A quantitative approximation for the quantum dynamics of hydrogen transfer: Transition state dynamics and decay in ClHCl^-

A general method for studying transition state spectroscopy and dynamics in hydrogen atom transfer reactions is presented. This approach is based on the time-dependent self-consistent field (TDSCF) approximation and is applied to a study of the ClHCl^- photodetachment experiments of Metz et al. [Metz et al., J. Chem. Phys. 88, 1463 (1988)]. Comparison of results of exact time-dependent and TDSCF calculations are made for collinear and three-dimensional (J=0) approximations for the quantum dynamics. When ClHCl is constrained to be collinear, the TDSCF calculation overcorrelates the motions in the H atom displacement and ClCl extension coordinates. This results in relatively poor agreement with the exact result for many properties of the wave function. In contrast, when the system is propagated in the three vibrational coordinates of the system, the transition state dynamics are effectively over much more rapidly. Consequently, the TDSCF approximation yields results of very good quantitative accuracy over the time required for most of the wave function to decay off of the transition state. Comparison is also made between the wave function that results from the exact propagation and from TDSCF when the wave function in the ClCl stretch coordinate is approximated by a Gaussian wave packet. Here the magnitude of the overlap between the two TDSCF. wave functions in the H atom coordinates, for quantum and semiclassical propagations of the wave function in the ClCl distance coordinate, is greater than 0.98 over the time of the propagations. These TDSCF calculations are repeated for a wave function that is approximated by a product of a two-dimensional wave function in the hydrogen atom coordinates and a one-dimensional wave function in the ClCl extension coordinate and even better quantitative agreement with the exact propagation is achieved. The success of this method for studying ClHCl gives us confidence that TDSCF will provide a general powerful tool for studies of hydrogen and proton transfer reactions in large systems.