Semiclassical limit of quantum mechanical transition state theory for nonseparable systems

The semiclassical limit of quantum mechanical transition state theory is derived by invoking the classical path approximation for the Boltzmann density operator and making use of the stationary phase approximation; separability of motion along a reaction coordinate is not assumed. The resulting expression for the rate constant bears an interesting similarity to that of conventional transition state theory, although all quantities in it refer to the full classical dynamics on the potential energy surface. In place of the vibrational frequencies of the ’’activated complex’’ which appear in the conventional theory, for example, the semiclassical expression contains characteristic frequencies related to the stability properties of a periodic classical trajectory. Conservation of total angular momentum is easily accounted for in a rigorous manner so that the semiclassical model can be applied to three−dimensional dynamical systems.