Elimination of the asymptotic fractional dissociation problem in Kohn-Sham density functional theory using the ensemble-generalization approach

TL;DR

This paper demonstrates that the ensemble-generalization approach removes fractional dissociation errors in Kohn-Sham density functional theory, even with simple approximations like LSDA, by inducing a spatial step in the potential.

Contribution

The study shows that ensemble generalization automatically introduces a step in the Kohn-Sham potential, eliminating fractional dissociation errors in simple density functionals.

Findings

Fractional dissociation is eliminated using ensemble generalization.

A spatial step in the potential emerges, reflecting the derivative discontinuity.

Even simple functionals like LSDA can correctly predict integer dissociation with this approach.

Abstract

Many approximations within density-functional theory spuriously predict that a many-electron system can dissociate into fractionally charged fragments. Here, we revisit the case of dissociated diatomic molecules, known to exhibit this problem when studied within standard approaches, including the local spin-density approximation (LSDA). By employing our recently proposed [E. Kraisler and L. Kronik, Phys. Rev. Lett. 110, 126403 (2013)] ensemble-generalization we find that asymptotic fractional dissociation is eliminated in all systems examined, even if the underlying exchange-correlation (xc) is still the LSDA. Furthermore, as a result of the ensemble generalization procedure, the Kohn-Sham potential develops a spatial step between the dissociated atoms, reflecting the emergence of the derivative discontinuity in the xc energy functional. This step, predicted in the past for the exact Kohn-Sham potential and observed in some of its more advanced approximate forms, is a desired feature that prevents any fractional charge transfer between the system's fragments. It is usually believed that simple xc approximations such as the LSDA cannot develop this step. Our findings show, however, that ensemble generalization to fractional electron densities automatically introduces the desired step even to the most simple approximate xc functionals and correctly predicts asymptotic integer dissociation.