Raman overlap

The quantity < f m > e has been termed Raman overlap (Myers and Mathies, 1987). It is the product of the modulus of a time-dependent Franck-Condon factor between the final state and the initial wavefunction propagated on the electronic surface, i. e. I < f m > I and a damping function e which decreases exponentially with time. 

Figure 6.1-2 The time-dependent picture of resonance Raman scattering panel A interaction of the incident photon with the electronic transition moment sends the initial vibrational state / > to the excited electronic surface, where it is propagated by the excited-state vibrational Hamiltonian panel B the Raman overlap < /li(i) as a...

Since the Raman intensity If, (Eq. 6.1-2) is proportional to the modulus. square of ayj and the latter is obtained by integration over the Raman overlap function (Eq. 6.1-17) the Raman excitation profile Ij = /yi(wo)) can be directly calculated by a half Fourier transformation of the Raman overlap. This has been done in panel C of Fig. 6.1-2, where for the case discussed in panels B and C the Raman intensity is plotted as a function of excitation energy E( =liuJo). 

A RIKES experunent is essentially identical to that of CW CARS, except the probe laser need not be tunable. The probe beam is linearly polarized at 0° (—>), while the polarization of the tunable pump beam is controlled by a linear polarizer and a quarter waveplate. The pump and probe beams, whose frequency difference must match the Raman frequency, are overlapped in the sample (just as in CARS). The strong pump beam propagating tlirough a nonlinear medium induces an anisotropic change in the refractive mdices seen by tlie weaker probe wave, which alters the polarization of a probe beam [96]. The signal field is polarized orthogonally to the probe laser and any altered polarization may be detected as an increase in intensity transmitted tlirough a crossed polarizer. When the pump beam is Imearly polarized at 45° y), contributions... 

The infra-red measurements were of two types, normal-film measurements with the sample sandwiched between KBr plates, and tilted-film experiments with the sample sandwiched between 45° prisms of KBr, in each case with layers of Nujol to provide optical matching. Whereas the 1616 cm 1 Raman line occurs in a region well clear of other lines so that it was satisfactory to measure peak intensities, the infra-red spectrum of PET shows many overlapping bands. Accurate assessment of absorption intensities therefore requires the computer separation of the spectrum into a set of overlapping peaks (shown to be Lorentzian in profile) and a linear background. The procedures adopted and the band assignments are discussed in detail by Hutchinson et al. 6). 

Storer model used in this theory enables us to describe classically the spectral collapse of the Q-branch for any strength of collisions. The theory generates the canonical relation between the width of the Raman spectrum and the rate of rotational relaxation measured by NMR or acoustic methods. At medium pressures the impact theory overlaps with the non-model perturbation theory which extends the relation to the region where the binary approximation is invalid. The employment of this relation has become a routine procedure which puts in order numerous experimental data from different methods. At low densities it permits us to estimate, roughly, the strength of collisions. 

The components of the low lying Raman doublet (h2g> b ) at about 30 cm exhibit a different temperature dependence which gives rise to a reverse assignment at 300 K [103, 104] in comparison to the low temperature studies (< 20 K) see Figs. 2 and 3. In fact, the bands overlap at about 50 K [114]. 

The basic methods of the identification and study of matrix-isolated intermediates are infrared (IR), ultraviolet-visible (UV-vis), Raman and electron spin resonance (esr) spectroscopy. The most widely used is IR spectroscopy, which has some significant advantages. One of them is its high information content, and the other lies in the absence of overlapping bands in matrix IR spectra because the peaks are very narrow (about 1 cm ), due to the low temperature and the absence of rotation and interaction between molecules in the matrix. This fact allows the identification of practically all the compounds present, even in multicomponent reaetion mixtures, and the determination of vibrational frequencies of molecules with high accuracy (up to 0.01 cm when Fourier transform infrared spectrometers are used). 

The TED and XRD patterns revealed that the deposit is not amorphous carbon but nanocrystalline diamond. Nonetheless, the 514-nm excited Raman spectra do not exhibit a clear diamond peak at 1332 cm though the peak due to the sp -bonded carbon network appears at 1150 cm The Raman cross section of the sp -bonded carbon network with visible excitation is resonantly enhanced [43, 48-50]. It consequently makes the 1332 cm diamond peak overlap with the peaks due to sp -bonded carbon. 

Raman and IR spectra taken from the same a-C(N) H film [10], showing an almost perfect overlapping of the two bands. 

The identification of xanthophylls in vivo is a complex task and should be approached gradually with the increasing complexity of the sample. In the case of the antenna xanthophylls, the simplest sample is the isolated LHCII complex. Even here four xanthophylls are present, each having at least three major absorption transitions, 0-0, 0-1, and 0-2 (Figure 7.4). Heterogeneity in the xanthophyll environment and overlap with the chlorophyll absorption add additional complexity to the identification task. No single spectroscopic method seems suitable to resolve the overlapping spectra. However, the combination of two spectroscopic techniques, low-temperature absorption and resonance Raman spectroscopy, has proved to be fruitful (Ruban et al., 2001 Robert et al., 2004). 

An example of a RRS spectrum from the yellow solution with Xj=488 nm (u> =20 492 cm-l) is shown in Fig. 4. Also shown are spectra in the v =C regions. The Raman modes of interest are the 667 cra l CHCI3 peak which is used for polymer mode normalization, VC=C at 1520 cm-l and v =C at 2120 cm-l. Analysis of the peaks in the yellow solution is straightforward because the Raman bands do not overlap. 

Raman spectroscopy has been used by several authors as an indent-ification method by comparing spectra of solutions with spectra of solid phases of known structure (85, 92-95). The heptamolybdate could be clearly identified (cf. below) and its spectrum in the solid state and aqueous solution is well characterized (93, 94). Other polyanions seem to be more difficult to identify because overlapping equilibria tend to conceal small changes in the spectrum upon acidification. 

In the preceeding section mention was made of ion association (ion-pairing) which, for the purposes of this paper, will refer to coulombic entities with or without cosphere overlap. Experimental support for ion-pairing has come from sound attenuation (2). Raman spectroscopy (2) and potentiometry (2, 2). Credibility has resulted from the model of Fuoss (2) applied by Kester and Pytkowicz (2). 

In resonant Raman spectroscopy, the frequency of the incident beam is resonant with the energy difference between two real electronic levels and so the efficiency can be enhanced by a factor of 10 . However, to observe resonant Raman scattering it is necessary to prevent the possible overlap with the more efficient emission spectra. Thus, Raman experiments are usually realized under nonresonant illumination, so that the Raman spectrum cannot be masked by fluorescence. 

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