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, 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 underlying model spaces. These difficulties can alleviated by approximate coupled-pair (ACP) theories, in which selected $(T_2)^2$ diagrams CCSD amplitude equations are removed, but there is generally accepted and robust way incorporating connected triply excited ($T_3$) clusters within ACP framework. It also not clear if specific combinations that work well for minimum-basis-set systems optimum when larger basis sets employed. This study explores these topics considering a few novel schemes with active-space full treatments $T_3$ correlations scale factors depending on numbers occupied unoccupied orbitals. The performance proposed illustrated examining symmetric dissociations $\text{H}_6$ $\text{H}_{10}$ rings using triple- double-$\zeta$ quality $\text{H}_{50}$ linear chain treated minimum basis, conventional CCSDT methods fail.