Analysis and extension of a model for constraining zero-point energy flow in classical trajectory simulations

Abstract

In previous work a method, based on an instantaneous normal mode analysis and time reversal of the momentum of any local normal mode whose energy falls below its quantum harmonic zero-point value, has been proposed for controlling zero-point energy flow during classical trajectory simulations. From the previous work it is not clear that this ZPE constraint method, which was developed for nonrotating systems, conserves linear and angular momenta. The projection of infinitesimal rotations and translations from the Cartesian force constant matrix, during the instantaneous normal mode analysis, results in specific orthogonality relations for the vibrational eigenvectors. Since the vibrating molecular system is defined to obey the instantaneous Eckart conditions, it is shown that these orthogonality relations have a form which preserves the linear and angular momenta as constants of motion when the ZPE constraint is applied. Based on this property, an extended ZPE constraint scheme is proposed for molecular systems with nonzero angular momentum. This extended scheme is successfully tested in a study of vibrationally and rotationally excited Al3 and C2H6. Descriptions are given of the effect of the ZPE constraint on Hamiltonians that (1) are separable in normal mode coordinates and momenta, (2) have ergodic dynamics, and (3) have tori which are not described by normal mode coordinates and momenta. The ZPE constraint scheme, when applied to a normal mode Hamiltonian, does not affect the trajectories which satisfy the ZPE condition. For ergodic Hamiltonians, preliminary analyses indicate the scheme gives microcanonical unimolecular rate constants which are in agreement with the quantum values. This suggests that the scheme may be a practical approach for evaluating quantum microcanonical unimolecular rate constants for anharmonic and vibrationally/rotationally coupled Hamiltonians with ergodic dynamics. However, more studies need to be completed to determine whether it is a general conclusion. For the latter Hamiltonian, the ZPE constraint may induce transitions between tori and between tori and chaotic trajectories.