Method of Moments of Coupled Cluster Equations Employing Multi-Reference Perturbation Theory Wavefunctions: General Formalism, Diagrammatic Formulation, Implementation, and Benchmark Studies

Abstract

A new class of non-iterative single-reference coupled-cluster (CC) and equation-of-motion CC (EOMCC) methods that combines the idea of energy corrections due to higher-order excitations defining the method of moments of CC equations (MMCC) with the multi-reference many-body perturbation theory, which is used to provide information about the most essential correlation effects relevant to electronic quasi-degeneracies, is described. The key elements of the resulting theory, termed MMCC/PT, are formulated using diagrammatic methods. The performance of the basic MMCC/PT approximations, in which inexpensive corrections due to triple (MMCC(2,3)/PT) or triple and quadruple (MMCC(2,4)/PT) excitations are added to ground- and excited-state energies obtained with the CC/EOMCC singles and doubles (CCSD/EOMCCSD) approach, is illustrated by the results of bench-mark calculations including bond breaking in HF, H2O, and F2, and excited states of CH+. The efficient, highly vectorized implementations of the triply and quadruply excited moments of the CCSD/EOMCCSD equations that enter the MMCC(2,3)/PT and MMCC(2,4)/PT energy formulas and other approaches based on the MMCC formalism, including other externally corrected MMCC theories and renormalized CC/EOMCC approaches, are discussed, and the most essential details of the MMCC/PT algorithm are presented.