Zirconium oxide (ZrO2) deposition on the Si(100)-(2 x 1) surface is investigated using density functional theory (DFT). The reactants investigated in this study are ZrCl4 and H2O. The atomistic mechanisms of the two different deposition cycles are investigated: (1) First, ZrCl4 is deposited on the clean Si(100)-(2 x 1) surface. Upon adsorption, ZrCl4 is shown to dissociate into ZrCl3(a) and Cl(a) with an activation barrier that is below the entrance channel. Next, water is deposited and reactions on the Si-Cl* and Zr-Cl* surface sites are investigated, where the asterisks denote the surface species. Alternatively, (2) H2O is first deposited on the Si(100)-(2 x 1) surface. As previously determined, we also find that H2O dissociates into OH(a) and H(a) upon adsorption. Subsequent reactions of ZrCl4 with the resulting Si-OH* and Si-H* sites are then investigated. Reactions on Si-H* sites also provide insight into the growth on hydrogen-terminated Si surfaces. Upon investigation of the two different deposition cycles, the structure of the interfacial layer between silicon and zirconium oxide is then investigated.