Axially symmetric powder pattern

Fig. 5. 75.4-MHz l3C cross-polarization spectra of the acetylium ion 1 on TaCl5 acquired at 298 K. The nonspinning spectrum shows a broad and axially symmetric powder pattern. The MAS spectrum shows that ca. 80% of the starting material (acetyl-f-13C chloride) was ionized to form the acetylium ion (<5lso = 153 ppm), and the rest formed the donor-acceptor complex with TaCls ( lso = 189 ppm). The nonspinning spectrum requires 20 times more scans to acquire than the MAS spectrum. The principal components of the l3C shift tensor of 1 were measured from both spectra, and the results are in very good agreement.

Chemical shift spectra of PTFE obtained at 259° are shown in Figure 1. These lineshapes, for three different samples of varying crystallinity, may be seen to be a linear combination of two lineshapes one is characteristic of an axially symmetric powder pattern and the other of an isotropic chemical shift tensor. At this temperature these two lineshapes differ greatly and may be numerically decomposed. 

In Figure 2, these lineshapes are decomposed into the isotropic lineshape and the axially symmetric powder pattern lineshape. This same procedure was used for eight samples. 

The narrow component corresponds to the amorphous fraction of the polymer and the axially symmetric powder pattern to the crystalline fraction of the polymer. Moreover, the amorphous as well as the crystalline line shapes extracted from samples of different crystallinity are essentially identical, which indicates that the structure and dynamics in the crystalline and amorphous fractions are independent of the degree of crystallinity. 

In a series of V wideline NMR studies, Mastikhin and coworkers have explored the chemical nature of the catalytically active species 37 2]. While the spectra of industrial catalysts from various sources are found to be substantially different, these differences more or less disappear after exposure to the reaction mixture. This result confirms the previously held view that the catalytically active species forms under operating conditions. Figure 4 shows typical spectra recorded at a field strength of 7.0 T, at which the lineshape is dominated by the chemical shift anisotropy. The principal contribution to the spectrum in Fig. 4 arises from an axially symmetric powder pattern with approximate 81 and 8 values of — 300 and — 1300 ppm, respectively. Based on comparative studies of model preparations, Mastikhin et al. suggest that the key compound formed has the composition K3VO2SO4S2O7. The anisotropic chemical shift parameters of... 

Fig. 18. The dashed curves represent the axially-symmetric powder pattern for the dangling bond observed at Si-SiOj interfaces (Caplan et al 1979) for several values of isotropic broadening W. The solid curve is the ESR spectrum in a-Si H. [Reprinted by permission of the publisher from Electron spin resonance studies of amorphous silicon, by D.K. Biegelsen, Proceedings of the Electron Resonance Society Symposium, Vol. 3, pp. 85 - 94. Copyright 1981 by Elsevier Science Publishing Co., Inc.]...

Finally, structural investigations of a human calcitonin-derived carrier peptide in a membrane enviromnent by solid-state NMR have been reported. The typical axially symmetric powder patterns of NMR spectra were used to confirm the presence of lamellar bilayers in the samples studied. The chemical shift anisotropy of the NMR spectra was monitored in order to reveal weak interaction of the peptide with the lipid headgroups. In addition, paramagnetic enhancement of relaxation rates and NMR order parameters of the phospholipid fatty acid chains in the absence and presence of the carrier peptide were measured. All peptide signals were resolved and fully assigned in 2D proton-driven spin diffusion experiments. The isotropic chemical shifts of CO, C and provided information about the secondary structure of the carrier peptide. In addition, dipolar eoupling measurements indicated rather high amplitudes of motion of the peptide. 

In Figure 7-28(a) is shown the theoretical NMR spectmm in which the asymmetrical parameter(Ti) is 0.5. Peak separations Avj, Av2 and AV3 have different values from each other. If the symmetrical motion takes place, the molecular motion is reflected in the observed spectrum as an axially symmetrical powder pattern. Figure 7-28(b) shows the observed H NMR spectrum of PG-IO-N-D at 40 " C, where N-D means that the main-chain amide proton is substituted by H. The observed spectrum shows a typical powder pattern composed of the inner peaks(Avj), the shoulders(Av2) and the outermost wingsCAvj). Therefore, this means that molecular motion of PG-IO-N-D is restricted at 40 " C. 

