Vibration wavenumber

As expected, the frequency increases with k (the stiffness of the bond) and decreases with /r. More commonly, though, we use vibration wavenumber co, rather than frequency, where... 

Given that the vibration wavenumbers of the molecules HCl, SO and PN are 2991, 1149 and 1337 cm, respectively, calculate, from Equation (1.68), their force constants and hence comment on the comparative bond strengths. 

The centrifugal distortion constant depends on the stifthess of the bond and it is not surprising that it can be related to the vibration wavenumber co, in the harmonic approximation (see Section 1.3.6), by... 

Other general circumstances in which normal vibrations tend to be localized in a particular group of atoms arise when there is a chain of atoms in which the force constant between two of them is very different from those between other atoms in the chain. For example, in the molecule HC=C—CH=CH2 the force constants in the C—C, C=C and C=C bonds are quite dissimilar. It follows that the stretchings of the bonds are not strongly coupled and that each stretching vibration wavenumber is typical of the C—C, C=C or C=C group. 

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

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. 

Table 6.4 Fundamental vibration wavenumbers of crotonaldehyde obtained from the infrared and Raman spectra...

Figure 6.22 Symmetry species of some overtone and combination levels of H2O together with directions of polarization of transition moments. The vibration wavenumbers are cO] = 3657.1 cm a>2 = 1594.8 cm m3 = 3755.8 cm ...

The progression with v" = 1 may also be observed in absorption but only in a molecule with a vibration wavenumber low enough for the u" = 1 level to be sufficiently populated. This is the case in, for example, iodine for which cog = 213 cm. As a result the... 

The CO2 laser is a near-infrared gas laser capable of very high power and with an efficiency of about 20 per cent. CO2 has three normal modes of vibration Vj, the symmetric stretch, V2, the bending vibration, and V3, the antisymmetric stretch, with symmetry species (t+, ti , and (7+, and fundamental vibration wavenumbers of 1354, 673, and 2396 cm, respectively. Figure 9.16 shows some of the vibrational levels, the numbering of which is explained in footnote 4 of Chapter 4 (page 93), which are involved in the laser action. This occurs principally in the 3q22 transition, at about 10.6 pm, but may also be induced in the 3oli transition, at about 9.6 pm. 

Spectroscopists usually talk in terms of wavenumbers rather than frequencies or energies. A wavenumber is an energy divided by hco, or a frequency divided by C(j, and so we refer to the classical vibrational wavenumber rUe given by... 

Since vibrational spectra of S2O2 have not yet been observed, the force constants calculated by ab initio MO methods were used to predict the harmonic vibrational wavenumbers of ds-S202 (C2v) and trans-S202 (C2I1) see Table 3 [34, 57]. 

For a precise determination of the structures, ab initio calculations on the energies of formation and characteristic harmonic wavenumbers have been performed at the HF and MP2/6-31G(d,p) level of theory with the Gaussian 92 program for the species of interest . The ab initio calculated energies and harmonic vibrational wavenumbers are given in Table 5. 

TABLE 5. Ab initio calculated energies (Joule)" and harmonic vibrational wavenumbers (cm ) of the species of interest ... 

TABLE 6. Selected experimental and calculated vibrational wavenumbers (cm ) for PI13P = NSiMes and [Li(o-C6H4PPh2NSiMe3)]2 Et20 with their tentative assignments ... 

Some values of rotation and vibration wavenumbers and temperatures of small molecules, and the degeneracy in parentheses, are listed in table 4.16. One can see... 

Table 4.16 Rotation and vibration wavenumbers and temperatures for some small molecules...

Rotation wavenumber, cm Rotation temp., K Vibration wavenumber, cm Vibration temp., K... 

---