A natural orbital functional based on an explicit approach of the two‐electron cumulant. Issue 5 (23rd February 2012) - Piris, M.; Gidopoulos, Nikitas I.; Theophilou, Andreas K.
Abstract The cumulant expansion gives rise to an useful decomposition of the two‐matrix in which the pair correlated matrix (cumulant) is disconnected from the antisymmetric product of the one‐matrices. The cumulant can be approximated in terms of two matrices, Δ and Π, which are explicit functions of the occupation numbers of the natural orbitals. It produces a natural orbital functional (NOF) that reduces to the exact expression for the total energy in two‐electron systems. The N‐representability positivity necessary conditions of the two‐matrix impose several bounds on the matrices Δ and Π. Appropriate forms of these matrices lead to different implementations of the NOF known in the literature as PNOFi (i = 1–5). The basic features of these functionals are reviewed here. The strengths and weaknesses of the different PNOFs are assessed. © 2012 Wiley Periodicals, Inc.