronic density. We apply the approach to develop a correction scheme that fixes the asymptotic behavior of any approximated XC potential for finite systems. Additionally, the correction procedure gives the value of the derivative discontinuity; therefore it can directly predict the fundamental gap as a ground-state property.