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We start from the Bethe-Goldstone equation (BGE) to derive a simpleorbital-dependent correlation functional -- BGE2 -- which terminates the BGEexpansion at the second-order, but retains the self-consistent coupling ofelectron-pair orrelations. We demonstrate that BGE2 is size consistent andone-electron "self-correlation" free. The electron-pair correlation couplingensures the correct H$_2$ dissociation limit and gives a finite correlationenergy for any system even if it has a no energy gap. BGE2 provides a gooddescription of both H$_2$ and H$_2^+$ dissociation, which is regarded as agreat challenge in density functional theory (DFT). We illustrate the behaviorof BGE2 analytically by considering H$_2$ in a minimal basis. Our analysisshows that BGE2 captures essential features of the adiabatic connection paththat current state-of-the-art DFT approximations do not.

Wave-function inspired density functional applied to the H$_2$/H$_2^+$ challenge