Selection Rules for the Raman Effect

The selection rules for the Raman effect are quite different from those for IR spectroscopy. The mechanism involves interaction between the incident radiation and the fluctuating polarisability of the molecule, in contrast to the fluctuating dipole moment in IR absorption. The dipole moment is a vector quantity, and can be resolved into components along three Cartesian axes. The polarisability is a tensor quantity, whose components can be written as products of Cartesian axes. For a molecule having no symmetry at all, or having only a plane of symmetry, all... 

The selection rules for the Raman effect are obtained by replacing P in Eq. 8.37 by the components of induced dipoles. These components a,y are the nine elements of the polarizability tensor, where i, j = x, y, z. The aij form a basis for the same rep as ij, namely T(ij), so that a particular transition is allowed in the Raman effect if F(m) X F(>/) contains T ij). Many more necessary details regarding the intensities of IR and Raman spectra that are beyond the scope of the present work are given by Wilson, Decius, and Cross (5). 

For a harmonic oscillator, the selection rule for the Raman effect is the following. Let us assume that the harmonic oscillator is originally in the state a with quantum number n. Then the matrix element (ci R y) will be different from zero only if the state j has the quantum number nil. Similarly, if state h has the quantum number nij 0 R ) will be different from zero only if state y has the quantum number mil. Both matrix elements will be simultaneously different from zero only if m = n or m = n 2, so that we may conclude that the selection rule for Raman scattering by a harmonic oscillator is An = 0, 2. The first possibility corresponds to scattering of light of the incident frequency v the second corresponds to scattering of light of frequency v db 2vg, where is the fundamental frequency of the harmonic oscillator. 

In addition the reader may find tables with selection rules for the Resonance Raman and Hyper Raman Effect in the book of Weidlein et al. (1982). Special discussions about the basics of the application of group theory to molecular vibrations are given in the books of Herzberg (1945), Michl and Thulstrup (1986), Colthup et al. (1990) and Ferraro and Nakamoto (1994). Herzberg (1945) and Brandmiiller and Moser (1962) describe the calculation of thermodynamical functions (see also textbooks of physical chemistry). For the calculation of the rotational contribution of the partition function a symmetry number has to be taken into account. The following tables give this number in Q-... 

Since the occurrence of the Raman effect depends on the change in polarizability as vibration occurs, the selection rules are different for the Raman effect than they are for the infrared spectrum. In particular, in molecules with a center of symmetry the totally symmetric vibration is Raman-active, but is forbidden in the infrared since it produces no change in dipole moment. Thus the homonuclear diatomic molecules, H2, O2, N2, show the Raman effect but do not absorb in the infrared. There is also a purely rotational Raman eff ect in these molecules. However, in this case the selection rule is A J = 2. Thus we have for the rotational Stokes lines... 

Lucovsky (1972). Their basic unit is the As S3 molecule weakly coupled through a As-S-As bond to the next AsSa molecule (Figure 4.5a). Applying the selection rules for the AsSa molecule they were able to explain the observed difference between the effective phonon densities determined from the i.r. and Raman spectra (Figure 4.5b). Taylor etal (1973) interpret their extensive infrared and NMR studies as evidence for the remnants of the layers in the vitreous AS2S3 and AsaSea which persists into the liquid state (Tayloretal (1971)). 

For the Raman effect vibration in a harmonic oscillator potential leads to the same selection rule as for the normal IR spectrum... 

The selection rules for pure rotational transitions of symmetric tops are A7 = 1, AAi = 0 for direct absorption or emission, and A/= 1 or 2, AAi = 0 for the Raman effect. We obtain simple spectra in both cases, with a single series of lines (A/= +1) in absorption and two series (A7 = +1 and +2) in the Raman effect. Neglecting centrifugal distortion, these series have constant spacings of 2B or AB, and lines for all values of K coincide. If there is centrifugal distortion, separate lines can be observed for the different K values that are possible for each value of J, with frequencies (for A7 = 1) given by... 

According to section 8g, a frequency Vab is Raman active if one of the matrix elements of the type (a xy 6) is different from zero. Proceeding as above, we therefore have the selection rule for the appearance of fundamentals in the Raman effect The frequency Vi is Raman active if r(Q ) = r(a ), r(j/ ),r(3 ), V xy), T xz), or T yz), where T(Qi) is the irreducible representation to which the corresponding normal coordinate Qi belongs. 

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. 

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. 

The selection rules for fi hyper-Raman scattering were derived by Cyvin, Rauch, and Decius, 02) and those for y hyper-Raman scattering, which has not yet been detected experimentally, by Christie and Lockwood 103>. From their tables one can see that silent modes become 3-active for such important point groups as C6, D6, C3v, C6v, C. D, 0 and Oh. Examples of additional 7 activity can be found in the point groups C4v, C. D. D, and Oh. Long and Stanton 104) have derived a quantum-mechanical theory of the hyper-Raman effect which indicates several possibilities for resonance enhancement of hyper-Raman intensities. Iha and Woo 105) extended the theory of nonlinear... 

Infrared and Raman spectroscopy are often grouped together, since both techniques provide information on the vibrational modes of a compound. However, since the two spectroscopic techniques are based on different physical principles the selection rules are different. Infrared spectroscopy is an absorption phenomenon, while the Raman spectroscopy is based on a scattering phenomenon (Raman and Krishnan 1928). In general, infrared energy is absorbed by polar groups, while radiation is more effectively scattered in the Raman effect by symmetric vibrations and nonpolar groups (Colthup et al. 1990 Ferraro and Nakamoto 1994). For most molecules other... 

In the normal vibrational Raman effect it has been traditionally assumed that the scattering tensor is symmetric ( p = ffap). However, even in 92 Placzek (5) considered the consequences of antisymmetric contributions, which he termed magnetic-dipole scattering because of the agreement between the selection rules for an antisymmetric Raman process and for a magnetic-dipole transition. Placzek gave the expected value of the depolarisation ratio, p i = Ij /I = > for purely antisymmetric scat-... 

There have been a number of reports of analogous surface selection rules for Raman spectra [27-29]. However, for SERS, the situation is complicated by the essential roughness of the metal surface and the mixture of enhancement mechanisms, in addition to the facts that the Raman effect depends upon the molecular polarizability tensor and the excitation frequencies are typically high enough to reduce the metal conductivity to levels where finite parallel, as well as perpendicular, electric vectors are established at the surface. An excellent recent review of this subject has been written by Creighton [30]. Suffice it to say here that surface selection rules evidently do exist for Raman spectroscopy but they are more complicated than the rule for infrared and EELS. 

Another possible structure is that of a linear one with D h symmetry. In this case the selection rules for IR and Raman activity are mutually exclusive. Only one Raman line not coinciding with two IR lines would be expected. However, as a result of some crystal field effects, the mutual exclusive selection rules might break down. As a result, even in a linear structure all three lines mi t be observed both in the Raman and IR. 

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