It is well established that size-extensive approaches based on the exponential wave function ansatz of coupled-cluster (CC) theory and their extensions to open-shell, multiconfigurational, and excited states are among the best ways of treating many-electron correlation effects. This is especially true in applications involving structural and spectroscopic properties of molecular systems, chemical reaction pathways, noncovalent interactions, and photochemistry. In all these and similar cases, the CC hierarchy, including CCSD, CCSDT, CCSDTQ, and so on, and its equation-of-motion (EOM) and linear-response extensions rapidly converge to the exact, full configuration interaction (CI) limit. Unfortunately, the CCSDT, CCSDTQ, and similar methods, needed to achieve a quantitative description, incur a steep increase in computational costs, rendering their application to larger many-electron systems prohibitively expensive. To address this challenge, this dissertation explores the development of computationally practical alternative approaches based on the CC(P;Q) and externally corrected CC (ec-CC) frameworks, which allow us to study challenging chemical problems, such as molecular bond breaking, biradicals, transition states, and excited states dominated by two- and other many-electron excitations, while avoiding the well-known failures of perturbative CC approximations in the presence of electronic quasi-degeneracies.The first part of this dissertation introduces two novel CC(P;Q) approaches capable of rapidly converging high-level CC/EOMCC energetics of the CCSDT/EOMCCSDT, CCSDTQ/EOMCCSDTQ, and similar types, at tiny fractions of the computational costs in an automated fashion, even in cases of stronger correlations. The first methodology combines the CC(P;Q) moment expansions with the information provided by selected CI wave functions obtained using the algorithm abbreviated as CIPSI to systematically recover the results corresponding to any desired level of CC/EOMCC theory. The second approach, called adaptive CC(P;Q), eliminates the reliance on active orbitals or external non-CC information adopted in previous formulations of CC(P;Q) by executing a sequence of CC(P;Q) calculations aimed at converging high-level CC/EOMCC energetics guided solely by the mathematical structure of the moment expansions. We demonstrate the effectiveness of both the CIPSI-driven and adaptive CC(P;Q) methodologies through a number of molecular applications aimed at recovering the full CCSDT/EOMCCSDT energetics when the noniterative triples corrections to CCSD/EOMCCSD struggle or fail. For the CIPSI-driven approach, we examine the dissociation of F2, the automerization of cyclobutadiene, and the vertical excitation spectrum of CH+. The adaptive CC(P;Q) approach is tested on the stretched F2 and F2+ molecules, the automerization of cyclobutadiene, singlet–triplet gaps in organic biradicals, the degenerate Cope rearrangement of bullvalene, and the ground- and excited-state potential energy surfaces of water along the O–H bond-breaking coordinate. To illustrate the computational advantages of the adaptive CC(P;Q) approach, as implemented in the open-source CCpy software package, we also discuss the CPU timings characterizing our calculations for cyclobutadiene and CnH2n+2 linear alkanes with n=1-8.In the final part of this dissertation, we implement and test a new family of ec-CC approaches designed to recover the exact, full CI, energetics. These methods leverage information about higher-order correlations provided by selected CI wave functions and adopt moment expansions, similar to those used in CC(P;Q), to account for missing higher-order correlation effects. In this new class of ec-CC approaches, termed ec-CC-II, one solves CCSD-like equations for the one- and two-body clusters in the presence of their three-body (T3) and four-body (T4) counterparts extracted from the underlying CI wave function, after discarding T3 and T4 amplitudes corresponding to CI coefficients that are zero. In this dissertation, we focus on the ec-CC-II approach using T3 and T4 clusters extracted from CIPSI calculations, along with its ec-CC-II3 extension, which corrects the ec-CC-II energetics for missing T3 correlation effects using the appropriately defined CC(P;Q)-like moment expansions. To assess the performance of the CIPSI-based ec-CC-II and ec-CC-II3 methodologies, we apply them to the challenging symmetric dissociation in water, where even high-level CC methods, such as CCSDTQ, struggle to achieve a full-CI-level description.
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