In order to reveal the mechanism of the electrochemical machining process in ultrapure water, first-principles molecular-dynamics simulations of Si(001) surfaces interacting with OH molecules were carried out on the basis of the Kohn-Sham local-density-functional formalism. A plane-wave basis set was used, and the cut-off energy is 327eV(24Ry). A norm-conserving pseudopotential was also used. We adopt the standard molecular-dynamics method for the optimization of the ionic system and the preconditioned conjugate-gradient (CG) method for the quenching procedure of the electronic degrees of freedom. We determined the optimized ionic configurations and electronic distributions for OH chemisorbed Si(001) surfaces and clarify the elemental process of the chemical reactions. It was confirmed that the Si surface atom cannot bond with four OH molecules, so it cannot be etched as an Si(OH)4 molecule. In this simulation, it was also confirmed that two OH molecules react with each other producing an H2O molecule and an oxygen atom. The oxygen atom bonds with two Si surface atoms at the surface bridge site or back-bond. We concluded that the Si surface atom cannot be etched with Si(OH)4 molecule but oxidized by oxygen atom produced by two OH molecules. These results agree with the experimental results of anodic oxidation of Si surface.