Quantum mechanical transition state theory and a new semiclassical model for reaction rate constants

An ``exact'' quantum mechanical transition state theory is defined, i.e., a model which invokes the basic transition state idea to calculate the rate of a chemical reaction but which is free of any auxiliary approximations. Most importantly, for example, it is not necessary to assume that the Hamiltonian is separable about the saddle point. It is argued that this model should provide an accurate description of the threshold region of the reaction where quantum effects are most significant. Finally, an even more general model, a new kind of semiclassical approximation, is presented which is essentially a synthesis of this quantum mechanical transition state model and the completely classical trajectory procedure for determining the rate constant; at sufficiently high temperatures, quantum effects become negligible, so that the correct rate constant is obtained; while at low temperature, the correct result is obtained because the transition state model becomes valid.