Computation of vibrational frequencies for adsorbates on surfaces

A general strategy for computing the vibrational frequencies of adsorbates on surfaces is presented. Rather than use numerical fits to the surface energy, we advocate diagonalizing a mass weighted energy second-derivative matrix. The computation of energy derivatives has several advantages: It facilitates a more accurate treatment of the adsorbate/substrate mass ratios. The normal modes of the surface vibrations are given automatically in the diagonalization step. Finally, a major advantage of using energy derivatives is that they provide estimates of the range of the adsorbate/substrate interactions which can be used to ensure that the frequency values are converged. We illustrate the strategy for cluster calculations which simulate the H/Al(100), O/Al(111), H2O/Al(111), and Al/Si(111) surfaces.