Classical description of the level density and the relaxation behavior of multidimensional molecular curve-crossing systems

Based on the mapping formulation of nonadiabatic dynamics (Phys. Rev. Lett. 1997, 78, 578), explicit classical expressions for the total level density N(E) of a vibronically coupled molecular system as well as quantum corrections to it are derived. The analytical results for N(E) reveal the relative importance of the various molecular parameters of a curve-crossing system, such as the electronic bias, the reorganization energy, and the topology of the potential-energy surfaces. To study the accuracy of the approximate description, numerical studies employing various spin-boson models as well as a two-state, three-mode model of the ultrafast S-2 --> S-1 electronic relaxation in pyrazine are presented. Comparing exact quantum and approximate classical data, the connection between the level density of a vibronically coupled molecular system and its nonadiabatic relaxation behavior is discussed in some detail.