Accelerating the convergence and reducing the variance of path integral calculations of quantum mechanical free energies by using local reference Potentials

We present two new methods to accelerate the convergence of Feynman path integral calculations of thermodynamic partition functions. The first enhancement uses information from instantaneous normal mode (INM) calculations to decrease the number of discretized points necessary to represent the Feynman paths and is denoted the local generalized Pitzer-Gwinn (LGPG) scheme. The second enhancement, denoted harmonically guided variance reduction (HGVR), reduces the variance in Monte Carlo (MC) calculations by exploiting the correlation between the sampling error associated with the sum over paths at a particular centroid location for the accurate potential and for the INM approximation of a model potential, the latter of which can be exactly calculated. The LGPG scheme can reduce the number of quadrature points required along the paths by nearly an order of magnitude, and the HGVR scheme can reduce the number of MC samples needed to achieve a target accuracy by more than an order of magnitude. Numerical calculations are presented for H ₂O ₂, a very anharmonic system where torsional motion is important, and H ₂O, a system more amenable to harmonic reference treatment.