Coupled-Channels Approach to the Quantum-Mechanical Treatment of Chemical Exchange Reactions

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Abstract
A formalism for the quantum-mechanical treatment of chemical exchange reactions of the type A+BC→AB+C based on the coupled-channels technique of solving the Schrödinger equation is developed. Essentially, the method consists of expanding the stationary-state wavefunction describing the reaction as a linear combination of linearly independent functions satisfying the relevant Schrödinger equation and also initial conditions specified on a “surface” of a particular arrangement channel. These linearly independent functions are generated by integrating the close-coupled equations throughout the various arrangement channels successively for linearly independent sets of initial conditions. The formalism is explicitly derived for collinear, electronically adiabatic encounters below the three-particle threshold. It is then applied to a simplified model for symmetric exchange reactions in which the center atom is very massive. The calculated transition and reaction probabilities are in agreement with recently reported results for the same model.