Phys. Rev. A [LCQ]

Abstract:

Capturing the discontinuous shift by Δ in the exact exchange-correlation (xc) potential is the standard proposal for calculating the fundamental gap Eg from the Kohn-Sham (KS) gap ɛg within KS density functional theory (DFT) as Eg=ɛg+Δ, yet this discontinuity is absent from existing approximations. The “N-centered” formulation of ensemble DFT artificially maintains a total electron number N in order to yield Eg not through a discontinuous shift in the xc potential but via the ensemble-weight derivative of the xc energy. Within the N-centered approach, we calculate exact xc potentials for a one-dimensional finite system and show analytically that Δ can in fact be interpreted as a discontinuous shift in the exact N-centered ensemble xc potential, thereby extending to charged excitations an exact property of uncharged excitations. We show that applying the Levy-Zahariev “shift-in-potential” procedure in this context relocates the discontinuous shift to the unimportant periphery of the system, so that the exact xc potential in effect is free of discontinuities and thus the inability of a local functional to capture discontinuous behavior is inconsequential.

Reference:

M. J. P. Hodgson, J. Wetherell, and Emmanuel Fromager

Exact exchange-correlation potentials for calculating the fundamental gap with a fixed number of electrons

Phys. Rev. A 103, 012806 – Published 12 January 2021, DOI: https://doi.org/10.1103/PhysRevA.103.012806

Contact :

Emmanuel Fromager, équipe LCQ, Institut de Chimie (UMR 7177).