Accelerating equilibrium isotope effect calculations: II. Stochastic implementation of direct estimators

Abstract

Path integral calculations of equilibrium isotope effects and isotopic fractionation are expensive due to the presence of path integral discretization errors, statistical errors, and thermodynamic integration errors. Whereas the discretization errors can be reduced by high-order factorization of the path integral and statistical errors by using centroid virial estimators, two recent papers proposed alternative ways to completely remove the thermodynamic integration errors: Cheng and Ceriotti [J. Chem. Phys. 141, 244112 (2015)] employed a variant of free-energy perturbation called "direct estimators," while Karandashev and Van\'ıček [J. Chem. Phys. 143, 194104 (2017)] combined the thermodynamic integration with a stochastic change of mass and piecewise-linear umbrella biasing potential. Here we combine the former approach with the stochastic change of mass in order to decrease its statistical errors when applied to larger isotope effects, and perform a thorough comparison of different methods by computing isotope effects first on a harmonic model, and then on methane and methanium, where we evaluate all isotope effects of the form ${\mathrm{CH}}_{4-\mathrm{x}}{\mathrm{D}}_{\mathrm{x}}/{\mathrm{CH}}_4$ and ${\mathrm{CH}}_{5-\mathrm{x}}{\mathrm{D}}_{\mathrm{x}}^{+}/{\mathrm{CH}}_5^{+}$, respectively. We discuss thoroughly the reasons for a surprising behavior of the original method of direct estimators, which performed well for a much larger range of isotope effects than what had been expected previously.

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• Efficient methods and practical guidelines for simulating isotope effects
• Direct path integral estimators for isotope fractionation ratios
• Monte Carlo evaluation of the equilibrium isotope effects using the Takahashi-Imada factorization of the Feynman path integral
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• Accelerating equilibrium isotope effect calculations: I. Stochastic thermodynamic integration with respect to mass

Cited by in corpus (1)

• Accelerating equilibrium isotope effect calculations: I. Stochastic thermodynamic integration with respect to mass