Page 340 - Instant notes

Physical Chemistry 326

The molecule does not need to have a permanent electric dipole since the selection rule
only requires a change in electric dipole during the vibration. Molecular vibrations which
give rise to observable vibrational spectra are called infrared active modes. The
vibrations of all heteronuclear diatomics are infrared active because the magnitude of
the permanent electric dipole changes as the bond length changes during vibration.
Conversely, all homonuclear diatomics (e.g. O 2, N 2) are infrared inactive because they
have no permanent dipole and none arises during vibration. The polyatomic molecule
CO 2 has no permanent dipole but its asymmetric stretching vibration and two bending
vibrations give rise to oscillating electric dipoles and are therefore infrared active (see
Topic I5). The symmetric stretching vibration of CO 2 is infrared inactive.
The specific selection rule for the allowed transitions between vibrational energy
levels of a harmonic oscillator is:
∆υ=±1 only

The positive value corresponds to absorption of energy from a lower to higher energy
level, the negative value to emission.
Applying the selection rule, the energy of the transition between vibrational states with
quantum numbers υ+1 and υ is:

Since the transition energy is independent of quantum number, all transitions associated
with a particular harmonic molecular vibration occur at a single frequency
, as shown in Fig. 2. Molecules with strong bonds (large k)
between atoms of low masses (small µ) have high vibrational frequencies. Bending
vibrations are generally less stiff than stretching vibrations, so tend to occur at lower
frequencies in the spectrum. At room temperature, application of the Boltzmann
distribution law shows that almost all molecules are in their vibrational ground states
and since all vibrational energy levels are singly degenerate (in contrast to rotational
energy levels, Topic I3) the dominant spectral transition in absorption arises from υ=0 to
υ=1.
A molecule can undergo a change in rotational energy level at the same time as it
undergoes the change in vibrational energy level, subject to the appropriate rotational
selection rules. It is often possible to resolve the rotational fine structure on either side of
the position of the vibrational transition (similar in appearance to a pure rotational
spectrum) in high resolution infrared spectroscopy of small molecules with large
rotational constants.