The development of accurate and computationally efficient wave function methods that can capture and balance dynamical and non-dynamical many-electron correlation effects to describe multi-reference problems, such as potential energy surfaces involving bond breaking, biradicals, and excited states characterized by dominant many-electron excitations, is one of the main goals of quantum chemistry. Among the promising approaches in this endeavor are the completely renormalized and active-space coupled-cluster (CC) and equation-of-motion (EOM) CC methods. While the completely renormalized and active-space CC and EOMCC approaches have been very successful in many applications, there are some cases where they do not capture the dynamical or non-dynamical many-electron correlation effects in a satisfactory manner. In this dissertation, we introduce the CC(P;Q) formalism, which alleviates this concern by combining the completely renormalized and active-space together. The CC(P;Q) scheme provides a systematic approach to correcting energies obtained in the active-space CC and EOMCC calculations that recover much of the non-dynamical and some dynamical many-electron correlation effects for the remaining, mostly dynamical, correlation effects missing in the active-space CC and EOMCC considerations. We discuss the development of the CC(t;3), CC(t,q;3), CC(t,q;3,4), and CC(q;4) methods, which use the CC(P,Q) formalism to correct energies obtained with the CC and EOMCC approaches with singles, doubles, and active-space triples (CCSDt/EOMCCSDt) for missing triple excitations (CC(t;3)), or to correct energies obtained with the CC and EOMCC approaches with singles, doubles, and active-space triples and quadruples (CCSDtq/EOMCCSDtq) for missing triples (CC(t,q;3)) or missing triples and quadruples (CC(t,q;3,4)), or even to correct energies obtained with the CC and EOMCC approaches with singles, doubles, triples, and active-space quadruples (CCSDTq/EOMCCSDTq) for correlation effects due to the missing quadruple excitations (CC(q;4)). By examining the double dissociation of water, the Be + H2 -> HBeH insertion, and the singlet-triplet gaps in the strongly biradical (HFH)- system and the BN molecule, we demonstrate that the CC(t;3), CC(t,q;3), and CC(t,q;3,4) methods reproduce the total and relative energies obtained with the parent full CC/EOMCC approaches with singles, doubles, and triples or singles, doubles, triples, and quadruples to within fractions of a millihartree at the tiny fraction of the computer cost, even when the electronic quasi-degeneracies become substantial.The CC(P;Q) formulation prompted the development of efficient CCSDt, CCSDtq, and CCSDTq programs. In this dissertation, we describe the technique of spin-integration for both closed and open shells, and how the resulting equations for CCSDTQ were automatically derived and implemented in a factorized form. We also discuss how the efficiency of the code was improved by removing unnecessary operations through, in particular, the reorganization of the relevant loops. Finally, we explain how the CCSDTQ code was transformed to obtain the active-space CCSDtq and CCSDTq approaches, which are the most essential parts of the CC(t,q;3), CC(t,q;3,4), and CC(q;4) calculations.
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