A theoretical study of intra-molecular vibrational effects on fractionation factors for molecules containing intra-molecular low-barrier hydrogen bonds

The fractionation factor is defined as the equilibrium constant for the reaction; R-H+DOH ⇌ R-D+HOH. Of interest are values of fractionation factors that obtain for reactions where reactants and/or products form intra-molecular low-barrier hydrogen bonds. Experimentally measured isotopic fractionation factors are usually interpreted via a one-dimensional potential energy surface along the intrinsic proton hydrogen bond coordinate. Here we show that coupling the intrinsic proton coordinate to an intra-molecular vibrational mode has large effects on the values of isotopic fractionation factors and offer a picture for the fractionation factor for low-barrier hydrogen bonds based on the one-dimensional potential of mean force on the intrinsic proton coordinate.