Akutsu et al. (1980) have reported P-NMR studies of lipid-containing viruses (e.g., bacteriophage PM2) that are spherical in shape with a hydrated diameter of 600 A and possessing a lipid bilayer. The virus contains only four proteins, namely, proteins I, II, III, and IV. The representative P-NMR spectra are shown in Fig. 14, where a 60% sucrose solvent was used to eliminate the influence of the overall rotational motion of the virus on the spectrum. It is clear firom the spectra A and C that there are two major components an axial symmetric powder pattern superimposed on the broad component. Akutsu and co-workers assigned these two components to a liquid-crystalline bilayer and the DNA inside the virus. Simulated spectrum B b d on the spectra of extracted lipids and T4 phage, which is known to have no lipid membrane, is in good agreement with the observed spectrum A or C. In the presence of 4-6 Af urea, the nucleocapsid was... 

Fig. 12. 5 P-NMR spectra (121.47 MHz) of a phosphonolipid - DPPC mixture (1 4, w/w) in water at pH 7.0 at S0°C. (A) 90° pulses, 2400 accumulations at 1 scan s. (B) As in (A) but using a DANTE pulse sequence at the indicated frequency (arrow) with 4° pulses separated by SO fts and a total saturation time of800 ms. (Q Difference spectrum of (A)- (B). (D) Computer simulation of spectrum (A) in terms of two axially symmetric powder patterns characterized by a difference in isotropic chemical shift of 28 ppm, angular-independent and angular-dependent linewidths of 70 Hz, chemical-shift anisotropies of +46 and +30 ppm for phospho- and phosphonolipid, respectively. From Jarrell et al. (1981).

Fig. 13. (Upper) ip-NMR spectrum (121.5 MHz) of the purple membrane from Halobacterium cutirubrum obtained with high-power H decoupling at IS C spectral width 125 kHz acquisition time 6 ms recycle time 1 s pulse width 45° decoupler on 4 fts before acquisition and during acquisition but off during remainder of cycle Fourier transform of 16,384 data points after zero iilling. (Lower) Computer simulation of the above in terms of two axially symmetric powder patterns characterized by effective chemical-shift anisotropies of -I-61 and 4-18.5 ppm the angular-independent and -dependent linewidths were 300 and 200 Hz, and 350 and 250 Hz, for the phosphomonoester and phosphodiester, respectively. The broken curves are the powder patterns for the two types of phosphate ester present. From Ekiel et al. (1981).

Figure 7.8. Simulated fijll- and half-field powder pattern ESR spectra of triplet states for different values of E/D (see text) [59] (a) = 0 the triplet wavefunction is axially symmetric. The pattern contains singularities at // (hv D/2 - /8hv)/gli and steps at D)/gP. (b) 0 E <. D/i the axial symmetry of the wavefunction is broken. The singularities occur at...

The NMR experiments were performed using the quadrupolar echo pulse sequence 7i/2x—Ti—7i/2y—T2—acquisition with phase-cycling and quadrature detection. A Bruker MSL 400 spectrometer was used for the high pressure studies operating at a resonance frequency of 61.4 MHz. In the liquid-crystalline phase, perdeuterated lipids display NMR spectra, which are superpositions of axially symmetric quadrupolar powder patterns of all C-D bonds.From the sharp edges, the quadrupolar splittings... 

Fig. 4. Quadrupolar powder patterns (a) Spin NMR powder pattern showing that the central -)<- ) transition is broadened only by dipolar coupling, chemical shift anisotropy, and the second-order quadrupolar interactions, (b) Spin 1 NMR powder pattern for a nucleus in an axially symmetric electric field gradient (see text). The central doublet corresponds to 6 = 90° in Eq. (10). The other features of low intensity correspond to 6 = 0° and 6 = 180°. (c) Theoretical line shape of the ) - -) transition of a quadrupolar nuclear spin in a powder with fast magic-angle spinning for different values of the asymmetry parameter t (IS) ...

