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. Relative anharmonic densities of state are calculated by the multiple histogram/Nose 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 Al_n→Al_n+Al dissociation threshold, where only one Aln_j conformation is energetically accessible and the harmonic model is 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 states. However, at higher energies anharmonicity for Al_n-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.