Neutral electronic excitations and derivative discontinuities: An extended $N$-centered ensemble density functional theory perspective

TL;DR

This paper develops an extended ensemble density functional theory that unifies different ensemble types to accurately describe neutral and charged electronic excitations, emphasizing derivative discontinuities without relying on asymptotic density behavior.

Contribution

It introduces a general, exact extended N-centered ensemble DFT framework combining multiple ensemble types for electronic excitations, applicable to lattice and mesoscopic systems.

Findings

Revisits the density-functional derivative discontinuity concept for neutral excitations.

Derives an exact, general ensemble DFT framework for charged and neutral excitations.

Highlights the role of weight dependence in ensemble Hartree-exchange-correlation energy.

Abstract

This work merges two different types of many-electron ensembles, namely the Theophilou-Gross-Oliveira-Kohn ensembles of ground and neutrally-excited states, and the more recent $N$-centered ensembles of neutral and charged ground states. On that basis, an in-principle exact and general, so-called extended $N$-centered, ensemble density-functional theory of charged and neutral electronic excitations is derived. We revisit in this context the concept of density-functional derivative discontinuity for neutral excitations, without ever invoking nor using the asymptotic behavior of the ensemble electronic density. The present mathematical construction fully relies on the weight dependence of the ensemble Hartree-exchange-correlation density-functional energy, which makes the theory applicable to lattice models and opens new perspectives for the description of gaps in mesoscopic systems.