Infrared-active

A particular vibration will give an absorption peak in the IR spectrum only if the dipole moment of the molecule changes dunng the vibration Which vibration of carbon dioxide the sym metric stretch or the antisymmetric stretch is infrared active 2... 

In the case of H2O it is easy to see from the form of the normal modes, shown in Figure 4.15, that all the vibrations Vj, V2 and V3 involve a change of dipole moment and are infrared active, that is w=l-0 transitions in each vibration are allowed. The transitions may be labelled Ig, 2q and 3q according to a useful, but not universal, convention for polyatomic molecules in which N, refers to a transition with lower and upper state vibrational quantum numbers v" and v, respectively, in vibration N. 

Inspection of the normal modes shows that only V3 and Vj involve a change of dipole moment and are infrared active. 

Although we have been able to see on inspection which vibrational fundamentals of water and acetylene are infrared active, in general this is not the case. It is also not the case for vibrational overtone and combination tone transitions. To be able to obtain selection mles for all infrared vibrational transitions in any polyatomic molecule we must resort to symmetry arguments. 

Having assigned symmetry species to each of the six vibrations of formaldehyde shown in Worked example 4.1 in Chapter 4 (pages 90-91) use the appropriate character table to show which are allowed in (a) the infrared specttum and (b) the Raman specttum. In each case state the direction of the transition moment for the infrared-active vibrations and which component of the polarizability is involved for the Raman-active vibrations. 

Figure 9.32 illustrates the isotopic enrichment of SFe following irradiation with a pulsed CO2 laser in the 3g vibrational band, at 945 cm, of SFe, V3 being a strongly infrared active bending vibration. The natural abundances of the isotopes of sulphur are (95.0 per cent), (4.24 per cent), (0.74 per cent) and (0.017 per cent). The figure shows that depletion of SFg has been achieved to such an extent that equal quantities of SFg and SFa remain. 

At higher frequencies (above 200 cm ) the vibrational spectra for fullerenes and their cry.stalline solids are dominated by the intramolecular modes. Because of the high symmetry of the Cgo molecule (icosahedral point group Ih), there are only 46 distinct molecular mode frequencies corresponding to the 180 6 = 174 degrees of freedom for the isolated Cgo molecule, and of these only 4 are infrared-active (all with Ti symmetry) and 10 are Raman-active (2 with Ag symmetry and 8 with Hg symmetry). The remaining 32 eigcnfrequencies correspond to silent modes, i.e., they are not optically active in first order. 

The Raman and infrared spectra for C70 are much more complicated than for Cfio because of the lower symmetry and the large number of Raman-active modes (53) and infrared active modes (31) out of a total of 122 possible vibrational mode frequencies. Nevertheless, well-resolved infrared spectra [88, 103] and Raman spectra have been observed [95, 103, 104]. Using polarization studies and a force constant model calculation [103, 105], an attempt has been made to assign mode symmetries to all the intramolecular modes. Making use of a force constant model based on Ceo and a small perturbation to account for the weakening of the force constants for the belt atoms around the equator, reasonable consistency between the model calculation and the experimentally determined lattice modes [103, 105] has been achieved. 

Of these many modes there are only 7 nonvanishing modes which are infrared-active (2A2 + 5 i ) and 15 modes that are Raman-active. Thus, by increasing the diameter of the zigzag tubules, modes with different symmetries are added, though the number and symmetry of the optically active modes remain the... 

Activity R = Raman-active, ir = infrared-active, S = optically silent, observed in neutron scattering. tCarbon atom displacement il or J. to C. 

The Raman spectrum of aqueous mer-cury(I) nitrate has, in addition to lines characteristic of the N03 ion, a strong absorption at 171.7 cm which is not found in the spectra of other metal nitrates and is not active in the infrared it is therefore diagnostic of the Hg-Hg stretching vibration since homonuclear diatomic vibrations are Raman active not infrared active. Similar data have subsequently been produced for a number of other compounds in the solid state and in solution. 

The PIA spectra obtained show an electronic transition peaking at 0.26 eV (see Fig. 9-17) accompanied by infrared active vibrational modes which reveal the charged nature of the observed states [31]. The dependence of the PIA intensity on temperature is depicted in Figure 9-17. 

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. 

Infrared activity of vibrations is readily deduced. The symmetric stretching vibration has no associated dipole moment change during the vibration and is, therefore, infrared inactive. The asymmetric stretching vibration has an associated dipole moment which fluctuates with the frequency of the vibration. The vibration is, therefore, infrared active. 

