This dissertation details the results of theoretical investigations of the mechanism of an interesting organometallic reaction that stereoselectively couples aldehydes and alkynes to synthesize allylic alcohols and the mechanisms of S-nitrosothiol decompositions, the construction of computer clusters for quantum mechanical calculations, and the benchmarking of the B3LYP functional for studying organometallic reactions with medium-sized basis sets. In Chapter 1, the proposed mechanisms for Ni0-catalyzed alkyne-aldehyde couplings in the presence of phosphine ligands are discussed. Oxidative cyclization is the lowest energy pathway for alkyne-aldehyde coupling. The presence of a Lewis acid reductant (BEt3) was shown to be important in the catalysis of the reaction. In Chapter 2, the factors affecting regioselectivity in this reaction are studied through quantum mechanical calculations. Regioselectivities in agreement with experimental results are predicted and they are determined primarily by a balance of steric interactions present in the transition state. Chapter 3 reports a study of the enantioselectivity of the reaction involving a chiral phosphine that yields chiral allylic alcohols. A systematic procedure maintained diversity in a small sample of conformations of the oxametallacycle product, which are fully optimized using DFT. Strong interactions between Ni and the reductant is possible only in the oxametallacycle diastereomer leading to the major product enantiomer. Chapter 4 discusses the trends and considerations necessary for the construction and management of computing clusters for quantum mechanical problems. Chapter 5 focuses on the reactivity of S-nitrosothiols and provides alternative radical mechanisms that agree with experimental observations of stability. Dimerization reactions and other radical processes studied require at least one reaction step of DeltaGact=+30 kcal/mol. Chapter 6 describes the transnitrosation reaction involving the reaction of thiolate with S-nitrosothiols. A novel intermediate, nitroxyl disulfide, was discovered that helps explain the role of S-nitrosothiols in transporting NO. Chapter 7 assesses the accuracy of the widely used DFT method B3LYP with the LANL2DZ basis set and pseudopotential for metals and the 6-31G* basis set for main group atoms using transition metal benchmark sets and a review of available literature. The accuracy of B3LYP energies and bond lengths is 10 kcal/mol and 0.03 A respectively.