SOME ESTIMATES OF TUNNELING SPLITTINGS IN SMALL CLUSTERS

A simple treatment is used to estimate the tunneling splittings caused by rearrangements in a variety of model cluster systems, including (H F)2, benzene-Ar, benzene-Ar2, C5H5+, B8H82-, and homoatomic clusters b ound by the Lennard-Jones and Morse potentials. Given sufficient gener ators to represent all the point group operations and feasible rearran gements, the effective molecular symmetry group is calculated along wi th the connectivity of the minima on the potential energy surface. Thi s defines the secular determinant which provides the best solutions to the multiminima problem that may be written as linear combinations of localized functions. A Huckel-type approximation is then employed, as suming that the only non-zero off-diagonal Hamiltonian matrix elements are between minima which are directly linked by are arrangement. The magnitude of this matrix element is estimated from properties of the c alculated reaction pathways, using a model one-dimensional Schrodinger equation. Solving the Huckel-type secular equations gives the splitti ng pattern for each rigid-molecule energy level and also an estimate o f the magnitude of the effect, along with the electric dipole allowed transitions. The results compare satisfactorily with experiment where data are available (i.e. the splittings are of the right order of magn itude), and a number of other cases are identified where tunneling eff ects might be observable.