A first principles total energy calculation is performed to study hydrogen in an hcp metal, Y, under a Born-Oppenheimer approximation between Y and H. The equilibrium interstitial location, heat of formation, the change in the lattice constants and the bulk moduli, and the vibration frequencies of hydrogen are in excellent agreement with the experiment. However, the Born-Oppenheimer approximation is unable to make a quantitative prediction about the energy level splitting and hydrogen energy barrier between the interstitial sites. It would be out of reach to address these problems via a first principles technique. With this in mind, an empirical tight binding model is constructed for the simpler Si:H system and applied in a molecular dynamics simulation to study the hydrogen vibration on Si(111) surface. Our empirical tight binding model is able to provide an efficient and yet accurate description of hydrogen vibrations in the SiH[subscript]4 molecule and on the Si(111) surface. The frequency shift of the hydrogen stretching mode with temperature is investigated. The coupling between the hydrogen wagging mode and the Si substrate mode is verified. Also we have observed that there is a strong coupling between the hydrogen stretching mode and the wagging mode. It is hoped that this model would find greater use as computational capacity continues to grow rapidly.