Nuclear Magnetic Dipole Interactions

Solids give rise to the "wide-line" or (broad-line) spectra, because the local fields arising from nuclear magnetic dipole interactions contribute significantly to the total field experienced by a nucleus in the solid state. A measure of this direct spin-spin interaction is the spin-spin relaxation time T2 (see Sect. 12.2.1.3), which is much shorter in solids than in liquids, and thus gives rise to broader lines (of the order of 10-6 to 10 4 T, depending on the kind of nucleus). Now the contour of the absorption line provides information as to the relative position of the neighbouring nuclei. 

Tohnan JR et al (1995) Nuclear magnetic dipole interactions in field-oriented proteins -information for structure determination in solution. Proc Natl Acad Sci USA 92(20) 9279-9283... 

The connection between the rate constants W and molecular parameters is a complex subject that can only be outlined here. Basically, the dipole-dipole interaction is a through-space effect in which one nuclear magnetic dipole interacts with the local field created by a second nucleus. The value of W depends upon the component of this field that fluctuates at the frequency of the transition, that is at 0, (o and 2Larmor frequency. Working out the algebra shows that the cross-relaxation rates are proportional to spectral densities, which are Fourier transforms of time correlation functions that describe molecular motions ... 

A nucleus in a state with spin quantum number 7 > 0 will interact with a magnetic field by means of its magnetic dipole moment p. This magnetic dipole interaction or nuclear Zeeman effect may be described by the Hamiltonian... 

Magnetic dipole interaction Hm (4.47) and electric quadmpole interaction //q (4.29) both depend on the magnetic quantum numbers of the nuclear spin. Therefore, their combined Hamiltonian may be difficult to evaluate. There are closed-form solutions of the problem [64], but relatively simple expressions exist only for a few special cases [65]. In Sect. 4.5.1 it will be shown which kind of information can be obtained from a perturbation treatment if one interaction of the two is much weaker than the other and will be shown below. In general, however, if the interactions are of the same order of magnitude, eQV Jl, and... 

Fig. 7.3 Effect of magnetic dipole interaction (7/m), electric quadmpole interaction (Hq), and combined interaction// = Hu + //q, Em> q on the Mossbauernuclear levels of Ni. The larger spacings between the sublevels of the ground state are due to the somewhat larger magnetic dipole moment of the nuclear ground state as compared to the excited state. The relative transition probabilities for a powder sample as well as the relative positions of the transition lines are indicated by the stick spectra below...

Apart from the determination of nuclear parameters, the Mossbauer transition in Os, especially the 36.2 and 69.6 keV transitions, are suited for chemical applications. As shown below, the 36.2 keV level, in spite of its large half-width, can be well used for the measurement of isomer shifts, whereas the 69.2 keV state is favorable for the characterization of electric quadrupole or magnetic dipole interactions. Both Mossbauer levels are populated equally well by the parent isotope lr, and simultaneous measurement is possible by appropriate geometrical arrangement. 

The physical interpretation of the anisotropic principal values is based on the classical magnetic dipole interaction between the electron and nuclear spin angular momenta, and depends on the electron-nuclear distance, rn. Assuming that both spins can be described as point dipoles, the interaction energy is given by Equation (8), where 6 is the angle between the external magnetic field and the direction of rn. 

The magnetic hyperfine splitting, the Zeeman effect, arises from the interaction between the nuclear magnetic dipole moment and the magnetic field H at the nucleus. This interaction gives rise to six transitions the separation between the peaks in the spectrum is proportional to the magnetic field at the nucleus. 

Nuclear Overhauser effect—The nuclear Overhauser effect (NOE) occurs only between nuclei that share a dipole coupling, i.e., their nuclei are so close that their magnetic dipoles interact. Techniques that use NOE enhance spectra and allow spacial relationships of protons to be determined. 

Fig. 7.4 Top Nuclear energy levels of Fe as shifted by electrical monopole (left), or as split by electrical quadrupole (center) or by magnetic dipole interaction (right), schematized for hematite at room temperature (5 > 0 vs. a-Fe, EQ < 0, Bhf 0). Bottom Schematic Mossbauer spectra corresponding to the energy levels schematized on top (J. FriedI, unpubl.).

Further evidence for this mechanism of spin-spin coupling in liquids is the fact that the coupling dies off as the number of chemical bonds separating the two nuclei increases. Moreover, the fact that couplings between trans protons in olefins are greater than between cis protons is incompatible with a direct interaction between the two nuclear magnetic dipoles. 

NMR transitions are between energy levels that correspond to different orientations of the nuclear magnetic dipole moment in an applied magnetic field B. The classical energy of interaction between an isolated nuclear magnetic moment fiN and B is2... 

This term is called the Fermi contact term. That part of the electron-nucleus magnetic-dipole interaction represented by (8.104) depends on the angular coordinates of the electron and is therefore anisotropic in contrast, the Fermi contact energy (8.108) is isotropic. The contact term plays an important role in the electron-coupled nuclear spin-spin interactions seen in the NMR spectra of liquids. 

Spectra of solids arc complicated, because of the multiplicity of parameters involved, especially by anisotropic interactions as dipolar coupling. Many techniques both experimental or computational have been developed for interpretation. A technique particularly useful for catalysis permits to selectively suppress anisotropic contributions by mechanical rotation of the sample (magic angle spinning, MASNMR) and by rotation of the nuclear magnetic dipoles with sequences of radiofrcqucncy pulses. 

The nuclear spin magnetic dipole interactions are listed in equation (4.18) in a space-fixed coordinate system of arbitrary origin. The two forms of the electric quadrupole... 

We recall from chapter 4 that there are many individual types of interaction which involve the nuclear magnetic dipole and electric quadrupole moments. Let us take just three of these to exemplify how the effective Hamiltonian is constructed. They are as follows ... 

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