Bending vibrations, number

In this section, we briefly discuss spectroscopic consequences of the R-T coupling in tiiatomic molecules. We shall restrict ourselves to an analysis of the vibronic and spin-orbit structure, detennined by the bending vibrational quantum number o (in the usual spectroscopic notation 02) and the vibronic quantum numbers K, P. 

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

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. 

The quantum numbers va, vc denote local stretching vibrations, while the quantum numbers, vb, denote the doubly degenerate bending vibrations (Figure 4.5). Equation (4.52) can be converted, using Eq. (4.53), to... 

The introduction of the algebra of U(2) both for stretching and for bending vibrations allows one to do a complete study of all molecular vibrations within this framework.2 Consider again the case of benzene. The total number of vibrational degrees of freedom is 3n - 6 = 30, while the total number of coordinates is 3n = 36. It is convenient to introduce the coordinates of Wilson, Decius, and Cross (1955), shown in Table 6.5. Since there are 36 of these coordinates but only 30 vibrational degrees of freedom, six coordinates must be spurious. The set of spurious coordinates can be determined using the method of Wilson, Decius, and Cross (1955), and is also shown in Table 6.5. 

Fig. 7.1 Infrared spectra of iron oxides in the range 400 to 4000 cm (ca. 1 mg in 300 mg KBr). a) Wave number range 1000-4000 cm b) wave number range 400-1000 cm The insert in the goethite spectrum shows that the two OH bending vibrations shift to higher wave...

Figure 9. Vibrational level spacing for HCP X S, A2G(D2) = G(0, u2 + 1,0)G(0, u2L0) plotted (open circles) vs. the bending quantum number vj. Also plotted l(open squares) is the reduced A2G, A2G(o2) - 2jc22i>2, which would be a horizontal line for a Morse oscillator.

---