Addressing Strong Correlation by Approximate Coupled-Pair Methods with Active-Space and Full Treatments of Three-Body Clusters

When the number of strongly correlated electrons becomes larger, the single-reference coupled-cluster (CC) CCSD, CCSDT, etc. hierarchy displays an erratic behavior, while traditional multi-reference approaches may no longer be applicable due to enormous dimensionalities of the underlying model spaces. These difficulties can be alleviated by the approximate coupled-pair (ACP) theories, in which selected $(T_2)^2$ diagrams in the CCSD amplitude equations are removed, but there is no generally accepted and robust way of incorporating connected triply excited ($T_3$) clusters within the ACP framework. It is also not clear if the specific combinations of $(T_2)^2$ diagrams that work well for strongly correlated minimum-basis-set model systems are optimum when larger basis sets are employed. This study explores these topics by considering a few novel ACP schemes with the active-space and full treatments of $T_3$ correlations and schemes that scale selected $(T_2)^2$ diagrams by factors depending on the numbers of occupied and unoccupied orbitals. The performance of the proposed ACP approaches is illustrated by examining the symmetric dissociations of the $\text{H}_6$ and $\text{H}_{10}$ rings using basis sets of the triple- and double-$\zeta$ quality and the $\text{H}_{50}$ linear chain treated with a minimum basis, for which the conventional CCSD and CCSDT methods fail.