23.7 Raman Spectroscopy 987
The polarizability can be described by anellipsoid of polarizability.^23 This ellipsoid
is a surface such that the distance to the surface from the origin in any direction is
proportional toα−^1 /^2 in that direction. The ellipsoid of polarizability will generally
possess all of the symmetry elements of the molecule. If a rotational or vibrational
motion modulates the polarizability the value of the polarizability in some direction
varies periodically as the motion occurs. This corresponds to changes in the shape or
orientation of the ellipsoid of polarizability.Rotational Raman Spectra
There are two contributions to the polarizability of a molecule: the distortion of the
electronic wave function and the distortion of the nuclear framework. The major con-
tribution is from the electrons, and can be considered to be the sum of contributions
from the individual electrons. The contributions of the inner-shell electrons are nearly
independent of orientation and these contributions can be ignored. The polarizability
of electrons in a bond parallel to the bond direction is different from the polarizabil-
ity perpendicular to that bond. As a diatomic molecule or linear polyatomic molecule
rotates, the components of the polarizability in fixed directions are modulated (fluc-
tuate periodically) as the ellipsoid of polarizability rotates. The rotation of a diatomic
or linear polyatomic molecule will beRaman active(produce a Raman spectrum).
In a nonlinear polyatomic molecule, the polarizabilities of the individual bonds add
vectorially to make up the total polarizability. If the molecule is a symmetric top, the
total polarizability is the same in all directions and the ellipsoid of polarizability is a
sphere. A spherical top molecule has no rotational Raman spectrum. Symmetric tops
and asymmetric tops have anisotropic polarizabilities and produce rotational Raman
spectra.EXAMPLE23.12
Which of the following will have a rotational Raman spectrum?
a.CHCl 3
b.IF 3
c.CS 2
Solution
a.CHCl 3 is a symmetric top, and will have a rotational Raman spectrum.
b.IF 3 is predicted by the VSEPR theory to be T-shaped, and will have a rotational Raman
spectrum.
c.CS 2 is linear, like CO 2 , and will not have a rotational Raman spectrum.Vibrational Raman Spectra
The stretching or compression of a bond changes the electronic wave function and
therefore changes the polarizability. The vibration of a diatomic molecule is Raman
active, whether the molecule is homonuclear or heteronuclear. A vibrational normal(^23) N. B. Colthup, L. H. Daly, and S. E. Wiberley,Introduction to Infrared and Raman Spectroscopy,
3rd ed., Academic Press, San Diego, 1990, p. 65ff.