Path integral virial estimator based on the scaling of fluctuation coordinates: Application to quantum clusters with fourth-order propagators

摘要

We first show that a simple scaling of fluctuation coordinates defined interms of a given reference point gives the conventional virial estimator indiscretized path integral, where different choices of the reference point leadto different forms of the estimator (e.g., centroid virial). The merit of thisprocedure is that it allows a finite difference evaluation of the virialestimator with respect to temperature, which totally avoids the need ofhigher-order potential derivatives. We apply this procedure to energy and heatcapacity calculation of the (H_2)_22 and Ne_13 clusters at low temperatureusing the fourth-order Takahashi-Imada and Suzuki propagators. This type ofcalculation requires up to third-order potential derivatives if analyticalvirial estimators are used, but in practice only first-order derivativessuffice by virtue of the finite difference scheme above. From the applicationto quantum clusters, we find that the fourth-order propagators do improve uponthe primitive approximation, and that the choice of the reference point plays avital role in reducing the variance of the virial estimator.