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

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 first 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 H 2 + D ⇌ H + HD and H 2 + D 2 ⇌ 2 HD .