Steric effects and cones of reaction in gas-phase reactions

Information on steric effects is most easily seen through the dependence of the molecule-fixed reaction cross section on the mutual orientation of the reactants. However, the observed cross sections in oriented molecule molecular beam reactions are laboratory-fixed quantities and depend on the orientation of the ‘‘diatom’’ with respect to the relative velocity of the atom–diatom collision pair. In this work, the laboratory-fixed cross section has been determined using the venerable line of centers model for two idealized potentials which describe the dependence of the threshold energy on reactant orientation. For the painted-sphere and the linear-barrier model (here, a painted sphere with a linear dependence on the cosine of the angle of attack), the molecule-fixed cross section is nearly trivial whereas the laboratory-fixed cross section is not. In the painted-sphere model, the orientation-dependent laboratory-fixed cross section was calculated analytically and exactly and is accurately approximated by a three-term Legendre expansion. For the painted sphere with the linear barrier, we have calculated the critical angle at which the laboratory-fixed cross section vanishes. This critical angle is the laboratory-fixed cone of reaction and is in contrast with the molecule-fixed, true steric cone. At high energies, the laboratory-fixed cross section for the linear-barrier potential was represented as an energy-corrected painted-sphere model. In the energy-corrected painted-sphere approximation, the anisotropy moments of the laboratory-fixed cross section illustrate the properties of the barrier and the cone of reaction.