Time-dependent self-consistent field approximation for intramolecular energy transfer. I. Formulation and application to dissociation of van der Waals molecules

The time-dependent self-consistent field method (TDSCF) is formulated and applied to the study of intramolecular dynamics and unimolecular decomposition processes. The method is illustrated by calculations on vibrational predissociation in van der Waals molecules, such as I₂(v) Ne→I₂(v′) + Ne. The TDSCF has the advantage of achieving formal separability of the modes by associating a time-dependent Hamiltonian with each mode, while permitting (possibly extensive) energy transfer among the modes via the time-dependent mean potential which acts on each mode. We present quantal, semiclassical, and classical versions of the method; a proper classical limit of the quantum TDSCF replaces the averages over wave functions by averages over self-consistently obtained bundles of trajectories. In all three versions, considerable computational economy is retained in comparison with full dynamics calculation. A detailed study is made of those properties which can be correctly obtained in such a time-dependent mean field theory. Attention is drawn to problems such as the occurrence of spurious states in the asymptotic region, and a simple method for avoiding them is suggested. We find for the I₂(v)Ne vibrational predissociation that the TDSCF compares well with corresponding full dynamics calculations for average single mode properties such as dissociation lifetimes and the translational energy release. Moreover, comparison with classical trajectory calculations shows that the TDSCF method reproduces the essential dynamical mechanism of the dissociation (in-phase impulsive I⋯Ne collision following several ineffective vibrations). The self-consistent bundle trajectories and the time-dependent mean fields are analyzed, and provide insight into the process dynamics. It is concluded that the TDSCF approach in both quantal and quasiclassical versions is a potentially powerful tool in the study of intramolecular energy transfer and unimolecular dissociation.