An explicitly spin-free compact open-shell coupled cluster theory using a multireference combinatoric exponential ansatz: formal development and pilot applications

In this paper, we present a comprehensive account of an explicitly spin-free compact state-universal multireference coupled cluster (CC) formalism for computing the state energies of simple open-shell systems, e.g., doublets and biradicals, where the target open-shell states can be described by a few configuration state functions spanning a model space. The cluster operators in this formalism are defined in terms of the spin-free unitary generators with respect to the common closed-shell component of all model functions (core) as vacuum. The spin-free cluster operators are either closed-shell-like n hole-n particle excitations (denoted by T(mu)) or involve excitations from the doubly occupied (nonvalence) orbitals to the singly occupied (valence) orbitals (denoted by S(e)(mu)). In addition, there are cluster operators with exchange spectator scatterings involving the valence orbitals (denoted by S(re)(mu)). We propose a new multireference cluster expansion ansatz for the wave operator with the above generally noncommuting cluster operators which essentially has the same physical content as the Jeziorski-Monkhorst ansatz with the commuting cluster operators defined in the spin-orbital basis. The T(mu) operators in our ansatz are taken to commute with all other operators, while the S(e)(mu) and S(re)(mu) operators are allowed to contract among themselves through the spectator valence orbitals. An important innovation of this ansatz is the choice of an appropriate automorphic factor accompanying each contracted composite of cluster operators in order to ensure that each distinct excitation generated by this composite appears only once in the wave operator. The resulting CC equations consist of two types of terms: a "direct" term and a "normalization" term containing the effective Hamiltonian operator. It is emphasized that the direct term is almost quartic in the cluster amplitudes, barring only a handful of terms and termination of the normalization term depends on the valence rank of the effective Hamiltonian operator and the excitation rank of the cluster operators at which the theory is truncated. Illustrative applications are presented by computing the state energies of neutral doublet radicals and doublet molecular cations and ionization energies of neutral molecules and comparing our results with the other open-shell CC theories, benchmark full CI results (when available) in the same basis, and the experimental results. Highly encouraging results show