The generalized transition state method

Current theories of unimolecular reaction rates are based on the transition state method which replaces internal reactant dynamics by an assumption of internal equilibrium. The present work is devoted to the development of generalized transition state method which allows effects such as nonergodicity and non-exponential decay to be accounted for within a simple theoretical framework. The derivation is quantum mechanical and not limited by any weak perturbation assumption. An effective hamiltonian is constructed for the reactant dynamics. The loss of amplitude due to reaction is accounted for by a dissipative term in the hamiltonian which is obtained on a phenomenological basis. The diagonalization of the hamiltonian allows the decay of reactant state to be predicted. The decay information is then used to set up a non-markovian master equation which in turn yields the rate coefficient for the reaction. The accuracy of the method is tested in one-dimensional model calculations in which particular attention is paid to decay by quantum mechanical tunneling through a potential barrier.