Extrapolation and perturbation schemes for accelerating the convergence ofquantum mechanical free energy calculations via the Fourier path-integral Monte Carlo method

We present two simple but effective techniques designed to improve the rate of convergence of the Fourier path-integral Monte Carlo method for quantum partition functions with respect to the Fourier space expansion length, K, especially at low temperatures. The first method treats the high Fourier c omponents as a perturbation, and the second method involves an extrapolatio n of the partition function (or perturbative correction to the partition fu nction) with respect to the parameter K. We perform a sequence of calculati ons at several values of K such that the statistical errors for the set of results are correlated, and this permits extremely accurate extrapolations. We demonstrate the high accuracy and efficiency of these new approaches by computing partition functions for H2O from 296 to 4000 K and comparing to the accurate results of Partridge and Schwenke. (C) 2000 American Institute of Physics. [S0021-9606(00)01320-9].