Page 345 - Instant notes

Applied vibrational spectroscopy 331

Vibrational Raman spectroscopy: selection rules and transitions

Raman spectroscopy occurs when a photon of incident radiation loses or gains energy in
an interaction with a molecule (see Topic I1). The incident radiation must be
monochromatic and intense and is typically provided by a laser.
The magnitude of the allowed energy exchange for vibrational Raman spectroscopy
is determined by the same specific selection rule as for infrared spectroscopy:
∆υ=±1

Therefore vibrational Stokes and anti-Stokes radiation occur at frequencies v ex−v and
v ex+v, respectively, where v ex is the frequency of the incident excitation radiation. Anti-
Stokes scattering can only arise if the molecule is already in an excited state. Since the
proportion of molecules in vibrationally excited states is considerably smaller than in the
ground state (determined by the Boltzmann distribution law), anti-Stokes transitions are
much less intense than Stokes transitions. For small molecules, which have widely spaced
vibrational and rotational energy levels, it may be possible to resolve rotational fine
structure around the Stokes and anti-Stokes vibrational lines arising from the
simultaneous loss and gain of rotational as well as vibrational energy in the scattering
interaction.
In addition, a vibrational Raman line only occurs if

the polarizability of the molecule changes during the vibration.

The polarizability of a molecule is a measure of the extent to which an applied electric
field, such as a photon of electromagnetic radiation, can induce an electric dipole (Topic
H6). It is determined, in part, by the distribution of electron density in the molecular
orbitals. A mode is Raman active if the vibration causes a change in either the
magnitude or the three-dimensional shape of the polarizability. Both homonuclear and
heteronuclear diatomic molecules swell and contract during vibration and the electron
density changes non-symmetrically between the two extremes of displacement. Therefore
fore all homonuclear and heteronuclear diatomics have Raman active vibrations, in
contrast to infrared vibrational spectroscopy, in which homonuclear diatomic vibrations
are inactive. The symmetric stretch of CO 2 is likewise Raman active. The asymmetric
stretching and bending modes of CO 2 are not Raman active because the electron density
changes symmetrically between the extremes of vibrational displacement in each mode
and hence polarizability does not vary with small displacements from equilibrium.

Rule of mutual exclusion

The infrared and Raman activities of CO 2 vibrations are summarized in Table 3. The data
demonstrate the rule of mutual exclusion for vibrational spectroscopy: