Nuclear spin interactions

Bermudez, A., Jelezko, F., Plenio, M.B. and Retzker, A. (2011) Electron-mediated nuclear-spin interactions between distant nitrogen-vacancy centers. Phys. Rev. Lett., 107, 150503. 

Fundamental constants (Cx), spatial tensors in the principal axis frame ((fi3 m,)F), and spin tensors (Tjm) for chemical shielding (a), J coupling (J), dipole-dipole (IS), and quadrupolar coupling (Q) nuclear spin interactions (for more detailed definition of symbols refer to [50])... 

Although the same nuclear spin interactions are present in solid-state as in solution-state NMR, the manifestations of these effects are different because, in the solid, the anisotropic contribution to the spin interactions contributes large time-independent terms to the Hamiltonian that are absent in the liquid phase. Therefore, the experimental methods employed in solids differ from the ones in the liquid state. The spin Hamiltonian for organic or biological solids can be described in the usual rotating frame as the sum of the following interactions ... 

Bloembergen and Rowland (78) have also shown that associated with the exchange interaction is a pseudo-dipolar interaction, which as the name implies, has the same functional form as the dipolar interaction. This interaction arises from the presence of the electron-coupled nuclear spin interaction and the dipole-dipole interaction and its magnitude is dependent on the relative amount of p- or d-character of the electronic wave functions in the solid. 

Type I and 2 mononuclear copper centers in enzymes and proteins are distinguished by theit different EPR spectra for Cu(ll). Type 1 and 2 spectra exhibit comparatively narrowly and widely spaced hyperfine lines, respectively, for the electton-nuclear spin interaction. The more narrow the spacing, the weaker is the interaction. Type 1 cupric centers generally have an intensely blue color, whereas type 2 centets are virtually colotless. 

Finally, the nuclear spins interact with the external field resulting in... 

The relationship to the s character of the bond is to be expected, since the primary mechanism for spin-spin coupling in this case involves electron-spin-nuclear-spin interaction. Only s electrons have any probability of being found at the nucleus, and so only these electrons are able to transmit information concerning nuclear spin states. 

The molecular interpretation of this result is as follows above the glass temperature T0 the molecular segments are in vigorous motion and change their positions frequently. Hence, the average nuclear spin interaction is reduced to a minimum. This causes a narrow absorption line. As the kinetic motion of the molecules is decreased by cooling, the frequency of position changes is reduced, and... 

However, if Q(Qea) does not involve nuclear spin interactions, another symmetry group for tf(Qea) may be found. We let be the point group which acts on electronic spin coordinates and which is isomorphic to sp. The double group of is denoted and is obtained from double group contains twice as many elements as The two groups sp and may be combined to give an inner subdirect product which is denoted sp < a-i and is defined to contain elements of the form... 

Woessner and Trewella (132) observed indirect (electron-coupled) nuclear spin interactions in the 29Si MAS NMR spectra of low albite. Three signals were measured, corresponding to T2M, T20, and T,M silicon sites, respectively. The last two signals were split and the magnitude of the splitting was field independent. This is the first time such effects, which are not normally observed in true solids (3), have been found for the 29Si nucleus. 

There is a completely analogous development for a system of nuclear spins interacting with a time-dependent magnetic field polarized along the x axis. 

Magnetic fields are generated by the rotation of a molecular magnetic moment and modulated by molecular collisions. Nuclear spin interacts with the fluctuating magnetic field. 

High-resolution NMR in solution requires the sample to be soluble in a solvent such that the various nuclear spin interactions can be averaged or removed by molecular micro-Brownian motions. Unfortunately, elastomers used in various applications are normally crosslinked materials and therefore not soluble in any solvent. Thus, solid state NMR with magic angle-spinning technique has been used with great success in the study of cured elastomers. However, this technique demands extended instrument facilities and expertise. 

Motions with rates of the order of the nuclear spin interaction anisotropy can be assessed via lineshape analysis. These are generally motions of intermediate rates, a few kHz to tens of kHz for chemical shift and dipolar interactions, higher for quadrupolar interactions. 

Finally, higher-rate motions (106—109 Hz) can be examined by spin-lattice relaxation time studies. Spin-lattice relaxation (as other relaxation processes) relies on fluctuations in nuclear spin interactions induced by molecular motion. Thus, in cases where relaxation is dominated by one particular nuclear spin interaction, the spin-lattice relaxation times can be calculated for different motions and compared with experimentally derived values. 

The other general way of resolving powder patterns from different chemical sites is to generate multidimensional NMR spectra in which the desired powder patterns (or magic-angle spinning sideband patterns) are resolved in one dimension, separated according to (for instance) isotropic chemical shift in another dimension. These techniques are discussed below in the relevant section for each type of nuclear spin interaction. 

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