Differential reaction cross sections from rotationally resolved quantum scattering calculations: application to gas-phase SN2 reactions

Abstract

Differential reaction cross sections have been computed based on previous rotationally resolved time-independent quantum-mechanical scattering calculations for the complex-forming S_N2 reaction Cl⁻ + CH₃Br → ClCH₃ + Br⁻. The results show almost isotropic cross sections for reactant molecules with high rotational quantum numbers. Backward scattering is disfavoured for reaction out of states with small rotational excitation, in particular the rovibrational ground state. This is a quantum-mechanical effect (interference of partial waves) that can partly be rationalized by simple classical arguments. In particular for higher vibrational excitations, an umbrella effect can be observed that favours the backward direction. It can be explained by the strong enhancement of the reactivity by opening a direct mechanism. The ion–dipole interaction exerts a torque onto the molecule which carries out a rotation by about 90° and then completes the reaction.