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 Φ 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 Φ 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 [R. H. McKenzie, Chem. Phys. Lett. 535, 196 (2012)]. We consider the relative contributions of the O–H stretch vibration, O–H bend vibrations (both in plane and out of plane), tunneling splitting effects at finite temperature, and the secondary geometric isotope effect. We compare our total Φ as a function of R with NMR experimental results for enzymes, and in particular with an earlier model parametrization Φ(R), used previously to determine bond lengths.
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One might also consider whether the fact that X-ray crystal structures are refined with classical molecular dynamics using force fields that are parametrised for weak H-bonds may also be a problem. Such refinements may naturally bias towards weak bonds, i.e., the longer bond lengths that are common in proteins.
