Figure 9.14
Classical analogy of polyatomic molecule.can be considered as approximating to a diatomic molecule A–X, and the wavenumber of the vibration
is then given by
where fA–X is the force constant of the A–X bond and
Hence, to a good approximation
and the wavenumber of the vibration is therefore independent of the masses of the other atoms in the
molecule. This type of stretching vibration is exemplified by hydrogen atoms linked to carbon, oxygen,
nitrogen or sulphur, and results in absorption bands around 3000 cm–^1. The wavenumber ranges of a
number of such groups are given in Table 9.6(a). Also shown in the table are the wavenumbers of the
bending modes, and it should be noted that the energies involved, and hence the wavenumbers, are
significantly lower than those of the corresponding stretching vibrations.
(b)—
Force Constant Effect
Considering the same model as that shown in Figure 9.14, if the force constant of the A—B bond is
significantly higher than those for the rest of the molecule, one stretching vibration will occur at a
higher wavenumber as σe is directly proportional to fA–B. This situation arises in molecules with
unsaturated groups such as C C, C C and C O because the magnitude of the force constant
increases significantly with bond order. Examples of the wavenumber ranges for some unsaturated and
saturated groups are compared in Table 9.6(b). Differences between the force constants of single