Elements of Modern Physics
202
Since Raman effect is a two-step process, the selection rules can be deduced
from those for the two separate steps. In particular, the selection rules for the
transition between the rotational states of molecules, are ∆J = ± 1 for emission
or absorption of photons, and hence Raman effect is observed for transitions
with
∆J = ± 2, 0
(6.106)
For purely rotational transitions, only the ∆J = ± 2 transitions need be
considered (∆J = 0 does not involve changes in energy). The change in the
energy in the case of diatomic molecules, is given by
∆E =
2
[ (
1) (
2) (
1)]
2
J J
J
J
I
±
+ −
−
−
= ±
−
≥
2
(2
1)
2
2
J
J
I
(6.107)
where J refers to the higher state. For J = 2, ∆ω = ± 3
2
/I, for J = 3, ∆ω = ± 5
2
/I, for
J = 4, ∆ω = ± 7
2
/I, etc. These lines are illustrated in Fig. 6.8. It is instructive to
compare them with the equi-spaced rotational levels in absorption spectra [see
Fig. 5.13(a)].
For transitions which involve changes in the vibrational states, ∆J can be
0 or 2. These involve larger changes in energy and hence anti-Stokes lines are
generally very faint. The frequency shift for a change in the vibrational state
but with ∆J = 0, corresponds to the missing central line in the vibrationalrotational spectrum. The spacing of the ∆J = 2 lines about the ∆J = 0 is given by
Eq. (6.107). Raman spectra, involving changes in the vibrational states, provide
useful information about the structure of the molecules.
Raman spectra are characteristic of the molecules (and atoms) and are
extremely useful in the analysis of the complicated mixtures of molecules,
especially of organic molecules. They are also important in the determination
of the rotational and vibrational levels, and in the analysis of the structures of
the molecules.
J = 4
3
2
1
0
n
n
– 5 1
n
n
+ 5 1
n
n
– 7 1 n
n
– 3 1 n
n
n
+ 3 1
n
n
+ 7 1
Fig. 6.9 The Raman spectrum for transitions within the rotational levels,
v 1 is the spacing of the rotational levels (see Fig. 5.13).