Lineshape analysis

Lineshape analysis of or NMR signals arising from the quadrupolar interaction or chemical shifts anisotropy, respectively, can yield invaluable information about amplitude and motions in the solid [3,150-156]. The quadrupolar interaction, in particular, dominates the spectral pattern in NMR. The frequency of a deuterium resonance in the absence of molecular motion is given by 

In the presence of rapid molecular motion, the NMR line shape is modified by the reduced EFG tensor depending on the rate of reorientation and the orientations of the principal axes of the EFG tensor relative to the rotation axis. A calculation of the averaged tensor is performed by transformation of the EFG tensor in motion to a final reference frame in terms of Euler angles a, and y [151,154,155]. The spectral frequency in the fast 

The time dependence of a quadrupole echo NMR experiment with two pulse separated by time t can be derived from Eq. (1.55) yielding 

The diagonal matrix Q contains the frequencies (Oi 0, p) for site i, which are calculated by WEBLAB, a collection of programs freely available over the internet at http //wwww.mpip-mainz.mpg.de/weblab40/. The diagonal element IIjj is the probabihty of a repopulation of site j from all other sites. One therefore has 

On the basis of this procedure, 180° flip frequencies of Tyr side chains for a variety of [ HsJPhe-labeUed Leu - or Met -enkephaline crystals have been evaluated (5.0 x 10 to 2.4 x 10 Hz) [157]. 

We now consider some specific features of the most widely used 2H NMR technique - lineshape analysis - as well as other important 2H NMR techniques. More detailed discussion can be found in other review articles [27,28]. By employing appropriate combinations of these techniques, and exploiting the complementarity between them, a detailed understanding of the dynamic properties may be established. 

An example concerns the hydrogen bond dynamics in selectively deuterated ferrocene-1,l -diylbis(diphenylmethanol-d1). In this structure, the molecules form hydrogen bonded dimers, with the oxygen atoms of four hydroxyl groups involved in a folded trapezium hydrogen bonding arrangement [33] shown schematically in Fig. 2 as a square. 

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This lineshape analysis also implies tliat electron-transfer rates should be vibrational-state dependent, which has been observed experimentally [44]- Spin-orbit relaxation has also been identified as an important factor in controlling tire identity of botli electron and vibrational-state distributions in radiationless ET reactions. 

Fig. 23. Experimental room temperature Raman spectrum from a sample consisting primarily of bundles or ropes of single-wall nanotubes with diameters near that of the (10,10) nanotube. The excitation laser wavelength is 514.5 nm. The inset shows the lineshape analysis of the vibrational modes near 1580 cm . SWNT refers to singlewall carbon nanotubes [195].

A unique situation is encountered if Fe-M6ssbauer spectroscopy is applied for the study of spin-state transitions in iron complexes. The half-life of the excited state of the Fe nucleus involved in the Mossbauer experiment is tj/2 = 0.977 X 10 s which is related to the decay constant k by tj/2 = ln2/fe. The lifetime t = l//c is therefore = 1.410 x 10 s which value is just at the centre of the range estimated for the spin-state lifetime Tl = I/Zclh- Thus both the situations discussed above are expected to appear under suitable conditions in the Mossbauer spectra. The quantity of importance is here the nuclear Larmor precession frequency co . If the spin-state lifetime Tl = 1/feLH is long relative to the nuclear precession time l/co , i.e. Tl > l/o) , individual and sharp resonance lines for the two spin states are observed. On the other hand, if the spin-state lifetime is short and thus < l/o) , averaged spectra with intermediate values of quadrupole splitting A q and isomer shift 5 are found. For the intermediate case where Tl 1/cl , broadened and asymmetric resonance lines are obtained. These may be the subject of a lineshape analysis that will eventually produce values of rate constants for the dynamic spin-state inter-conversion process. The rate constants extracted from the spectra will be necessarily of the order of 10 -10 s"F... 

These surface kinetics studies initially focused on the dissociation of NO. For instance, Comelli and co-workers reported on the kinetics of the isothermal decomposition of NO on Rh(110) at temperatures ranging from 198 to 240 K and NO coverages below 0NO 0.3 ML [45], Auger electron spectroscopy (AES) lineshape analysis was used to measure the amount of undissociated NO as a function of time, and the resulting 0NO(t)... 

Fig. 60. Crossover from single-chain to many-chain relaxation at T = 343 K. Lineshape analysis for PDMS/d-benzene at c = 5 and 18% double logarithmic plot of — ln/S(Q,t)/S(Q,0) vs. t/s. (Reprinted with permission from [116]. Copyright 1982 J. Wiley and Sons, Inc., New York)...

Several methods have been developed to determine the chemical shift anisotropies in the presence of small and large quadrupolar broadenings, including lineshape analysis of CT or CT plus ST spectra measured under static, MAS, or high-resolution conditions [206-210]. These methods allow for determination of the quadrupolar parameters (Cq, i)q) and chemical shift parameters (dcs, //cs> <5CT), as well as the relative orientation of the quadrupolar and chemical shift tensors. In this context, the MQMAS experiment can be useful, as it scales the CSA by a factor of p in the isotropic dimension, allowing for determination of chemical shift parameters from the spinning sideband manifold [211],... 

The 170 chemical shift data obtained for the W(IV) are summarized in Fig. 11, while further kinetic information from lineshape analysis of the above study is described in Section III. 

NMR lineshape analysis, 39 376-378 Butyronitrile, hydrogenation over Raney-type nickel catalysts, 36 370... 

The ethylene bromonium and 1-bromoethyl cations and their neutral and anionic counterparts have been the subject of a tandem mass spectrometric study of dissociation and gas-phase redox reactions. IR and Raman studies of the bioactive bromonium cation (19), as its hydrogensulfate salt, agree with the results of an X-ray structure determination, and theoretical calculations are also in agreement, except for the details of the NO2 groups. The azaallenium ion (22) is an intermediate in the photolysis of (20) (21) and (22) could both be seen. Flash photolysis of (23) leads to (24), (25), and (26), all of which could be trapped by nucleophiles (27) was not an intermediate. NMR lineshape analysis of the spectmm of (28) leads to reaction rate constants of formation for both the intimate ion pair (29) and the solvent-separated ion pair (30). ... 

A unique feature of NMR is its sensitivity for dynamic processes. Using different techniques, from the well-known lineshape analysis to the application of relaxation time measurements, the correlation times of dynamic processes which can be studied span a... 

Temperature-dependent lineshape changes were observed in an early study of the fluo-renyllithium(TMEDA) complex. A detailed study by lineshape analysis, which was also applied to the TMEDA complex of 2,3-benzofluorenyllithium(TMEDA) (Figure 29f, yielded barriers AG (298) of 44.4 and 41.9 kJmoD for the 180° ring flip in these systems, respectively . A second dynamic process, which was detected via the temperature dependence of, the spin-lattice relaxation time in the rotating frame, is characterized by barriers of 35.1 and 37.6 kJmoD, respectively, and may be ascribed to the ring inversion process. For the fluorenyl complex, a barrier AG (298) of 15.9 kJmoD for the methyl rotation in the TMEDA hgand was determined from temperature-dependent NMR spectra of the deuteriated system. 

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