Dipolar interactions powder pattern

Dipolar interaction can lead to an EPR line broadening (Fig. 6). The spectrum of the interacting spins can be treated as the convolution of the non-interacting powder pattern spectrum with a dipolar broadening function which is known as Pake pattern in randomly oriented samples. 

The Tte of the 3Fe-4S centre in succinate ubiquinone reductase between 4 and 8 K is decreased by interaction with paramagnetic cytochrome b.98 To mitigate the impact of spectral diffusion the relaxation times were measured by a picket-fence sequence with 100 pulses. Analysis of the powder pattern distribution of relaxation times indicated that the anisotropic dipolar interaction dominated over isotropic scalar interaction and a lower limit of 10 A was estimated for the distance between the iron-sulfur cluster and the heme. 

Efforts to understand the state of hydrogen in metals and metal hydrides have involved the use of NMR for many years. This study combines the conventional solid state NMR techniques with more recently developed high-resolution, solid state NMR techniques (5,6). Conventional NMR techniques furnish information on dipolar interactions and thus can furnish static geometrical information on hydrogen positions and information on proton motion within such solids. The newer multiple pulse techniques suppress proton-proton dipolar interaction and allow information on other, smaller interactions to be obtained. This chapter reports what the authors believe is the first observation of the powder pattern of the chemical shift tensor of a proton that is directly bonded to a heavy metal. 

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) ...

More recently, the static NMR spectra of 16 potassium compounds have been obtained by Bastow (1991) using a solid pulse echo sequence. Most of these compounds have relatively small dipolar coupling, resulting in sharp powder pattern features of the observed central transition. Accurate simulations allowed the values of xq and T to be determined and also indicated very small CSA contributions. Most of these model compounds contain only 1 potassium site, but even those compounds with 2 inequivalent K sites could be sufficiently resolved to allow accurate and unambiguous simulation (Bastow 1991). The NMR interaction parameters for potassium compounds are collected in Table 8.8. 

Two-dimensional PISEMA spectra experimentally obtained from powder samples are analyzed by comparison with simulations to determine Euler angles that define the orientation of the CSA tensor in the molecular frame, while the magnitudes of the CSA tensor is measured from a ID chemical shift powder pattern. Some examples of PISEMA spectra of powder samples simulated using SIMPSON program 5 are shown in Fig. 6. PISEMA spectra correlating the N chemical shift and the ll 5r dipolar coupling interactions associated with an amide site of a peptide (Fig. 6(A)) and with the N -H bond of the imidazole ring in histidine (Fig. 6(B)) were simulated. 

Rotary resonance recoupling of heteronuclear C- H dipolar interactions in NMR spectra (recorded under conditions of H decoupling at frequency vi and MAS at frequency Vr) has been studied for three examples of molecular solids (adamantane, ferrocene and hexamethylbenzene) in which substantial molecular motion is known to occur. It has been shown that when rotary resonance conditions are satisfied (i.e. l Vr = , for n = 1 or 2), the recoupling can lead to motionally averaged Pake-like powder patterns from which information on C- H intemuclear distances and/or molecular motion can be derived. 

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... 

In the NMR spectrum, the dipolar interaction represents itself as a line splitting. For isolated pairs of unlike spins, the i and j spin resonances are each split into a doublet with a splitting of 2d , for like spins a doublet with a splitting of 3d is found. For powder samples a so called Pake powder pattern is found instead of the doublet. Resolved splittings are only observable for fairly well isolated spin systems consisting of two or a very few spins (e.g., the proton pair of the crystal water in gypsum [9]). For extended spin systems, a broad and rather featureless resonance line is observed. 

Fig. 6.4.3. chemical shift powder pattern spectra of labeled gramicidin A. (A) Trpn gramicidin A—experimental data obtained with cross-polarization and H dipolar decoupling at 20.3 MHz for N. (B) spectral simulation with o-n = 36, saturated solution of NH4N03. (C) [ C,]Leuio-[ N ]Trpn gramicidin A—experiment as in (A) displaying a combination of N chemical shift anisotropy and the — " C dipolar interaction. (D) spectral simulation with the same an values as in (B) and with = 0° and Pu = 106°. 

The small, but significant, increase in the anisotropy or width of the powder pattern suggests that at room temperature librational averaging is occurring. Consequently, it is important to have the dynamics characterized. Note, that for a molecular site, it is only necessary to characterize the dynamics once and then for the range of interactions observed at that site the motionally-averaged dipolar magnitudes can be calculated. 

For example, the carbonyl carbon powder pattern of [l- C]Gly silk fibroin is modified by dipolar interaction with the N nucleus of the Ala residue bonded directly in the peptide. From a simulation which takes into account such a dipolar interaction, a cN and )8dcn values for the carbonyl carbon are determined. The results are also listed in Table 23.1 together with the values for other sites. 

The basic principles are well established isolated pairs of nuclei in a rigid solid experience a mutual dipolar interaction directly proportional to the average of the inverse cube of the internuclear distance. For a powder sample of an H2 complex, a normal Pake doublet line shape results (Fig. 20.3C), which can be used to calculate internuclear H-H distances within 1%. The patterns are quite sensitive to anisotropic motion, that is hindered rotation or torsion of the side-bound H2 about the M-H2 axis. This will not affect the H2 dipolar splitting when this axis is parallel to the applied magnetic field. One pair of temperature-independent... 

It is well known from theory and experiment that the interaction of ethylene with silver is nearly repulsive (711. This weak adsorption can be investigated with solid-state C NMR (72], and an illustration of such spectra for 1- C-C2H4 and 1, 2- C2 C2H4 is depicted in Fig. 36. The value extracted from the chemical shift/dipolar powder patterns of these spectra is 1.34 A. This result is close to the value of 1.335-1.340 A for ethylene in the gas phase (731, a bond distance that reflects the weak interaction between the silver and the adsorbed ethylene. 

Signal enhancements were obtained in H — O cross-polarization experiments without spinning, and reliable second-order quadrupolar powder patterns were observed [1291. Relaxation parameters involved in cross-polarization transfer were shown to be characteristic of the various sites, so that they can be used for signal assignment. In addition, in some cases the differences in crosspolarization rates were used to edit spectra by a selective enhancement of protonated oxygen resonances, such as those from surface hydroxyl groups in amorphous silica. The latter method can be applied to complicated systems, provided dipolar H — O interactions for the various sites are different. We illustrate this procedure by using a static H — O CP spectrum [126] of talc. 

In typical applications, say of organic solids by NMR, microcrystaUine sohds or amorphous samples are studied in which all orientations of molecules are present Each in a molecule is represented by a distribution of resonances, a powder pattern, which reflects the orientation dependence of the chemical shift and H C dipolar interactions. The experimental spectrum is the sum of powder patterns from all the resonances in the spectrum, and as such usually presents a... 

Fig. 7.8 Solid-state C NMR "powder pattern" line shape for the case of C— H dipolar interaction and an ensemble of randomly oriented C- H units. The frequency axis is...

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