Rule of mutual exclusion

Wavenumbers (unsealed cm ) and relative infrared/Raman intensities as follows. Infrared intensities very strong-strong-medium-weak-very weak-0. Raman intensities 0-100 (sh shoulder). In the case of the centrosymmetric point group C2h the rule of mutual exclusion applies... 

The chair-like Se molecule is of symmetry [147] and due to the center of inversion in this point group the rule of mutual exclusion applies. Therefore,... 

The rule of mutual exclusion states that for a molecule with a center of symmetry, a given vibrational transition cannot appear in both the IR and Raman spectra. (For the proof, see Chapter 9.) Some fundamentals may be both IR and Raman inactive their frequencies can often be determined from IR or Raman combination bands. 

This was first investigated by Huang n). Long-wave optical phonons are those with small k values. A polar phonon is an infrared-active phonon. Polar phonons therefore can only be observed in the Raman effect for crystals having no center of symmetry in the elementary cell. For centro-symmetric crystals the rule of mutual exclusion applies infrared-active phonons are forbidden in Raman scattering and vice versa. The elementary cells of NaCl and LiF have a center of symmetry, but GaP has none. The following considerations may therefore be applied to GaP as an example. This crystal has two atoms in the elementary cell and is cubic. It can be treated as an optically isotropic medium. 

Both models have the same numbers of infrared, Raman, and polarized Raman bands. However, they can be distinguished by the fact that the T2 mode in the 7d structure is both IR and Raman active (there is one coincidence), whereas the rule of mutual exclusion holds for the centrosymmetric D4h structure. 

Since benzene has a center of symmetry, the rule of mutual exclusion applies i.e., bands that appear in the IR are absent in the Raman and vice versa. Thus, just from symmetry considerations, one predicts four infrared-active and seven Raman-active fundamental transitions, with no required coincidences among these frequencies. 

Eq. (35-7)]. For molecules of symmetry, these elements belong to the symmetry species, Fly, and so that the condition for a Raman-active transition is that the product F(i/fj) X include one of these species. Thus, from the Xg ground state of acetylene, Raman transitions to the (10000) Xg, (01000) 2, and (00010) Il levels are allowed and can be used to determine the nj, V2, and V4 fundamental frequencies, respectively. As can be seen in Table 1, these three modes do not produce a dipole change as vibration occurs, and thus these transitions are absent from the infrared spectrum. This is an example of the rule of mutual exclusion, which applies for IR/Raman transitions of molecules with a center of symmetry... 

An important consequence of molecular symmetry concerns molecules which have a center of symmetry. It is the rule of mutual exclusion ... 

Figure 4.1-3 Symmetric and antisymmetric stretching vibrations of zig-zag chains. In the C-C chain, both vibrations are IR inactive and Raman active (rule of mutual exclusion at the center of each bond there is a local center of symmetry). As the Si-O-Si chain vibrates, on the other hand, all Si atoms move against all O atoms both vibrations are IR active. Both vibrations are Raman allowed i/j causes the greater polarizability change. The frequencies of these vibrations are affected by the substituents the listed values correspond to polyethylene and polydimethylsiloxane, respectively (Fig. 4.1-2C).

In the infrared spectrum of polyethylene (Fig. 4.1-2A) this band is split into a doublet at 720 and 731 cm This factor group splitting (Fig. 2.6-1 and Sec. 2.7.6.4) is a result of the interaction between the molecules in crystalline lattice areas. It may be used to investigate the crystallinity of polymers (Drushel and Iddings, 1963 Luongo, 1964). Polyethylene has a unit cell of the factor group Dih (compare Secs. 2.7.5 and 2.7.6.3) which contains a -CH2-CH2- section of two neighboring chains. Each of these sections has a center of inversion in the middle of the C-C bond (Fig. 4.1-3). Therefore the rule of mutual exclusion (Sec. 2.7.3.4) becomes effective The vibrations of the C-C bonds cannot be infrared active and further there are no coincidences of vibrational frequencies in the infrared and Raman spectrum of linear polyethylene. 

All iy(C=C) vibrations give rise to sharp and narrow Raman bands of high intensity. IR spectra, on the other hand, frequently exhibit comparatively weak C=C vibrations. A symmetrical substitution in trans position introduces a center of inversion at the center of the C=C bond due to the rule of mutual exclusion (Sec. 2.7.3.4) the C=C vibration must then be forbidden in the infrared spectrum. 

The 7 isomer of 1,2,3,4,5,6-hexachlorocyclohexane (Fig. 4.1-9A), an insecticide, gives rise to a large number of sharp bands which have the same IR and Raman frequencies. The 0 isomer (Fig. 4.1-9B), on the other hand, exhibits fewer bands and shows no bands which coincide in the IR and the Raman spectrum. This confirms its structure, which possesses a center of symmetry (rule of mutual exclusion). The insecticide endrine, too, shows a complicated pattern of bands, but due to the low symmetry the IR and Raman spectrum coincide to a large extent (Fig. 4.1-9 C). 

The vibrational selection rules treated in Sec. 2.7 are strictly valid in the gas phase, because intermolecular interactions are mostly absent. As an example we present the rotation-vibration infrared and Raman spectra of benzene CgHg in Fig. 4.3-1 on a common scale. According to the rule of mutual exclusion (see Sec. 2.7.3.4), none of the fundamentals should coincide in the two spectra. Of the 20 normal vibrations of QHf, four are infrared active (1A2 , 3 i ), seven Raman active (24 E g, and nine... 

