Comparison of zero-point energy constrained and quantum anharmonic Rice-Ramsperger-Kassel-Marcus and phase space theory rate constants for Al₃ dissociation

The ZPE constrained trajectory model is found to retain the ergodicity and intrinsic Rice-Ramsperger-Kassel-Marcus (RRKM) behavior observed previously [J. Chem. Phys. 101, 8535 (1994)] in unconstrained trajectories of Al₃ decomposition. Microcanonical unimolecular rate constants for Al₃ decomposition are calculated from the ZPE constrained trajectories and compared with the predictions of the vibrator and flexible transition state models of RRKM theory, phase space theory, and the orbiting transition state model of phase space theory (OTS/PST). Quantum anharmonic Al₃ vibrational densities of state, determined by a semiclassical approach, are used to calculate these statistical rate constants. Anharmonicity increases the density of states threefold for total energies 1-2 kcal/mol above the classical product asymptotic limit, but has a negligible effect on the Al₂ - Al transition state sum of states. The ZPE constrained trajectory unimolecular rate constants are in poor agreement with the quantum anharmonic OTS/PST and flexible RRKM rate constants. This is because the ZPE constraint is too restrictive and some of the ZPE constrained trajectories are temporarily trapped in the ZPE forbidden region of phase space. The ZPE constrained trajectory rate constants are smaller than their purely classical counterparts, since Al₂ is not formed without its ZPE and thus the effective dissociation threshold is larger for the ZPE constrained trajectories. ZPE constrained sums and densities are calculated by including the ZPE constraint when solving the classical phase integral. RRKM rate constants calculated from these ZPE constrained sums and densities are in much better agreement with the quantum anharmonic OTS/PST and flexible RRKM rate constants, than are those calculated from the ZPE constrained trajectories. The difference between the ZPE constrained RRKM and quantum flexible RRKM rate constants becomes small and much less than the anharmonic correction, for energies slightly in excess of the Al₂+Al classical asymptotic limit. This is because the number of real frequencies in the instantaneous normal mode analysis decreases as the total energy is increased, which makes the ZPE constrained RRKM rate constant more accurate. Product energy partitioning from the ZPE constrained trajectories is in good agreement with the predictions of quantum phase space theories, except that the product diatom is formed too rotationally excited. The ZPE constraint scheme retains a spurious frequency and zero-point energy for the Al₂ - Al bending motion at large separations, which increases the Al₂ product rotational energy. The work reported here supports the proposal that a ZPE constraint model, based on an instantaneous normal mode analysis, may be a valid approach for including zero-point energy effects in trajectory simulations of ergodic anharmonic coupled systems. However, additional work needs to be done to remove some of the numerical problems with the current ZPE constraint model and to make the model less restrictive.