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

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.