There is a high demand for the development of processes for the conversion of ubiquitous molecules into industrially useful commodities. Transition metal catalysts are often utilized for the activation and functionalization of small organic molecules due to their diverse nature and proven utility with a myriad of chemical transformations. The functionalization of methane (CH4) and dinitrogen (N2) to methanol (CH3OH) and ammonia (NH3) respectively is of particular interest; however, both methane and dinitrogen are essentially inert due to the inherit strength of their bonds. In this dissertation a series of computational studies is performed to better understand the fundamental chemistry behind the functionalization of methane and the activation of dinitrogen in a homogeneous environment. A catalytic cycle is proposed for the oxy-functionalization of methane to methanol. The cycle consists of two key steps: (1) C-H activation across a metal-alkoxide bond (M-OR), and (2) regeneration of the M-OR species through an oxy-insertion step utilizing external oxidants. The C-H activation step has been extensively studied; however, the latter step is not as well understood with limited examples. For this work, we focus on the oxy-insertion step starting with a class of compounds known to do C-H activation (i.e., Pt(II) systems). Computational studies …