STATISTICAL ANHARMONIC UNIMOLECULAR RATE CONSTANTS FOR THE DISSOCIATION OF FLUXIONAL MOLECULES - APPLICATION TO ALUMINUM CLUSTERS

Anharmonic densities of state are determined for the Al-n (n = 5,6,12, 13) clusters using a model analytic potential energy function. Relativ e anharmonic densities of state are calculated by the multiple histogr am/Nose dynamics method. Absolute densities for Al-5 and Al-6 are dete rmined by Monte Carlo evaluation of the phase integral, while for Al-1 2 and Al-13 they are determined by adiabatic switching. The anharmonic densities of state are orders of magnitude larger than harmonic value s based on the deepest potential energy minimum. At an energy equal to the cluster dissociation threshold, the anharmonic density is 56 and 4600 times larger than the harmonic density for Al-6 and Al-13, respec tively. The anharmonic densities of state are used to determine anharm onic phase space theory rate constants for Al-6-->Al-5+Al and Al-13--> Al-12+Al dissociation. These rate constants are within a factor of 2 o f the anharmonic microcanonical rate constants determined by using cla ssical trajectories to calculate the initial decay rates for microcano nical ensembles of Al-6 and Al-13 clusters. The trajectories also show that the Al-6 and Al-13 dissociations have ergodic unimolecular dynam ics. At the Al-n-->Al-n-1+Al dissociation threshold, where only one Al -n-1 conformation is energetically accessible and the harmonic model i s accurate for the Al-n-1 density of states, the anharmonic correction to the unimolecular rate constant is that for the Al-n density of sta tes. However, at higher energies anharmonicity for Al-n-1 also becomes important and the anharmonic correction to the unimolecular rate cons tant becomes smaller. A modified Rice-Ramsperger-Kassel rate constant expression, with all degrees of freedom active and A and/or E(0) made energy dependent, fits anharmonic microcanonical unimolecular rate con stants for Al-3 Al-6 and Al-13 dissociation. A simple Rice-Ramsperger- Kassel-Marcus model, used to analyze the experimental studies of alumi num cluster dissociation, gives accurate rate constants as a result of a fortuitous cancellation of errors. (C) 1996 American Institute of P hysics.