The force constants for homeotropic surface anchoring of a model Gay-Berne nematic liquid crystal are derived by a local density functional method with data from molecular dynamics simulations. For the molecule-surface interaction both an anisotropic and an isotropic one-particle potential is taken. It is found that the values of the anchoring strengths are barely affected by the anisotropy of the surface potential, which indicates predominance of packing effects. Additionally, a surface-induced smectic A phase is being observed even though the phase is unstable in the bulk.