Path-integral virial estimator for reaction rate calculation based on the quantum instanton approximation

Abstract

The quantum instanton approximation is a type of quantum transition state theory that calculates the chemical reaction rate using the reactive flux correlation function and its low order derivatives at time zero. Here we present several path-integral estimators for the latter quantities, which characterize the initial decay profile of the flux correlation function. As with the internal energy or heat capacity calculation, different estimators yield different variances (and therefore different convergence properties) in a Monte Carlo calculation. Here we obtain a virial-type estimator by using a coordinate scaling procedure rather than integration by parts, which allows more computational benefits. We also consider two different methods for treating the flux operator, i.e., local-path and global-path approaches, in which the latter achieves a smaller variance at the cost of using second-order potential derivatives. Numerical tests are performed for a one-dimensional Eckart barrier and a model proton transfer reaction in a polar solvent, which illustrates the reduced variance of the virial estimator over the corresponding thermodynamic estimator.

23 pages, 5 figures, 1 table

References in corpus (4)

• Path integral virial estimator based on the scaling of fluctuation coordinates: Application to quantum clusters with fourth-order propagators
• Heat capacity estimators for random series path-integral methods by finite-difference schemes
• Optimal Energy Estimation in Path-Integral Monte Carlo Simulations
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Cited by in corpus (3)

• Direct evaluation of the temperature dependence of the rate constant based on the quantum instanton approximation
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• Accelerating quantum instanton calculations of the kinetic isotope effects