Normal mode analysis of van der Waals vibrations

Two algorithms are presented for calculation of the van der Waals modes of weakly bound clusters. Both methods rely on the harmonic normal mode approximation and a chosen intermolecular potential. These calculational techniques differ specifically in the form of the force field employed: one method uses the total (both intra- and intermolecular) force field for the cluster and the other uses only the intermolecular force field. Both methods require rather elaborate coordinate transformation and their first and second partial derivatives; these are provided in detail. The two calculations generate eigenvalues and eigenvectors that are in complete agreement with one another for a given potential. The methods insure that the van der Waals modes are calculated at the proper cluster equilibrium configuration for which all torques and forces on molecules and/or atoms are effectively zero. Examples are presented for (H2O)n (n=2,...,7), benzene clustered with water, methane, and ammonia, and a number of different intermolecular potentials. Some of the observed heterogeneous cluster van der Waals modes are reassigned in light of these new results.