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

TL;DR

This paper introduces BGE2, a new density functional derived from the Bethe-Goldstone equation, which accurately describes H$_2$ and H$_2^+$ dissociation by capturing key electron-pair correlation effects.

Contribution

BGE2 is a novel orbital-dependent correlation functional that terminates at second-order but maintains self-consistent electron-pair coupling, improving dissociation predictions.

Findings

BGE2 is size consistent and free of one-electron self-correlation.

BGE2 accurately describes H$_2$ and H$_2^+$ dissociation.

Analytical analysis shows BGE2 captures essential adiabatic connection features.

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 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.