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

The analytical quantum mechanics of chemically reactive linear collisions is treated in the vibrationally near-adiabatic approximation. The ``reaction coordinate'' in this approximation is found to be the curve on which the classical local vibrational and internal centrifugal forces balance. Expressions are obtained for the calculation of transmission coefficients for these nonseparable systems. Some implications for tunneling calculations in the literature are noted. Expressions for nonadiabatic corrections are derived, the latter being associated with vibrational transitions undergone by the transmitted and reflected waves. When the system does not have enough energy to react, the last results refer to the vibration—translation energy-transfer problem in linear collisions. Two novel features are the introduction of an actual coordinate system which passes smoothly from one suited to reactants to one suited to products and the introduction of an adiabatic-separable method, a method which includes curvilinear effects. Extensions to collisions in higher dimensions are given in later papers.