Vibrational intensity

There are cases where the variation of the electtonic ttansition moment with nuclear configuration caimot be neglected. Then it is necessary to work with equation (B 1.1.6) keeping the dependence of on Q and integrating it over the vibrational wavefiinctions. In most such cases it is adequate to use only the tenns up to first-order in equation (B 1.1.7). This results in modified Franck-Condon factors for the vibrational intensities [12]. 

In general, the -dependent variations of natural atomic charges in dative bonds are significantly larger than those in covalent bonds. Indeed, the Q (R) variations in dative bonds resemble those in ionic bonds (cf. Fig. 2.9), to which they are evidently related by similarities in donor-acceptor character. The strong AQ /AR dependence tends to be associated with enhanced infrared vibrational intensity and other spectroscopic signatures characteristic of ionic bonding. 

Person, W.B., and Zerbi, G. Eds., Vibrational intensities in Infrared and Raman Spectroscopy, Elsevier, Amsterdam (1982). 

Vibrational intensity distributions have not been measured in any of the room... 

Galabov BS, Dudev T (1996) Vibrational intensities. Elsevier Science, Amsterdam... 

More recently, the PCM has been amply extended to the treatment of vibrational spectroscopies, by taking into account not only solvent-induced vibrational frequency shifts, but also vibrational intensities in a unified and coherent formulation. Thus, models to treat IR [8], Raman [9], IR linear dichroism [10], VCD [11] and VROA [12] have been proposed and tested, by including in the formulation local field effects, as well as an incomplete solute-solvent regime (nonequilibrium) and, when necessary, by extending the model to the treatment of specific solute-solvent (or solute-solute) effects. 

The quantities of interest in vibrational spectra are frequencies and intensities. Within the double harmonic approximation, vibrational frequencies and normal modes for solvated molecules are related, within the continuum approach, to free energy second derivatives with respect to nuclear coordinates calculated at the equilibrium nuclear configuration. The QM analogues for vibrational intensities , depend on the spectroscopy under study, but in any case derivative methods are needed. 

In order to formulate a theory for the evaluation of vibrational intensities within the framework of continuum solvation models, it is necessary to consider that formally the radiation electric field (static, Eloc and optical E[jc) acting on the molecule in the cavity differ from the corresponding Maxwell fields in the medium, E and Em. However, the response of the molecule to the external perturbation depends on the field locally acting on it. This problem, usually referred to as the local field effect, is normally solved by resorting to the Onsager-Lorentz theory of dielectric polarization [21,44], In such an approach the macroscopic quantities are related to the microscopic electric response of... 

From the two preceding sections, it is clear that VCD and ROA are measured in entirely different ways. Most of these differences stem from the way in which the parent vibrational intensity is measured. In the case of ROA, the spectral region is the visible, where it is possible to reach photon-limited background... 

Pearson, W. Serbi, G. Vibrational Intensities in Infrared and Raman Spectroscopy, Amsterdam Elsevier, 1982. 

Since the intensity calculation can be reduced to calculating a and for deformed molecules, the availability of quantum chemical methods immediately led to attempts to employ them to determine vibrational intensities (Segal and Klein, 1967). The polarizability is the proportionality factor between the induced dipole moment and the inducing electric field. It is therefore necessary to use a perturbation treatment which takes the electric field into account. Two different approaches were explored the Finite... 

Near-infrared absorption is therefore essentially due to combination and overtone modes of higher energy fundamentals, such as C-H, N-H, and O-H stretches, which appear as lower overtones and lower order combination modes. Since the NIR absorption of polyatomic molecules thus mainly reflects vibrational contributions from very few functional groups, NIR spectroscopy is less suitable for detailed qualitative analysis than IR, which shows all (active) fundamentals and the overtones and combination modes of low-energy vibrations. On the other hand, since the vibrational intensities of near-infrared bands are considerably lower than those of corresponding infrared bands, optical layers of reasonable size (millimeters, centimeters) may be transmitted in the NIR, even in the case of liquid samples, compared to the layers of pm size which are detected in the infrared. This has important consequences for the direct quantitative study of chemical reactions, chemical equilibria, and phase equilibria via NIR spectroscopy. 

Inspection of the density and the temperature dependence of the vibrational intensity B (see Eq. 6.2-3) provides further evidence of the weakness of intermolecular interactions in compressed carbon monoxide. Thus, the spectroscopic properties in the dense fluid phase are either quite similar to the corresponding gas phase values or are closely related to these values and may be derived from data of the gas phase spectrum. Fig. 6.2-6 shows the density dependence of the reduced vibrational intensity for the first and second overtones of CO. 

Figure 6.2-6 Density dependence of the reduced vibrational intensity BIBq of the first overtone (triangles) and second overtone (circles) of pure CO Bq is the respective vibrational intensity in the gas phase.

The vibrational intensities B(0 v) of fundamental and overtone modes may be related to the electric dipole moment function M(r) around the equilibrium internuclear distance of the diatomic molecule (Chackerian, 1976) via rotationless matrix elements... 

The vibrational intensities and their dependence on the temperature and the pressure are of special interest to quantitative analysis covering an extended region of states. Fig. 6.2-11 shows the vibrational intensity of the 31 3 second overtone, B (6700-7300), which has been determined by integration of the experimental absorbance spectra in the wavenumber region between 6700 cm and 7300 cm. The data points are mean values for the temperature range from 25 °C to 227 °C. A temperature dependence of the vibrational intensity at constant density cannot be detected. 

Figure 6.2-11 Density dependence of the vibrational intensity of pure CO2 in the wavenumber range from 6700 cm to 7300 cm. The data points are mean values for the temperature range between 25 °C and 227 °C.

Up to a density of about 1.0 g cm the vibrational intensity is found to be independent of the temperature and the density (or pressure). At the highest densities, B (6700-7300) slightly decreases. This behavior, which is also observed in several other near-infrared bands of CO2 (Buback et al., 1986a, 1986b), seems to indicate that repulsive interactions are becoming important in highly compressed fluid CO2. This assumption is supported by an inspection of the density dependence of the band maximum positions. In Fig. 6.2-12, the wavenumbers of maximum absorption in the P and the R branch, i>p(max) and i> (max), of the component around 4980 cm (see Fig. 6.2-8) are plotted versus the density. The arithmetic mean values of the P and R branch maxima, i> , which are shown as full circles in the lower density spectra, linearly decrease with the density. They can be... 

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