Transition state theory, Siegert eigenstates, and quantum mechanical reaction rates

The "good" action variables associated with a transition state (i.e., the saddle point of a potential energy surface), on which a general semiclassical transition state theory is based, are shown to be the semiclassical counterpart of the Siegert eigenvalues of the system. (Siegert eigenvalues are the complex eigenvalues of the Schrödinger equation with outgoing wave boundary conditions.) By using flux correlation functions, it is then shown how the exact quantum mechanical reaction rate can be expressed in terms of the Siegert eigenvalues (and eigenfunctions). Applications to some test problems show these Siegert-based rate expressions to be rapidly convergent with respect to the sum over Siegert states.