Coupled cluster with singles, doubles, and partial higher-order excitations based on the corresponding orbitals: The formulation and test applications for bond breaking processes

An approximate coupled-cluster (CC) method-CC singles, doubles, triples, and quadruples involving up to five-pair indices [CCSDTQ(5P)] based on the unrestricted Hartree-Fock (UHF) reference is presented. The key concept is to transform canonical molecular orbitals into corresponding orbitals so that all spin orbitals are grouped into pairs. An approximation to CCSDTQ(5P) is CCSDT(5P), in which none of quadruples are included. These two methods, CCSDT(5P) and CCSDTQ(5P), are approximations to the full CCSDT and CCSDTQ methods, respectively. Both methods computationally scale as the seventh power of the system size. They have been applied to study the bond breaking potential energy surfaces in several closed-shell molecules (HF, F-2, CH4, H2O, and N-2) and two open-shell molecules (OH and CH3). In comparison with full configuration interaction results, both methods are demonstrated to provide accurate descriptions for single-bond breaking processes, whose performance is significantly better than that of the UHF-based CCSD(T) method. For multiple bond breaking processes in H2O and N-2, CCSDTQ(5P) or CCSDT(5P) also provides slightly better results than CCSD(T).