Organic reactions are systematically examined experimentally and theoretically to determine the role dynamics plays in the outcome of the reaction. It is shown that trajectory studies are of vital importance in understanding reactions influenced by dynamical motion. This dissertation discusses how a combination of kinetic isotope effects, theoretical calculations, and quasiclassical dynamics trajectories aid in the understanding of the solvolysis of p-tolyldiazonium cation in water, the cycloadditions of cyclopentadiene with diphenylketene and dichloroketene, and the cycloaddition of 2- methyl-2-butene with dichloroketene. In the solvolysis of p-tolyldiazonium cation, significant 13C kinetic isotope effects are qualitatively consistent with a transition state leading to formation of an aryl cation, but on a quantitative basis, the isotope effects are not adequately accounted for by simple SN1 heterolysis to the aryl cation. The best predictions of the 13C isotope effects for the heterolytic process arise from transition structures solvated by clusters of water molecules. Dynamic trajectories starting from these transition structures afford products very slowly. The nucleophilic displacement process for aryldiazonium ions in water is determined to be at the boundary of the SN2Ar and SN1 mechanisms. The reaction of cyclopentadiene with diphenylketene affords both [4 + 2] and [2 + 2] cycloadducts directly. This is surprising. There is only one low-energy transition structure for adduct formation. Investigation of this reaction indicates that quasiclassical trajectories started from a single transition structure afford both [4 + 2] and [2 + 2] products. Overall, an understanding of the products, rates, selectivities, isotope effects, and mechanism in these reactions requires the explicit consideration of dynamic trajectories.

Non-statistical recrossing in ketene cycloadditions with alkenes, heavy-atom tunneling and the mechanism of the decarboxylation of Mandelylthiamin is investigated in this dissertation. A combination of experimental kinetic isotope effects and theoretical models and kinetic isotope effects is utilized for this endeavor. This dissertation also describes how the use of quasiclassical dynamic trajectories, microcanonical RRKM calculations, and canonical variational transition state theory in combination with small-curvature tunneling approximations is utilized to help advance our research methodology to better understand mechanism. In the cycloaddition of dichloroketene with cis-2-butene, significant amounts of recrossing is observed using quasiclassical dynamic trajectories. An unusual inverse 13C intramolecular KIE lead us to investigate the role that heavy atoms play in non-statistical recrossing. More importantly, this discovery has uncovered a new phenomena of entropic intermediates that not only applies to ketene cycloadditions, but can also be applicable to other "concerted" reactions such as Diels-Alder reactions. The ring-opening of cyclopropylcarbinyl radical has revealed that heavy-atom tunneling plays a major role. The intramolecular 13C kinetic isotope effects for the ring-opening of cyclopropylcarbinyl radical were unprecedentedly large and in combination with theoretical predictions and multidimensional tunneling corrections, the role of tunneling in this reaction can be better understood. The mechanism decarboxylation of mandelylthiamin has been extensively studied in the literature. However, until the use of theoretically predicted KIEs and theoretical binding motifs the rate-limiting step of this reaction has been hotly debated. In this dissertation, a discussion of how the theoretical KIEs indicate the initial C-C bond as the rate-limiting step and chelating binding motifs of pyridinium and mandelylthiamin to explain the observed catalysis is given.