Line width parameter

The nitroxide moiety of 16-SASL and 16-PC exhibits such a great deal of motion that the rotational correlation time can be calculated (Berliner 1978). The rotational correlation time (assuming isotropic rotational diffusion of the nitroxide fragment) can be calculated from the linear term of the line width parameter ... 

If the g- and hyperfine anisotropies are known from analysis of a solid-state spectrum, the line-width parameters (1, and yt can be used to compute the rotational correlation time, tr, a useful measure of freedom of motion. Line widths in ESR spectra of nitroxide spin labels, for example, have been used to probe the motional freedom of biological macromolecules.14 Since tr is related to the molecular hydrodynamic volume, Ft, and the solution viscosity, r, by a relationship introduced by Debye 15... 

Fig. 6.9. A Spontaneous Raman spectrum of d62-DPPC lipids and its decomposition into Lorentzian line profiles. B Normalized multiplex CARS spectra (dots) of a planar-supported bilayer and monolayer formed by d62-DPPC on a glass-water interface for parallel-polarized input beams, together with the fit using the center frequency and line width parameters extracted from the decomposition analysis in (A) (solid line). The spectrum exposure time was 0.64 s. Error bars indicate the shot-noise standard deviation (Copyright American Chemical Society [70])...

In Eq. (10), E nt s(u) and Es(in) are the s=x,y,z components of the internal electric field and the field in the dielectric, respectively, and p u is the Boltzmann density matrix for the set of initial states m. The parameter tmn is a measure of the line-width. While small molecules, N<pure solid show well-defined lattice-vibrational spectra, arising from intermolecular vibrations in the crystal, overlap among the vastly larger number of normal modes for large, polymeric systems, produces broad bands, even in the crystalline state. When the polymeric molecule experiences the molecular interactions operative in aqueous solution, a second feature further broadens the vibrational bands, since the line-width parameters, xmn, Eq. (10), reflect the increased molecular collisional effects in solution, as compared to those in the solid. These general considerations are borne out by experiment. The low-frequency Raman spectrum of the amino acid cystine (94) shows a line at 8.7 cm- -, in the crystalline solid, with a half-width of several cm-- -. In contrast, a careful study of the low frequency Raman spectra of lysozyme (92) shows a broad band (half-width 10 cm- -) at 25 cm- -,... 

Phonon signals which do not overlap too much with other bands in the spectrum can be analysed using Least Squares routines. For most applications it is sufficient to use an overall line width parameter Y for TO and LO phonons and to approximate the spectral function by an oscillator profile which is a simple Lorentzian for T Oo according to... 

The next series of experiments consisted in measuring the variations in the line width parameters - a2 as a function of temperature. Figure 14 shows the superposition... 

Based on the presented research it can be stated, that the excited state line width parameter has an important influence on the CT2pa in the case of the moderate positive solvatochromic molecules, as the individual parameters may cancel each other. In the case of strongly negative solvatochromic molecule, the T probably just confirmed the tendency established by the three other parameters. 

Fig. 3.15, The CARS spectrum rotational width versus methane density for various values of parameter y (1) y = 0, (2) y = 0.3, (3) y = 0.5, (4) y = 0.7, (5) y = 0.75, (6) y = 0.9, (7) y = 0.95, (8) y = 1. Curves (4) and (6) are obtained by subtraction of the dephasing contribution from the line width calculated taking account of vibrational broadening. The other dependences are found assuming purely rotational broadening (vibrational relaxation neglected).

For homonuclear molecules s = / — j takes only even values whereas j is even for para modification and odd for ortho modification of the molecules. With a proper choice of fitting parameters any fitting law reproduces experimental line width rather well. Hence the good fit to their -dependence may not be considered as a criterion of quality of a fitting law. To discriminate between models it is necessary to gain agreement with experimental data on te or xE, which are much more... 

The spectra are calculated by numerical diagonalization of the nuclear Hamiltonian (4.49) and powder summation over the distribution of the EFG for different values of the asymmetry parameter rj. The line width was 0.25 mm s h... 

The 9Be NMR spectroscopy has been used in determination of the chiral binaphthyldiimine Be(II) complex [49].118 The measured 8Be value of 4.84 ppm and the line width of 40 Hz indicated the presence of a four-coordinate complex. The calculated 9Be NMR parameters were in good agreement with experimental results. 

Figure 4.14 shows the ESR spectrum of [Mn(CO)(dmpe)Cp]+. Clearly, the parallel features are rather variable in line width, with the low-field lines broad and the high-field lines narrow. The ESR parameters for this spectrum49 are given in Table 4.15 where (j is the angle between the g-matrix z-axis and the hyperfine matrix z-axis. 

Reproduced from ref. 48, with permission.) (a) Experimental spectrum at 120 K, (b) simulation with parameters of Table 4.15 and constant 4.1 G Gaussian line widths, (c) simulation with constant 4.1 G line widths, wg = 0.0049. (Reproduced with permission from ref. 48, copyright (1997) American Chemical Society.)... 

The values of A1/2 v for water protons in the D2O-solutions of the s- and p-fractions under discussion were measured over a temperature range from 20 to 55 °C [27]. The heat-induced variations of the A1/2 v parameter for these two copolymers are different (Fig. 5a and b). For instance, at temperatures from 20 to 24 °C, the line width of the water proton signal in the solution of the fraction p (Fig. 5a) broadens from 1.88 to 3.5 Hz, it narrows further... 

Several general observations can be made from the spectra and the calculated ESR parameters. First, the Na+- smectites possess narrower resonance line widths than the Ca +-smectites, with the exception of the saponite. Since Ca +-smectites, unlike Na+ -smectites, do not disperse into individual platelets in aqueous suspension, the Na+-smectite films formed by drying suspensions onto a smooth flat surface have the silicate surfaces more perfectly oriented in the plane of the film. As a result, less angular variation of the z-axis of Cu + relative to the plane of the film would narrow the spectra. One can see evidence of hyperfine splitting in the gj component of the Na+-smectite spectra, but not in the Ca +-smectite spectra. Saponite, unlike the other smectites, has very similar spectral linewidths for the Na+ and Ca + form (Figure 16). Since this Na+-saponite sample does not disperse completely in water (Table II), the alignment of Na+-saponite platelets in the clay film may be no better than that of the Ca +-saponite. 

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