Quantum-Mechanical Calculation of the Probability of an Exchange Reaction for Constrained Linear Encounters

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Abstract
A numerical procedure suitable for use with a high‐speed computing machine is developed for calculating the average quantum‐mechanical probability of the exchange reaction BC+A→B+CA for constrained linear encounters at temperature T when BC is initially in its ground or first excited vibrational state. The average refers to the average over the relative momentum frequency distribution of collisions between BC and A at temperature T. The procedure, which involves the numerical solution of the time‐dependent Schrödinger equation, is sufficiently general so that any three‐atom potential energy surface may be used. Two sample calculations have been performed using a simple potential energy surface. The results of these quantum‐mechanical calculations for the average probability of reaction are compared with the corresponding classical quantities which are obtained in an elementary fashion.

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