Raman overtone

Scalable Resonances in Global Treatment of IR, Raman, Overtone, and SEP Data for Standard Normal-Mode Hamiltonian... 

Since the Raman operators are derived from the electric dipole operators, the Raman intensity can be described in terms of the slope, (3, of the IR intensities. As a result, if the infrared intensity decreases by a factor of g for an overtone transition of +1, the corresponding Raman intensity (if active) will decrease by a factor of g. Although such a result is merely an approximate rule of thumb, it does seem to correlate well with the few available experimental data for Raman overtone transitions. A similar analysis can be carried out for any molecular point group. For example, an analysis of the CH stretching modes of benzene would involve using... 

Far from resonance, a fundamental (Au = 1) Raman transition is allowed if the normal mode involved corresponds to the same species as one of the components of the scattering tensor, provided this component is not antisymmetric. As we have seen, this last restriction does not apply under resonance conditions. In practice, Raman overtones are usually extremely weak far from resonance although they are not strictly forbidden. Under resonance conditions, they may be strong. 

Fig. 25. Excitation profiles (solid lines) and depolarization ratios (broken lines) of the first Raman overtone (w = 2) ofa molecule with fourfold symmetry subject to x e x eRenner-Teller coupling (after Siebrand and Zgierski, 1979c).

Figure 6 Raman spectra from different types of sp -hybridized nanocarbons, which are labeled. The main features (radial breathing mode (RBM), disorder-induced D band, the first-order Raman-allowed G and, and the second-order Raman overtones G ) are identified. (Reproduced from Ref. 9. American Chemical Society, 2010.)...

W Knippers, K van Helvoort, S Stolte, J Reuss. Raman overtone spectroscopy of ethylene. Chem Phys 98 1-6, 1985. 

Polyenes 1660-1580 6.02-6.33 in-w s br, often more than one band. In Raman, overtone bands may easily be observed... 

Albrecht A C, Clark R J H, Oprescu D, Owens S J R and Svensen C 1994 Overtone resonance Raman scattering beyond the Condon approximation transform theory and vibronic properties J. Chem. Phys. 101 1890-903... 

With broad-band pulses, pumping and probing processes become more complicated. With a broad-bandwidth pulse it is easy to drive fundamental and overtone transitions simultaneously, generating a complicated population distribution which depends on details of pulse stmcture [75], Broad-band probe pulses may be unable to distinguish between fundamental and overtone transitions. For example in IR-Raman experiments with broad-band probe pulses, excitation of the first overtone of a transition appears as a fundamental excitation with twice the intensity, and excitation of a combination band Q -t or appears as excitation of the two fundamentals 1761. 

Equations (6.5) and (6.12) contain terms in x to the second and higher powers. If the expressions for the dipole moment /i and the polarizability a were linear in x, then /i and ot would be said to vary harmonically with x. The effect of higher terms is known as anharmonicity and, because this particular kind of anharmonicity is concerned with electrical properties of a molecule, it is referred to as electrical anharmonicity. One effect of it is to cause the vibrational selection mle Au = 1 in infrared and Raman spectroscopy to be modified to Au = 1, 2, 3,. However, since electrical anharmonicity is usually small, the effect is to make only a very small contribution to the intensities of Av = 2, 3,. .. transitions, which are known as vibrational overtones. 

One effect of mechanical anharmonicity is to modify the Au = t infrared and Raman selection rule to Au = 1, 2, 3,. .., but the overtone transitions with Au = 2, 3,... are usually weak compared with those with Au = t. Since electrical anharmonicity also has this effect both types of anharmonicity may contribute to overtone intensities. 

In addition to bands in the infrared and Raman spectra due to Au = 1 transitions, combination and overtone bands may occur with appreciable intensity, particularly in the infrared. Care must be taken not to confuse such bands with weakly active fundamentals. Occasionally combinations and, more often, overtones may be used to aid identification of group vibrations. 

In Section 6.1.3 it was noted that vibrational overtone transitions, whether observed by infrared or Raman spectroscopy, are very weak. They become even weaker as the vibrational quantum number increases. The high sensitivity of CRDS makes it an ideal technique for attempting to observe such transitions. 

