Adsorption of a water molecule on a Si (001) surface and its dissociation were studied using density functional theory to study the distribution of .OH fragments on the Si surface. The Si (001) surface was composed of Si dimers, which buckle in a zigzag pattern below the order.disorder transition temperature to reduce the surface energy. When a water molecule approached the Si surface, the O atom of the water molecule favored the down-buckled Si atom, and the H atom of the water molecule favored the up-buckled Si atom. This is explained by the attractions between the negatively charged O of the water and the positively charged down-buckled Si atom and between the positively charged H of the water and the negatively charged up-buckled Si atom. Following the adsorption of the first water molecule on the surface, a second water molecule adsorbed on either the inter-dimer or intra-dimer site of the Si dimer. The dipole-dipole interaction of the two adsorbed water molecules led to the formation of the water dimer, and the dissociation of the water molecules occurred easily below the order-disorder transition temperature. Therefore, the 1/2 monolayer of .OH on the water-terminated Si (001) surface shows a regular distribution. The results shed light on the atomic layer deposition process of alternate gate dielectric materials, such as HfO2.