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Abstract
One of the advantages of computational quantum chemistry is its ability to leverage theoretical models to extract insights from the study of challenging chemical systems. In particular, the trends that manifest along groups or rows of the periodic table have been of interest to chemists for many years. Comprehensive understanding of these kinds of trends has the potential to evolve our chemical intuition of many systems that are at the cutting edge of experimental research. This work begins with a summary of the foundational theoretical details of the ab initio methods employed throughout this body of research. The first application examines atmospherically relevant binary complexes formed between hypohalous acids and water, with close examination of the competition between hydrogen and halogen bonding. Next, motivated by the impressive synthetic work of Cummins, we characterize the Pn(CH)3 (Pn = N, P, As, Sb, Bi) tetrahedrane molecules and lay a firm foundation for future experimental work on these systems. Significant attention is given to the electronic structure motifs exhibited by these molecules and how they change with increasing pnictogen size. The third project examines the HNCO + H2O reactions which are of significant importance for industrial polymer design. Key stationary points are characterized with energy predictions approaching the CCSDT(Q)/CBS limit. Using \textit{ab initio} composite methods, the changes in barrier heights for a collection of 24 substituted RNCO species as well as the presence of additional catalyst waters are determined, and the patterns are analyzed with the aim of informing novel material design. The final project concerns the design of an upper-level physical chemistry lab that focuses on the tension between cost and accuracy by means of an \textit{ab initio} study of methane combustion energy. The components of the exercise are explained in detail with an emphasis on its intentional design which prioritizes pedagogical flexibility, accessibility, and learning goals that can be generalized to many computational science fields.