In this dissertation, density functional theory (DFT) calculations were used to investigate (1)NO2 adsorption on BaO in NOx Storage Reduction (NSR) catalyst affected by the morphology of BaO and the γ-Al2O3 support, (2) energy barrier of H2 dissociative adsorption over Mg clusters affected by its electronic structure, and (3) comparison of the activities of CeO2 clusters affected by two different supports--monoclinic ZrO2 and non-spinel γ-Al2O3. Our results showed that the electronic effect caused by the non-stoichiometry of the bare BaO clusters and surfaces improves their reactivities toward NO2 adsorption greatly, whereas the geometric structure of the catalyst has only minor effect on the activity; we also found that the γ-Al2O3 substrate improves the reactivities of the supported BaO clusters and at the same time the interface between BaO and γ-Al2O3 provided a unique and highly reactive environment for NO2 adsorption. Hydrogen dissociation barrier over pure Mg clusters is greatly affected by the electronic structure of the clusters--closed shell clusters such as Mg10 and Mg92- have higher energy barrier toward H2 dissociation; however, H2 dissociation over clusters that are two electrons shy from the closed electronic shell are relatively easier. As substrates, neither ZrO2(111) nor γ-Al2O3(100) affects the reactivity of the supported Ce2O4 toward CO2 adsorption and CO physisorption significantly; whereas the reactivity of Ce2O4 toward CO reactive adsorption were found to be affected by the two substrates very differently.