A new Fourier path integral method, a more general scheme for extrapolation, and comparison of eight path integral methods for the quantum mechanicalcalculation of free energies

Using an isomorphism of Coalson, we transform five different discretized pa th integral (DPI) methods into Fourier path integral (FPI) schemes. This al lows an even-handed comparison of these methods to the conventional and par tially averaged FPI methods as well as a new FPI method. It also allows us to apply to DPI methods a simple and highly effective perturbative correcti on scheme (previously presented for FPI methods) to account for the error d ue to retaining only a finite number of terms in the numerical evaluation o f the propagator. We find that in all cases the perturbative corrections ca n be extrapolated to the convergence limit with high accuracy by using a co rrelated sequence of affordable calculations. The Monte Carlo sampling vari ances of all eight methods studied are very similar, but the variance of th e perturbative corrections varies markedly with method. The efficiencies of the new FPI method (called rescaled fluctuation FPI) and one of Fourier an alog methods compare favorably with that of the original FPI method. The re scaled fluctuation method not only proves practically successful, but it al so gives insight into the origin of the dominant error in the conventional FPI scheme. (C) 2001 American Institute of Physics.