Fitting ab initio total energies, obtained within the generalized gradient approximation with spin-orbit coupling and a correction that includes Coulomb repulsion, we calculate the anisotropy parameters D and E of an effective spin model that describes 3d magnetic impurities separated from the Cu(100) surface by a monolayer of Cu₂N. Assuming a general exchange interaction between conduction and 3d electrons we construct an effective Kondo model which depends on D and E. We discuss the specific cases for Mn, Fe, and Co impurities.