Generalization of Activated-Complex Theory. III. Vibrational Adiabaticity, Separation of Variables, and a Connection with Analytical Mechanics

Abstract

In Part I, activated‐complex theory was extended by including the possibility of a curvilinear reaction coordinate. A separation‐of‐variables approximation was made in the neighborhood of the activated‐complex region of configuration space. In the present paper a more general yet simpler derivation of the final equation is given. It permits subsequent introduction of analytical mechanics in the above neighborhood in a variety of ways such as separation of variables, vibrational adiabaticity, or a method combining certain features of both, the separable—adiabatic approximation. The relationship of these methods is discussed. Some numerical quantum‐ and classical‐mechanical results obtained for transmission coefficients of nonrotating atom‐transfer reactions (linear complexes), using computers, are interpreted in terms of an adiabatic approximation with reasonable agreement. Attention is also called to a modified WBK expression for the transmission coefficient, which generalizes the usual WBK formula in a simple way.