Application of Hilbert-space coupled-cluster theory to simple (H2)2model systems. II. Nonplanar models

In this series, the recently developed explicit formalism of orthogonally spin-adapted Hibert space (or state universal), multireference (MR) coupled-cluster (CC) theory, exploiting the model space spanned by two closed-shell-type reference configurations, is applied to a simple minimum-basis-set four-electron model system consisting of two interacting hydrogen molecules in various geometrical arrangements. In this paper, we examine the nonplanar geometries of this system, generally referred to as the T4 models, and their special cases designated as P4 and V4 models. They correspond to different cross sections of the ${\mathrm{H}}_4$ potential-energy hypersurface, involving the dissociation or simultaneous stretching of two H—H bonds. They involve various quasidegeneracy types, including the orbital and configurational degeneracies, the twofold degeneracy of the ground electronic state and interesting cases of broken-symmetry solutions. We employ the CC with singles and doubles (SD) approximation, so that the cluster operators are approximated by their one- and two-body components. Comparing the resulting CC energies with exact values, which are easily obtained for these models by using the full configuration-interaction method, and performing a cluster analysis of the exact solutions, we assess the performance of various MRCC Hilbert-space approaches at both linear and nonlinear levels of approximation, while a continuous transition is being made between the degenerate and nondegenerate or strongly correlated regimes. We elucidate the sources and the type of singular behavior in both linear and nonlinear versions of MRCC theory, examine the role played by various intruder states, and discuss the potential usefulness of broken-symmetry MRCCSD solutions.