Quantum phase space theory for the calculation of v⋅j vector correlations

Abstract

The quantum state-counting phase space theory commonly used to describe ‘‘barrierless’’ dissociation is recast in a helicity basis to calculate photofragment v⋅j correlations. Counting pairs of fragment states with specific angular momentum projection numbers on the relative velocity provides a simple connection between angular momentum conservation and the v⋅j correlation, which is not so evident in the conventional basis for phase space state counts. The upper bound on the orbital angular momentum, l, imposed by the centrifugal barrier cannot be included simply in the helicity basis, where l is not a good quantum number. Two approaches for an exact calculation of the v⋅j correlation including the centrifugal barrier are described to address this point, although the simpler helicity state count with no centrifugal barrier correction is remarkably good in many cases. An application to the photodissociation of NCCN is consistent with recent classical phase space calculations of Klippenstein and Cline. The experimentally observed vector correlation exceeds the phase space theory prediction. We take this as evidence of incomplete mixing of the K states of the linear parent molecule at the transition state, corresponding to an evolution of the body-fixed projection number K into the total helicity of the fragment pair state. The average over a thermal distribution of parent angular momentum in the special case of a linear molecule does not significantly reduce the v⋅j correlation below that computed for total J=0. Predictions of the v⋅j correlations for the unimolecular dissociation of NCNO and CH2CO are also provided.