Monte Carlo evaluation of the equilibrium isotope effects using the Takahashi-Imada factorization of the Feynman path integral

Abstract

The Feynman path integral approach for computing equilibrium isotope effects and isotope fractionation corrects the approximations made in standard methods, although at significantly increased computational cost. We describe an accelerated path integral approach based on three ingredients: the fourth- order Takahashi-Imada factorization of the path integral, thermodynamic integration with respect to mass, and centroid virial estimators for relevant free energy derivatives. While the frst ingredient speeds up convergence to the quantum limit, the second and third improve statistical convergence. The combined method is applied to compute the equilibrium constants for isotope exchange reactions H2+D=H+HD and H2+D2=2HD.

References in corpus (5)

• Efficient first-principles calculation of the quantum kinetic energy and momentum distribution of nuclei
• Efficient methods and practical guidelines for simulating isotope effects
• The inefficiency of re-weighted sampling and the curse of system size in high order path integration
• Path integral evaluation of equilibrium isotope effects
• Three applications of path integrals: equilibrium and kinetic isotope effects, and the temperature dependence of the rate constant of the [1,5] sigmatropic hydrogen shift in (Z)-1,3-pentadiene

Cited by in corpus (7)

• Nuclear quantum effects enter the mainstream
• Committee neural network potentials control generalization errors and enable active learning
• High Order Path Integrals Made Easy
• Direct path integral estimators for isotope fractionation ratios
• Accelerating quantum instanton calculations of the kinetic isotope effects
• Accelerating equilibrium isotope effect calculations: I. Stochastic thermodynamic integration with respect to mass
• Accelerating equilibrium isotope effect calculations: II. Stochastic implementation of direct estimators