Optical Theory of Raman Intensities

The valence-optical theory of Raman intensities (VOTR) is the first comprehensive theoretical formalism for interpreting vibrational intensities in the Raman 

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B. Valence Optical Theory of Raman Intensities An Example... 

The indices 1, 2 and 3 correspond to the numbering of unit vectors as defined above. At diis stage important approximations are introduced. It is required diat the unit vector e Ik) lies always along the bond k and that the bond polarizability tensor preserves its simple representation when the bond participates in vibrational motion. These approximations are kept in order to reduce the number of intensity parameters. A generalized version of the valence-optical theory of Raman intensities which considers ofiT-diagonal elements of the bond polarizability tensor has been discussed by Rupprecht [299]. 

Cartesian reference fiame, geometrical data, definition of internal and symmetry coordinates and a matrix for sulfiir dioxide were already given in Section 9.I1.B. The application of valence-optical theory of Raman intensities results in the set of electro-optical parameters given by Eq. (9.43). If these quantities are substituted inside the brace of Eqs. (9.33) and (9.34), the elements of ([a]) array are obtained... 

Skoog et al. [2] emphasized the instmmentation advances of the 1980s and early 1990s. Both Fourier-transform Raman (FT-Raman) spectrometers and single-stage spectrographs are discussed. There is some discussion of optical fiber probes, but none of the Raman microprobe. The authors sketch the theory of Raman scattering and present a classical (polarizability derivative) treatment of selection rules and intensity. Resonance enhancement and surface enhancement are treated briefly. In a textbook noted for its emphasis on instrumentation, there is little discussion of current applications. 

As was shown in Chapter 8, the experimental gas phase differential Raman scattering cross sections are directly related to the molecular polarizability derivatives wifli respect to normal coordinates forming the supeitensor intensity analysis die dot/dQj derivatives are usually further transformed into different types of parameters. The eventual goal is to transfonn the experimental observables into molecular quantities reflecting electro-optical properties of simple molecular sub-units. Several formulations for parametric interpretation of Raman intensities have been put forward. In this chapter the basic principles and characteristics of the theories developed will be discussed. The mathematical formalism inherent of each theoretical approach will be illustrated with examples. 

The present book appears more than ten years since the publication of "Vibrational Intensities in Infrared and Raman Spectroscopy," a volume edited by W. B. Person and G. Zerbi. It contains comprehensive reviews describing major developments in the field made during the seventies. Though not at a very fast pace, advances in the field, especially in theoretical approaches, have been made during the past fifteen years. In 1988 the monograph of L. A. Gribov and W. J. Orville-Thomas "Theory and Methods of Calculation of Molecular Spectra" was published. This volume presents, in detail, the progress achieved within the valence optical theory of infrared and Raman intensities. 

These results apply specifically to Rayleigh, or elastic, scattering. For Raman, or inelastic, scattering the same basic CID expressions apply but with the molecular property tensors replaced by corresponding vibrational Raman transition tensors between the initial and final vibrational states nv and rn . In this way a s are replaced by (mv aap(Q) nv), where aQ/3(<3) s are effective polarizability and optical activity operators that depend parametrically on the normal vibrational coordinates Q such that, within the Placzek polarizability theory of the Raman effect [23], ROA intensity depends on products such as (daaf3 / dQ)0 dG af3 / dQ) and (daaf3 / dQ)0 eajS dAlSf / dQ)0. 

This article reviews all the published work concerned with the study of vibrational optical activity in chiral molecules from measurements of a small difference in the intensity of Raman scattering in right and left circularly polarized incident light. The history and basic theory are described briefly, followed by an account of the instrumentation and the precautions that must be observed in order to suppress spurious signals. The various theories that have been proposed in order to relate stereochemical features to the observations are then outlined, this being followed by a survey of all reported Raman optical activity spectra. 

Thus the polarizability tensor of the molecule is written as a sum of local atomic polarizabilities, each modified through dipolar interactions with the electric dipole moments on all the other atoms induced by the electric vector of the incident light wave. Similarly for the local atomic polarizabilities appearing in the origin-dependent parts of the optical activity tensors. But unlike the bond polarizability development, no allowance can be made for intrinsic local optical activity tensors Gj ap and Aj since these now pertain to spherical atoms. We refer to the original articles for the explicit Raman intensity and optical activity expressions generated by the atom dipole interaction theory. 

Hecht et al. (1992) published the ROA spectra of pinanes and pinenes. They reported the SCP and ICP Raman optical intensities for right angle scattering in the four naturally occuring substances. The intensities for both experimental techniques in each case were identical within the noise level of the experiments, well in agreement with theory for far from resonance conditions. 

Some optical modes, contributing to the vibrational energy of the 3n-dimensional system, may not be observable by Raman scattering or infrared absorption for symmetry reasons (see Sec. V.E) or because of a weak scattered intensity. In fact, group theory is unable to predict exact intensities, because it is unable to predict frequencies. Only measurements can allow such determinations. 

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