Vibrational Raman effect, classical

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

A classical description of the vibrational Raman effect (which was the main process studied before the introduction of lasers) has been developed by Placek [8.8]. It starts from the relation... 

While the vibrational Raman effect has the same selection rule as the IR transitions, different rules apply for the rotational Raman effect (compare with the classical picture )... 

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 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. 

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 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. 

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). 

Fig. 1.32. Classical theory for the origin of the Raman effect. In (a) we see a diatomic molecule where represents protons and represents the center of gravity of the electrons. The electrons are displaced by the external field of the photon and an induced dipole moment is generated which changes when the bond length changes during the molecular vibration. The induced dipole moment is plotted in (b) as an amplitude modulated wave with steady amplitude components shown in (c) from which scattered radiation is generated.

The theoretical basis of the inelastic scattering, or Raman effect, as it is known nowadays, can be understood involving physical approaches the classical, where the contributions of the elastic and the inelastic effects can be seen clearly, and the quantum approach, where it seems very clear that the effect can be explained on the basis of a mixture of electronic and vibrational states of the matter, giving rise to the vibronic model to explain the physical vision. 

We have described our most recent efforts to calculate vibrational line shapes for liquid water and its isotopic variants under ambient conditions, as well as to calculate ultrafast observables capable of shedding light on spectral diffusion dynamics, and we have endeavored to interpret line shapes and spectral diffusion in terms of hydrogen bonding in the liquid. Our approach uses conventional classical effective two-body simulation potentials, coupled with more sophisticated quantum chemistry-based techniques for obtaining transition frequencies, transition dipoles and polarizabilities, and intramolecular and intermolecular couplings. In addition, we have used the recently developed time-averaging approximation to calculate Raman and IR line shapes for H20 (which involves... 

A classical treatment of Raman scattering (3,4) is based on the effects of molecular vibrations on the polarizability, a, in Eq. (2.1). Consider the incident optical electric field to be governed by Eq. (2.2) ... 

Vibrational dynamics are dominantly represented with normal modes that are coherent harmonic oscillations of all degrees of freedom at the same frequency [Wilson 1964 Califano 1981 Long 2002 Ferraro 2003], In the classical regime, normal coordinates - the eigenvectors of the dynamical matrix -are determined only to an arbitrary proportionality factor. In other words, the effective mass associated to a normal mode is arbitrary. This is of no consequence for optical spectroscopy techniques (infrared and Raman) that cannot probe masses, because of tiny momentum transfer values. Only recently, effective masses have been determined thanks to vibrational spectroscopy with neutrons [Ikeda 2002], The existence of well-defined (of course) effective masses should be included in further theoretical developments. 

In their now classic study of the effect of surface forces on adsorbed molecules, Sheppard and Yates (26) found that some of the Raman-active vibrations of methane, ethylene, and hydrogen appeared in the infrared when these materials were adsorbed on silica. The frequency shifts for the molecule on going from the gas phase to the adsorbed phase were all rather small, indicating that no chemical change in the species was brought about by the adsorption. 

The effect can be described by classical mechanics in terms of forced vibrations of harmonic oscillators. Here since the molecular polarizability t. changes slightly as Ihe bond distorts, nonlinear effects give rise to dipole oscillations at frequencies other than the imposed frequency. Raman himself seems to have been led to this discovery, at least In part, by his theoretical studies of Ihe vibrations of musical instruments such as the violin. 

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