A realistic tight-binding model for chemisorption on semiconductor surfaces is presented. The model is quantitatively accurate, computationally very simple, free from adjustable parameters, and can be applied to a wide variety of problems. The basic assumption underlying the model, which is based on the Hückel approximation, is that the local bond (i.e., the chemisorption bond) at the surface is similar to the corresponding bond in an appropriately chosen molecule. While the Hamiltonian matrix elements between substrate atomic orbitals are determined from the well-known bulk energy bands, the matrix elements between chemisorbate and substrate orbitals are obtained from molecular energy levels. The matrix elements thus obtained show reasonable chemical trends. The validity of the above procedure for the determination of the matrix elements is demonstrated by the good agreement of the theoretical spectra with experiment obtained without further adjustment of parameters. The sensitivity of the spectra to changes in the parameters is described in detail. The surface-energy bands and local density of states have been calculated for the chemisorption of atomic hydrogen on the (111) surfaces of Si and Ge. The apparent photoelectron density-of-states spectrum has been calculated taking into account the escape probability, the secondary electrons, and the variation of the oscillator strength near the surface (local oscillator strength). The calculated spectra are in excellent agreement with experiment. © 1976 The American Physical Society.