title: Efficient Calculation of Free Energy Differences Associated with Isotopic Substitution Using Path-Integral Molecular Dynamics.
abstract: The problem of computing free energy differences due to isotopic substitution in chemical systems is discussed. The shift in the equilibrium properties of a system upon isotopic substitution is a purely quantum mechanical effect that can be quantified using the Feynman path integral approach. In this paper, we explore two developments that lead to a highly efficient path integral scheme. First, we employ a mass switching function inspired by the work of Ceriotti and Markland [ J. Chem. Phys. 2013, 138, 014112] that is based on the inverse square root of the mass and which leads to a perfectly constant free energy derivative with respect to the switching parameter in the harmonic limit. We show that even for anharmonic systems, this scheme allows a single-point thermodynamic integration approach to be used in the construction of free energy differences. In order to improve the efficiency of the calculations even further, however, we derive a set of free energy derivative estimators based on the fourth-order scheme of Takahashi and Imada [ J. Phys. Soc. Jpn. 1984, 53, 3765]. The Takahashi-Imada procedure generates a primitive fourth-order estimator that allows the number of imaginary time slices in the path-integral approach to be reduced substantially. However, as with all primitive estimators, its convergence is plagued by numerical noise. In order to alleviate this problem, we derive a fourth-order virial estimator based on a transferring of the difference between second- and fourth-order primitive estimators, which remains relatively constant as a function of the number of configuration samples, to the second-order virial estimator. We show that this new estimator converges as smoothly as the second-order virial estimator but requires significantly fewer imaginary time points.
authors.affiliation: Department of Chemistry, New York University , New York, New York 10003, United States.
authors.forename: Ondrej
authors.initials: O
authors.lastname: Marsalek
authors.affiliation: Department of Chemistry, New York University , New York, New York 10003, United States.
authors.forename: Pei-Yang
authors.initials: PY
authors.lastname: Chen
authors.affiliation: Géosciences Environnement Toulouse, OMP-Université Paul Sabatier , 14 avenue Edouard Belin, 31400 Toulouse, France.
authors.forename: Romain
authors.initials: R
authors.lastname: Dupuis
authors.affiliation: CEMES-CNRS-UPR 8011, 29 rue Jeanne Marvig, 31055 Toulouse, France.
authors.forename: Magali
authors.initials: M
authors.lastname: Benoit
authors.affiliation: Géosciences Environnement Toulouse, OMP-Université Paul Sabatier , 14 avenue Edouard Belin, 31400 Toulouse, France.
authors.forename: Merlin
authors.initials: M
authors.lastname: Méheut
authors.affiliation: Department of Chemistry, New York University , New York, New York 10003, United States.|NYU-ECNU Center for Computational Chemistry at NYU Shanghai , Shanghai 200062, China.
authors.forename: Zlatko
authors.initials: Z
authors.lastname: Bačić
authors.affiliation: Department of Chemistry and Courant Institute of Mathematical Sciences, New York University , New York, New York 10003, United States.|Institute for Pure and Applied Mathematics , 460 Portola Plaza, Los Angeles, California 90095, United States.|NYU-ECNU Center for Computational Chemistry at NYU Shanghai , Shanghai 200062, China.
authors.forename: Mark E
authors.initials: ME
authors.lastname: Tuckerman