The thirty-two silent modes of Coo have been studied by various techniques [7], the most fruitful being higher-order Raman and infra-red spectroscopy. Because of the molecular nature of solid Cqq, the higher-order spectra are relatively sharp. Thus overtone and combination modes can be resolved, and with the help of a force constant model for the vibrational modes, various observed molecular frequencies can be identified with specific vibrational modes. Using this strategy, the 32 silent intramolecular modes of Ceo have been determined [101, 102]. 

Kwiatkowski and Lesczcynski and (2) Nowak, Adamowicz, Smets, and Maes. Within the harmonie approximation, ab initio methods yield very aeeurate frequeneies for the fundamental vibrations (normal eoor-dinate ealeulations) although in most eases the values need to be sealed (sealing faetor 0.9 to 0.98 depending on the theoretieal method used). The eomparison with the experimental speetrum suffers for the following reasons (1) most tautomerie eompounds are studied in solution while the ealeulated speetrum eorresponds to the gas phase (2) eombination, overtone, and Fermi resonanee bands are not eomputed and (3) ealeulations are mueh less aeeurate for absolute intensities than for frequeneies. This last problem ean be partially overeome by reeording the eomple-mentary Raman speetrum. Some representative publications are shown in Table V. 

Raman spectroscopy can in principle be applied to this problem in much the same manner as infrared spectroscopy. The primary difference is that the selection rules are not the same as for the infrared. In a number of molecules, frequencies have been assigned to combinations or overtones of the fundamental frequency of the... 

Figure 3. Energy schemata of transitions involving vibrational states (a excitation of 1st vibrational state - mid-IR absorption b excitation of overtone vibrations - near-IR absorptions c elastic scattering - Rayleigh lines d Raman scattering - Stokes lines e Raman scattering - Anti-Stokes lines f fluorescence).

At resonance with an electric dipole allowed transition, the Stokes resonance Raman scattering, I(tt/2), associated with a single totally symmetric mode and its overtones is proportional to... 

Fig. 2 Jablonski energy level diagram illustrating possible transitions, where solid lines represent absorption processes and dotted lines represent scattering processes. Key A, IR absorption B, near-IR absorption of an overtone C, Rayleigh scattering D, Stokes Raman transition and E, anti-Stokes Raman transition. S0 is the singlet ground state, S, the lowest singlet excited state, and v represents vibrational energy levels within each electronic state.

The number of fundamental vibrational modes of a molecule is equal to the number of degrees of vibrational freedom. For a nonlinear molecule of N atoms, 3N - 6 degrees of vibrational freedom exist. Hence, 3N - 6 fundamental vibrational modes. Six degrees of freedom are subtracted from a nonlinear molecule since (1) three coordinates are required to locate the molecule in space, and (2) an additional three coordinates are required to describe the orientation of the molecule based upon the three coordinates defining the position of the molecule in space. For a linear molecule, 3N - 5 fundamental vibrational modes are possible since only two degrees of rotational freedom exist. Thus, in a total vibrational analysis of a molecule by complementary IR and Raman techniques, 31V - 6 or 3N - 5 vibrational frequencies should be observed. It must be kept in mind that the fundamental modes of vibration of a molecule are described as transitions from one vibration state (energy level) to another (n = 1 in Eq. (2), Fig. 2). Sometimes, additional vibrational frequencies are detected in an IR and/or Raman spectrum. These additional absorption bands are due to forbidden transitions that occur and are described in the section on near-IR theory. Additionally, not all vibrational bands may be observed since some fundamental vibrations may be too weak to observe or give rise to overtone and/or combination bands (discussed later in the chapter). 

Fig. 9. (a) Infrared spectra of outgassed thin pellets of Ti-free silicalite (curve 1) and TS-1 with increasing Ti content x (curves 2-5). Spectra were normalized by means of the overtone bands between 1500 and 2000 cm-1 (not shown) and vertically shifted for clarity. The thick horizontal line represents the fwhm of the 960 cm-1 band for sample 2. By assuming that this band has a constant fwhm for any x, the absorbance W obtained is plotted as the ordinate in panel b, where the band has the same fwhm as in curve 2 (horizontal thin lines), (b) Intensity W of the 960 cm-1 infrared band (normalized absorbance units) as a function of x (full squares) and corresponding Raman counts (open squares) [Reprinted from Ricchiardi et al. (41) with permission. Copyright (2001) American Chemical Society]. 

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