Broadening resonance

Ben-Reuven A. Resonance broadening of spectral lines. Phys. Rev. A4, 2115-20 (1971). 

Collisional or pressure broadening and resonance broadening. These are caused by collisions between unlike and like atoms respectively in the sample vapour. Only the former is significant in flames. 

However, upon cooling, the signals for the three allylic and two bridgehead resonances broaden, and at 183 K they separate into 10 different signals. The coalescence temperature for the central allyl H resonance is 225 K. 

Other broadening processes also exist. Holtsmark (resonance) broadening arises from collisions between atoms of the same kind and is therefore negligible when compared with other collisions. 

Different behavior was found for the p-toluenesulfonate and chloride derivatives containing ligands derived from pyrimidine. This could be due to a competitive coordination of these anions against the heterocyclic ligands. For the chloride complexes, a clear resonance broadening is observed at room temperature. Considering the chemical shifts it must be accepted that the free ligand is the dominant species. 

Fig. 17. The C-13 spectra over a 200 K temperature range for DGEBA epoxy cured with piperidine. The chemical structure on the left shows one half of the (symmetrical) monomer (top half) and a possible curing structure with piperidine (bottom half). In the spectra the methyl resonance broadens and then disappears at low temperature the remaining peak at about 25 x 10 6 is assigned to the piperidine. The low-temperature splittings of peaks c and d.collapse at higher temperature, indicating reorientation of the phenyl group with respect to the backbone 641...

Further evidence for isotropic chemical shifts was found in variable temperature studies. The aromatic carbon ortho to the oxygen resolved into two peaks at low temperatures. The aromatic carbons meta to the oxygen have two peaks, but these peaks are not as well resolved. As the temperature was raised, the splittings in both coalesced into one peak, indicating that there is rapid sampling from two magnetic environments. This is indicative of the motion of the phenyl group with respect to the backbone. At lower temperatures, the methyl resonance broadens and eventually... 

Below 200 K the 13Ci resonances broaden differentially with decreasing temperature, indicating a slowing down of the intra-aggregate C—Li exchange at different rates for different species. 

Thomas and coworkers showed that f-butyllithium in pentane consists exclusively of cubic tetramers. Below 251 K, the 13C NMR of 6Li bound carbon consists of a 1 3 6 7 6 3 1 multiplet with 7(13C,6 Li) = 5.1 Hz, the familiar signature of a cubic tetramer24. On increasing the temperature above 251 K, this resonance broadens and resolves again by 268 K into a nonet with splitting of 4.1 Hz due to fast intraaggregate C—Li exchange. Carbon-13 NMR line shape analysis established AH = 25 1 kcalmol-1 and AS1 = 44 eu. 

When the quasistatic contribution to the absorption coefficient, as described by eq. (1), is incorporated in the LTE model (5.) a more realistic emission spectrum of the HPS discharge results (de Groot and Woerdman, to be published). This is already evident when the quasistatic absorption spectrum is compared with the extrapolated dispersive, resonantly broadened Na D absorption profile (see Figure 3). In the far red wing (X > 650 nm) the contribution of the A Sj, - X Zg transition is much larger than the dispersive contribution in a LTE model the same holds for the emission spectrum. In the far blue wing (X< 560 nm) the contribution of the Ilg - transition likewise dominates the dispersive contribution. 

Figure 21 H resonances ofheme methyl groups ofHydrogenobac-ter thermophilus ferricytochrome C552 at (a) 26, (b), 11 (c) 1, (d) —6 °C. The chemical shifts observed are an average of shifts for two different axial methionine orientations in fast exchange on the NMR timescale. Upon lowering the temperature, the exchange process is slowed so that resonance broadening is evident as the process approaches the intermediate exchange regime. Samples for (b)-(d) are in 20% methanol...

Examination of the NMR spectrum of vinyl acetate and vinyl propionate copolymers with Eu(hfc)3 or Pr(hfc)3 indicated that linkages within the polymer were racemic in nature. The H (400 MHz) and (100 MHz) NMR spectra of 3-amino-l,2-dicarba-c/oio-dodecaboranes exhibited enantiomeric discrimination in the presence of Eu(hfc)3. The resonances broadened in the presence of the shift reagent, but it was still possible to observe signal separation for the two enantiomers. 

In indirect methods, the resonance parameters are determined from the energy dependence of the absorption spectrum. An important extra step — the non-linear fit of (t E) to a Lorentzian line shape — is required, in addition to the extensive dynamical calculations. The procedure is flawless for isolated resonances, especially if the harmonic inversion algorithms are employed, but the uncertainty of the fit grows as the resonances broaden, start to overlap and melt into the unresolved spectral background. The unimolecular dissociations of most molecules with a deep potential well feature overlapping resonances [133]. It is desirable, therefore, to have robust computational approaches which yield resonance parameters and wave functions without an intermediate fitting procedure, irrespective of whether the resonances are narrow or broad, overlapped or isolated. 

Guanine cytosine, G.C, (11 to 13 ppm) and adenine uracil, A.U, (13 to 15 ppm) NH resonances are shifted by the ring currents of nearby bases, and calculations [42] indicate that the solid-state clover leaf structure is appropriate in solution. NH Resonances disappear when the helices melt and Mg helix stabilisation is readily observed by NMR [43] but optical melting points are higher than the temperature range over which NH resonances broaden and disappear [44]. for the double helix of d(A-A-C-A-A) with d(T-T-G-T-T), for example, is 28°C but resonances have disappeared by 9°C T is thymine. 

The thermal development of amorphous sialon fibres from polyaluminocarbosilane gels at 1000°C and their crystallisation to p-sialon fibres at 1400-1500°C has been studied by Al and Si NMR (Soraru etal. 1993). The gel precursor shows the typical 3-peak Al spectrum, with resonances at 3.2, 32 and 57.4 ppm but the amorphous fibres formed at 1000°C contain only tetrahedral Al. On crystallisation of p-sialon, the tetrahedral Al resonance broadens due to the occurrence of mixed AIO4 - xNx sites (Soraru eta/. 1993). 

Above 450 K, the NMR spectrum of Rb3C6o contains 2 sharp resonances arising from mbidium in non-equivalent octahedral and tetrahedral sites (Walstedt etal. 1993). The octahedral peak appears at about 52 ppm and the tetrahedral peak is at about 195 ppm with an octahedraktetrahedral intensity ratio of 1 2, consistent with the known crystal structure. As the temperature is lowered these resonances broaden and shift slightly and a third tetrahedral resonance appears at 200 K the 3 resonances occur at 40 ppm (octahedral), 165 ppm (tetrahedral) and 270 ppm (new tetrahedral). The formation of the second tetrahedral site has been explained in terms of alkali-metal vacaneies which occur only in the tetrahedral positions (Apostol et al. 1996). Measurements of the Rb and Rb relaxation rates indicate a quadrupole relaxation mechanism involving phonons, and no change in either the NMR spectrum or the relaxation rates was found in the vicinity of Tc for this compound (Corti 1993). 

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