On the use of pair interactions to model vibrations of an adatom on a transition-metal surface

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Abstract
The dependence of the adatom vibration frequency on the change in the local density of states between sites is examined. Adsorption on a surface of the same species with a half-filled band is assumed. The adatom bond length R is less than the bulk spacing and it decreases with decreasing coordination z. The short-range repulsion and hopping integral between the adatom and near neighbours are assumed to vary with R as exp(-pR) and exp(-qR) respectively. For p/q=2, the adsorption energy Ead0 is independent of z, and the force constant for vibration normal to the surface is k=pq cos2 theta Ead0, where theta is the angle between the bond and the surface normal. If Ead0 varies little between sites, a much used approximation is to take k dependent on theta but not on z. This is exact in the present model for p/q=2. This value is typical of simple molecules, but rather larger values are appropriate for transition metals. For all p/q the dependence on z of k is less than the linear variation obtained with an additive site-independent pair potential.