Virtual space level shifting and correlation energies

Abstract

Adding a nonlocal operator to the true Hamiltonian is used to define an adiabatic coupling between a noninteracting (e.g., Kohn–Sham) reference system and the real one. By using the Hellmann–Feynman theorem, it is shown that when the operator added is shifting upward the virtual (noninteracting) levels the correlation energy is related to the number of electrons displaced into the virtual levels. To construct approximations, calculations were performed for the uniform electron gas. The expectation that atomic systems would behave locally like a uniform electron gas with the unoccupied levels shifted up by a constant close to the atomic excitation energies is not confirmed by exploratory calculations on atoms. Some perturbation theory expressions are also given and suggest an approach to self-interaction free-correlation energy functionals. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 581–590, 1998