Chemistry Reference
In-Depth Information
The selection rules allow us to determine the number of bands to expect in vibrational spec-
tra, since only vibrations belonging to certain irreducible representations lead to bands in
the spectra.
In the second part (Sections 6.4-6.7) we will consider what the vibrations belonging
to a given irreducible representation 'look like'. This involves the construction of linear
combinations of the basis of atomic movements that are consistent with the characters of
the irreducible representation. These combinations are known as symmetry adapted linear
combinations (SALCs). SALCs are a general way to visualize the molecular properties
that correspond to the objects with the irreducible symmetries identified by the reduction
formula. The method we shall use to obtain these SALCs is the projection operator, which
is introduced in Section 6.6 and will also be employed in Chapter 7 to find molecular
orbitals.
Finally, in Section 6.8, examples of vibrational analysis and its use in differentiating
molecular isomers will be given.
6.2 Selection Rules
Selection rules are used in spectroscopy to determine whether a transition between two
energy states within a molecule will show up in its spectrum. To be seen the transition has
to be able to couple to the light which is used as a probe. This coupling is controlled by
integrals over the initial and final states for the transition and the appropriate molecular
property for the type of spectroscopy.
IR absorption occurs when the transition between two vibrational states of a molecule
has an energy matching the photon energy of the probe radiation
and
the transition causes a
change in the molecular dipole moment. If there is no change in molecular dipole moment
during the vibration, then there will be no absorption and we say that the mode is not
allowed by the selection rules.
Raman spectroscopy uses higher energy probe radiation and the spectrum is caused by
the link between the vibrational and electronic states of the molecule through molecular
polarizability. If the vibration causes no change in polarizability then the selection rule
will not be satisfied and no spectral signature is observed for that vibration.
Symmetry controls the yes/no decision of the selection rules, determining which vibra-
tions will lead to absorption and, hence, the number of bands to expect. However,
symmetry does not allow the calculation of the band position (frequency) or intensity,
as these are controlled by physical properties of a molecule such as bond strengths and the
masses of the constituent atoms.
In the next two sections we consider the selection rules for IR and Raman spectroscopies
in more detail.
6.2.1
Infrared Spectroscopy
When the irreducible representations for the vibrations of a molecule have been identified,
the collective motions of the atoms that constitute each mode can be thought of as a simple
oscillator to be described with quantum mechanics. As the molecule vibrates in a given
mode it moves through a potential energy surface that is set by the chemical bonds of
the system. For small displacements, which are all that occur at room temperature, we
