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Abstract:
We start from the Bethe–Goldstone equation
(BGE) to derive a simple orbital-dependent correlation functional—BGE2— which terminates the BGE expansion at the second-order, but retains the self-consistent coupling of electron-pair correlations. We demonstrate that BGE2 is size consistent and
one-electron 'self-correlation' free.
The electron-pair correlation coupling ensures the correct H2 dissociation limit and gives a finite correlation energy for any system even if it has a no energy gap.
BGE2 provides a good description of both H2 and H2+ dissociation, which is regarded as a great challenge in density functional theory (DFT). We illustrate the behavior of BGE2 analytically by considering H2
in a minimal basis. Our analysis shows that BGE2 captures essential features of the
adiabatic connection path that current state-of-the-art DFT approximations do not.
