Initial surface reaction mechanism for atomic layer deposition of HfO2 on the hydroxylated GaAs(001)-4x2 surface using HfCl4 and H2O as precursors is investigated using hybrid density functional theory. The reaction between HfCl4 and H2O with the hydroxylated GaAs(001)-4x2 surface consists of two half-reactions: (1) HfCl4 with GaAs-OH sites and (2) H2O with Hf-Cl sites. The two half-reactions proceed through the formation of stable chemisorbed states, resulting in high activation barriers of 17.1 and 17.6 kcal/mol for HCl formation, respectively. Additional energies are also needed to desorb the respective physisorbed states HCl from the substrate surfaces.