Raman intensity frameworks

As is evident from the previous discussion, application of the algebraic framework to the calculation of Raman intensities is far from being comprehensive. First, one cannot use the simple expectation values of dipole operators (3.106) directly when dealing with higher-order terms in f. A proper treatment of these objects would require (at least in certain cases) using the exact form of matrix elements of T. Second, the onedimensional approach does not include rotations, so it lacks information... 

It has been found that the above theory is quite useful in predicting the correct overall behavior of matter in the presence of electromagnetic radiation. However, in order to predict correctly Raman intensities, it has been found necessary to refine the theory by accounting for small deviations in the electronic wave functions with nuclear motion. In the framework of the Herzberg-Teller theory, it is assumed that the corrected electronic wave functions may be obtained by the use of a first-order perturbation expansion as a linear combination of the complete set of zero-order Born-Oppenheimer functions, discussed above. Since here we are mainly interested in the normal Raman effect, we shall consider only corrections to the second term in Eq. (41). If we first examine corrections to the state X, the resulting expression for the derivative of the transition moment with motion along a normal mode is ... 

The IR spectra of silicon oxides, in the framework region mode, is dominated by a strong absorption around 1000 cm due the anti-symmetric stretching of the Si - 0 - Si unit (Raman inactive mode) and by a less intense absorption around 800cm due the symmetric stretching of the Si-O-Si unit (Raman active mode). In the transparency window between these two modes, the IR spectra of TS-1 shows an additional absorption band located at 960 cm ... 

In the early 1990s Raman spectroscopy was applied to the characterization of TS-1 catalysts [55,56]. In such experiments, beside the 960 cm band, already observed by IR spectroscopy (see Sect. 3.5), a new component at 1125 cm was detected by Scarano et al. [55] (see Fig. 2f). The 1125 cm band was recognized to be a fingerprint of the insertion of Ti atoms in the ze-olitic framework [55]. This band could not be observed in the IR studies as totally overshadowed by an extremely intense band around 1000 cm due to Si02 framework modes (Fig. 2e). 

On the basis of these assignments, the two bands must be associated with the presence of isolated Ti atoms in tetrahedral coordination within the silicalite framework. Consequently, a quantitative linear correlation between the Ti02 content and the intensities of both the infrared and Raman bands at 960 cm-1 is expected—and this is indeed observed, as shown in Fig. 9b. 

Furthermore, both the resonant (Fig. 6b) and non-resonant (Fig. 6a) Raman spectra give a constant value for the ratio of the intensity of IR band at 1125 cm-1 to that at 960 cm-1 (7(1125)//(960)) ratio of 0.25 and 11, respectively, for samples with varying TKU contents. This result suggests that the two bands should be related to two different spectroscopic manifestations of the same phenomenon, namely, incorporation of Ti in the silicalite framework (41). 

Bolis et al (43) reported volumetric data characterizing NH3 adsorption on TS-1 that demonstrate that the number of NH3 molecules adsorbed per Ti atom under saturation conditions was close to two, suggesting that virtually all Ti atoms are involved in the adsorption and have completed a 6-fold coordination Ti(NH3)204. The reduction of the tetrahedral symmetry of Ti4+ ions in the silicalite framework upon adsorption of NH3 or H20 is also documented by a blue shift of the Ti-sensitive stretching band at 960 cm-1 (43,45,134), by a decrease of the intensity of the XANES pre-edge peak at 4967 eV (41,43,134), and by the extinction of the resonance Raman enhancement of the 1125 cm-1 band in UV-Raman spectra (39,41). As an example, spectra in Figs. 15 and 16 show the effect of adsorbed water on the UV-visible (Fig. 15), XANES (Fig. 16a), and UV-Raman (Fig. 16b) spectra of TS-1. 

What is remarkable is that all of these early measurements of the UV resonance Raman spectra of nucleic acid components involved computational and theoretical support to their experimental findings. For example, Spiro used CINDO calculations to determine the nature of the excited electronic states of the nucleotides [157], In the early and mid 1970 s, many researchers were also attempting to understand resonance Raman spectroscopy, the types of information it could provide, and a unifying theoretical framework to the intensities [147, 159-172], UV resonance Raman spectra provided some of the first experimental evidence to test the various theoretical models. Peticolas attempted to fit the observed experimental excitation profiles of AMP [156], UMP [151, 154] and CMP [152, 153] to the sum-over-states model for the resonance Raman cross-sections. From these simulations, they were able to obtain preliminary excited-state structural dynamics of the nucleobase chromophores of the nucleotides for UMP [151, 153, 158] and CMP [153], For AMP, the experimental excitation profiles were simulated with an A-term expression, but the excited-state structural changes were not obtained. Rather, the goal of that work was to identify the electronic transitions within the lowest-energy absorption band of adenine [156],... 

Vibrational spectroscopy measures atomic oscillations practically on the scale as the scale of proton dynamics, 10-15 to 10 12 s. Fillaux et al. [110] note that optical spectroscopies, infrared and Raman, have disadvantages for the study of proton transfer that preclude a complete characterization of the potential. (However, the infrared and Raman techniques are useful to observe temperature effects inelastic neutron spectra are best observed at low temperature.) As mentioned in Ref. 110, the main difficulties arise from the nonspecific sensitivity for proton vibrations and the lack of a rigorous theoretical framework for the interpretation of the observed intensities. 

A series of ZSM-5 samples with differing framework aluminium contents (containing tetrapropylammonium cations, [TPA]+) have been characterised by Raman spectroscopy. Difference Raman spectra reveal evidence for two distinct occluded species in samples with non-zero framework aluminium content. These species have been Identified as [TPA]+ cations associated with framework anionic sites and non-framework anions such as Br or OH-, on the basis of correlations between the integrated intensities of difference spectra and zeolite aluminium content. The relative abundance of the two forms have been determined semi-quantitatlvely and empirical evidence for [TPA]+ disordering is reported. 

We assume that (i) the 960 cm band does not saturate for the TS-1 sample with lowest Ti content and (ii) the true Full Width at Half Maximum (FWHM) of this band is constant over all set of TS-1 samples. The former assumption is supported by the fact that the intensity of the 960 cm band, for the x = 1.0 sample, is less than 1.5 in absorbance units, while the latter is exactly what expected for a band associated to different concentrations of a unique species. Assumption (i) allows us to measure the true FWHM of the 960 cm band in TS-1 samples (27 cm ). Now, following assumption (ii), we were able to estimate for all samples reported in Fig. 3, the absorbance (W) at the height where the width of the band corresponds to 27 cm. This method minimize the errors due to the instrument sensibility and allows a quantitative estimation of the band intensity. Such obtained values plotted against x in the Fig. 3d ( data), give a high linear correlation (r = 0.9998) and validate assumption (i) and (ii). A further, and definitive, validation comes from the similar linearity found for the intensities of the Raman band, which can not be affected by saturation problems, see Fig. 3d ( data). These results implies that the 960 cm band is well a fingerprint of the insertion of Ti in the zeolitic framework, even if not... 

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