Approximate account of connected quadruply excited clusters in single-reference coupled-cluster theory via cluster analysis of the projected unrestricted Hartree-Fock wave function

Extension of the applicability of the closed-shell coupled-cluster (CC) theory with doubly (CCD) or singly and doubly (CCSD) excited clusters to quasidegenerate situations requires the inclusion of the connected triply and quadruply excited cluster components T-3 and T-4. Since an explicit consideration of those clusters for larger systems is computationally very demanding, we explore the possibility of estimating the T-4 contribution using the projected unrestricted Hartree-Fock (PUHF) wave function. The resulting CCDQ' and CCSDQ' approaches are shown to correctly approximate the effect of the quadruply (Q') excited T-4 clusters, even when the PUHF wave function itself cannot serve as a good source of the lower-order pair-cluster components. It is important that the results of the cluster analysis of the PUHF solution are used directly and no further approximations are made. Only when both pair-cluster and T-4 cluster components are reasonably well approximated by the PUHF wave function, the T-4 cluster contributions cancel out certain CCSD diagrams, and good CC results can be obtained with the approximate coupled-pair approaches. It is also demonstrated that it may be more difficult to balance T-3 and T-4 clusters relying on simple perturbative approaches, such as CCSDQ'+T(CCSDQ'). The results of formal considerations, including a thorough investigation of the cluster structure of the PUHF wave function, are illustrated on several examples. These include a few model systems composed of four and eight hydrogen atoms in various geometrical arrangements, as described using minimum and double zeta plus polarization basis sets, for which the exact full configuration interaction data are available. The orthogonally spin-adapted formulation of CC theory is used throughout.