Quantum-classical reaction rate theory

A correlation function formalism for the calculation of rate constants in mixed quantum-classical systems is presented. The full quantum equilibrium density is retained in the rate expressions and quantum-classical Lionville dynamics is used to propagate the species variables in time. Results for a model two-level system coupled to a nonlinear oscillator that is coupled to a harmonic bath and for a proton transfer reaction in a polar liquid solvent are presented. The rate coefficients for these systems are computed using surface-hopping dynamics based on the solution of the quantum-classical Lionville equation.