Charged excitations made neutral: N-centered ensemble density functional theory of Fukui functions

TL;DR

This paper derives an exact equation within N-centered ensemble DFT to accurately compute Fukui functions, overcoming fractional electron number issues and enabling improved functional approximations.

Contribution

It introduces a novel exact working equation for Fukui functions in N-centered ensemble DFT, addressing derivative discontinuity problems.

Findings

Derivation of an exact equation for Fukui functions in Nc-ensemble DFT

Circumvents kernel derivative discontinuity issues in fractional electron calculations

Enables development of new approximation strategies for functional design

Abstract

An in-principle exact working equation to compute electronic affinity and ionization Fukui functions is derived within the $N$-centered (Nc) ensemble extension of density functional theory (DFT). It circumvents the kernel derivative discontinuity problem of DFT for fractional electron numbers, whose contribution is recovered through weight derivatives of the ensemble density functional potential. Thus, it allows for the design of alternative and effective approximations, such as the weight-dependent scaling of regular functionals or the interpolation between known limits of Nc ensembles