Optical Model Analysis of Nonreactive Collisions of Reactive Molecules: Scattering of K, Rb, and Cs from CCl4, CH3I, and SnCl4

Abstract

Crossed beam studies of nonreactive scattering of K, Rb, and Cs atoms from CCl4, CH3I, and SnCl4 have been carried out and the differential cross sections compared with calculations based on a phenomenological optical model analysis. The models employed make use of a parameterized “reference” potential which is intended both to represent a multipole expansion of the potential surface of the reactants for internuclear distances greater than the radius of chemical interaction, and to provide a systematic means of calculating the real parts of the optical phase shifts. A new semiclassical method for calculating nonreactive differential cross sections for an isotropic central potential (reference) and a parameterized probability of reaction (opacity) function, P(β), is presented and applied to the scattering of M+CCl4. It is found that the observed cross sections are consistent with a Lennard-Jones reference potential and a P(β) which is a rounded-off step function. A better description of the reactivity for these systems was obtained by expressing the opacity function in terms of y, the reduced distance of closest approach, instead of the impact parameter β. The velocity dependence of the opacity function was virtually removed upon making this transformation, and the reactivity for a given alkali atom was found to resemble a diffuse “black sphere” of radius yc, the opacity becoming less diffuse in the order Cs<Rb<K. The optical model has been extended to include an anisotropic term in the reference potential for analysis of the nonreactive scattering of M+CH3I. The magnitude of the anisotropic term was found to be much larger than that predicted from long-range dispersion forces alone. It is shown that the large anisotropy can account for the sudden decrease in the wide angle nonreactive scattering, which was previously interpreted as a reaction threshold angle. Probability of reaction functions were derived from the data, and the results were consistent with the steric effect found in experiments which employ oriented CH3I molecules. The cross sections for M+SnCl4 are interpreted on the basis of orbiting from an “electron jump” potential, which is the adiabatic potential resulting from the crossing of covalent (M+SnCl4) and ionic (M++SnCl4−) curves. Parameters for the potential are extracted from the data and used to estimate the electron affinity of the SnCl4 molecule. The value obtained, 2.1 ± 0.2, is in fair agreement with a recent estimate from direct measurement of the threshold for ion-pair formation.