Monte Carlo Trajectories: The Dynamics of Harpooning in Alkali–Halogen Reactions

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Abstract
An analysis is presented of the dynamical properties of a model meant to represent the “harpooning,” or electron-jump mechanism that has been proposed to describe the alkali-metal–halogen-molecule reactions (M + X2→MX + X). Individual trajectories are computed from classical equations of motion with the starting conditions chosen by Monte Carlo procedures. With 500 or so trajectories for each trial, a comparison can be made with available observations from molecular-beam experiments; the way in which the reaction energy is distributed between kinetic energy of translation and the internal modes of the product, along with a measure of the differential cross section, are of particular concern. The trajectories include a sudden crossing from an initial homopolar surface to a final surface with the long-range forces required of an M+X− bond to simulate electron transfer. Two different potential functions are used as the final surface: one has a phenomenological form to include various types of X–X forces after transition, and the other has a simple induced-dipole term as an interaction of the departing X with the resulting charges (M+,X−). Except for an extreme trial closely approximating pure stripping, nine trials of the first potential failed to agree with experiment. The last potential gave good results for trials of K + Br2,K + I2,Rb + Br2,Rb + I2, and Cs + Br2.