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The quantum instanton approximation is a type of quantum transition statetheory that calculates the chemical reaction rate using the reactive fluxcorrelation function and its low order derivatives at time zero. Here wepresent several path-integral estimators for the latter quantities, whichcharacterize the initial decay profile of the flux correlation function. Aswith the internal energy or heat capacity calculation, different estimatorsyield different variances (and therefore different convergence properties) in aMonte Carlo calculation. Here we obtain a virial-type estimator by using acoordinate scaling procedure rather than integration by parts, which allowsmore computational benefits. We also consider two different methods fortreating the flux operator, i.e., local-path and global-path approaches, inwhich the latter achieves a smaller variance at the cost of using second-orderpotential derivatives. Numerical tests are performed for a one-dimensionalEckart barrier and a model proton transfer reaction in a polar solvent, whichillustrates the reduced variance of the virial estimator over the correspondingthermodynamic estimator.Comment: 23 pages, 5 figures, 1 tabl

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