%0 Journal Article
%T Isotopic fractionation in proteins as a measure of hydrogen bond length
%A Ross H. McKenzie
%A Bijyalaxmi Athokpam
%A Sai Ramesh
%J Quantitative Biology
%D 2015
%I arXiv
%R 10.1063/1.4927391
%X If a deuterated molecule containing strong intramolecular hydrogen bonds is placed in a hydrogenated solvent it may preferentially exchange deuterium for hydrogen. This preference is due to the difference between the vibrational zero-point energy for hydrogen and deuterium. It is found that the associated fractionation factor $\Phi$ is correlated with the strength of the intramolecular hydrogen bonds. This correlation has been used to determine the length of the H-bonds (donor-acceptor separation) in a diverse range of enzymes and has been argued to support the existence of short low-barrier H-bonds. Starting with a potential energy surface based on a simple diabatic state model for H-bonds we calculate $\Phi$ as a function of the proton donor-acceptor distance $R$. For numerical results, we use a parameterization of the model for symmetric O-H.... O bonds. We consider the relative contributions of the O-H stretch vibration, O-H bend vibrations (both in plane and out of plane), tunnelling splitting effects at finite temperature, and the secondary geometric isotope effect. We compare our total $\Phi$ as a function of $R$ with NMR experimental results for enzymes, and in particular with an empirical parametrisation $\Phi(R)$, used previously to determine bond lengths.
%U http://arxiv.org/abs/1504.04939v2