Exchange and Correlation in Open Systems of Fluctuating Electron Number

TL;DR

This paper investigates the failure of semi-local density functionals in modeling open systems with fluctuating electron numbers and proposes a correction method using a local hybrid functional.

Contribution

It develops an exact-exchange theory and an exchange-hole sum rule to explain these failures and suggests a correction approach.

Findings

Semi-local density functionals curve upward for open systems, unlike the linear exact energy.

Exact-exchange theory and sum rule explain the functional failures.

Proposed local hybrid functional corrects the energy predictions.

Abstract

While the exact total energy of a separated open system varies linearly as a function of average electron number between adjacent integers, the energy predicted by semi-local density functional approximations curves upward and the exact-exchange-only or Hartree-Fock energy downward. As a result, semi-local density functionals fail for separated open systems of fluctuating electron number, as in stretched molecular ions A$_2^{+}$ and in solid transition metal oxides. We develop an exact-exchange theory and an exchange-hole sum rule that explain these failures and we propose a way to correct them via a local hybrid functional.