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In its usual classical form activated complex theory assumes a particular expression for the kinetic energy of the reacting system one 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.

In its usual form activated complex theory assumes a quasi-equilibrium between reactants and activated complex, a separable reaction coordinate, a Cartesian reaction coordinate, and an absence of interaction of rotation with internal motion in the complex. In the present paper a rate expression is derived without introducing the Cartesian assumption. The expression bears a formal resemblance to the usual one and reduces to it when the added assumptions of the latter are introduced. The new equation for the transmission coefficient contains internal centrifugal terms. The derivation employs an extension of the Stackel-Robertson formalism for separation of variables in mechanics. The fourth assumption can also be weakened and a rotational interaction included in the formalism. In applications of the rate equation use is made of the recent findings that in the immediate vicinity of a saddle-point or a minimum a potential energy surface can be imitated in some major topographical respects by a surface permitting separation of variables. The separated wave equation for the reaction coordinate is then curvilinear because of the usual curvature of the path of steepest ascent to the saddle-point. Calculations of transmission coefficients and rates can be made and compared with those obtainable from the usual one-dimensional …