Fundamental frequencies Raman selection rules

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.. 

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... 

The infra-red and Raman spectra of molecules are dominated by transitions between the ground state and the fundamental levels but, in practice, the number of fundamental frequencies observed does not reach 3JV—6 since (a) some of the Xt are identical (leading to degenerate fundamental levels) and (b) selection rules forbid certain transitions. Both (a) and (b) are determined by the symmetry of the molecule. 

The XY,-type molecules are veiy rare. Both IF, and ReF, arc known to be pentagonal-bipy rami dal (D ,), and their vibrational spectra have been assigned completely, as shown in Table II-9. The A, ", and , vibrations are Raman active, and the A 2 and , vibrations are infrared active. According to Eysel and Seppelt, IF, undergoes minor dynamic distortions from 0 symmetry which cause violation of the Djj, selection rules for combination bands but not for the fundamentals. Normal coordinate analysis shows that the axial bonds are definitely stronger and shorter t ian the equatorial ones. Table 11-9 also lists the frequencies and assignments of the [U02Fs] ion of Dj, symmetry. 

The values for Eq have been obtained from the overtones of the O-H stretching mode which occur at approximately twice, thrice, four times etc. the frequency of the O-H fundamental and in part consist of IR + Raman combination bands. Being forbidden by the dipole selection rules their intensities decrease rapidly, by about two orders of magnitude for each increment. As a consequence the higher overtone bands are very... 

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. 

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. 

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... 

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