Crystal growth of gallium nitride on GaN(0 0 0 1) surface by hydrogen vapor phase epitaxy (HVPE) was modeled using ab initio quantum mechanical density functional theory (QM DFT) calculations. These calculations employed SIESTA package, suitable for bulk and surface calculations [J.M. Soler, E. Artacho, J.D. Gale, Alberto Garcia, J. Junquera, P. Ordejon, D. Sanchez-Portal, J. Phys.: Condens. Matter 14 (2002) 2745; P. Ordejon, D.A. Drabold, M.P. Grumbach, R.M. Martin, Phys. Rev. B 48 (1993) 14,646; P. Ordejon, D.A. Drabold, M.P. Grumbach, R.M. Martin Phys. Rev. B 51 (1995) 1456]. The GaN(0 0 0 1) surface model was 2-d supercell, consisting of a GaN slab and an empty zone, perfectly suited for the simulations of the surface properties and surface processes. The simulations include the impingement of the ammonia molecule on the GaN(0 0 0 1) face. The influence of the presence of hydrogen was analyzed. The simulation results indicate that the adsorption of ammonia occurs without energy barrier. Since, ammonia dominates in the vapor phase during HVPE growth, the state of GaN (0 0 0 1) surface is nitrogen-rich (N-rich). Subsequently, the adsorption of other chemical species, such as HCl, GaCl and H-2 of the GaN surface was considered. These calculations were made for GaN surface covered by N atoms and by NH2 radicals. Additionally, the desorption process of the gallium from GaN(0 0 0 1) face was also modeled. These results indicate that GaCl molecule is strongly attached to the surface. In addition, the Ga desorption from the surface is extremely costly process in terms of the energy. These results indicate that the growth rate of gallium nitride is determined by the magnitude of gallium flux as observed in typical MOVPE and HVPE processes. (C) 2007 Elsevier B.V. All rights reserved.