The development and implementation of electronic structure methods based on the exponential wave function ansatz of the single-reference coupled-cluster (CC) theory and its extensions to excited states exploiting the equation-of-motion (EOM) and linear responseframeworks have witnessed great success in a wide range of applications, but there are areas of chemistry, especially studies of chemical reaction pathways and photochemistry, where further improvements in the existing CC and EOMCC methodologies are needed. In order to make progress in this area, it is important to evaluate the quality of the results that the existing CC/EOMCC methods provide, particularly in applications involving the interpretation and prediction of photochemical phenomena and electronic excitations spectra involving closed- and open-shell molecules. Thus, in the rst part of this PhD project we use a database set of 28 organic molecules ranging from linear polyenes, unsaturated cyclic hydrocarbons, aromatic hydrocarbons, and heterocycles to aldehydes, ketones, amides, and nucleobases to examine the performance of the completely renormalized (CR) EOMCC approaches forexcited electronic states, in which the relatively inexpensive non-iterative corrections due to triple excitations are added to the energies obtained with the standard EOMCC approach with singles and doubles, abbreviated as EOMCCSD. We focus on two variants of the approximately size-intensive CR-EOMCC methodology with singles, doubles, and noniterative triples, abbreviated as delta-CR-EOMCCSD(T), and the analogous two variants of the newer, rigorously size-intensive, left-eigenstate delta-CR-EOMCC(2,3) approach based on the biorthogonal formulation of the method of moments of CC equations.In the second part of this dissertation, we focus on the development of new EOMCC methods that are particularly well-suited for accurate calculations of diradical electronic spectra and single bond breaking. They are the cost-effective variants of the doubly electron-attached (DEA) EOMCC methodologies with up to 3-particle---hole (3p-1h) or 4-particle--2-hole (4p-2h) excitations, abbreviated as DEA-EOMCC(3p-1h)fNug and DEA-EOMCC(3p-1h,4p-2h){Nu}, respectively, which utilize the idea of applying a linear electron-attaching operator to the correlated CC ground state of an (N -2)-electron closed-shell reference system in order to generate the ground and excited states of the N-electron open-shell species of interest, while using Nu active unoccupied orbitals to select the dominant 3p-1h and 4p-2h terms. We demonstrate that the relatively inexpensive DEA-EOMCC(3p-1h,4p-2h){Nu} method signicantly reduces the computational costs of the parent active-space DEA-EOMCC(4p-2h){Nu} and full DEA-EOMCC(4p-2h) approaches, which are needed to obtain highly accurate results for open-shell systems having two electrons outside the closed-shell cores, such as diradicals, with virtually no loss in accuracy of the resulting excitation and dissociation energies. We also show that the active-space DEA-EOMCC(3p-1h){Nu} method accurately reproduces the results of the parent DEA-EOMCC(3p-1h) calculations at the small fraction of the cost. In addition to a series of benchmark examples that illustrate the performance of the DEA-EOMCC(3p-1h){Nu}, DEA-EOMCC(3p-1h,4p-2h){Nu}, and other DEA-EOMCC approaches with 3p-1h and 4p-2h excitations, including singlet{triplet gaps in methylene, trimethylenemethane, and several antiaromatic diradicals and bond breaking in the fluorine molecule, we provide the most essential details of DEA-EOMCC equations with an active-space treatment of 3p-1h and 4p-2h terms, as implemented in the compactcodes developed in this work and interfaced with the GAMESS package.
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