A compact spin-free combinatoric open-shell coupled cluster theory applied to single-reference doublets

Abstract

In this article, we present an explicitly spin-free compact coupled cluster (CC) theory for simple open-shell systems, e.g., doublets, biradicals, which can be described either by a single open-shell determinant or by a configuration state function (CSF) which corresponds to a single spatial configuration but is a linear combination of determinants with different spin allocations. A new cluster expansion Ansatz for the wave-operator is introduced, in which the spin-free cluster operators are either of the form of closed-shell-like n hole-n particle excitations or contain valence excitations, which may involve exchange spectator scatterings. These latter type of operators are allowed to contract among themselves through the spectator orbitals. The novelty of the Ansatz is in the choice of a suitable automorphic factor accompanying each composite of noncommuting operators, ensuring that each such composite appears only once. The resulting CC equations consist of two types of terms: one is direct and the other is folded and the latter involves the effective Hamiltonian operator. We emphasize that while the direct term terminates exactly at the quartic power of the cluster amplitudes, termination of the folded term is dictated by the valence rank of the effective Hamiltonian operator, just as in the spin-free open-shell CC theory with a normal ordered exponential Ansatz. Example applications are presented by computing the core and valence-ionized state energies of H₂O molecule and comparing the results with benchmark full CI results. The results show the efficacy of the method.