We studied the reaction of tri-methylaluminum (TMA) on hydroxyl (OH)-terminated Si (001) surfaces for the initial growth of aluminum oxide thin-films using density functional theory. TMA was adsorbed on the oxygen atom of OH due to the oxygen atom’s lone pair electrons. The adsorbed TMA reacted with the hydrogen atom of OH to produce a di-methylaluminum group (DMA) and methane with an energy barrier of 0.50 eV. Low energy barriers in the range of 0 - 0.11 eV were required for DMA migration to the inter-dimer, intra-dimer, and inter-row sites on the surface. A unimethylaluminum group (UMA) was generated at each site with low energy barriers in the range of 0.21 - 0.25 eV. Among the three sites, the inter-dimer site was the most probable for UMA formation.