In this review we address (1) the co-adsorption of group V (As, Sb, Bi) atoms and molecular oxygen on the Si(0 0 1) surface and (2) the adsorption and dynamics of Sb, Bi, Si and Ge ad-dimers on the Si(0 0 1) and Ge(0 0 1) surfaces. The adsorption and diffusion processes of group IV and V atoms on the (0 0 1) surfaces of group IV semiconductor surfaces have been studied using multi-configuration self-consistent field methods and density functional theory calculations. Results obtained by various types of first-principle total energy calculations are mutually compared and discussed. Our results demonstrate the capability of these quantum chemistry methods to provide relevant and reliable information on the interaction between adsorbate and semiconductor surfaces.