Anisotropy and asymmetry

Table 1 chemical shift tensor components, anisotropies and asymmetries for... 

In the heterocycle 16, P and Se high-resolution solid-state NMR spectroscopy was used to study structural properties. Both P CP/MAS and Se CP/ MAS experiments revealed that the asymmetric unit consists of two independent molecules with a different geometry around phosphorus and selenium centres. The established values of anisotropy and asymmetry parameters reflected the distortion of the phosphorus environment, and correlated with X-ray diffraction data. P NMR spectroscopy has been used to follow a new type of P-decomposi-tion in diphosphorylated amines and to characterise new organophosphorus compounds with -N-P(0)-N- linkages. A series of dioxaphosphocin-6-oxides (17), of varying substituent X, have been characterised by using P NMR and... 

The traditional definitions of the three principal value components (5i 1, 22, and 533), isotropy 5iso, anisotropy and asymmetry of the chemical shift are equivalent to those of the magnetic shielding. This traditional scheme is indefinite. It leads to a loss of physical and chemical generality which is disadvantageous. Therefore, besides the isotropy two new parameters, span Q and skew k, are often introduced and used instead of the anisotropy A3 and... 

Conventional X-ray diffraction measures a space and time average of the electronic density. Therefore, any dynamical disorder will be transformed into spatial disorder between positions whose probabilities are determined by the average time spent on each position. Certainly, one of the most tremendous advantages of NMR compared to X-ray diffraction is its ability to measure the occurrence of motion at different time-scales. Whether the motion correlation time is on the Larmor frequency scale, the linewidth scale or much slower (exchange NMR) will affect differently the NMR parameters like relaxation rates, apparent anisotropy and asymmetry of the interaction and ID or 2D lineshape. With suitable sequences, the motion correlation times and site probabilities as a function of an external parameter (temperature or pressure) can be explicitly measured. 

The nature of the orientational disorder in phases III and II was investigated first by powder experiments to give an overview of the evolution of the anisotropy and asymmetry parameter of the averaged EFG interaction. In all phases, the EFG asymmetry parameter is different from zero, and continuously decreases as temperature increases, with no observed anomaly at the transition temperature. That the asymmetry is definitively nonzero over the whole temperature range shows that the planar reorientational motion consists of jumps over six asymmetric potentials wells, which retain the centrosymmetry on average, and that the population of the different sites continuously evolves with temperature. The authors argued that a precise estimation of the two unknown occupation probabilities cannot be drawn from powder spectra without simplifying assumptions. The reasons come from the model of sixfold jump around the axis normal to the benzene... 

The beauty of CP MAS solid-sate NMR spectra comes from the useful chemical information can be extracted from the envelope of narrow lines. Using methods developed by Maricq and Waugh (126) or by Herzfeld and Berger (91), the diagonal tensor elements an, 022, and CT33 can be extracted when the isotropic shift is known. Using the tensor elements, the shielding anisotropy and asymmetry are calculated, as shown in Eqs. 5 and 6. 

Fig. 21. (a) H-decoupled NMR spectrum of polycrystalline N-labelled N-methyldiphenylphosphoiamidate, without sample rotation. The P-shielding anisotropy and asymmetry parameters are -21.24 kHz and 0.19, respectively, (b) With ma c-angle sample rotation at 1.5 kHz. (c)-(e) indicate when an r.f. irradiation is on at the N-15 isotropic shift frequency. The irradiation intensity fulfils the rotary resonance conditions [Pg.82]

In principle, it is possible to extract the anisotropy and asymmetry of the CSA by fitting the observed MAS sideband intensities. This is referred to as a Herz-feld—Berger analysis [23]. Such an approach is restricted to relatively small molecules, since it is necessary to be able to resolve, at a low yj, the sidebands of different resonances. As the number of distinct resonances increases, the ID spectrum becomes increasingly more crowded the advantage of extending the experiment to a second dimension in such cases will be discussed in Section 9.5. 

Solid state NMR spectroscopy was applied to measure the isotropic chemical shifts, chemical shift anisotropies and asymmetry parameters of three phosphorylated amino acids, O-phospho-L-serine, O-phospho-L-threonine and O-phospho-L-tyrosine. The CP buildup rates and longitudinal relaxation times of P and H were determined and compared with the values measured for a triphosphate bound to a crystalline protein. It was shown that the phosphorylated amino acids are well-suited model compounds, e.g. for the optimisation of experiments on crystalline proteins. In addition, from 2D exchange experiments on O-phospho-L-tyrosine the existence of an exchange between the two different conformations of the molecule was deduced. 

Using lateral force microscopy on Langmuir-Blodgett films, we found unexpected friction anisotropies and asymmetries in the frictional behavior. The data were found not to be related to the hexagonal packing of the molecules, but rather related to a small molecular tilt. 

Are the anisotropy and asymmetry related to molecular orientation Electron diffraction demonstrated that the condensed molecules are hex onally packed, and the upper limit for the tilt from the normal was fifteen degrees. Brewster angle microscopy determined that the tilt from the normal was approximately ten degrees, and the azimuthal tilt direction was along the subdomain boundary, as sketched in Fig.4. 

Figure 2. Anisotropic dipole radiation profile modeling a fluorophore at a glass-water interface. The critical angle is indicated by straight lines. Depending on distance and dipole orientation, this radiation profile shows a pronounced anisotropy and asymmetry.

Unfortunately, there are different conventions for the ordering of the principal shielding axes which can lead to much confusion when comparing literature values of anisotropies and asymmetries. To circumvent these problems it has been proposed that shielding tensor results should be reported in terms of the span and the skew, defined as (Mason 1993) ... 

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