Towards simple orbital-dependent density functionals for molecular dissociation

Density functional theory (DFT) is one of the leading first-principles electronic-structure theories. However, molecular dissociation remains a challenge, because it requires a well-balanced description of the drastically different electronic structure at different bond lengths. One typical and well-documented case is the dissociation of both H$_2^+$ and H$_2$, for which all popular DFT functionals fail [1,2]. We start from the Bethe-Goldstone equation to propose a simple orbital-dependent correlation functional which generalizes the linear adiabatic connection approach. The resulting scheme is based on second-order perturbation theory (PT2), but includes the self-consistent coupling of electron-hole pairs, which ensures the correct H$_2$ dissociation limit and gives a finite correlation energy for systems with a (near)-degenerate energy gap. This coupling PT2-like (CPT2) approximation delivers a significant improvement over all existing functionals for both H$_2$ and H$_2^+$ dissociation. We will demonstrate the reason for this improvement analytically for H$_2$ in a minimal basis. [1] A. J. Cohen {\it et al.}, \emph{Chem. Rev.} \textbf{112} 289 (2012), [2] F. Caruso {\it et al.}, \emph{Phys. Rev. Lett.} \textbf{110} 146403 (2013).