Raman effect treatment

The heavy alkali molybdates and -tungstates are known to exist in an orthorhombic modification as well, having the space group D h, Z =4) (55). The IR and Raman data 84), reproduced in Table 9, show clearly that vi and vz appear in the spectra for all these substances and that vz and vi are spht into three bands in the Raman effect. These comply for the most part with the simple site symmetry treatment where the anion has Cs S5nnmetry. 

Long, D. A., The Raman Effect A Unified Treatment of the Theory of Raman Scattering by Molecules, J. Wiley Sons, New York, 2002. 

A complete discussion of the theory of the coherent Raman effects is not possible in the available space. There are many excellent introductions and reviews for a more detailed treatment (2,3,4). Let us simply outline some basic considerations pertinent to the following discussion. The electronic polarization of a medium can be expressed as a power series in the electric field as in Equation (1). 

Thus it is seen that m varies not only with vq, the frequency of the incident light, but also with the frequencies vq H- and Vq — v. The molecule will therefore emit radiation, not only with the frequency equivalent to the frequency of the absorbed radiation, but also with frequencies vq -j-and Vq — v. This elementary treatment of the Raman effect shows that the appearance of Raman lines is to be associated with a change of polarizability during oscillation. A more detailed treatment of the Raman effect involves the use of a more complex expression than 9.9 for the variation of a. 

The interactions of electromagnetic radiation with the vibrations of a molecule, either by absorption in the infrared region or by the inelastic scattering of visible light (Raman effect), occur with the classical normal vibrations of the system (Pauling and Wilson, 1935). The goal of our spectroscopic analysis is to show how the frequencies of these normal modes depend upon the three-dimensional structure of the molecule. We will therefore review briefly in this section the nature of the normalmode calculation more detailed treatments can be found in a number of references (Herzberg, 1945 Wilson etal., 1955 Woodward, 1972 Cali-fano, 1976). We will then discuss the component parts that go into such calculations. 

An e1ementary but complete introduction to the Raman effect appears in a text by Guillory (2) which also discusses several other molecular spectroscopic structural probes. More rigorous treatments of the subject may be found in works dealing primarily with vibrational spectroscopic methods (3)-(6). A brief introduction to the theory of Raman spectroscopy follows and is based on the inelastic scatter ng of light by a nonabsorbing medium. 

Silver is an example of a metal that shows the surface-enhanced Raman effect. After a special surface treatment, the signal of a molecular group on the surface of the metal is enhanced by several orders of magnitude. One successful surface treatment is deposition of silver. So, after starting silver deposition from a cyanide electrolyte on a platinum electrode, a Raman signal of the CN-stretch vibration develops and reaches a limiting value (Figure 7.28). ... 

The rigorous derivation of the intensity formulas for the Raman effect or, indeed, for the infrared would require a completely satisfactory quantum mechanical theory of radiation, which does not appear to have been developed at this time. There seems to be little doubt, however, that essentially correct treatments of both these phenomena have been obtained, using as a foundation either the Dirac theory of radiation or the correspondence principle. There is not space to give the detailed... 

Partial Quantum Mechanical Treatment of the Raman Effect... 

Tensor representations, synonymous for product representations and their decomposition into irreducible constituents, are useful concepts for the treatment of several problems in spectroscopy. Important examples are the classification of the electronic states in atoms and the derivation of selection rules for infrared absorption or the vibrational Raman or hyper-Raman effect in crystals. In the first case the goal is to reduce tensors which are defined as products of one-particle wave functions, while in the second case tensors for the dipole moment, the electric susceptibility or the susceptibilities of higher orders have to be reduced according to the irreducible representations of the relevant point groups. 

D. Long, The Raman effect a unified treatment of the theory of Raman scattering by molecules (Wiley, Chichester, 2002)... 

Recent developments in Raman equipment has led to a considerable increase in sensitivity. This has enabled the monitoring of reactions of organic monolayers on glassy carbon [4.292] and diamond surfaces and analysis of the structure of Lang-muir-Blodgett monolayers without any enhancement effects. Although this unenhanced surface-Raman spectroscopy is expected to be applicable to a variety of technically or scientifically important surfaces and interfaces, it nevertheless requires careful optimization of the apparatus, data treatment, and sample preparation. 

A vibronic coupling model for mixed-valence systems has been developed over the last few years (1-5). The model, which is exactly soluble, has been used to calculate intervalence band contours (1, 3, 4, 5), electron transfer rates (4, 5, 6) and Raman spectra (5, 7, 8), and the relation of the model to earlier theoretical work has been discussed in detail (3-5). As formulated to date, the model is "one dimensional (or one-mode). That is, effectively only a single vibrational coordinate is used in discussing the complete ground vibronic manifold of the system. This is a severe limitation which, among other things, prevents an explicit treatment of solvent effects which are... 

V. Skakalova, A. B. Kaiser, U. Dettlaff-Weglikowska, K. Hrncarikova, S. Roth, Effect of chemical treatment on electrical conductivity, infrared absorption, and Raman spectra of single-walled carbon nanotubes, J. Phys. Chem. B, vol. 109, pp. 7174-7181, 2005. 

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