The adsorption of the different species X and CX(3) on an X-terminated diamond (111) surface (X = H, F,Cl, Br) has been investigated structurally and energetically, using a cluster approach and two different types of quantum mechanical methods : the ab initio molecular orbital (MO) method and the first-principle density functional theory (DPT) method, respectively. The halogen species F and Cl, as well as hydrogen H, were all shown to be able to sustain the sp(3) structural configuration of the surface carbon atoms. Furthermore,the adsorption energies were much larger for the H and F species than for other species like Cl and Br, indicating that H and F species stabilize the diamond(lll) surface better than the Cl and Br species do. For Br large sterical hindrances are induced, and the diamond (111) surface cannot be stabilized. The adsorption of CH3 or CF3 to a radical carbon on a H- or F-terminated diamond (111) surface stabilizes also the sp(3) structural configuration of the radical carbon atom. The large difference in adsorption energy of the species CH3 and CF3 indicates that the probability for diamond growth, based on the CF3 species as a dominant growth species on a F-terminated diamond (111) surface, is much lower than for growth based on the CF3 species as a dominant growth species on a H-terminated surface. There is no tendency for the gaseous species CCl3 and CBr3 to adsorb on a Cl- or Br-terminated diamond (111) surface.