Raman intensities of lattice modes and the oriented gas model (original) (raw)
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Journal of Physics: Condensed Matter, 1998
Polarized Raman spectra of (Rb x (NH 4 ) 1−x ) 2 SO 4 crystals (x = 0.1 and 0.7) were studied in the temperature range 10-300 K. Thorough site-symmetry analysis of internal SO 2− 4 and NH + 4 vibrations combined with factor-group analysis based on hexagonal pseudosymmetry allowed us to make an assignment of the observed modes. The spectra of the x = 0.1 sample are compatible with those of pure (NH 4 ) 2 SO 4 including the features of the disorder in the paraelectric phase above 220 K (the broad central peak of the relaxator type and high mode damping) and ordering in the ferroelectric phase. The spectra of the x = 0.7 sample show a much smaller disorder at high temperatures (no broad central mode and lower mode damping) due to the lower ammonium content, but clearly confirm the onset of the dynamic dipolar glass transition (short-range correlations inducing the appearance of long-lived dipolar clusters) near 220 K.
Physical Review E, 2010
The orientational order parameters in liquid crystals have been a subject of interest during the last decades since they quantify the degree of intrinsic long range orientational order, which is characteristic of all liquid crystal phases. In the earliest attempts to explain the anisotropic properties of nematic liquid crystal several assumptions had to be made, for instance, rigid rod-like molecular structure and uniaxiality of the nematic phase . The theoretical efforts for modeling a nematic phase led to an anisotropic orientational distribution function (ODF), f(T). The ODF is expanded in terms of Legendre polynomials and their expansion coefficients may be viewed as the orientational order parameters. The first two non-trivial orientational order parameters, <P 2 > and <P 4 >, are of particular interest since they can be measured experimentally. As a matter of fact, the molecular field theories such as Maier-Saupe (MS) or Humphries-James-Luckhurst (HJL) impose conditions in the possible behavior of these order parameters . Several experimental techniques have been developed for obtaining reliable values of <P 2 >. However, only few of them can also determine the value of <P 4 > [4-14], Raman spectroscopy and X-ray diffraction are among these methods. Measurements of vibrational Raman depolarization ratio in different orthogonal linear polarization conditions is a traditional method to find the order parameters <P 2 > and <P 4 > in liquid crystals . In their pioneering work, Jen et al. laid the foundations to determine simultaneously <P 2 > and <P 4 > by Raman spectroscopy in a backscattering configuration . Even though the values for <P 2 > with this method were in agreement with previous results derived by several other methods , the values for <P 4 > were rather in disagreement with those results and beyond experimental uncertainty. In fact, <P 4 > was unexpectedly negative in many cases . Several attempts were made trying to explain these results [9]; however, there could not be found a convincing argument. Other more reasonable ideas regarding internal field correction were suggested . Although these corrections improved the results of <P 4 >, they were not enough to fit the values in any of the molecular field theories. Moreover, the values for <P 4 > were still lower than those predicted by the Maier-Saupe model, suggesting a theoretical overestimation in this model. Therefore, there was a deep mystery concerning the value of <P 4 > and its sign anytime it was determined by the Raman technique. In recent years, Jones et al. extended the experimental work done by Jen et al and developed a theoretical method to determine <P 2 > and <P 4 > by a fitting procedure . Basically, a detailed intensity profile over a particular angular distribution of the scattered Raman signal and under two different polarization conditions is measured. Thus, the order parameters and the differential polarizability ratio r can be obtained from a simultaneous fitting procedure of such intensities profiles, I ZZ and I YZ . The main advantage of this method is that only one planar cell is required unlike the method by Jen et al., where three different alignment geometries are required. On the other hand, X-ray as mentioned above is another conventional method to obtain <P 2 > and <P 4 > . However, X-ray and Raman experiments probe features of the sample differently. On one hand, the X-ray diffraction pattern arises because of the interaction between the X-ray beam and the electron density distribution inside the sample; on the other
2014
David Tuschel In this second installment of a two-part series we present polarized Raman spectra and discuss the association of the symmetry species of the normal vibrational mode and the depolarization ratio of Raman scattering. We discuss those aspects of molecular symmetry and Raman polarization rules that can be applied with normal Raman instrumentation. Materials include liquids, single crystals, and polycrystalline compounds. Practical Group Theory and Raman Spectroscopy, Part II: Application of Polarization Molecular Spectroscopy Workbench
A New Approach to the Vibronic Spectra of Molecular Crystals
physica status solidi (b), 1967
A study is made of the experimental consequences of the theory of the vibrational spectra of molecular crystals presented recently in [3]. A discussion is also given of the model used in this theory. A detailed comparison is made between the theory and experimental results for pure and isotropic doped naphthalene crystals in the M‐band region. The theory accounts for the decay of electronic‐vibrational intra‐molecular excitations into pure electronic and intra‐molecular vibrational excitations by a resonance interaction. In this case the crystal spectrum should exhibit a wide absorption band corresponding to two‐particle excitation. If the reduction of the vibrational frequencies of the molecule accompanying its electronic excitation is comparable with the pure electronic excitation band width, the spectrum should also show a narrow band corresponding to a one‐particle excitation. These bands should be associated with the vibrational band which is observed experimentally. This idea ...
Practical Group Theory and Raman Spectroscopy, Part II: Application of Polarization
In this second installment of a two-part series we present polarized Raman spectra and discuss the association of the symmetry species of the normal vibrational mode and the depolarization ratio of Raman scattering. We discuss those aspects of molecular symmetry and Raman polarization rules that can be applied with normal Raman instrumentation. Materials include liquids, single crystals, and polycrystalline compounds.
The prediction of Raman spectra by density functional theory. Preliminary findings
Chemical Physics Letters, 1995
We report the first calculations of Raman vibrational intensities by density functional theory, implemented within the Q-Chem program. Local (S-VWN) and gradient-corrected (B-LYP) DF'I" results are compared with experimental and Hartree-Fock results for the N 2, HF and C2H 6 molecules. Preliminary indications are that local DFT compares less favorably to experiment than either Hartree-Fock or gradient-corrected DF'I'. The Hartree-Fock and B-LYP results are generally similar except for the HF molecule, where B-LYP is somewhat better. For all methods, best results were obtained by augmenting the basis set with diffuse polarization functions.
The Journal of Physical Chemistry A, 2001
A methodology for the theoretical evaluation of vibrational Raman scattering intensities for molecules in solution in the polarizable continuum model (PCM) framework is presented. Raman intensities are expressed in terms of derivatives of the dynamic effective polarizability with respect to nuclear coordinates. Local field effects are included by considering both the solvent polarization induced by the probing field (cavity field) and the solvent reaction field. The dependence of computed Raman intensities on the parameters of the calculation (basis set, exchange-correlation functional for DFT calculations, and cavity size) is discussed. A comparison between PCM and semiclassical values for simple molecules in various solvents is made.