Efficient calculation of free energy differences associated with isotopic substitution using path-integral molecular dynamics

Ondrej Marsalek, Pei Yang Chen, Romain Dupuis, Magali Benoit, Merlin Méheut, Zlatko Bacic, Mark Tuckerman

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1440-1453
Number of pages14
JournalJournal of Chemical Theory and Computation
Volume10
Issue number4
DOIs
StatePublished - Apr 8 2014

Fingerprint

estimators
Free energy
Molecular dynamics
Substitution reactions
free energy
substitutes
molecular dynamics
Derivatives
Switching functions
Thermodynamics
harmonics
thermodynamics
shift
configurations

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry
  • Computer Science Applications

Cite this

Efficient calculation of free energy differences associated with isotopic substitution using path-integral molecular dynamics. / Marsalek, Ondrej; Chen, Pei Yang; Dupuis, Romain; Benoit, Magali; Méheut, Merlin; Bacic, Zlatko; Tuckerman, Mark.

In: Journal of Chemical Theory and Computation, Vol. 10, No. 4, 08.04.2014, p. 1440-1453.

Research output: Contribution to journalArticle

Marsalek, Ondrej ; Chen, Pei Yang ; Dupuis, Romain ; Benoit, Magali ; Méheut, Merlin ; Bacic, Zlatko ; Tuckerman, Mark. / Efficient calculation of free energy differences associated with isotopic substitution using path-integral molecular dynamics. In: Journal of Chemical Theory and Computation. 2014 ; Vol. 10, No. 4. pp. 1440-1453.
@article{5e95995359c04abd849a612a43f1be95,
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.",
author = "Ondrej Marsalek and Chen, {Pei Yang} and Romain Dupuis and Magali Benoit and Merlin M{\'e}heut and Zlatko Bacic and Mark Tuckerman",
year = "2014",
month = "4",
day = "8",
doi = "10.1021/ct400911m",
language = "English (US)",
volume = "10",
pages = "1440--1453",
journal = "Journal of Chemical Theory and Computation",
issn = "1549-9618",
publisher = "American Chemical Society",
number = "4",

}

TY - JOUR

T1 - Efficient calculation of free energy differences associated with isotopic substitution using path-integral molecular dynamics

AU - Marsalek, Ondrej

AU - Chen, Pei Yang

AU - Dupuis, Romain

AU - Benoit, Magali

AU - Méheut, Merlin

AU - Bacic, Zlatko

AU - Tuckerman, Mark

PY - 2014/4/8

Y1 - 2014/4/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84898410430&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898410430&partnerID=8YFLogxK

U2 - 10.1021/ct400911m

DO - 10.1021/ct400911m

M3 - Article

AN - SCOPUS:84898410430

VL - 10

SP - 1440

EP - 1453

JO - Journal of Chemical Theory and Computation

JF - Journal of Chemical Theory and Computation

SN - 1549-9618

IS - 4

ER -