Quantum dynamical stereochemistry of atom–diatom reactions

Abstract

We have used density matrix techniques and angular momentum algebra to obtain quantum–mechanical equations describing the dynamical stereochemistry of the atom–diatom reaction A+BC⇌AB+C. The relative motions of reagents and products are specified by four vectors: rotational angular momenta of diatomic molecules and relative velocities of reagents and products. Our equations show how the correlations between the spatial distributions of these four vectors are related to the scattering matrix determined in quantum scattering calculations. We present three different expressions for the four-vectors correlation. One of them is appropriate to the helicity representation of the scattering matrix, while the others are appropriate to the orbital angular momentum representation with either space-fixed or body-fixed reference frames. The formulation adopted allows for a rigorous comparison between theory and experiment. It takes mixed quantum–mechanical states and unobserved quantum-numbers into account, and all vector distributions are expressed in terms of measurable quantities (scattering angles and polarization moments of rotational angular momenta). Explicit expressions for most of the lower-order vector correlations obtained by direct reduction of the four-vectors correlation formulas are also presented.