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

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 orrelations. We demonstrate that BGE2 is size consistent and one-electron “self-correlation” free. The electron-pair correlation coupling ensures the correct H${}_2$ 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 H${}_2$ and H${}_2^{+}$ dissociation, which is regarded as a great challenge in density functional theory (DFT). We illustrate the behavior of BGE2 analytically by considering H${}_2$ 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.