It is well established that the exponential wave function ansatz of coupled-cluster (CC) theory and its equation-of-motion (EOM) extension to excited states are among the most appealing ways to describe the electronic structure of molecules. One of the key challenges in the development of the CC and EOMCC methodologies is the incorporation of many-electron correlation effects due to higher–than–two-body components of the cluster and EOM ex- citation operators, needed to achieve a quantitative description, without running into the usually prohibitive computational costs of the CC approach with singles, doubles, and triples (CCSDT) and its excited-state EOMCCSDT extension, the CC method with singles, doubles, triples, and quadruples (CCSDTQ) and its excited-state EOMCCSDTQ extension, etc., and without resorting to perturbative CCSD(T)-type ideas that fail in multireference situations, such as bond breaking and excited states dominated by two-electron transitions. One of the most promising approaches in this area is the semi-stochastic CC(P;Q) methodology that identifies the most important higher–than–doubly excited determinants needed in the high- level CC/EOMCC calculations with the help of the stochastic configuration interaction (CI) and CC Quantum Monte Carlo (QMC) wave function propagations and uses the suitably designed deterministic iterative and noniterative steps of the CC(P;Q) formalism to converge the desired CCSDT/EOMCCSDT, CCSDTQ/EOMCCSDTQ, etc., energetics. In this dis- sertation, we first discuss our recent work on extending the semi-stochastic, CIQMC-driven, particle-conserving CC(P;Q) framework to excited electronic states and open-shell systems. We tested performance of the resulting methods by examining their ability to recover the high-level CCSDT/EOMCCSDT energetics in calculations of the electronic excitation spec- tra of the CH+, CH, and CNC molecules and singlet–triplet gaps in a few biradical systems, including methylene, (HFH)−, cyclobutadiene, cyclopentadienyl cation, and trimethylen- emethane. The second part of this dissertation focuses on an alternative way of determining ground and excited states of open-shell systems within the EOMCC framework by turning to the single and double electron attachment (EA) and single and double ionization potential(IP) EOMCC schemes. By generating ground and excited states of open-shell species, such as radicals and biradicals, with the help of suitably designed operators that can formally add electrons to or remove electrons from the parent closed-shell cores (an operation pro- ducing the appropriate multi-configurational reference space within a single-reference frame- work, while relaxing the remaining electrons), the resulting EA/IP- and DEA/DIP-EOMCC methods offer several advantages over the particle-conserving CC/EOMCC treatments, in- cluding rigorous spin and symmetry adaptation of the calculated electronic states and the ability of handling high- and low-spin states in an accurate and well-balanced manner. We demonstrate how to utilize the stochastic CIQMC wave function propagations, which are of particle-conserving character, in identifying the dominant higher-order 3-particle-2-hole (3p- 2h)/3-hole-2-particle (3h-2p) and 4-particle-2-hole (4p-2h)/4-hole-2-particle (4h-2p) compo- nents of the respective particle-nonconserving electron attaching/ionizing operators, needed to obtain a quantitative description, without having to resort to the previously exploited user- and system-dependent active-space concepts. The effectiveness of the semi-stochastic, CIQMC-driven, EA/IP/DEA/DIP-EOMCC approaches will be illustrated by examining the adiabatic excitations in the C2N, CNC, N3, and NCO radicals and by revisiting the singlet– triplet gaps in methylene and trimethylenemethane.
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