Isotopic fractionation in proteins as a measure of hydrogen bond length

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.Comment: Final version, accepted for publication in Journal of Chemical Physics. Minor changes, including more extensive discussion of relevant of model to protein

Effect of quantum nuclear motion on hydrogen bonding

This work considers how the properties of hydrogen bonded complexes, D-H....A, are modified by the quantum motion of the shared proton. Using a simple two-diabatic state model Hamiltonian, the analysis of the symmetric case, where the donor (D) and acceptor (A) have the same proton affinity, is carried out. For quantitative comparisons, a parametrization specific to the O-H....O complexes is used. The vibrational energy levels of the one-dimensional ground state adiabatic potential of the model are used to make quantitative comparisons with a vast body of condensed phase data, spanning a donor-acceptor separation (R) range of about 2.4-3.0 A, i.e., from strong to weak bonds. The position of the proton and its longitudinal vibrational frequency, along with the isotope effects in both are discussed. An analysis of the secondary geometric isotope effects, using a simple extension of the two-state model, yields an improved agreement of the predicted variation with R of frequency isotope effects. The role of the bending modes in also considered: their quantum effects compete with those of the stretching mode for certain ranges of H-bond strengths. In spite of the economy in the parametrization of the model used, it offers key insights into the defining features of H-bonds, and semi-quantitatively captures several experimental trends.Comment: 12 pages, 8 figures. Notation clarified. Revised figure including the effect of bending vibrations on secondary geometric isotope effect. Final version, accepted for publication in Journal of Chemical Physic

Alkyl hydrogen atom abstraction reactions of the CN radical with ethanol

We present a study of the abstraction of alkyl hydrogen atoms from the beta and alpha positions of ethanol by the CN radical in solution using the Empirical Valence Bond (EVB) method. We have built separate 2 x 2 EVB models for the H-beta and H-alpha reactions, where the atom transfer is parameterized using ab initio calculations. The intra- and intermolecular potentials of the reactant and product molecules were modelled with the General AMBER Force Field, with some modifications. We have carried out the dynamics in water and chloroform, which are solvents of contrasting polarity. We have computed the potential of mean force for both abstractions in each of the solvents. They are found to have a small and early barrier along the reaction coordinate with a large energy release. Analyzing the solvent structure around the reaction system, we have found two solvents to have little effect on either reaction. Simulating the dynamics from the transition state, we also study the fate of the energies in the HCN vibrational modes. The HCN molecule is born vibrationally hot in the CH stretch in both reactions and additionally in the HCN bends for the H-alpha abstraction reaction. In the early stage of the dynamics, we find that the CN stretch mode gains energy at the expense of the energy in CH stretch mode. Published by AIP Publishing

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