Since the intrinsic lineshape has finite width, the experimentally observed lineshape is the convolution of 1(f) with one of the lineshape functions g(f). A powder lineshape for an axially symmetric chemical shielding tensor is shown in Fig. 4 and a typical example of a general powder lineshape is shown in Fig. 5. Many systems yield lineshapes close to that of a powder pattern and the mathematical properties of these lineshapes are discussed in detail by Alexander et al.iA... 

The powder pattern for an / = 1 quadrupolar interaction can be obtained by reflecting the axially symmetric chemical shielding powder pattern about its average value,53 as shown in Fig. 8. This follows from Eqs (42a) and (42b) having the same functional form as that of Eq. (24). From Eq. (42b) we obtain... 

FIGURE 7.10 2H (D) NMR spectrum of polycrystalline alanine-d3 at three temperatures. The line shape variation results from reorientation of the CD3 group, (a) At 123 K the powder pattern represents a nearly static CD3. (b) At 177 K, the line shape is distorted by motional averaging, (c) At 293 K, motion is fast enough to produce an undistorted axially symmetric averaged powder pattern. Spectra courtesy of Dennis A.Torchia (National Institutes of Health). 

As mentioned earlier, the symmetry at Si is slightly distorted octahedral, the site being surrounded by 6 oxide ions. Therefore, Nff at Si and CuH (also in a similar environment are expected to have similar e.s.r. spectra. The spectrum of CuH ion would be the more complex, however, because of hyperfine interaction with the magnetic nuclei Cu and Cu s. In contrast, all but 1-2 % (Ni i) of the Ni nuclei are non-magnetic. The e.s.r. spectrum of a sodium-reduced Ni (5 %)Y sample in which most of the Ni ions are believed to be at Si is shown in fig. 8. This powder-pattern spectrum is characteristic of a system with an axially symmetric -tensor ... 

This term is anisotropic and produces a powder pattern. It has been derived under the assumptions that first-order perturbation of the S-states is sufficient, that the J tensor is axially symmetric and that the unique axis of J is aligned with the intemuclear vector. Under MAS this term will be scaled but, as it is not proportional to P2(cos0), it cannot be completely removed. Hence the MAS spectrum will still have some residual width, but the most profound effect is to leave an isotropic term which can be calculated by averaging the powder lineshape. Hence for a J-coupled system with an axially symmetric quadrupole interaction, the spectrum is shifted from the isotropic chemical shift by ... 

Figure 4.15 Chemical shift powder patterns for (a) asymmetric and (b) axially symmetric anisotropies (After Emerson and Bray, 1993).

As shown in Fig. 1, a typical 15N powder pattern of a peptide reveals axial symmetry because the electronic structure around the nitrogens of the peptide bonds is nearly symmetrical around the axes of the N-H bonds. In such cases, the orientation of the principal axis is difficult to determine even from a singlecrystal study. The directions of the two principal values, crn and dipolar interactions between the nitrogen and the adjacent... 

One-dimensional quadrupole echo NMR lineshape analysis of powder samples is particularly informative when fast, discrete jumps occur between sites of well-defined geometry as, for example, in a phenyl group undergoing two-site exchange. In this case, the characteristic Pake-pattern is transformed into an axially asymmetric lineshape with an apparent asymmetry parameter r] 9 0 (see Equation (6.2.3)) [1-8]. The asymmetric lineshapes, shown on the left in Fig. 6.2.2, can be derived by considering how the individual components of the principal EFG tensor become averaged by the discrete jumps. Within the molecular frame, and in units of as defined by Equation (6.2.2), the static axially symmetric tensor consists of the components = 1, = — 1/2, and V y = — 112. This traceless tensor satisfies the... 

Figure 1 Solid-state NMR powder patterns, dominated by chemical shift anisotropy effects (a) spherically symmetric chemical shift tensor, (b) axially symmetric chemical shift tensor, (c) asymmetric chemical shift tensor. Top traces theoretical powder patterns bottom traces powder patterns broadened by other anisotropic interactions or chemical shift distribution effects.

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