Small clusters/particles of metal dispersed on high surface-area metal oxide supports are commonly used in industrial catalysis. To advance catalyst design, an understanding of how the interaction between metals and supports influences active site structure, composition, and activity is required. In this thesis, molecular-level density functional theory (DFT) simulations and periodic supercell and cluster models are used to describe a trinuclear rhenium (Re3) cluster adsorbed on an alumina (Al2O3) support as a function of reaction environments. To compare the effects of surface hydroxylation on cluster-support binding, periodic supercell simulations are performed on Re3 clusters adsorbed on a hydrogen-free ('dry') and fully hydroxylated ('wet') ÌøåÁ-alumina (0001) surface. Calculations demonstrate that both a Re atom and the Re3 cluster bind more strongly on the 'dry' than the 'wet' surface. Electronic structure analysis shows that the metal-support interaction on 'dry' surface is strengthened by electron flow from cluster to the empty orbitals of nearby relaxed first layer Al atoms, whereas on the 'wet' surface there is a strong thermodynamic drive for hydrogen to undergo 'reverse' spillover from the surface to the supported metal clusters. These calculations show that Re-Re bonding is preserved and the clusters are stable to dissociation when adsorbed on both the dry and wet ÌøåÁ-alumina (0001) surfaces. The supercell results demonstrate that the Re3 clusters have a strong affinity for hydrogen, a characteristic expected to be important in their operation as hydrogenation catalysts. A HxRe3(OH)3 model was used to simulate hydrogen uptake on an alumina-supported Re3 cluster. Calculations of successive H additions show that H atoms adsorb exothermically and prefer to distribute evenly across Re atoms: the first three hydrogen ligands adsorb atop each Re; the next three hydrogen ligands prefer bridge bonding in the Re3 plane; additional hydrogen ligands again adsorb atop Re atoms. The average Re-Re distance is constant up to six H ligands; additional hydrogen uptake significantly elongates the Re-Re bonds. A first-principles thermodynamic model based on these results shows that there is a strong thermodynamic driving force for the supported Re3 cluster to adsorb hydrogen, and equilibrium is reached when there are 6~8 H ligands.