Computational methods serve as a powerful complement to experimental studies in the field of catalysis. Of particular interest in catalysis is the development of transition state-finding methods because they allow for the determination of activation energies and rate constants, thereby leading to an understanding of catalytic mechanisms. The present work has led to the development of a more computationally efficient method for locating transition states and has applied this new method, as well as existing methods, to the analysis of methanol oxidation on isolated vanadate sites supported on metal oxides. The first part of the research effort has been devoted to using existing computational methods to study the selective oxidation of methanol to formaldehyde over isolated VOx sites supported on SiO 2, TiO2, and bilayered TiOx/SiO 2. Previous experimental studies have demonstrated that supported VO x catalysts are one of the best materials for methanol oxidation and that superior performance is achieved when the catalytic centers are present as isolated VOx sites, however there is little understanding of the detailed reaction mechanism. The aim of this research is to present a comprehensive catalytic mechanism that is fully consistent with experimental work. A model of the active site on each support was developed and shown to be in good agreement with geometric parameters and vibrational frequencies obtained from spectroscopic measurements. The calculation of reactant, product, and transition state species were carried out using density functional theory (DFT) to determine reaction energetics. Statistical mechanics and absolute rate theory were used to determine equilibrium constants and rate coefficients for each elementary reaction step. The formation of formaldehyde was found to involve two keys steps: the reversible adsorption of methanol followed by the rate-limiting step of H-abstraction. The release of formaldehyde and water from the active V center leads to a two electron reduction of V from V5+ to V3+. Rapid reoxidation of the reduced V center has been proposed to occur by adsorption of O2 to form a peroxide species, followed by migration of one of the O atoms associated with the peroxide across the surface of the support. Experimental work has also shown that VOx supported on TiO2 is 103 more active than when supported on SiO2, although DFT calculations in the present study have shown that the increased activity is not due to an intrinsic electronic effect. Instead, the presence of surface O-vacancies associated with the active site have been shown to offer a plausible explanation of the increased activity, and serve to reduce the activation energy of the rate-limiting step. This result suggests that O-vacancies play a role in the rate of formaldehyde formation, which is further evidenced by a strong correlation between the turnover frequency for methanol oxidation and the energy required to form an O-vacancy on different metal oxide supports. The role of surface O-vacancies is also found to play a role when Ti is present as a surface modifier on the bilayered TiO x/SiO2 support. The calculated thermodynamics and overall kinetics in each of these studies are in good agreement with those determined experimentally. The second part of the research effort has been focused on improving the computational efficiency of the growing string method (GSM) for finding transition states so that it can be used more effectively for large systems. The advantage of the GSM is that it does not require an initial guess of the transition state or the reaction pathway, unlike other common transition state-finding methods, although it is still...