Group vibration

An A-atomic molecule has 3A — 5 normal modes of vibration if it is linear, and 3A — 6 if it is non-linear these expressions were derived in Section 4.3.1. 

Even with this simple model it is clear that if one of the nuclei is given a sudden displacement it is very likely that the whole molecule will undergo a very complicated motion, a Lissajous motion, consisting of a mixture of angle-bending and bond-stretching. The Lissajous motion can always be broken down into a combination of the so-called normal vibrations of the system which, in the Lissajous motion, are superimposed in varying proportions. 

For the vibrational numbering scheme, see Chapter 4, footnote 4 (page 93). 

In an approximation which is analogous to that which we have used for a diatomic molecule, each of the vibrations of a polyatomic molecule can be regarded as harmonic. Quantum mechanical treatment in the harmonic oscillator approximation shows that the vibrational term values G(v ) associated with each normal vibration i, all taken to be nondegenerate, are given by 

As for a diatomic molecule, the general harmonic oscillator selection mle for infrared and Raman vibrational transitions is 

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These compounds have infrared spectra that are greatly complicated by harmonics and combination bands in the region of carbonyl group vibrations. 

Table 6.3 lists a number of group vibration wavenumbers for both bond-stretching and angle-bending vibrations. 

In addition to the descriptions of group vibrations as stretch and bend (or deformation) the terms rock, twist, scissors, wag, torsion, ring breathing and inversion (or umbrella) are used frequently these motions are illustrated in Figure 6.13. 

Table 6.3 Typical bond-stretching and angle-bending group vibration wavenumbers co...

Just as group vibration wavenumbers are fairly constant from one molecule to another, so are their intensities. For example, if a molecule were being tested for the presence of a C—F bond there must be not only an infrared absorption band due to bond-stretching at about 1100 cm but also it must be intense. A weak band in this region might be attributable to another normal mode. 

In addition to bands in the infrared and Raman spectra due to Au = 1 transitions, combination and overtone bands may occur with appreciable intensity, particularly in the infrared. Care must be taken not to confuse such bands with weakly active fundamentals. Occasionally combinations and, more often, overtones may be used to aid identification of group vibrations. 

What group vibrations would you hope to identify in the infrared and Raman spectra of... 

The concept of a chromophore is analogous to that of a group vibration, discussed in Section 6.2.1. Just as the wavenumber of a group vibration is treated as transferable from one molecule to another so is the wavenumber, or wavelength, at which an electronic transition occurs in a particular group. Such a group is called a chromophore since it results in a characteristic colour of the compound due to absorption of visible or, broadening the use of the word colour , ultraviolet radiation. 

Like group vibrations, the wavelength at which a chromophore absorbs can be employed as an analytical tool, but a rather less useful one. 

In the undisturbed state, the halophosphates can be classified by the following point groups (vibrational species in brackets) ... 

DFT calculations were performed on Mo dinitrogen, hydra-zido(2-) and hydrazidium complexes. The calculations are based on available X-ray crystal structures, simplifying the phosphine ligands by PH3 groups. Vibrational spectroscopic data were then evaluated with a quantum chemistry-assisted normal coordinate analysis (QCA-NCA) which involves calculation of the / matrix by DFT and subsequent fitting of important force constants to match selected experimentally observed frequencies, in particular v(NN), v(MN), and 8(MNN) (M = Mo, W). Furthermore time-dependent (TD-) DFT was employed to calculate electronic transitions, which were then compared to experimental UVATs absorption spectra (16). As a result, a close check of the quality of the quantum chemical calculations was obtained. This allowed us to employ these calculations as well as to understand the chemical reactivity of the intermediates of N2 fixation (cf. Section III). 

For isolated molecules a variety of approaches have proved useful in the interpretation of vibrational spectra. Firstly, a species may approximate to a symmetry higher than its actual. In such cases a correlation with-descent in symmetry from — the higher symmetry usually simplifies the interpretation of its spectra. Secondly, local group vibrations, essentially uncoupled from the vibration of other equivalent or near-equivalent groups, may occur. Thirdly, chemically distinct groups may couple... 

In very small molecules such as CH4 or C2H2 the molecule vibrates as a whole and all atoms are involved equally in vibrational excitation and not all vibrations can be seen. Generally different groups of large molecules are not excited to the same extent. Polar groups takes preference and as a result the IR spectra of large molecules show IR bands of group vibration rather than of molecular vibration. 

The FTIR reflection spectra of DDTC (solid) and FeDs are shown in Fig. 4.45. Only at the 700-2000 cm region most of the important functional groups vibrations of diethyl dithiocarbamate are observed. From Fig. 4.44, it can be seen... 

UZM-5 samples show two distinct Si-OH-Al bands which are due to OH groups vibrating in the different size cages of these zeolites. Depending on the structure of the zeolite, the spectrum can have multiple Si-OH-Al vibrational bands and they can vary in position. 

Table 12.2 Assignment of hydroxyl group vibrations for alumina from different models.

Methods for treating the factor group vibrations have been given by Davydov (25), as well as by Bhagavantam and Venkatarayudu (22). A simple analysis is possible through what is known as the correlation method (20, 26, 27) by which one is able to write the irreducible representations and thereby classify k=0 phonons directly and simply. The number of A = 0 phonons is 3 N, where N is taken to be the number of atoms in the entire unit cell. However, there are only 3 N-3 optically active phonons because the acoustic vibrations have approximately... 

Despite the fact that a full assignment of all the observed absorptions to the respective macromolecule s natural frequencies is not possible in all cases - in particular for complex co- and terpolymers, stereoregular polymers, crosslinked systems, composites, compounds or blends this is very difficult - there are many bands caused by local group vibrations of a few atoms which can be interpreted very nicely. As an example, the C=0 band (stretching vibration) is usually observed as an intense absorption between v = 1850-1650 cm. Because of the coupling with other vibrations of the molecule its frequency is characteristic for the constitution and the neighborhood of the observed atom group. 

A number of systematic structural analyses have been described for families of saturated oxazolones. First, as mentioned previously, detailed smdies of NMR long-range coupling in 2,4-disubstimted-5(47/)-oxazolones and in 5(27/)-oxazo-lones have been reported." Similarly, detailed NMR studies of the kinetics of racemization of 2,4-disubstimted-5(47/)-oxazolones have been performed. A theoretical study of the spectral-luminescence properties of some 4-alkyl-2-phenyl-5(47/)-oxazolones has been reported and an investigation of the infrared (IR) and Raman spectra of 5(4//)-oxazolones, particularly of the carbonyl group vibration, has been reported. Electron impact mass spectra of saturated 5(47/)-oxazolones have been published. More recently this technique has been used to distinguish between the stereoisomers of some spirocyclopropane oxazolones 352 (Fig. 7.36). Finally, several studies of the HPLC behavior of 5(47/)-oxazolones complete a general view for this family of compounds. " " ... 

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