Classical Raman effect

If coherent radiation with a very high intensity is applied continuously or as pulse, non-linear effects can be observed which produce coherent Raman radiation. This is due to the quadratic and cubic terms of Eq. 2.4-14, which describe the dipole moment of a molecule induced by an electric field. Non-linear Raman spectroscopy and its application are described in separate chapters (Secs. 3.6 and 6.1), since this technique is quite different from that of the classical Raman effect and it differs considerably in its scope. 

The classical Raman effect produces only very weak signals. There are two techniques which very successfully enhance this effect. The resonance Raman spectroscopy RRS is making use of the excitation of molecules in a spectral range of electronic absorption. The surface-enhanced Raman spectroscopy SERS employs the influence of small metal particles on the elementary process of Raman scattering. These two techniques may even be combined surface-enhanced resonance Raman effect SERRS. Such spectra are recorded with the same spectrometers as classical Raman spectra, although different conditions of the excitation and special sample techniques are used (Sec. 6.1). 

Raman effect (continued) spectral activity, 339-341 terminology of, 295 vibrational wavefunctione, 339-341 Raman lines, 296 weak, 327-330 Raman scattering, 296 classical theory, 297-299 quantum mechanical theory, 296, 297 Raman shift, 296... 

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. 

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... 

The following classical description [21], while failing to explain many of the quantitative aspects of the Raman effect, is able to capture its qualitative behavior and provides a useful basis for understanding this phenomena. As in the case of Rayleigh scattering theory, the source of the scattering is the oscillating dipole moment,... 

The Raman effect can be seen, from a classical point of view, as the result of the modulation due to vibrational motions in the electric field-induced oscillating dipole moment. Such a modulation has the frequency of molecular vibrations, whereas the dipole moment oscillations have the frequency of the external electric field. Thus, the dynamic aspects of Raman scattering are to be described in terms of two time scales. One is connected to the vibrational motions of the nuclei, the other to the oscillation of the radiation electric field (which gives rise to oscillations in the solute electronic density). In the presence of a solvent medium, both the mentioned time scales give rise to nonequilibrium effects in the solvent response, being much faster than the time scale of the solvent inertial response. 

The fundamentals of the Raman effect can be understood by consideration of a classical model, in which an incident beam of radiation (i.e., laser beam, for all practical purposes, in flame diagnostics) passes through an ensemble of molecules. The resultant laser beam electric field distorts the electronic cloud distribution of each molecule, causing oscillating dipoles these induced dipoles are related to the incident laser beam electric field by the molecular polarizability. The dipoles, in turn, produce a secondary radiating field at essentially the same frequency as that for the incident beam. This radiation is termed Rayleigh scattering. 

As mentioned above, the basic theory of the Raman effect was developed before its discovery. However, at this time numerical calculations of the intensity of Raman lines were impossible, because these require information on all eigenstates of a scattering system. Placzek (1934) introduced a semi-classical approach in the form of his polarizability theory. This provided a basis for many other theoretical and experimental studies. Physicists and chemists worldwide realized the importance of the Raman effect as a tool for qualitative and quantitative analysis and for the detennination of structure. 

Placzek s theory (1934) which treats molecules as quantum objects and electromagnetic fields classically, satisfactorily describes the Raman effect on the condition that the exciting frequency differs considerably from the frequencies of electronic as well as of vibrational transitions. 

In the ordinary Raman effect, few molecules are found in their excited vibrational state. The strong pumping action of a laser beam changes this situation drastically, so that an appreciable fraction of all molecules in the laser beam are soon made available for anti-Stokes emission. Classically, the anti-Stokes radiation is generated by the interaction of the laser beam with molecular vibrations, but the phase of the latter is established by the still more intense Stokes radiation. As a consequence, an index-matching requirement... 

The classical theory of Raman scattering offered a mechanistic way of understanding the Raman effect but was unable to provide information on the intensity of Raman... 

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. 

To conclude this section, there is one other phenomenon we should like to discuss, viz. the Raman effect. Let it be mentioned beforehand, however, that this is not a revolutionary discovery, like, for example, the discovery of the wave nature of the electron, but an effect which was predicted by the quantum theory (Smekal (1923), Kramers-Heisenberg) some years before it was found experimentally, though it can also be explained within the framework of classical physics (Cabannes (1928), Rocard, Placzek) its great importance rests rather on the facility with which it can be applied to the study of molecules, and on the colossal amount of material relating to it which has been accumulated so quickly. The effect was discovered simultaneously (1928) by Raman in India, and by Landsberg and Mandelstam in Russia. They found that scattered light contains, in addition to the frequency of the incident light, a series of other frequencies. 

The classical argument for the Raman effect can be expressed mathematically as follows. Let fi be the dipole moment induced by an electric field E then the polarizability, a, is defined by... 

The quantum yield of the classical (or so-called linear) Raman effect is rather poor. Only a fraction of to 10 of the exciting photons are converted into Raman photons. This excludes the detection of low concentration analytes. Moreover, due to the quantum yield of fluorescence, even traces of fluorescent impurities may mask the Raman signal by their fluorescence. Therefore, there has been much scientific effort towards the development of Raman based methods which allow one to overcome this problem. Methods to overcome these problems are Resonance Raman Scattering and Surface Enhanced Raman Scattering. 

The mechanism by which the Raman effect occurs can be understood classically, although a quantum mechanical derivation is necessary for understanding the variation in line intensities and developing selection rules for predicting which vibrational modes are Raman active. Both descriptions are based upon an interaction between the oscillating induced polarization or dipole moment of the molecule (P) and the time-dependent electric field vector of the incident radiation (E). 

The Raman effect can be described by an elementary classical theory. When a... 

In the simple classical theory of the vibrational Raman effect [1] the electric vector is taken as the real expression... 

Quantum-mechanical expressions for the polarizability and other higher-order molecular response tensors are obtained by taking expectation values of the operator equivalent of the electric dipole moment (2.5) using molecular wavefunctions perturbed by the light wave (2.4). This particular semi-classical approach avoids the complications of formal time-dependent perturbation theory it has a respectable pedigree, being found in Placzek s famous treatise on the Raman effect [9], and also in the books by Born and Huang [lO] and Davydov [ll]. Further details of the particular version outlined here can be found in my own book [12]. 

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