A compact spin-free coupled-cluster theory for open-shell systems

We present in this Paper a brief account of a novel spin-free compact coupled cluster (CC) theory for simple open-shell configurations, e.g. doublet and biradicals, which are not necessarily single determinants. A new cluster Ansatz for the wave-operator is introduced, in which the spin-free cluster operators are either of the type of closed-shell-like n hole-n particle excitations or contain valence excitations, which may involve exchange spectator scatterings. The cluster operators with exchange valence spectator scatterings and the pure valence excitation 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 non-commuting operators, ensuring that each such composite appears only once. This leads to CC equations which terminate exactly at the quartic power of the cluster amplitudes, reminiscent of the closed-shell CC theory. As example applications, we compute the state energies of the ground state of OH and NH2 radicals with cc-pVDZ basis set and assess the performance of the theory by comparing the results with the benchmark full Cl results in the same basis set. The results show the power and the efficacy of the method.