IR Frequency Depends on Type of Bond

As we have seen in the previous sections, a molecule with many atoms has a mode for each degree of freedom in molecular vibrations. A mode is seldom clean in the sense that it is formed by only a single interatomic vibration, as is the case for diatomic molecules. For large molecules, a mode may correspond to a complicated nuclear motion pattern involving, for example, five covalent bonds, as in hexatriene. 

In the vibronic (vibrational + electronic) ground state, the molecule is in its lowest electronic state, while the vibrational modes have the lowest quantum numbers (vi,V2. V3N ( ) = (0,0. 0). The quantum numbers Vi,V2.V3n 6 are ordered according to vibration quantum. The first excited vibronic state is thus (1,0,0. 0). Next state is either (0,1,0,.. 0) or (2,0,0. 0). Due to the selection rules (Av, = 1), only the former can be reached from the ground stale and is visible in the spectrum. 

These values are obtain in Hartree-Fock calculations. The experimental value for the lowest ethane stretch frequency is 995 cm .  

FIGURE 4.5 Vibrational spectra for some small molecules. Hartree-Fock calculation of PES ab initio, 6-31G). 

FIGURE 4.6 Raman spectrum (Stokes) for organic molecule. Origin is at the Rayleigh scattering. 

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