Computational approaches have made significant contributions to our understanding of heterogeneous catalysis. These calculations reveal insights regarding the reactivity and stability of catalytic systems that may otherwise be difficult or impossible to observe experimentally. In this collection of work, computational techniques are applied to understand the reactivity and stability of three types of catalytic systems: (1) metal surfaces, (2) plasma-assisted reactions, and (3) zeolites. First, I describe and present several approaches to evaluate the free energy and entropy of adsorbed atoms and molecules on metal surfaces. I developed a Python-based utility that numerically evaluates the Schrödinger equation to compute the density of states (DOS) for a particle in an arbitrary potential. The DOS can be used with standard statistical mechanical models to evaluate the free energy and entropy of an adsorbate. Using this method, we can obtain accurate free energies and entropies as compared to analytical approximate methods, at no additional computational cost.  Next, I discuss my contribution toward characterizing products made from plasma-assisted catalysis. Our experimental collaborators report inelastic neutron scattering (INS) observations of Ni particles after treatment with nitrogen and hydrogen plasmas. I modes of various species on the surface and present predicted INS spectra to facilitate the characterization of the products generated. Our results show that we can overcome reaction barriers that are thermally inaccessible when a plasma is present. Finally, I present two projects related to zeolite stability. First, I show that current models to predict the zeolite phase a templating molecule will crystallize are not always reliable. I introduce a new augmented scheme to predict the affinity a templating molecule has to crystallize one topology over another. I also show that the coocclusion of alkali surrogates has an impact on how the template molecules fit in the zeolite cavities. Second, I present results regarding the stability of defects in zeolites post-dealumination. We find that energies are sensitive to proton arrangements in the defect, but the location a defect can form is independent of the locations of other Brønstead and defect sites in the framework. These observations can then be extended to better understand how hydrolysis occurs in zeolites.