Transformation from angle-action variables to Cartesian coordinates for polyatomic reactions

Abstract

The transformation from angle-action variables to Cartesian coordinates is an important step of the semiclassical description of bimolecular collisions and photofragmentations. The basic reason is that dynamical conditions corresponding to molecular beam experiments are ideally generated in angle-action variables, whereas the classical equations of motion are ideally solved in Cartesian coordinates by standard numerical approaches. To our knowledge, this transformation is available in the literature only for atom-diatom arrangements. The goal of the present work is to derive it for diatom-polyatom ones. The analogous transformation for any type of arrangement may then be straightforwardly deduced from that presented here.