Overview

As has already been shown, the problem of ab initio methods consists in the derivation of the potential energy surface (Eq. 2.12) and finding its local minima dependent on the 3N co-ordinates of the N nuclei. Using the pair potential approximation or even many-body potentials with the molecular mechanics method significantly reduces the effort for obtaining the potential energy surface, while the problem of detecting the saddle points still remains the same. Though there are a lot of different strategies available, there are no (or at least very few) systematic algorithms that localize the energetically best fitting configurations within an acceptable time.

However, while molecular mechanics as well as ab initio methods are very popular and successful in the description of more or less complex systems (molecules, clusters, etc.) most often known from organic chemistry the treatment of the many-particle problem is handled, nevertheless, in a static way, i.e. the results are only valid for temperatures equal to zero. Even by including temperature dependent potentials molecular mechanics calculations can never deliver dynamic values. But especially with respect to nanostructures consisting of non-bonded materials or metals, such dynamic effects are of considerable interest.

Since the harmonic approximation for crystalline solids known from solid state physics is not well suited for an adequate description of surface phenomena at higher temperatures either [Schommers, 1986], the only method at disposal is the classical solution of Hamilton's equations of motion for N particles

where q _i and p