A comparison of classical trajectory and statistical unimolecular rate theory calculations of Al₃ decomposition

Classical trajectories are used to simulate the dissociation of microcanonical ensembles of Al₃ clusters with 0.25-2.00 kcal/mol energy in excess of the dissociation threshold. Unimolecular lifetime distributions for the ensembles are in accord with the random lifetime prescription of Rice-Ramsperger-Kassel-Marcus (RRKM) theory and Al₃ is identified as an intrinsic RRKM molecule. Unimolecular rate constants determined from the trajectories are compared with the predictions of variational RRKM theory with harmonic vibrator and flexible transition state models, phase space theory (PST), and the orbiting transition state model of phase space theory (OTS/PST). The flexible RRKM model, PST, and OTS/PST give Al₂- - -Al transition state sums of state which agree to within 1%. The harmonic vibrator RRKM model gives a sum of states which varies from only 40% to 10% larger as the excess energy is increased from 0.25 to 2.0 kcal/mol. Adiabatic switching and direct integration of the phase integral are used to determine the reactant Al₃ anharmonic density of states. For the energies considered in this work, anharmonicity determined by adiabatic switching increases the Al₃ density of states from the harmonic value by a factor of 2.5-2.9. The anharmonic density of states determined by solving the phase integral depends on where the reactant/product phase space boundary is positioned. Placing it at the vibrator transition state gives an anharmonic density of states nearly the same as that determined by adiabatic switching, while placing it at the looser flexible transition state gives a density of states 35% larger at the highest energy. Using this latter anharmonic density of states gives OTS/PST and flexible RRKM Unimolecular rate constants which agree with the trajectory results to within 25% at the lowest energy and 10% at the highest energy. Product energy partitioning distributions determined from the trajectories are compared with the predictions of PST, OTS/PST, and the Engelking model. Both OTS/PST and PST give product energy partitioning distributions which are in near quantitative agreement with the trajectory results.