Document Type


Date of Original Version



We perform a thorough analysis on the choice of estimators for random series path integral methods. In particular, we show that both the thermodynamic (T-method)and the direct (H-method)energy estimators have finite variances and are straightforward to implement. It is demonstrated that the agreement between the T-method and the H-method estimators provides an important consistency check on the quality of the path integral simulations. We illustrate the behavior of the various estimators by computing the total, kinetic, and potential energies of a molecular hydrogen cluster using three different path integral techniques. Statistical tests are employed to validate the sampling strategy adopted as well as to measure the performance of the parallel random number generator utilized in the Monte Carlo simulation. Some issues raised by previous simulations of the hydrogen cluster are clarified.

Publisher Statement

© 2003 American Institute of Physics.This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Predescu, Cristian, Dubravko Sabo, J. D. Doll and David L. Freeman. ʺEnergy Estimators for Random Series Path-Integral Methods.ʺ Journal of Chemical Physics. 119(20):10475-10488. 22 November 2003.and may be found at