Quantum theory of angular momentum coupling in reactive collisions

Quantum scattering theories of chemical reaction usually require, at some stage, a transformation from the quantum states of reactants to those of the products. We show that it is useful to separate this transformation into angular momentum coefficients and translational-vibrational integrals. The angular momentum coefficients thus defined are general kinematic factors, depending only on the masses of the atoms and the product vibrational and translational distances, but not on the particular potential surface. Analytic formulas are derived for these angular momentum coefficients, both for reactions confined to a plane and for three-dimensional motion. Various selection rules, symmetry properties, orthogonality conditions, normalization rules, and recursion relations are derived from these formulas. An efficient and numerically stable method is derived for numerical evaluation of the angular momentum coefficients. Examples are given for several specific reactions and the trends with varying mass combinations are rationalized in terms of limiting cases. These results display the kinematic aspects of angular momentum transfer in chemical reactions. Comparison with classical trajectories, which include both dynamic and kinematic effects, shows the extent to which dynamic effects alter the distributions of rotational and orbital angular momenta from those given by the kinematic effects alone. Finally, the integral for the transformation of the vibrational and radial dependence of the scattering wavefunction is discussed qualitatively.