Application of Hilbert-space coupled-cluster theory to simple (H2)2model systems: Planar models

The recently developed explicit formalism of orthogonally-spin-adapted, Hilbert-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 four-electron model system consisting of two interacting hydrogen molecules. Four planar minimum-basis-set ${\mathrm{H}}_4$ models are examined, each characterized by a single parameter that fully determines its geometry, assuming the trapezoidal (H4 model), rectangular (P4 model), linear (D4 model), and square (S4 model) nuclear configuration. Varying this geometry-determining parameter, in each case we obtain different cross sections of the ${\mathrm{H}}_4$ potential-energy hypersurface, involving the dissociation of one, two, or all four H-H ‘‘bonds.’’ Comparing the resulting CC energies with exact values that are easily obtained for this model using the full configuration-interaction method, we can assess the performance of various MRCC Hilbert-space approaches at both the linear and nonlinear levels of approximation, while a continuous transition is being made between the degenerate and nondegenerate regimes. This enables us to elucidate the sources and the type of singular behavior in both linear and nonlinear versions of MRCC theory, to examine the role played by various intruder states, the existence and types of multiple solutions and their ability to describe various excited states, and, by performing a cluster analysis of the exact solutions, to assess the quality of the MRCC wave functions as well as the energies.