Statistical anharmonic unimolecular rate constants for the dissociation of fluxional molecules: Application to aluminum clusters

Abstract

Anharmonic densities of state are determined for the Aln (n=5,6,12,13) clusters using a model analytic potential energy function. Relative anharmonic densities of state are calculated by the multiple histogram/Nosé dynamics method. Absolute densities for Al5 and Al6 are determined by Monte Carlo evaluation of the phase integral, while for Al12 and Al13 they are determined by adiabatic switching. The anharmonic densities of state are orders of magnitude larger than harmonic values 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 Al6 and Al13, respectively. The anharmonic densities of state are used to determine anharmonic phase space theory rate constants for Al6→Al5+Al and Al13→Al12+Al dissociation. These rate constants are within a factor of 2 of the anharmonic microcanonical rate constants determined by using classical trajectories to calculate the initial decay rates for microcanonical ensembles of Al6 and Al13 clusters. The trajectories also show that the Al6 and Al13 dissociations have ergodic unimolecular dynamics. At the Aln→Aln−1+Al dissociation threshold, where only one Aln−1 conformation is energetically accessible and the harmonic model is accurate for the Aln−1 density of states, the anharmonic correction to the unimolecular rate constant is that for the Aln density of states. However, at higher energies anharmonicity for Aln−1 also becomes important and the anharmonic correction to the unimolecular rate constant becomes smaller. A modified Rice–Ramsperger–Kassel rate constant expression, with all degrees of freedom active and A and/or E0 made energy dependent, fits anharmonic microcanonical unimolecular rate constants for Al3, Al6, and Al13 dissociation. A simple Rice–Ramsperger–Kassel–Marcus model, used to analyze the experimental studies of aluminum cluster dissociation, gives accurate rate constants as a result of a fortuitous cancellation of errors.