Generalized dipolar coupling

As anticipated in Sections 2.2.2 and 3.1, the unpaired electrons should not be considered as point-dipoles centered on the metal ion. They are at the least delocalized over the atomic orbitals of the metal ion itself. The effect of the deviation from the point-dipole approximation under these conditions is estimated to be negligible for nuclei already 3-4 A away [31]. Electron delocalization onto the ligands, however, may heavily affect the overall relaxation phenomena. In this case the experimental Rm may be higher than expected, and the ratios between the Rim values of different nuclei does not follow the sixth power of the ratios between metal to nucleus distances. In the case of hexaaqua metal complexes the point-dipole approximation provides shorter distances than observed in the solid state (Table 3.2) for both H and 170. This implies spin density delocalization on the oxygen atom. Ab initio calculations of R m have been performed for both H and 170 nuclei in a series of hexaaqua complexes (Table 3.2). The calculated metal nucleus distances in the assumption of a purely metal-centered dipolar relaxation mechanism are sizably smaller than the crystallographic values for 170, and the difference dramatically increases from 3d5 to 3d9 metal ions [32]. The differences for protons are quite smaller [32]. 

R m calculations in the presence of ligand-centered contributions are possible for metal complexes with ligands having dominant ti spin density delocalization mechanisms. With certain approximations, the relaxation rates of protons and carbon atoms in sp2 CH moieties can be expressed [33-35] as the sum of a 

Crystallographic values of metal-hydrogen and metal-oxygen distances in hexaaqua complexes of divalent 3d metal ions compared with calculated effective distances 

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In spite of the apparent simplicity of the method, its drawback comes from the fact that a two-spin system has been assumed. It provides merely global information spanning all protons prone two interact by dipolar coupling with the considered carbon. Selective information requires pulsed experiments stemming from the general solution of Equation (14) given below. 

For protons (ADD) = 0, so that the dipolar coupling is determined by the two- and three-center contributions. Recently, Keijzers and Snaathorst1271 have shown that the three-center contributions (ADD)3 should not, in general, be neglected in the computation of anisotropic proton hf coupling constants. In most ENDOR work, however, only the two-center contribution (ADD)2>, ( distant term) has been considered. 

Spin labels contain unpaired electrons that by highly efficient electron-nuclear spin dipolar coupling lead to accelerated transverse or longitudinal relaxation. The effect is rather far-reaching (at least up to 10 A), and its general use is described in Chapt. 15. 

The dependence of the residual dipolar coupling on the angle that the vector forms with a reference axis explains why the use of dipolar couplings makes possible the determination of the relative orientation of different domains in a multidomain protein and facilitates nucleic acid structure determination. Dipolar couplings can constitute up to 50% of the total structural data available for nucleic acids, while this number drops to 10-15% in proteins. Thus, the impact of the use of dipolar couplings on the structure determination of nucleic acids is generally more substantial than in the case of proteins. Furthermore, the presence or absence of tertiary structure in a protein or nucleic acid does not have a major influence on the number of dipolar couplings that can be measured, in contrast to the case of the NOE. 

If the paramagnetic center is part of a solid matrix, the nature of the fluctuations in the electron nuclear dipolar coupling change, and the relaxation dispersion profile depends on the nature of the paramagnetic center and the trajectory of the nuclear spin in the vicinity of the paramagnetic center that is permitted by the spatial constraints of the matrix. The paramagnetic contribution to the relaxation equation rate constant may be generally written as... 

As mentioned in Sections I.B.2.b and II.A, the dipolar coupling between Li- C may complicate solid state NMR spectra of organolithium compounds and its elimination is often desirable. On the other hand, dipolar coupling constants are related to atomic distances and their determination can yield important structural information. It is therefore of general interest that the REDOR technique, briefly described in Section I.B.2.b, provides a means to determine these parameters. 

Solids—Many polymers are either soluble or insoluble. NMR of solids generally give broad lines because of the effects of dipolar coupling between nuclei and the effect of chemical shift anisotropy (CSA). Both of these effects are greatly reduced for polymers in solution and allow for decent spectra of soluble polymers in solution. 

Dipolar coupling (vectorial coupling) only occurs between spatially close nuclei and acts through space. Generally, however, signal splitting does not occur in solution because... 

The natural line-width of the proton resonances is determined by the nuclear spin relaxation times. Nuclear relaxation in solutions of diamagnetic molecules comes mainly from intramolecular proton-proton dipolar coupling modulated by the rotational tumbling of the molecules, and will be discussed in more detail in section VII. Suffice it here to say that the line-width increases in general with increasing size of the molecule. For a small organic molecule a line-width at half height of the resonances of less than one cps would be expected, whereas the resonances... 

While keeping in mind the general picture of nuclear relaxation in paramagnetic systems as described in Section 3.1, it is appropriate to consider first the simple case of dipolar coupling between two point-dipoles as if the unpaired electrons were localized on the metal ion. The enhancement of the nuclear longitudinal relaxation rate Rim due to dipolar coupling with unpaired electrons can be calculated starting from the Hamiltonian for the system ... 

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