Interactions pseudo-dipolar interaction

D SAxSB (asymmetric exchange or Moriya-Dzialoshinski interaction +SA K SB (anisotropic exchange or pseudo-dipolar interaction)... 

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. 

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. 

Perhaps the most detailed studies of both the isotropic and anisotropic exchange interactions have been made for InP, where the anisotropic (pseudo-dipolar) part of the 31P-115In exchange coupling was shown to reduce the measured 31P second moments from theoretical values calculated from dipolar couplings alone [255, 256]. Double and triple resonance 31P MAS-NMR experiments have also provided much information as a result of the existence of the two nearly identical isotopes of... 

The interplay between the local Pb polarization and B-site ions may be described by a simple model. As discussed above the magnitude of the local off-centering of Pb " ions is always about 0.5 A, and does not depend on the environment. Thus it could be described as a pseudo-spin, and justifies the pseudo-spin model with the dipolar-dipolar interaction and the local anisotropy energy ... 

In general, induced shifts Ad may arise by contact interaction (through-bond interaction) or by dipolar (pseudo-contact) interaction (through-space interaction)87. In rare earth ions the inner/electrons are well shielded and do not participate in covalent bonding (contact interaction). Thus induced shifts originate mainly from pseudo-contact interactions. 

A pseudo solid-like behavior of the T2 relaxation is also observed in i) high Mn fractionated linear polydimethylsiloxanes (PDMS), ii) crosslinked PDMS networks, with a single FID and the line shape follows the Weibull function (p = 1.5)88> and iii) in uncrosslinked c/.s-polyisoprenes with Mn > 30000, when the presence of entanglements produces a transient network structure. Irradiation crosslinking of polyisoprenes having smaller Mn leads to a similar effect91 . The non-Lorentzian free-induction decay can be a consequence of a) anisotropic molecular motion or b) residual dipolar interactions in the viscoelastic state. 

Since this dipolar interaction remains in isotropic media as similarly found for the contact shift (see sect. 2.1), it is often termed as the pseudo-contact shift. For the general case of a complex possessing an anisotropic magnetic susceptibility tensor, Kemple et al. (1988) show that the pseudo-contact shift spherical coordinates of the resonating nucleus in an arbitrary axes system with the lanthanide metal ion i (III) located at the origin (fig. 1)... 

RDCs belong to the so-called anisotropic NMR parameters which cannot be observed in isotropically averaged samples as, for example, is the case in liquids. Besides RDCs, a number of other anisotropic parameters can be used for structure elucidation, like residual chemical shift anisotropy, residual quad-rupolar couplings for spin-1 nuclei, or pseudo-contact shifts in paramagnetic samples. Here, we will focus on RDCs where we give a brief introduction into the dipolar interaction, then into the averaging effects with the description by the alignment tensor and concepts to deal with the flexibility of molecules. For the other anisotropic NMR parameters, we refer the reader to ref 19 for an introduction and to refs. 6-8 for a detailed description. 

Nuclear magnetic resonance spectra of these compounds are highly informative in this regard. The lineshapes of the Sn and resonances are dominated by the coupling of the nuclei with the unpaired electron spins. This interaction results in large resonance shifts arising from both the Fermi contact and the pseudo-contact (dipolar) interaction. 

The pseudo-dipolar exchange interactions, which are anisotropic and vary rapidly with the increasing interatomic distance, are one of origins of the Joule magnetostriction. 

It has been known for some time that the FIDs of such systems often decay in a way that is well represented for the most part by a Weibullian [60,61]. Arguments based on consideration of correlation functions suggested that the FID of high molecular weight polydimethyl siloxane in the melt should decay for the most part with a Weibullian power of between 1.25 and 1.5 [62], and the existence of residual static dipolar interactions in these systems was confirmed by the existence of the pseudo-solid echo [63]. This reference forms part of a much larger body of work on such systems by Cohen-Addad and co-workers which it is beyond the scope of this chapter to cover in any detail, but interested readers are directed to literature such as [64] and [65]. 

In solids, in addition to the classical dipolar interaction described above, interactions between the nuclear spins are also mediated by the bonding and/or conduction electrons. These exchange and pseudo-dipolar interactions were already included by Van Vleck (1948) in his general treatment, and specific application to NMR in solids was given by Bloembergen and Rowland (1953). These interactions are generally most consequential for relatively heavy nuclei. 

Note that this has identical spin operators to those involving in Equation [31]. This means that the spectra of anisotropic systems depend on (2D y + / ), and that these two interactions cannot be determined separately from the spectra. For this reason, Jfj is often referred to a pseudo-dipolar coupling. 

The direct dipolar coupling, and the anisotropic component of the indirect spin-spin interaction in the direction of the magnetic field, appear in the Hamiltonian in the same form. The splittings that arise in NMR spectra are the sum of these two quantities, called the experimental anisotropic coupling Ty= 2Dyzz + 7 )- It is therefore important to know experimentally, or to evaluate theoretically, the values of the pseudo-dipolar coupling in order to accurately determine Dy z, which is related... 

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