Block-Correlated Coupled Cluster Theory Based on the Generalized Valence Bond Reference for Singlet–Triplet Energy Gaps of Strongly Correlated Systems

A block-correlated coupled cluster (BCCC) method based on the triplet generalized valence bond (GVB) wave function (GVB-BCCC) has been implemented for the first time. By introducing several techniques, we have developed a practical and efficient GVB-BCCC code. The GVB-BCCC3 method (with up to three-pair correlation) can be used to deal with strongly correlated (SC) systems with triplet or singlet ground states, allowing singlet–triplet (S-T) energy gaps in the active space of SC systems computationally available. For selected SC systems, our calculations show that GVB-BCCC3 can always provide correct ground-state spin multiplicity as the complete active space configuration interaction (CASCI) or density matrix renormalization group (DMRG). Furthermore, we found that the S-T energy gaps from GVB-BCCC3 are quite consistent with CASCI or DMRG results. This work demonstrates that GVB-BCCC3 is a promising theoretical tool for describing S-T energy gaps within the active space of SC systems with large active spaces.