Exchange and Correlation in Open Systems of Fluctuating Electron Number

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.

4 pages, 2 figures

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