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

• Published in: The Journal of chemical physics 2006-02, Vol.124 (8), p.084102-084102-9
• Main Authors: Yang, Sandy, Yamamoto, Takeshi, Miller, William H.
• Format: Article
• ISSN: 0021-9606; 1089-7690
• DOI: 10.1063/1.2171693

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.