Merging Active-Space and Renormalized Coupled-Cluster Methods via the CC(P;Q) Formalism, with Benchmark Calculations for Singlet-Triplet Gaps in Biradical Systems.

Abstract

We have recently developed a flexible form of the method of moments of coupled-cluster (CC) equations and the CC(P;Q) hierarchy, which enable one to correct the CC and equation-of-motion CC energies obtained with unconventional truncations in the cluster and excitation operators [Shen, J.; Piecuch, P. Chem. Phys.2012, 401, 180; J. Chem. Phys.2012, 136, 144104]. One of the CC(P;Q) methods is a novel hybrid scheme, abbreviated as CC(t;3), in which the results of CC calculations with singles, doubles, and active-space triples, termed CCSDt, are corrected for the triple excitations missing in CCSDt using the expressions that are reminiscent of the completely renormalized (CR) CC approach known as CR-CC(2,3). We demonstrate that the total electronic energies of the lowest singlet and triplet states, and the singlet-triplet gaps in biradical systems, including methylene, (HFH)(-), and trimethylenemethane, resulting from the CC(t;3) calculations agree with those obtained with the full CC approach with singles, doubles, and triples to within fractions of a millihartree, improving the results of the noniterative triples CCSD(T), CCSD(2)T, and CR-CC(2,3) and hybrid CCSD(T)-h calculations, and competing with the best multireference CC data.