N-centered ensemble density-functional theory for open systems

TL;DR

This paper introduces two variants of N-centered ensemble density-functional theory that effectively describe systems with fractional electron numbers, addressing the derivative discontinuity issue in open systems.

Contribution

The paper presents novel left and right N-centered ensemble DFT formulations that incorporate a fictitious ensemble density and a grand canonical weight to handle fractional electrons.

Findings

Exact description of derivative discontinuity via ensemble dependence.

Framework for embedding open systems within pure-state N-electron wavefunctions.

Potential for in-principle-exact open fragment descriptions.

Abstract

Two (so-called left and right) variants of N-centered ensemble density-functional theory (DFT) [Senjean and Fromager, Phys. Rev. A 98, 022513 (2018)] are presented. Unlike the original formulation of the theory, these variants allow for the description of systems with a fractional electron number. While conventional DFT for open systems uses only the true electron density as basic variable, left/right N-centered ensemble DFT relies instead on (i) a fictitious ensemble density that integrates to a central (integral) number N of electrons, and (ii) a grand canonical ensemble weight $\alpha$ which is equal to the deviation of the true electron number from N. Within such a formalism, the infamous derivative discontinuity that appears when crossing an integral number of electrons is described exactly through the dependence in $\alpha$ of the left and right N-centered ensemble Hartree-exchange-correlation density functionals. Incorporating N-centered ensembles into existing density-functional embedding theories is expected to pave the way towards the in-principle-exact description of an open fragment by means of a pure-state N-electron many-body wavefunction. Work is currently in progress in this direction