Application of similar reasoning to the case of the bending mode of COj would indicate that the vibration is Raman inactive, infrared active. 

For a fundamental transition to occur by absorption of infrared dipole radiation, it is necessary that one or more of these integrals (and consequently the intensity) be nonzero. It follows from the selection rule given above that in order that a transition be infrared active p must have the same symmetry properties as at least one of x, y, or z. 

Hence we may conclude for a vibration to be active in the infrared spectrum it must have the same symmetry properties (i.e. transform in the same way) as, at least, one of x, y, or z. The transformation properties of these simple displacement vectors are easily determined and are usually given in character tables. Therefore, knowing the form of a normal vibration we may determine its symmetry by consulting the character table and then its infrared activity. 

The example of COj discussed previously, which has no vibrations which are active in both the Raman and infrared spectra, is an illustration of the Principle of Mutual Exclusion For a centrosymmetric molecule every Raman active vibration is inactive in the infrared and any infrared active vibration is inactive in the Raman spectrum. A centrosymmetric molecule is one which possesses a center of symmetry. A center of symmetry is a point in a molecule about which the atoms are arranged in conjugate pairs. That is, taking the center of inversion as the origin (0, 0, 0), for every atom positioned at (au, yi, z ) there will be an identical atom at (-a ,-, —y%, —z,). A square planar molecule XY4 has a center of symmetry at atom X, whereas a trigonal planar molecule XYS does not possess a center of symmetry. 

When one of the cartesian coordinates (i.e. x, y, or z) of a centrosymmetric molecule is inverted through the center of symmetry it is transformed into the negative of itself. On the other hand, a binary product of coordinates (i.e. xx, yy, zz, xz, yz, zx) does not change sign on inversion since each coordinate changes sign separately. Hence for a centrosymmetric molecule every vibration which is infrared active has different symmetry properties with respect to the center of symmetry than does any Raman active mode. Therefore, for a centrosymmetric molecule no single vibration can be active in both the Raman and infrared spectrum. 

Centrosymmetric molecules represent a limiting case as far as molecular symmetry is concerned. They are highly symmetric molecules. At the other extreme, molecules with very low symmetry should produce a set of Raman frequencies very similar to the observed set of infrared frequencies. Between these two extremes there are cases where some vibrations are both Raman and infrared active and others are active in Raman or infrared but not in both. Nitrate ion is an example of a molecule in this intermediate class. 

The relationship between Raman and infrared activity and molecular symmetry is summarized diagramatically in Fig. 6. 

We do not, in general, have to depend on conceptual approaches or on qualitative generalizations. Symmetry and group theory have provided us with a general method, called symmetry analysis, of determining the number of Raman active vibrations, the number of infrared active vibrations, and... 

Vibrations of the symmetry class Ai are totally symmetrical, that means all symmetry elements are conserved during the vibrational motion of the atoms. Vibrations of type B are anti-symmetrical with respect to the principal axis. The species of symmetry E are symmetrical with respect to the two in-plane molecular C2 axes and, therefore, two-fold degenerate. In consequence, the free molecule should have 11 observable vibrations. From the character table of the point group 04a the activity of the vibrations is as follows modes of Ai, E2, and 3 symmetry are Raman active, modes of B2 and El are infrared active, and Bi modes are inactive in the free molecule therefore, the number of observable vibrations is reduced to 10. 

Ra = Raman active, IR = infrared active, ia = inactive molecular vibration. R and T denote rotations and translations, respectively... 

The factor group Dzh of orthorhombic Sg includes an inversion operation therefore, the g-u exclusion principle works resulting in modes of either Raman (gerade, g) or infrared activity (ungerade, u). 

Summarizing, in the crystal there are 36 Raman active internal modes (symmetry species Ug, hig, 2g> and 26 infrared active internal modes (biw b2w hsu) as well as 12 Raman active and 7 infrared active external vibrations (librations and translations). Vibrations of the type are inactive because there appears no dipole moment along the normal coordinates in these vibrations of the crystal. 

Infrared active are modes of symmetry bi, h2u> 3u> and Raman active are those of symmetry flg, big, b2g, b ... 

Wavenumbers scaled by optimized factors. Intensities for Raman active modes classified by the present authors on the basis of the calculated values. The intensities of two IR active vibrations were calculated to be equal (Ra) = Raman active, (IR) = infrared active [181]... 

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