The interaction of a hydrogen atom with the silicon (111) surface is studied with cluster models. On the basis of ab initio Hartree-Fock-LCAO (linear combination of atomic orbitals) theory the electronic structure of silicon-hydrogen clusters with up to four silicon atoms is calculated where the embedding of the clusters into the substrate is simulated by surrounding hydrogen atoms. The distance of the adsorbing hydrogen perpendicular to the surface is optimized with respect to the total energy of each cluster. The adsorbate-substrate binding which is always highly convalent seems to be quite localized so that the cluster approach should be reasonable for this system. From the calculations, the adsorbate energy and the energy for adsorbate vibrations perpendicular to the surface can be determined. Our cluster results are in good agreement with those of band-structure-type studies and with experimental data. © 1979 The American Physical Society.