Romain Dupuis

+34 694476999
DIPC, Paseo Manuel de Lardizabal, 4. 20018 SAN SEBASTIÁN

J. Chem. Theory Comput., 2014, 10 (4), pp 1440–1453

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 ; Bačić, Zlatko ; Tuckerman, Mark E.


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. 2013138, 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. 198453, 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.

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