Proton distances evaluation

Here AiS - AEi is the solvent reaction coordinate distance between the TS and reactant, and AE - AE is the corresponding distance between the product and reactant, (cp) is the quantum average over the proton and H-bond vibrations of Cp, the limiting product contribution to the electronic structure. The electronic structure for each critical point (c = R, P, and ) is evaluated at the respective critical point position AE (AE = AEp, AEp, or A ) along the reaction coordinate. The structural element is the quantum-averaged proton distance (over both... 

At longer mixing times many hirther contacts become detectable due to spin diffusion that carmot be used for a quantitative evaluation in terms of proton distances. However, these contacts allow a qualitative comparison of equivalent interactions - as e.g. 5 5, 6-6, and 5-6 contacts - between different adjacent nucleotides. 

This simple relaxation theory becomes invalid, however, if motional anisotropy, or internal motions, or both, are involved. Then, the rotational correlation-time in Eq. 30 is an effective correlation-time, containing contributions from reorientation about the principal axes of the rotational-diffusion tensor. In order to separate these contributions, a physical model to describe the manner by which a molecule tumbles is required. Complete expressions for intramolecular, dipolar relaxation-rates for the three classes of spherical, axially symmetric, and asymmetric top molecules have been evaluated by Werbelow and Grant, in order to incorporate into the relaxation theory the appropriate rotational-diffusion model developed by Woess-ner. Methyl internal motion has been treated in a few instances, by using the equations of Woessner and coworkers to describe internal rotation superimposed on the overall, molecular tumbling. Nevertheless, if motional anisotropy is present, it is wiser not to attempt a quantitative determination of interproton distances from measured, proton relaxation-rates, although semiquantitative conclusions are probably justified by neglecting motional anisotropy, as will be seen in the following Section. 

In the above expression, vR and Vp are the frequencies associated with the rath level of reacting proton in the reactant state and the mth level in the product state, and q is the frequency associated with the low-frequency mode developed in the BH model. The term AQ reflects the change in equilibrium distance between the reactant and product states and Cmpm(Q) is the tunneling matrix element from the nth level in the reactant state to the mth level in the product state. An explicit evaluation of the tunneling matrix element Cmpm(Q) is obtained within the WKB semiclassical framework and is given by... 

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