The spectra of the anti conformer will follow the rule of mutual exclusion, as the molecules possess an inversion centre. The selection rules predict five Raman active skeleton deformations for the anti conformer. For the crystalline state (Fig. 1), five deformations are observed, leaving no doubt that the anti conformer is energetically favored. Table 2 summarizes the calculated and observed skeleton stretching vibrations of both isotopomers. According to the correlation tables, Ag and Au vibrations of the anti conformer (point group 21) combine into A vibrations of point group C2, Bg, and B vibrations into vibrations belonging to symmetry species B. 

Fig. 2 depicts Raman spectra of rBuSiF2SiF2tBu at two temperatures. In accordance with the ab initio predictions no temperature-dependent rotational isomerism can be observed. Subsequently, the vibrational analysis of /BuSiF2SiF2/Bu was carried out for the point group C2, since the vibrational spectra obey the rule of mutual exclusion Cjh contains inversion as a symmetry operation). 

For highly symmetrical molecules and ions such as TiC (Tt), CeHe (T>6ti), and PtCH " (T>4h). both IR and Raman spectroscopies are required to obtain the full set of vibrational frequencies. If a molecule or an ion possesses a center of inversion, there is a rule of mutual exclusion-, no fundamental vibration that is active in the IR absorption can be active in the Raman scattering, and no fundamental vibration that is active... 

One finds that, in molecules of high symmetry, both IR and Raman spectroscopy are needed to observe the vibrational modes. Even with both techniques, there may still be some vibrations that are totally forbidden. The best known selection rule for IR and Raman spectroscopy is known as the Rule of Mutual Exclusion , which states that if a molecule has a centre of symmetry, vibrations cannot be active in both IR and Raman spectroscopy. This rule has often been applied in molecular structure investigations to determine whether a centre of symmetry is present. In general, vibrations that do not distort the molecular symmetry, symmetric vibrations , are intense in the Raman spectrum while those that maximize the distortion are most intense in the IR spectrum. If the atoms involved in these vibrations are highly polarizable (e.g., sulfur or iodine) then the Raman intensity is high. Some examples of... 

In addition to these two selection rules, molecules with a centre of symmetry (e.g. linear CO2, and octahedral SFe) are subject to the rule of mutual exclusion. 

For centros5mmetric molecules, the rule of mutual exclusion states that vibrations that are IR active are Raman inactive, and vice versa. 

PtCy in Figure 4.17, along with their appropriate symmetry labels. In the character table (see Appendix 3), the A2 and Eu representations contain z and (x,y) functions, respectively. Therefore, of the vibrational modes shown in Figure 4.17, only the A2u and Eu modes are IR active. Since [PtC ] " contains an inversion centre, the rule of mutual exclusion apphes, and the A2 and modes are Raman inactive. Similarly, the Aig, Big and B2g modes that are Raman active, are IR inactive. Among compounds of the />-block elements, 7)41, XY4 structures are rare the observation of absorptions at 586, 291 and 161cm in the IR spectrum of XeF4 is consistent with the structure predicted by the VSEPR model. 

Indeed, variable-temperature Raman spectra do not reveal spectral features due to a single conformer only. Vibrational spectra of solid tBuBr2SiSiBr2 Bu and Bul2SiSil2/Bu indicate that the anti conformation (point group Czh) is adopted in the solid state since the spectra obey the rule of mutual exclusion. Raman vibrational spectra of both disilanes are summarized in Tables 1 and 2, respectively. 

Raman spectra can now be routinely obtained for all types of materials. It is particularly useful for centrosymmetric species, such as octahedral SFg or Cr(CO)g, for which the rule of mutual exclusion applies. This rule states that vibrations which are Raman-active are IR-inactive, and vice versa . This means that a centrosymmetric species can be readily identified from the noncoincidence of the peaks appearing in its IR and Raman spectra. 

An XYfi molecule belonging to the On point group has (3 x 7) — 6 = 15 degrees of vibrational freedom. Figure 3.18 shows the modes of vibration of SFg along with their symmetry labels. Only the Ti modes are IR active this can be confirmed from the On character table in Appendix 3. Since the S atom in SF lies on an inversion centre, the Tiu modes are Raman inactive (by the rule of mutual exclusion). Of the Ti, modes shown in Fig. 3.18, one can... 

What is the rule of mutual exclusion Give two examples of molecular species to which this rule applies. 

The rule of mutual exclusion states that a centrosymmetric structure will not have the same normal mode active in both Raman and infrared. 

Oh- The existence of a center of symmetry for all molecules belonging to these groups carries an important implication for their infrared spectra, since it has been shown that for molecules with an inversion center transitions allowed in the infrared are forbidden in Raman spectra and vice versa. This is the so-called rule of mutual exclusion, which states that fundamentals appearing in the infrared spectra of these molecules will not appear in the Raman spectra, and conversely, those appearing in the Raman spectra will not appear in the infrared. It is also possible for certain transitions to be forbidden in both. 

The rule of mutual exclusion has been used extensively to establish the structure of many molecules. For example, planar C2H4, which belongs to group a center of symmetry. The... 

There is a rule of mutual exclusion, which states In a molecule with a center of symmetry, a normal mode that is seen in the infrared spectrum will not be seen in the Raman spectrum, and vice versa. The normal modes of carbon dioxide illustrate this rule. In molecules with more than three atoms, it is sometimes possible to determine whether a normal mode will be Raman active or IR active by inspection of the normal mode motions. Group theory is often used to simplify the analysis. ... 

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