Scanning tunneling microscopy observations of homoepitaxial growth on vicinal Si(001) and of coarsening of Si islands are used to develop a model of growth based on a configuration-dependent activation energy to hopping. In the model four contributions to this energy barrier are proposed: the activation energy to surface diffusion E(s), the dimer formation energy E(d) and two directional interaction energies between neighboring atoms not forming a dimer, E parallel-to and E perpendicular-to. Monte Carlo simulations are employed to compare experimental results with the results of the tested model and to deduce the atomic interaction energies: E(s) = (1.15 +/- 0.1) eV, E(d) = (0.45 +/- 0.10) eV, E parallel-to = (0.20(-0.14)+0.2) eV, E perpendicular-to = (0.01(0.07)+0.1) eV. Preliminary results of simulations, including anisotropic diffusion, are presented.