<i>n</i>-electron valence state perturbation theory: A spinless formulation and an efficient implementation of the strongly contracted and of the partially contracted variants

TLDR

The n‑electron valence state perturbation theory is reformulated in a spin‑free formalism that focuses on its strongly contracted and partially contracted variants. The new approach introduces average values of excitation operators in the unperturbed state, analogous to extended Koopmans’ theorem and EOM, enabling efficient evaluation of second‑order energy contributions when the unperturbed four‑particle spinless density matrix is available. An inequality between the second‑order energy contributions of the strongly and partially contracted variants is proven, and the method successfully reproduces the Cr₂ potential energy curve.

Abstract

The n-electron valence state perturbation theory is reformulated in a spin-free formalism, concentrating on the “strongly contracted” and “partially contracted” variants. The new formulation is based on the introduction of average values in the unperturbed state of excitation operators which bear resemblance with analogous ones occurring in the extended Koopmans’ theorem and in the equations-of-motion technique. Such auxiliary quantities, which allow the second-order perturbation contribution to the energy to be evaluated very efficiently, can be calculated at the outset provided the unperturbed four-particle spinless density matrix in the active orbital space is available. A noticeable inequality concerning second-order energy contributions of the same type between the strongly and partially contracted versions is proven to hold. An example concerning the successful calculation of the potential energy curve for the Cr2 molecule is discussed.