Dipolar couplings interactions

For a rigidly held, three-spin system, or when existing internal motion is very slow compared to the overall molecular tumbling, all relaxation methods appear to be adequate for structure determination, provided that the following assumptions are valid (a) relaxation occurs mainly through intramolecular, dipolar interactions between protons (b) the motion is isotropic and (c) differences in the relaxation rates between lines of a multiplet are negligibly small, that is, spins are weakly coupled. This simple case is demonstrated in Table V, which gives the calculated interproton distances for the bicycloheptanol derivative (52) of which H-1, -2, and -3 represent a typical example of a weakly coupled, isolated three-spin... 

The NOESY spectrum of 7-hydroxyfrullanolide reveals the spatial proximities between the various protons. Cross-peak D arises from the gemi-nal coupling between the exomethylenic geminal protons (8 5.71 and 6.06). Dipolar interaction between the 06 proton (8 4.97) and the allylic methyl protons (8 1.64) is inferred from cross-peak C. This interaction is possible only when the C-6 proton is a-oriented. The C-1/3 and 02/8 protons (8 1.31 and 1.45, respectively) exhibit cross-peaks... 

Instead of measuring only the time-dependent dipolar interaction via NOE, it is also possible to determine dipolar couplings directly if the solute molecule is partially aligned in so-called alignment media. The most important resulting anisotropic parameters are RDCs, but residual quadrupolar couplings (RQCs), residual chemical shift anisotropy (RCSA) and pseudo-contact shifts (PCSs) can also be used for structure determination if applicable. 

Nuclear spins can be considered as dipoles that interact with each other via dipolar couplings. While this interaction leads to strongly broadened lines in soUd-state NMR spectroscopy, it is averaged out in isotropic solution due to the fast tumbUng of the solute molecules. In Uquid-state NMR spectroscopy, the dipolar interaction can only be observed indirectly by relaxation processes, where they represent the main source of longitudinal and transverse relaxation. 

It is well-known that the hyperfine interaction for a given nucleus A consists of three contributions (a) the isotropic Fermi contact term, (b) the spin-dipolar interaction, and (c) the spin-orbit correction. One finds for the three parts of the magnetic hyperfine coupling (HFC), the following expressions [3, 9] ... 

In the solid, dynamics occurring within the kHz frequency scale can be examined by line-shape analysis of 2H or 13C (or 15N) NMR spectra by respective quadrupolar and CSA interactions, isotropic peaks16,59-62 or dipolar couplings based on dipolar chemical shift correlation experiments.63-65 In the former, tyrosine or phenylalanine dynamics of Leu-enkephalin are examined at frequencies of 103-104 Hz by 2H NMR of deuterated samples and at 1.3 x 102 Hz by 13C CPMAS, respectively.60-62 In the latter, dipolar interactions between the 1H-1H and 1H-13C (or 3H-15N) pairs are determined by a 2D-MAS SLF technique such as wide-line separation (WISE)63 and dipolar chemical shift separation (DIP-SHIFT)64,65 or Lee-Goldburg CP (LGCP) NMR,66 respectively. In the WISE experiment, the XH wide-line spectrum of the blend polymers consists of a rather featureless superposition of components with different dipolar widths which can be separated in the second frequency dimension and related to structural units according to their 13C chemical shifts.63... 

Whenever the system is no longer constituted by single non-interacting spins, the simple Bloch Equation (2) must be completed by additional coupling terms. Let us consider the dipolar interaction between two spins... 

The coupling term, traditionally denoted by cr B (which has however nothing to do with the screening coefficient of Section 2.2), is the so-called cross-relaxation rate and is a relaxation parameters which depends exclusively on the dipolar interaction between nuclei A and B, contrary to auto-relaxation rates which are compounds of several contributions. For instance, if A is a carbon-13, the auto-relaxation rate can always be written as... 

Further complicating the situation is the fact that the same term can arise from two quite different physical effects electron-electron dipolar interaction and spin-orbit coupling. 

We now will show that spin-orbit coupling can give a spin Hamiltonian term identical to that we obtained from the electron dipolar interaction. Consider the... 

Notice that the fine structure term found here has the same form (and the tensor is given the same symbol) as that obtained from the electron dipolar interaction. Unlike the dipolar D-tensor, however, the spin-orbit coupling D-tensor in general does not have zero trace. Nonetheless, we introduce analogous parameters ... 

Although it is unfortunate that spin-orbit coupling and the electron dipolar interaction give fine structure terms of the same form, it is possible to separate the effects. Since the spin-orbit contribution to D is related to the g-tensor ... 

Aniosotropic hyperfine coupling results primarily from dipolar interactions between a magnetic nucleus and an unpaired electron in a p, d, or f orbital. Such interactions give rise to a Hamiltonian... 

It should now be evident that the experimental tensor may be expressed as the sum of an isotropic term resulting from the contact interaction, and a tensor resulting from dipolar interactions and any indirect coupling via the orbital angular momentum. This may be written in the form of an equation ... 

NMR of solids usually give broad featureless absorptions due to the dipolar interactions which, at least in the case of protons, are orders of magnitude larger than the characteristic chemical shifts and spin-spin couplings used for structure elucidation... 

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