Generalization of the Activated Complex Theory of Reaction Rates. II. Classical Mechanical Treatment

In its usual classical form, activated‐complex theory assumes a particular expression for the kinetic energy of the reacting system, one being associated with a rectilinear motion along the reaction coordinate. The derivation of the rate expression given in the present paper is based on the general kinetic‐energy expression. A rate equation of the customary form is obtained: $k_{\mathrm{rate}}\mathrm{=(kT/h)}\exp {\mathrm{[-(F‡-F}}^r\mathrm{)/kT]}$ , where F‡ is the free energy of a system constrained to exist on a hypersurface in n‐dimensional space and F^r is the free energy of the reactants. The usual derivation is then reinterpreted, in terms of geodesic normal coordinates, to be somewhat more general than it appears. Normally, rotation—vibration interaction is neglected, as in the above derivation, although not in treatments of some special reactions in the literature for which the centrifugal potential is important. A derivation is given which includes the influence of this centrifugal potential but which omits Coriolis effects.