The Raman Effect

B) THE MICROSCOPIC HYPERPOLARIZABILITY IN TERMS OF THE LINEAR POLARIZABILITY THE KRAMERS-HEISENBERG EQUATION AND PLACZEK LINEAR POLARIZABILITY THEORY OF THE RAMAN EFFECT... 

Long D A 1988 Early history of the Raman effect Int. Rev. Phys. Chem. 7 314-49... 

It was predicted in 1923 by Smekal and shown experimentally in 1928 by Raman and Krishnan that a small amount of radiation scattered by a gas, liquid or solid is of increased or decreased wavelength (or wavenumber). This is called the Raman effect and the scattered radiation with decreased or increased wavenumber is referred to as Stokes or anti-Stokes Raman scattering, respectively. 

The incident radiation should be highly monochromatic for the Raman effect to be observed clearly and, because Raman scattering is so weak, it should be very intense. This is particularly important when, as in rotational Raman spectroscopy, the sample is in the gas phase. 

Long, D. A. (2002) The Raman Effect, John Wiley, Chichester. 

In the context of discussion of the Raman effect, Equation (5.43) relates the oscillating electric field E of the incident radiation, the induced electric dipole fi and the polarizability a by... 

Spectroscopic examination of light scattered from a monochromatic probe beam reveals the expected Rayleigh, Mie, and/or Tyndall elastic scattering at unchanged frequency, and other weak frequencies arising from the Raman effect. Both types of scattering have appHcations to analysis. 

Barkla, originally interested mainly in v-ray scattering, discovered characteristic x-rays by an experimental method similar in principle to that described above. His experimental arrangement (Figure 1-7) is reminiscent of that used today in studies of the Raman effect. By using an absorber in the form of sheets (Figure 1-7) to analyze the scattered beam in the manner of Figure 1-4, he obtained results that clarified the earlier experiments described above. 

Before discussing specific examples of the application of Raman spectroscopy to studying adsorbate-adsorbent interactions, it will be necessary, at this juncture, to explain the nature of the Raman effect. 

The nature of the spectrum and the terminology of the Raman effect are summarized in Fig. 1. 

Koningstein, J. A., Introduction to the Theory of the Raman Effect, Chapter I. Reidel Publ., Dordrecht, Netherlands, 1972. 

Additional experimental verification that molecules of hydrogen in condensed phases are in states approximating those for free molecules is provided by the Raman effect measurements of McLennan and McLeod.13 A comparison of the Raman frequencies found by them and the frequencies corresponding to the rotational transitions / = 0—>/ = 2 and/= 1— / = 3 (Table II) shows that the intermolecular interaction in liquid hydrogen produces only a very small change in these rotational energy levels. 

Since the Raman scattering is not very efficient (only one photon in 107 gives rise to the Raman effect), a high power excitation source such as a laser is needed. Also, since we are interested in the energy (wavenumber) difference between the excitation and the Stokes lines, the excitation source should be monochromatic, which is another property of many laser systems. 

In crystalline solids, the Raman effect deals with phonons instead of molecular vibration, and it depends upon the crystal symmetry whether a phonon is Raman active or not. For each class of crystal symmetry it is possible to calculate which phonons are Raman active for a given direction of the incident and scattered light with respect to the crystallographic axes of the specimen. A table has been derived (Loudon, 1964, 1965) which presents the form of the scattering tensor for each of the 32 crystal classes, which is particularly useful in the interpretation of the Raman spectra of crystalline samples. 

A molecule is composed of a certain number N of nuclei and usually a much larger number of electrons. As the masses of the electrons and the nuclei are significantly different, the much lighter elections move rapidly to create the so-called electron cloud which sticks die nuclei into relatively fixed equilibrium positions. The resulting geometry of die nuclear configuration is usually referred to as the molecular structure. The vibrational and rotational spectra of a molecule, as observed in its infrared absorption or emission and the Raman effect, are determined by this molecular geometry. 

Figure 2.52 Schematic representation of the transitions giving rise to the Raman effect. GS = ground electronic state, ES = excited electronic state, VS = virtual electronic stale, R = Rayleigh scattering, S = transitions giving rise to Stokes lines, AS = transitions giving rise to Anti-Stokes lines, RRS = transitions giving rise to resonance Raman.

The Raman effect arises when a photon is incident on a molecule and interacts with the electric dipole of the molecule. In classical terms, the interaction can be viewed as a perturbation of the molecule s electric field. In quantum mechanics the scattering is described as an excitation to a virtual state lower in energy than a real electronic transition with nearly coincident de-excitation and a change in vibrational energy. The scattering event occurs in 10 14 seconds or less. The virtual state description of scattering is shown in Figure 1. 

Inelastic scattering of light due to the excitation of vibrations had already been predicted in 1923 [37] and was confirmed experimentally a few years later by Raman [38], Because at that time the Raman effect was much easier to measure than infrared absorption, Raman spectroscopy dominated the field of molecular structure determination until commercial infrared spectrometers became available in the 1940s [10]. 

The Raman effect relates to scattering of light. Raman found that illuminating a transparent substance such as water causes a small proportion of the light to emerge... 

The Raman effect is tiny. At most, only one photon per 105 collides in an inelastic manner, the exact number depending on the energy (and hence frequency) of the incident light. 

The Raman effect by Neil Everett, Bert King and Ian Clegg in Chemistry in Britain, July 2000, p. 40, is a good general introduction, written for scientists with no prior experience of Raman spectroscopy. Each of the books cited above under general reading discuss Raman spectroscopy, but in greater depth. 

The Raman effect is produced when the frequency of visible light is changed in the scattering process by the absorption or emission of energy produced by changes in molecular vibration and vibration-rotation quantum states. 

The dominant tendency of my studies has been not so much to obtain and describe organic compounds but... to penetrate their mechanisms.. . . For undertaking this kind of problem, the classic methods of organic chemistry are far from sufficient. Physicochemical procedures become more and more necessary. I have been led to use especially optical methods (the Raman effect and ultraviolet spectra) and electrochemical techniques (conductibility, electrode potentials, and especially polarography).. . . The notion of reaction mechanism led almost automatically to envisioning the electronic aspect of chemical phenomena. From 1927, and working in common with Charles Prevost, I have directed my attention on the electronic theory of reactions." 56... 

Figure 1.14 The spectral manifestation of the Raman effect, (a) The spectrum of the incident light, (b) The spectrum due to scattered (Rayleigh and Raman) light, (c) The Raman spectrum. The relative intensities of the incident, Rayleigh, and Raman hnes are quite different in real...

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