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Some Estimates of Tunneling Splittings in Small Clusters

D. Wales
Journal / Anthology

Journal of the American Chemical Society
Year: 1993
Volume: 115
Page range: 11191-11201

A simple treatment is used to estimate the tunneling splittings caused by rearrangements in a variety of model cluster systems, including HF)2, benzene-AR, Benzene-AR2, C5H5^+, B8H8^2-, and homoatomic clusters bound by the Lennard-Jones and Morse potentials. Given sufficient generators to represent all the point group operations and feasible rearrangements, the effective molecular symmetry group is calculated along with the connectivity of the minima on the potential energy surface. This defines the secular determinant which provides the best solutions to the multiminima problem that may be written as linear combinations of localized functions. A Hückel-type approximation is then employed, assuming that the only non-zero off-diagonal Hamiltonian matrix elements are between minima which are directly linked by a rearrangement. The magnitude of this matrix element is estimated from properties of the calculated reaction pathways, using a model one-dimensional Schrödinger equation. Solving the Hückel-type secular equations gives the splitting pattern for each rigid-molecule energy level and also an estimate of 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 magnitude), and a number of other cases are identified where tunneling effects might be observed.

*Science > Physics > Nuclear and Particle Physics
*Science > Physics > Quantum Physics