## Abstract

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 Al_{5} and Al_{6} are determined by Monte Carlo evaluation of the phase integral, while for Al_{12} and Al_{13} 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 Al_{6} and Al_{13}, respectively. The anharmonic densities of state are used to determine anharmonic 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 of the anharmonic microcanonical rate constants determined by using classical trajectories to calculate the initial decay rates for microcanonical ensembles of Al_{6} and Al_{13} clusters. The trajectories also show that the Al_{6} and Al_{13} 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 E_{0} made energy dependent, fits anharmonic microcanonical unimolecular rate constants for Al_{3}, Al_{6}, and Al_{13} 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.

Original language | English |
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Pages (from-to) | 7432-7447 |

Number of pages | 16 |

Journal | Journal of Chemical Physics |

Volume | 105 |

Issue number | 17 |

DOIs | |

State | Published - 1996 |