Quantum mechanical canonical rate theory: A new approach based on the reactive flux and numerical analytic continuation methods

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Abstract
We present the reactive flux analytic continuation (RFAC) method, based on the quantum reactive flux formalism combined with a numerical analytic continuation approach to calculate quantum canonical rates in condensed phase systems. We express the imaginary time reactive-flux correlation function in terms of a frequency dependent rate constant, and use path integral formalism to derive a working expression suitable for Monte Carlo simulation techniques. The imaginary time data obtained by simulation is analytically continued to the real time using the maximum entropy method to obtain the reaction rate. Motivated by the success of the method to predict the rates for a simple one dimensional parabolic barrier model, we assess its accuracy for a condensed phase reaction modeled by a double-well coupled to a harmonic bath. We note that the method is applicable to a more general Hamiltonian as long as the reaction coordinate can be identified. The reaction rates computed in this fashion are in very good agreement with analytic and numerically exact results. We demonstrate the applicability of the method for a wide range of model parameters and temperatures.