Raman selection rules

Raman and IR spectroscopies are complementary to each other because of their different selection rules. Raman scattering occurs when the electric field of light induces a dipole moment by changing the polarizability of the molecules. In Raman spectroscopy the intensity of a band is linearly related to the concentration of the species. IR spectroscopy, on the other hand, requires an intrinsic dipole moment to exist for charge with molecular vibration. The concentration of the absorbing species is proportional to the logarithm of the ratio of the incident and transmitted intensities in the latter technique. 

Thus, Raman and IR spectra have different selection rules. Raman lines can be discovered where there is no IR absorption, and vice versa. 

Selection Rules Raman Rffecl. Since the intensities of Raman scattering are determined by the integrals... 

Is the transition between the ground and lowest excited singlet states of cyclobutadiene allowed by electric dipole selection rules, Raman selection rules, both, or neither ... 

The Si02 framework vibrations that occur at about 430, 800, 1070, and 1180cm in the fused silica spectrum (discussed in Section 1.4.2) can be explained by a vibrational calculation on a continuous random network (CRN) [36,37]. The 1070 and 1180 cm bands are assigned to the TO and LO modes of the Si-O asymmetric stretching vibration, respectively. Due to the selection rules, Raman-active modes involve symmetric vibrations, which... 

This spectrum is called a Raman spectrum and corresponds to the vibrational or rotational changes in the molecule. The selection rules for Raman activity are different from those for i.r. activity and the two types of spectroscopy are complementary in the study of molecular structure. Modern Raman spectrometers use lasers for excitation. In the resonance Raman effect excitation at a frequency corresponding to electronic absorption causes great enhancement of the Raman spectrum. 

CAHRS and CSHRS) [145, 146 and 147]. These 6WM spectroscopies depend on (Im for HRS) and obey the tlnee-photon selection rules. Their signals are always to the blue of the incident beam(s), thus avoiding fluorescence problems. The selection ndes allow one to probe, with optical frequencies, the usual IR spectrum (one photon), not the conventional Raman active vibrations (two photon), but also new vibrations that are synnnetry forbidden in both IR and conventional Raman methods. 

Perhaps the best known and most used optical spectroscopy which relies on the use of lasers is Raman spectroscopy. Because Raman spectroscopy is based on the inelastic scattering of photons, the signals are usually weak, and are often masked by fluorescence and/or Rayleigh scattering processes. The interest in usmg Raman for the vibrational characterization of surfaces arises from the fact that the teclmique can be used in situ under non-vacuum enviromnents, and also because it follows selection rules that complement those of IR spectroscopy. 

Another related issue is the computation of the intensities of the peaks in the spectrum. Peak intensities depend on the probability that a particular wavelength photon will be absorbed or Raman-scattered. These probabilities can be computed from the wave function by computing the transition dipole moments. This gives relative peak intensities since the calculation does not include the density of the substance. Some types of transitions turn out to have a zero probability due to the molecules symmetry or the spin of the electrons. This is where spectroscopic selection rules come from. Ah initio methods are the preferred way of computing intensities. Although intensities can be computed using semiempirical methods, they tend to give rather poor accuracy results for many chemical systems. 

In a diatomic or linear polyatomic molecule rotational Raman scattering obeys the selection rule... 

For a symmetric rotor molecule the selection rules for the rotational Raman spectmm are... 

One effect of mechanical anharmonicity is to modify the Au = t infrared and Raman selection rule to Au = 1, 2, 3,. .., but the overtone transitions with Au = 2, 3,... are usually weak compared with those with Au = t. Since electrical anharmonicity also has this effect both types of anharmonicity may contribute to overtone intensities. 

The rotational selection rule for vibration-rotation Raman transitions in diatomic molecules is... 

Because Raman scattering is also a two-photon process the selection rules for two-photon absorption are the same as for vibrational Raman transitions. For example, for a two-photon electronic transition to be allowed between a lower state j/" and an upper state... 

Graphite exhibits strong second-order Raman-active features. These features are expected and observed in carbon tubules, as well. Momentum and energy conservation, and the phonon density of states determine, to a large extent, the second-order spectra. By conservation of energy hut = huty + hbi2, where bi and ill) (/ = 1,2) are, respectively, the frequencies of the incoming photon and those of the simultaneously excited normal modes. There is also a crystal momentum selection rule hV. = -I- q, where k and q/... 

Raman spectroscopy can in principle be applied to this problem in much the same manner as infrared spectroscopy. The primary difference is that the selection rules are not the same as for the infrared. In a number of molecules, frequencies have been assigned to combinations or overtones of the fundamental frequency of the... 

Spectra of ra 5-Pt35Cl2F and the c/s-isomer show the simpler spectra expected from the trans-isomer (three Pt—F and two Pt—Cl stretches) compared with the m-isomer (four Pt—F and two Pt—Cl stretches). The complexity of the spectrum of the m-isomer is also the result of the lack of a centre of symmetry in the cis-form the selection rules allow all bands to be seen in both the IR and the Raman spectra (in theory, at least). 

The classical theory of scattering provides us with a relatively simple selection rule for Raman activity which can be compared with that for infrared activity. 

An important difference between the infrared and Raman selection rules... 

We may consider how this selection rule applies to the two cases of the infrared and Raman spectra ... 

The selection rules for isotropic Raman spectra ji = jf = j greatly simplify the formalism. The frequency matrix has only diagonal elements... 

W.G. Fateley, F. R. Dollish, N. T. Devitt, F. F. Bentley, Infrared and Raman Selection Rules for Molecular and Lattice Vibrations The Correlation Method, Wiley, New York, 1972... 

Thus the IR active modes will be determined by the matrix elements of the polarlsablllty matrix and not by a combination of the surface selection rule and the normal IR selection rules l.e. all of the Raman active modes could become accessible. This effect has been formalized and Its significance assessed In a discussion (12) which compares Its magnitude for a number of different molecules. In the case of acrylonitrile adsorption discussed In the previous section, the Intensity of the C=N stretch band appears to vary with the square of the electric field strength as expected for the Stark effect mechanism. 

Cyvin, S. J., Rauch, J. E. and Decius, J. C. (1965) Theory of hyper-Raman effects (nonlinear inelastic light scattering) selection rules and depolarization ratios for the second-order polarizability. 

Christie, J. H. and Lockwood, D. J. (1971) Selection rules for three- and four-photon Raman interactions. J. Chem. Phys., 54, 1141-1154. 

This broad band at 1500 cm was ascribed by Kaufman. Metin, and Saper-stein [10], to an IR observation of the amorphous carbon Raman D and G bands. This is forbidden by the selection rules, and has been attributed to the symmetry breaking introduced by the presence of CN bonds in the amorphous network. As carbon and nitrogen have different electronegativities, the formation of CN bonds gives the necessary charge polarity to allow the IR observation of the collective C=C vibrations in the IR spectrum. This conclusion was stated by the comparison of spectra taken from films deposited from N2 and N2. In the N2-film spectrum, no shift was observed for the 1500-cm band, whereas all other bands shifted as expected from the mass difference of the isotopes. Figure 25 compares... 

The hyperpolarizability tensor is obtained in a way similar to the case of SHG. However, the selection rules for an SFG resonance at the IR frequency implies that the vibrational mode is both IR and Raman active, as the SF hyperpolarizability tensor elements involve both an IR absorption and a Raman-anti-Stokes cross-section. Conversely, the DFG hyperpolarizability tensor elements involve an IR absorption and a Raman-Stokes cross-section. The hyperpolarizability tensor elements can be written in a rather compact form involving several vibrational excitations as [117] ... 

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