Line shape symmetry

Chemical shift anisotropy 5.5,5 xxr yy zz Line-shape analysis MAS-sidebands Coordination symmetry... 

Nuclear electric quadrupole QCC (quadrupole coupling constant), (asymmetry parameter) Line-shape analysis, nutation NMR Coordination symmetry... 

The analysis of XRPD patterns is an important tool studying the crystallographic structure and composition of powder compounds including the possibility to study deviation from ideal crystallinity, i.e. defects. Looking at an X-ray powder diffractogram the peak position reflects the crystallographic symmetry (unit cell size and shape) while the peak intensity is related to the unit cell composition (atomic positions). The shape of diffraction lines is related to defects , i.e. deviation from the ideal crystallinity finite crystallite size and strain lead to broadening of the XRPD lines so that the analysis of diffraction line shape may supply information about sample microstructure and defects distribution at the atomic level. 

If a molecule contains one or more unpaired electrons it is usually possible to detect an electron spin resonance signal and at a very low concentration of unpaired electrons, commonly 1018 spins with modem instruments. Several pieces of information can be obtained in this way. The number of unpaired spins can be found, the symmetry of the molecule in the region of the unpaired electron can be determined, and, if the unpaired electron is delocalized over nuclei with nuclear spins, then the extent of delocalization can be determined. Perhaps more importantly for our purpose, the rotational time of molecules can be determined from line shape studies. 

Sweeney, W. V., D. Coucouvanis et al. (1973). ESR of spin 5/2 systems with axial symmetry and moderately large zero-field splittings. Application of line-shape calculations to the interpretation of randomly oriented microcrystallite spectra. J. Chem. Phys. 59 369-379. 

Powder patterns of crystals with axial symmetry yield the value of qQ but do not, of course, give the direction of the axis of symmetry. Line shapes to be expected for the magnetic resonance in this situation have been calculated (95) and for / = %, the shape is illustrated in Fig. 11 for polycrystalline corundum (a-AbOs). 

Symmetries of local electrical environments of quadrupolar nuclei (/ 1) profoundly influence relaxation times and resonance line shapes of such nuclei (9, 116). Consider a nucleus for which I = % (Br79, Bn). In the absence of quadrupolar perturbation, the nuclear spin levels are evenly spaced, as shown in I below, and the three possible nuclear resonance transitions have equal energies (Am = 1). If, however, eqQ 0... 

Archaebacterial rhodopsins may provide models for signal transduction and ion transport.62 Spin labels were attached to sensory rhodopsin (pSRII) and its transducer (pHTrll) from Natronobacterium pharaonis. Interspin distance determined by line-shape analysis including a Gaussian distribution of distances revealed a 2 2 complex with 2-fold symmetry. Distances for 26 pairs of spin labels defined the orientation of the TM helices of pHtrll relative to the F and G helices of pSRII.63 Light excitation causes a flap-like movement of helix F of NpSRII that induces a rotary motion of a helix in the transmembrane domain of the transducer.62... 

Figure 7. Free-induction decay line shapes for H4Os4(CO)i2 near 100°K and room temperature. The lack of complete symmetry in the line shape may be caused by a probe impurity signal located slightly to the left of the spectra s...

We start with the basic relationships ( Ansatz ) of collision-induced spectra (Section 5.1). Next we consider spectral moments and their virial expansions (Section 5.2) two- and three-body moments of low order will be discussed in some detail. An analogous virial expansion of the line shape follows (Section 5.3). Quantum and classical computations of binary line shapes are presented in Sections 5.4 and 5.5, which are followed by a discussion of the symmetry of the spectral profiles (Section 5.6). Many-body effects on line shape are discussed in Sections 5.7 and 5.8, particularly the intercollisional dip. We conclude this Chapter with a brief discussion of model line shapes (Section 5.10). 

Now we turn to the measurements in zz polarization configuration. For our crystal two lines of Aig symmetry at 232 and 448 cm"1 are observed at room temperature as shown in Fig. 3. The disadvantage of the Sr-doped La2Ni04 system is that the dopant positions are fixed at relatively high temperature and may be random. At room temperature we do not see any dopant-induced extra features in the low frequency part of the spectra. The line shape of the Ni-0(2) bond stretching mode at 448 cm 1 is asymmetric. This asymmetry can be explained by a random distribution of holes on oxygen above Tco. 

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