Vibrations of adsorbates on metal surfaces from geometry optimizations.

We present a method to compute harmonic vibrations that uses the structures and the forces in the structures that are obtained from a geometry optimization. It does not require any additional electronic structure calculations. The method generally takes only on the order of minutes on a regular PC, but it does not guarantee the calculation of all vibrations of a system. Tests on small adsorbates on a transition metal surface show, however, that the most relevant vibrations are obtained. An important part of the method is the inclusion of several checks to determine the reliability of its results, which gives also error estimates of the vibrational frequencies.