Journal Articles The Journal of Chemical Physics Year : 2021

Variations of the Hartree-Fock fractional-spin error for one electron

Abstract

Fractional-spin errors are inherent in all current approximate density functionals, including Hartree-Fock theory, and their origin has been related to strong static correlation effects. The conventional way to encode fractional-spin calculations is to construct an ensemble density that scales between the high-spin and low-spin densities. In this article, we explore the variation of the Hartree-Fock fractional-spin (or ghost-interaction) error in one-electron systems using restricted and unrestricted ensemble densities, and the exact generalized Hartree-Fock representation. By considering the hydrogen atom and H 2 + cation, we analyze how the unrestricted and generalized Hartree-Fock schemes minimize this error by localizing the electrons or rotating the spin coordinates. We also reveal a clear similarity between the Coulomb hole of He-like ions and the density depletion near the nucleus induced by the fractional-spin error in the unpolarized hydrogen atom. Finally, we analyze the effect of the fractional-spin error on the Møller-Plesset adiabatic connection, excited states, and functional-and density-driven errors.

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hal-03228266 , version 1 (18-05-2021)

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Hugh G. A. Burton, Clotilde Marut, Timothy J Daas, Paola Gori-Giorgi, Pierre-Francois Loos. Variations of the Hartree-Fock fractional-spin error for one electron. The Journal of Chemical Physics, 2021, 155 (4), pp.054107. ⟨10.1063/5.0056968⟩. ⟨hal-03228266⟩
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