Stationary phase evaluations of quantum rate constants.

We compute the quantum rate constant based on two extended stationary phase approximations to the imaginary-time formulation of the quantum rate theory. The optimized stationary phase approximation to the imaginary-time flux-flux correlation function employs the optimized quadratic reference system to overcome the inaccuracy of the quadratic expansion in the standard stationary phase approximation, and yields favorable agreements with instanton results for both adiabatic and nonadiabatic processes in dissipative and nondissipative systems. The integrated stationary phase approximation to the two-dimensional barrier free energy is particularly useful for adiabatic processes and demonstrates consistent results with the imaginary-time flux-flux correlation function approach. Our stationary phase methods do not require calculation of tunneling paths or stability matrices, and work equally well in the high-temperature and the low-temperature regimes. The numerical results suggest their general applicability for calibration of imaginary-time methods and for the calculation of quantum rate constants in systems with a large number of degrees of freedom.