Electron-nuclear dipolar coupling

Figure 5. Li MAS NMR spectrum of the Mn(IV) spinel (Lio.5Zno.5)tet(Lio.5Mni 5)oct04 and the typical hyperfine shifts observed for lithium in a series of local environments. Hyperfine shifts are given next to the two isotropic resonances in the Li spectrum all other peaks are spinning sidebands, which are predominantly caused by the electron—nuclear dipolar coupling.

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... 

This is a very important result. The first term in the last line of (4.13) represents the so-called Fermi contact interaction between the electron and nuclear spin magnetic moments, and the second term is the electron-nuclear dipolar coupling, analogous to the electron-electron dipolar coupling derived previously in (3.151). The Fermi contact interaction occurs only when the electron and nucleus occupy the same position in Euclidean space, as required by the Dirac delta function S(-i Rai). This seemingly... 

Read carefully the discussion of the electron-nuclear contact coupling (pp 387-389) and make a similar analysis of the electron-nuclear dipolar coupling that arises from the term (11.7.9). Hence verify that the coupling with any nucleus is described by a coupling tensor whose components depend on the form of the spin density in the vicinity of the nucleus. [Hint Express the scalar products in terms of spherical components as in (11.7.3) and (11.7.4), and reduce the matrix elements (within the degenerate manifold of electron-nuclear product functions) in a parallel fashion, focusing attention on the coefficient of S l . The cartesian form can be obtained at the end.]... 

Here /, is the 13C nuclear spin, S is the unpaired electronic spin, and A j- is the Fermi contact hyperfine coupling tensor. This coupling is identical for all 13C nuclei as long as the C60 ion is spherical, but becomes different for different nuclei after the Jahn-Teller distortion leading to an inhomogeneous frequency distribution. The homogeneous width of the 13C NMR lines is, on the other hand, mainly determined by the electron-nuclear dipolar interaction... 

Frequency- and temperature-dependent studies may be employed to confirm that the system is in the fast-exchange limit on the n.m.r. time-scale. - - The second assumption may be validated by comparing - the ratio T T. As shown earlier, if the dipolar term is the only significant factor, the ratio T jT will be 7/6 = 1.17 1.00. If values are obtained that are greater than this value, there is some contribution from electron-nuclear scalar coupling. A third implicit assumption is that there is only one (unique) binding site on the molecule for the metal ion. 

In equation (bl. 15.24), r is the vector coimecting the electron spin with the nuclear spin, r is the length of this vector and g and are the g-factor and the Boln- magneton of the nucleus, respectively. The dipolar coupling is purely anisotropic, arising from the spin density of the impaired electron in an orbital of non-... 

P has been computed using Hartree-Fock atomic orbital wavefunctions and can be found in several published tabulations14 17 and in Appendix 1. Because of the (r 3) dependence of P, dipolar coupling of a nuclear spin with electron spin density on another atom is usually negligible. 

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 relaxivity enhancement of water protons in the aqueous solutions of paramagnetic complexes arises from time fluctuation of the dipolar coupling between the electron magnetic moment of the metal ion and the nuclear magnetic moment of the solvent nuclei (13,14). The dipolar interaction... 

In principle, there are several contributions to nuclear Tm" however, the dipolar coupling term often dominates (10,22). The dipolai contribution depends on the reciprocal of the sixth power of the distance between the resonating nucleus and the relaxing electron, on the square of the magnetic moments associated with the unpaired electrons (ge2 B S(S+l)) and with the nucleus on the magnetic field as expressed by the Larmor... 

Ms value but on different positions in space. This random motion of the electron around the nucleus is again seen as a fluctuating magnetic field that causes nuclear relaxation through dipolar coupling. 

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