A coupled cluster approach with a hybrid treatment of connected triple excitations for bond-breaking potential energy surfaces.

An approximate coupled cluster singles, doubles, and triples (CCSDT) method based on the unrestricted Hartree-Fock (UHF) reference, in which the contribution of triple excitations is approximately treated in a hybrid manner [denoted as CCSD(T)-h], is presented. In this approach, canonical UHF molecular orbitals are first transformed into corresponding orbitals so that each alpha-spin orbital is paired with only one beta-spin orbital. Then, active orbitals (occupied or virtual) are automatically selected by setting a threshold for the overlap integrals of corresponding orbitals. With the concept of active orbitals, triple excitations can be divided into two subsets: (1) "active" triples involving at least one occupied active orbital and one virtual active orbital and (2) the remaining triples. The amplitudes of these two classes of triple excitations are obtained via two different approaches. When the present method is employed to study bond-breaking processes, it computationally scales as the seventh power of the system size, because the number of active orbitals involved in such processes is relatively small compared to the total number of the orbitals, and is usually independent on the system size. It has been applied to study the bond-breaking potential energy surfaces in the H(8) model and five small molecules (HF, F(2), CH(4), H(2)O, and N(2)). For all systems under study, the overall performance of CCSD(T)-h is very competitive with that of CCSDT, and much better than that of the UHF-based CCSD(T).