An integrated path integral and free-energy perturbation-umbrella sampling method for computing kinetic isotope effects of chemical reactions in solution and in enzymes

An integrated centroid path integral and free-energy perturbation-umbrella sampling (PI-FEP/UM) method for computing kinetic isotope effects (KIEs) for chemical reactions in solution and in enzymes is presented. The method is based on the bisection sampling in centroid path integral simulations to include nuclear quantum effects to the classical potential of mean force. The required accuracy for computing kinetic isotope effects is achieved by coupled free-energy perturbation and umbrella sampling for reactions involving different isotopes. The use of FEP with respect to different masses results in relatively small statistical uncertainties, whereas if KIEs are computed directly by the difference in free energies obtained from the quantum mechanical potentials of mean force for different isotopes, the statistical errors are significantly greater. The PI-FEP/UM method is illustrated in two applications. The first reaction is the decarboxylation of N-methyl picolinate in water, for which the primary ¹³C and secondary ¹⁵N KIEs have been determined. The second reaction is the proton-transfer reaction between nitroethane and an acetate ion in water. In both cases, the computational results are in accord with experimental data, and the findings provide further insight into the mechanism of these reactions in water.