On the Analytical Mechanics of Chemical Reactions. Classical Mechanics of Linear Collisions

Abstract

The classical mechanics of chemically reactive linear collisions is investigated for vibrationally near-adiabatic reactions. A coordinate system which passes smoothly from one suited to the reactants to one suited to the products is used. The Hamilton—Jacobi equation is then solved in the adiabatic approximation by introduction of an ``adiabatic-separable'' method. Nonadiabatic corrections, which describe the probability of vibrational transitions, are also calculated. They involve the Fourier component of local internal centrifugal and vibration frequency-change terms. The reaction coordinate for the adiabatic system is shown to be that curve on which local vibrational and internal centrifugal forces balance pointwise. Applications can be made to the role of translational—vibrational energy interchange in reactions, reaction-cross-section theory, bobsled effect, and other topics. The results may be compared with electronic computer calculations as they become available.