The Interpretation of Lanthanide-Induced Shifts in 1H Nuclear The Interpretation of Lanthanide-Induced Shifts in 1H Nuclear Magnetic Resonance Spectra Magnetic Resonance Spectra

Summary Owing to the present accuracy of the data and various other factors, it is easy to obtain agreement with experimental results for lanthanide-induced shifts in lH n.m


The Interpretation of Lanthanide-induced Shifts in lH Nuclear Magnetic
Resonance Spectra By J. GOODISMAN and R. S. MATTHEWS* (Department of Chemistry, Syracuse University, Syracuse, New York, 13210) Summary Owing to the present accuracy of the data and various other factors, it is easy to obtain agreement with experimental results for lanthanide-induced shifts in lH n.m.r. spectra; some considerations in the formulation of such models which have been ignored previously are discussed.

LANTHANIDE-INDUCED
shifts are of considerable value in resolving n.ni.r. spectra of molecules containing various functional groups,lt2 although there is disagreement over the interpretation of the numerical values of the shifts. We here discuss certain facts which have been ignored previously. If the induced shift is pseudo-contact in nature, its value (8) is given by equation (l), where r is the lanthanideproton distance, and X is the angle between the principal magnetic axis of the complex and a vector from the magnetic moment to the proton. This equation assumes cylindrical symmetry about the bond from the substrate to the complex, which while reasonable, has not been verified. K depends on the concentrations of the lanthanide complex and the alcohol, the g-value of the ion, etc.
Equation ( has been ascribed to neglect of the angular factor 3 cos2 x x -1. We point out that measurement of the distance to oxygen rather than to the lanthanide ion also causes a decrease in this quantity. Since the distance Y (H-Eu) will in general be greater than the .p (O-H), one can write The effect of variation in angle is again neglected. If the shifts actually decrease as (i' + d)-3 they will fall off less quickly than the inverse cube as a function of 9. Indeed, any slope desired can be obtained by plotting log 6 us. ? + d and varying d , and the slope of -3 is obtained for adamantan-2-01 for d 3. 19 A. This is significantly larger than Eu-0 distances suggested by Sanders and WilliamslO and by Briggs et aE.,s so this formula also simulates an angular effect. We introduce it only to point out a danger in believing a model on the basis of log-log plots, since the quality of the fit to a straight line as measured by the residuals log &log Scale (see Table 1) is not greatly affected.
It is easy to obtain straight lines with low residuals in log-log plots for this kind of data so a fit of this kind may not be significant. While the residuals are generally < 0-1,  corresponding to errors of < lo%, log 6 values vary only over a range of ca. 1.5 units. Further, for any particular molecule for the protons the angular factors and the distances from oxygen (or Eu) are not independent since the molecular structure causes some correlation between them. E.g., if the magnetic axis is the molecular axis, for rigid molecules, x will be closer to zero for distant protons, and so 3cos2x -1 will be larger, while for flexible molecules the distant protons will be able to move off the axis and so the angular factor will be smaller. Finally, the effect on the shift of the change in Y is likely to dominate the effect of the angular factors because of the dependence upon y 3 .
The apparent slope of the plots of In 8 vs. In V should reflect molecular structure however. For the model in the preceding paragraph, rigid molecules give rise to slopes of greater than -3 and flexible molecules slopes less than -3. The deviation from -3 reflects, among other things, the angular effect, and we have found slopes greater than -3 for all published data on rigid molecules. For flexible molecules such as n-hexanol and heptanol, we calculated the proton-oxygen distance as a root-mean-square average over the configurations generated by free rotation about the incervening bonds, by the methods in ref. 9. In the present case, we assume tetrahedral bond angles and C-0, C-C, and C-H distances of 1.43, 1.59, and 1.lOA respectively. Table 2 gives calculated mean square distances and The shifts (in p.p.m.) for the protons on the rigid part of the molecule obey equation (2).

2)
The shift of 1.9p.p.m. for the side chain proton corresponds to Y = 20 A, so the shift falls off more quickly with Y than for the other protons, as expected.
Attempts have been made to fit spectra to more detailed models. Thus, Briggs, Hart, and Moss* considered the shift in borneol due to praseodymium THD. Three structural parameters together with K (equation 1) were varied to fit the 10 measured shifts. The C(0H)H shift was excluded although its value was quite well predicted from parameters determined from the others. They obtained a reasonable fit (see Table 3), but in light of some good fits obtained above using 6 = KTa this cannot be taken as proof of the model. As an experiment, we calculated a least-squares fit of the dependence of the logarithms of the ten shifts upon an expression with a quadratic dependence upon log f , the    Table 1 The flexible chain in this case consists of six carbon atoms, so the distance from the metal should be (see Table 2) ca. 5 A more than for the C(18) methyl proton, i.e., ca. 14 A. of -3.6.
proton-oxygen distance, a physically unreal procedure (see Table 3 It is thus difficult to derive a model in terms of its ability to fit the observed shifts. If there are three or more parameters in the model, the average error should be much less than 1 p.p.m. for the agreement to be considered good. This in no way implies that the model of Briggs et al. is incorrect, of course, since the poorer agreement may be due to errors in the measurement of the shifts (lo%, but may be as high as 50Yo6 for small shifts). This is especially true if one uses a dilution study to extrapolate the chemical shifts for each proton in the absence of the lanthanide reagent (e.g. ref. 4) since Shapiroll has recently shown conclusively that such dilution curves are not linear a t low concentrations of the reagent. Such problems and/or the presence of effects other than the pseudocontact shift may make it impossible to get highly acccurate values for the pseudocontact shift for comparison of experimental and theoretical results. Nevertheless, no model, however