Products' angular distribution for stereoselective reactions. Simple optical and kinematic considerations

Abstract

The angular distribution of reactive (and also of non-reactive) scattering has been shown to provide useful insights into the steric requirements of chemical reactions. In a simple optical model, the differential scattering cross-section, d²σ_R/d²w, and the differential orientation-dependent cross-section, dσ_R/d cos γ, are both derived from a common opacity function. The angle-dependent line-of-centres model has been used to compute both cross-sections. For the K + CH₃l reaction where the barrier, according to Bernstein, is a linear function of the cosine of the approach angle, the two differential cross-sections are closely related. Within the angle-dependent line-of-centres model one can also re-examine the optical mode analysis of the non-reactive scattering. This suggests a reinterpretation of the variable ‘the potential at the distance of closest approach’ as ‘the energy along the line of centres’. With this interpretation, the systematics in the opacity functions, determined from the observed non-reactive scattering, can be simply accounted for. In particular, for several reactions [e.g. K + CH₃Br, K +(CH₃)₃ CBr] the opacity analysis provides evidence for a [‘cone of nonreaction’] of a primarily geometrical nature reflecting presumably the steric hindrance of the organic group.

In the analysis of the reactivity of oriented molecules it has been shown to be necessary to distinguish carefully between the theoretical steric requirements defined in the molecular frame and the operational orientation defined in the laboratory frame. This distinction is readily implemented using a kinematic model. It is thereby found that for K + oriented CH₃l the reactivity is strongly dependent on the experimental orientation for backwards scattering. This dependence diminishes for less backwards scattering and is practically unobservable for sideways scattering. This loss in selectivity is, however, of purely kinematic origin: for higher impact parameters the relation between a given experimental orientation angle and the theoretical angle of attack is one-to-many. The kinematic model used incorporates an impulsive release of the exoergicity ála the DIPR model. The impulse is not directed along the old bond. A very definite polarization of the Kl angular momentum in the direction perpendicular to the plane of reaction is noted.