Restoration of the Derivative Discontinuity in Kohn-Sham Density Functional Theory: An Efficient Scheme for Energy Gap Correction

TL;DR

This paper introduces an efficient perturbation-based scheme to accurately evaluate the derivative discontinuity in Kohn-Sham DFT, enabling improved predictions of fundamental energy gaps without significant computational overhead.

Contribution

It presents a novel perturbation theory approach to estimate the derivative discontinuity directly from ground-state densities, improving gap predictions in KS-DFT.

Findings

Accurately predicts fundamental gaps for atoms and molecules.

Provides a universal functional for the first-order correction to the derivative discontinuity.

Achieves improved gap predictions with minimal additional computational cost.

Abstract

From the perspective of perturbation theory, we propose a systematic procedure for the evaluation of the derivative discontinuity (DD) of the exchange-correlation energy functional in Kohn-Sham density functional theory (KS-DFT), wherein the exact DD can in principle be obtained by summing up all the perturbation corrections to infinite order. Truncation of the perturbation series at low order yields an efficient scheme for obtaining the approximate DD. While the zeroth-order theory yields a vanishing DD, the first-order correction to the DD can be expressed as an explicit universal functional of the ground-state density and the KS lowest unoccupied molecular orbital density, allowing the direct evaluation of the DD in the standard KS method without extra computational cost. The fundamental gap can be predicted by adding the estimated DD to the KS gap. This scheme is shown to be accurate in the prediction of the fundamental gaps for a wide variety of atoms and molecules.