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Title: A whole-path importance-sampling scheme for Feynman path integral calculations of absolute partition functions and free energies

Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. In this paper, we now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH 4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. Finally, we also show that it is typically possible to reduce the overheadmore » associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function.« less
Authors:
ORCiD logo [1] ; ORCiD logo [1]
  1. Univ. of Minnesota, Minneapolis, MN (United States). Dept. of Chemistry. Chemical Theory Center. Supercomputing Inst.
Publication Date:
Grant/Contract Number:
FG02-86ER13579
Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 144; Journal Issue: 3; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Research Org:
Univ. of Minnesota, Minneapolis, MN (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; generalized functions; particle distributions; free energy; path integral formulation; quantum statistical mechanics; numerical algorithms; Monte Carlo methods; Planck constant; Feynman path integral; statistical thermodynamics
OSTI Identifier:
1469169
Alternate Identifier(s):
OSTI ID: 1235492

Mielke, Steven L., and Truhlar, Donald G.. A whole-path importance-sampling scheme for Feynman path integral calculations of absolute partition functions and free energies. United States: N. p., Web. doi:10.1063/1.4939869.
Mielke, Steven L., & Truhlar, Donald G.. A whole-path importance-sampling scheme for Feynman path integral calculations of absolute partition functions and free energies. United States. doi:10.1063/1.4939869.
Mielke, Steven L., and Truhlar, Donald G.. 2016. "A whole-path importance-sampling scheme for Feynman path integral calculations of absolute partition functions and free energies". United States. doi:10.1063/1.4939869. https://www.osti.gov/servlets/purl/1469169.
@article{osti_1469169,
title = {A whole-path importance-sampling scheme for Feynman path integral calculations of absolute partition functions and free energies},
author = {Mielke, Steven L. and Truhlar, Donald G.},
abstractNote = {Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. In this paper, we now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. Finally, we also show that it is typically possible to reduce the overhead associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function.},
doi = {10.1063/1.4939869},
journal = {Journal of Chemical Physics},
number = 3,
volume = 144,
place = {United States},
year = {2016},
month = {1}
}