Selection rules for Raman spectra

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. 

We will see later (p. 76) that the selection rules for Raman spectra are different from those for vibrational-rotational spectra. Thus a molecule giving no infrared spectrum may have a Raman spectrum and vice versa. 

Both infrared and Raman spectra are concerned with measuring molecular vibration and rotational energy changes. However, the selection rules for Raman spectroscopy are very different from those of infrared - a change of polarisability... 

The selection rules for Raman and IR active vibrations are different. A vibrational mode is Raman active if the polarizability of the molecule changes during the vibration. Changes in polarizability (for Raman spectra) are not as easy to visualize as changes in electric dipole moments (for IR spectra) and in most cases it is necessary to use group theory to determine whether or not a mode will be Raman active. 

Both Raman and IR spectra have been observed for all the XF cations. These spectra are rather simple ones since both the cations and MF anions are of the highly symmetrical octahedral structure, Oh, with a center of symmetry. Therefore the selection rules for Raman and IR active vibrations are mutually exclusive. Only three Raman lines, vi, V2 stretchings and 1 5 bending mode are expected, whereas two non-coinciding IR lines, stretching and P4 bendingmode are expected. Indeed, the imported spec-... 

By convention, these are often called infrared selection rules, to distinguish between the selection rules for vibrational spectra obtained by infrared absorption and Raman spectroscopy (described later in this section). We will stick to the more cumbersome electric dipole to avoid the suggestion that the rules are wavelength-dependent. 

When polymers possess helical symmetry, this symmetry changes the types of vibrational modes that can be observed in the IR and Raman spectra in a specific manner that can be used to determine the chain conformation (Fig. 6.9). Thus, for the planar 2i and 3i helices, differences in selection rules for Raman and IR spectra allow a direct determination of the conformation. For helical conformations with pitches greater than that of a 3i hehx, the selection rules do not change but the frequencies shift. 

We have now discovered that the selection rules for Raman and IR spectra are different. The IR selection rule requires a vibration to belong to the same irreducible representation as X, y, z, whereas vibrations are Raman active if they belong to irreducible representations for the products of axes. This means that vibrations that show up in IR spectra need not be present in Raman and vice versa. 

In the area of the elucidation of molecular structure the Raman method has proved particularly useful. The application of group theory leads to a set of selection rules for Raman and infrared spectra on the basis of a proposed molecular model. One can then determine the total number of theoretical frequencies which should appear in Raman and infrared spectra. This is then compared with the observed spectra. The procedure can be repeated with other models until a good match between theoretical and experimental spectra is obtained. The method is illustrated by Table III. On the basis of the selection rules, Lord picked structure D h as the most likely for the molecule IF . Recently x-ray work on IF has been published [ ]. 

The selection rule for Raman intensities (b) discussed in the previous section requires that the vibrational quantum number changes by +1 for the Stokes lines in the Raman spectra. This is, however, true for the fundamental lines, corresponding to transition 0->l, and for the "hot bands" related to transitions of the type l->2, 2->3, etc. These appear at the same frequency in the spectra as the fundamental bands. Thus, the frequencies associated with fundamental and "hot band" transitions are hardly discernible. All such transitions contribute to the intensity of a Raman band. A summation over all vibrational quantum numbers Vj from zero to infinity is needed to account for all contributions to the intensity I,. Following the considerations given in Section 1.1 [Eqs. (1.31) and (1.39)], the expression is obtained... 

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

The differences in selection rules between Raman and infrared spectroscopy define the ideal situations for each. Raman spectroscopy performs well on compounds with double or triple bonds, different isomers, sulfur-containing and symmetric species. The Raman spectrum of water is extremely weak so direct measurements of aqueous systems are easy to do. Polar solvents also typically have weak Raman spectra, enabling direct measurement of samples in these solvents. Some rough rules to predict the relative strength of Raman intensity from certain vibrations are [7] ... 

Donovan, B., Angress, F. Lattice vibrations. London Chapman and Hall 1971. Turrell, G. lniia.red and Raman spectra of crystals. New York Academic Press 1972. Fateley, W. G., Dollish, F. R., McDevitt, N. T., Bentley, F. F. Infrared and raman selection rules for molecular and lattice vibrations The correlation method. New York J. Wiley 1972. 

Derivation of selection rules for a particular molecule illustrates the complementary nature of infrared and Raman spectra and the application of group theory to the determination of molecular structure. 

Table 3-2 Selection Rules for IR, Raman and Hyper-Raman Spectra of Benzene (D6/l)...

Raman Selection Rules. For polyatomic molecules a number of Stokes Raman bands are observed, each corresponding to an allowed transition between two vibrational energy levels of the molecule. (An allowed transition is one for which the intensity is not uniquely zero owing to symmetry.) As in the case of infrared spectroscopy (see Exp. 38), only the fundamental transitions (corresponding to frequencies v, V2, v, ...) are usually intense enough to be observed, although weak overtone and combination Raman bands are sometimes detected. For molecules with appreciable symmetry, some fundamental transitions may be absent in the Raman and/or infrared spectra. The essential requirement is that the transition moment F (whose square determines the intensity) be nonzero i.e.. 

The experimental techniques most commonly used to measure the phonon distributions are IR absorption, Raman scattering and neutron scattering. The IR and Raman spectra of crystalline silicon reflect the selection rules for optical transitions and are very different from the phonon density of states. The momentum selection rules are relaxed in the amorphous material so that all the phonons contribute to the spectrum. 

It is always desirable to back up IR absorption spectroscopy with Raman measurements. The different selection rules for the two techniques means that, at least for symmetric species, it is often necessary to have data from both types of measurement to have a full picture of the vibrational spectrum. Raman spectroscopy has been used to study many matrix-isolated species although there are problems regarding intensity and photosensitivity. An excellent review exists on the subject that highlights both the applications and difficulties of the method. A molecule that has been well characterized by both IR and Raman spectroscopy is the matrix-isolated species Mo(C )s(N2) (15). Spectra for (15) are illustrated... 

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