Raman line shapes

Usually, particle size has relatively little effect on Raman line shapes unless the particles are extremely small, less than 100 nm. For this reason, high-quality Raman spectra can be obtained from powders and from polycrystalline bulk specimens like ceramics and rocks by simply reflecting the laser beam from the specimen surface. Solid samples can be measured in the 90° scattering geometry by mounting a slab of the solid sample, or a pressed pellet of a powder sample so that the beam reflects from the surface but not into the entrance slit (Figure 3). 

IR line shapes for this system have been measured at room and other temperatures. Isotropic, depolarized, and unpolarized Raman line shapes have also been measured. For this system all Raman line shapes are similar, peaking at about 3430 cm 1, with a shoulder at about 3625 cm 1 (at room temperature). The IR line shape is red-shifted by about 30 cm 1 and does not show the blue shoulder. Experimental IR [10] and unpolarized Raman [12] line shapes are shown in Fig. 3. 

Figure 3. Experimental [10, 12] and theoretical IR and unpolarized Raman line shapes for H0D/D20 at room temperature.

The Raman line shape is calculated with the bond polarizability model as described above. The unpolarized Raman line shape computed from the sum of the VV and VH line shapes is shown in Fig. 3. One again sees fair agreement between theory and experiment, with excellent peak position and evidence of a... 

In a recent experimental study involving the temperature dependences of the IR and Raman line shapes, Loparo et al. [14] confirmed that non-Condon effects are important in experimental (and theoretical ) line shapes, and they found a frequency dependence to the dipole derivative that is qualitatively similar to the form used in our work. 

IR and Raman line shapes have been measured for H0D/H20. They peak near 2500 cm 1 and have line widths in the 160 to 180 cm 1 range. Corcelli et al. [151] calculated these line shapes using the approaches described in Section III.C, for the SPC/FQ model, for temperatures of 10 90°C, finding quite good agreement with experiment. More recently, we have extended the method involving the quadratic electric field map for HOD/D20 [98] to HOD/H20 [52] and have calculated IR and unpolarized Raman line shapes. These line shapes, in comparison with experimental line shapes [12, 52], are shown in Fig. 7. Agreement between theory and experiment is excellent for both the IR and Raman. 

Vartiainen, E. M., Rinia, H. A., Muller, M., and Bonn, M. 2006. Direct extraction of Raman line-shapes from congested CARS spectra. Opt. Express 14 3622-30. 

J. Borysow and L. Frommhold, The Infrared and Raman Line Shapes of Pairs of Interacting Molecules, in Phenomena Induced by Intermolecular Interactions, G. Birnbaum, ed., Plenum, New York, 1985. 

We shall now briefly review the Kubo-Oxtoby theory of vibrational line-shape. The starting point for most theories of vibrational dephasing is the stochastic theory of lineshape first developed by Kubo [131]. This theory gives a simple expression for the broadened isotropic Raman line shape (/(< )) in terms of the Fourier transform of the normal coordinate time correlation function by... 

The majority of studies of vibrational dephasing have looked at the width or shape of the isotropic Raman line. The Raman line shape is the Fourier transform of the coherence decay function that characterizes dephasing (20,21). The coherence decay can also be measured directly in... 

A. One-Dimensional Measurements Raman Line Shape and Free Induction Decays... 

Thus the Raman echo adds vital new information on the dephasing process. This fact does not obviate Raman line shape or FID measurements. Because of their relative simplicity and experimental ease, these techniques remain valuable tools. However, using them in comparison with the Raman echo [Equations (11) and (12)] provides a much more complete and less model-dependent picture of vibrational dephasing than is possible with line shape or FID measurements alone. 

The third model assumes that the concentration fluctuations are long lived but not static. The dotted line in Fig. 12 shows good agreement with the data assuming a lifetime of 5 ps for the concentration fluctuations. A range of lifetimes from 4 to 7 ps is compatible with the data. This model not only agrees with the Raman echo data, it is also matches the FID and Raman line shape and peak position data as well. The lifetime found in the Raman echo implies that the Gaussian component of the line shape (4.25 cm-1) is actually motionally narrowed from the full distribution of frequencies (5.15 cm-1). 

Because density fluctuations produce a long-lived perturbation, whereas collisional dynamics are fast, the Raman echo is a definitive experiment for testing this prediction. An excellent system for this test is the sym-methyl stretch of acetonitrile (3). There have been many Raman line shape studies of this mode, which concluded that the IBC theory of collisional dynamics alone can account for the linewidth (84,90,91,133,134). On the other hand, calculations by George and Harris using Schweizer and Chandler s theory predicted that a substantial fraction of the linewidth is due to density fluctuations (135). 

Figure 13 Raman FID of the sym-methyl stretch in CH3CN (points). The exponential fit (solid curve) is consistent with the isotropic Raman line shape. (Adapted from Ref. 3.)...

I thank the coworkers who helped with the original work discussed here Prof. David A. Vanden Bout, Dr. Laura J. Muller, Dr. John E. Freitas, Dr. Xiaotian Zhang, and Hugh H. Hubble. I also thank Dr. Xun Pan and Prof. Richard MacPhail of Duke University for providing the Raman line shape data on CH3ECDCI3. This work was supported by the National Science Foundation. 

B. Hegemann and J. Jonas. Temperature study of Rayleigh and Raman line shapes in liquid carbonyl sulfide. J. Phys. Chem., 5 5851-5855 (1984),... 

Note that the exact form of the above ansatz is not critical for obtaining the general behavior of C(t), as described below, the important parameters being the decay time of the modulation correlation function and the mean square modulation depth . The analytical expression for C(t) is now differentiable to second order and exponential decay is followed only at long times t > Tp. Exjjerimental nonjjerfectly Lorentzian Raman line shapes can often be fitted with this equation. 

Very recently Shafer et al. (1973) have extended the analysis of Riehl (1973) using essentially the IIP of Gengenbach (1972) and, as additional experimental input, the Raman line shapes of May (1961) and Cooper (1970). It was possible to explain all experimental material very well by a potential function for the AIP which is in satisfying agreement with theoretical requirements at long and short range. 

M. Musso, F. Matthai, D. Keutel, and K. L. Oehme, Critical Raman line shape behavior of fluid nitrogen. PureAppl. Chem., 76 (2004), 147—155. 

In CS2 T2 can be measured by C n.m.r, relaxation measurements and from the Raman line shape [78]. The n.m.r. measurements correspond to the value of T2 obtained by integration and the Raman measurements to the value of T2 from the slope of C2(t). As we expect the simulated and experimental values obtained from the slopes are 10% larger than the values obtained by integrating under C2(t). For CS2 the agreement between simulation and experiment is good at room temperature, but the simulated values are 15% too high at the triple point. 

IR and Raman line shapes of ice Ih have also been recently studied by Skinner et al. [118-121]. The results of their calculations for isotopically substituted HOD in either H O or D O were presented in Ref. 118. The calculations, which exploit a mixed quantum/classical approach and a new TIP4P water model [122], yield... 

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