Physical Chemistry Third Edition

23.8 Other Types of Spectroscopy 997

which leads to a spectrum of equally spaced lines with a spacing in terms of

reciprocal wavelength equal to 2 ̃Be. Molecules with no permanent dipole moment give

no microwave spectrum. The microwave spectra of nonlinear polyatomic molecules

are more complicated but the presence of a permanent dipole moment is required for

a microwave spectrum to occur.

Transitions between vibrational levels lead to spectra in the infrared region. For

diatomic molecules with permanent dipole moments, the selection rule is

∆v± 1

leading to a “fundamental” band centered at a reciprocal wavelength equal to ̃νe. Since

the selection rule is only an approximation, “overtone” bands at multiples of this recip-

rocal wavelength also occur.

The infrared spectra of polyatomic molecules contain one fundamental band for

each normal mode whose motion modulates the dipole moment of the molecule. Nor-

mal modes that do not modulate the dipole moment of the molecule are not seen in

the infrared spectrum. Overtone bands occur as with diatomic molecules, along with

combination bands, which are produced when two normal modes make simultaneous

transitions.

Atomic and molecular spectra in the visible and ultraviolet regions arise from tran-

sitions from one electronic state to another. Vibrational and rotational transitions occur

simultaneously with the electronic transitions, producing complicated band spectra.

The electronic transitions take place rapidly compared with rotational and vibrational

periods, and conform to the Franck–Condon principle: The nuclei remain stationary

during the transition.

Raman spectroscopy involves inelastic scattering of light instead of absorption

or emission. The selection rules for Raman transitions are different from those of

absorption and emission spectroscopy, so that many transitions that are forbidden in

absorption and emission occur in Raman scattering. Raman scattering requires that the

motion modulate the polarizability of the molecule. For rotational Raman transitions

in diatomic and linear polyatomic molecules

∆J0,± 2

which leads to a rotational Raman spectrum with lines whose reciprocal wavelengths

have equal spacing of 4 ̃Bebetween them.

Almost every diatomic molecule has a vibrational Raman spectrum. The vibrational

selection rule for diatomic molecules is

∆v± 1

A nonlinear polyatomic molecule will exhibit a rotational Raman spectrum only if it

has different values of polarizability in different directions. Most molecules exhibit a

rotational Raman spectrum, except for highly symmetric molecules such as spherical

tops.

A normal mode must modulate the polarizability to be seen in the vibrational Raman

spectrum. The “rule of exclusion” states that in a molecule with a center of symmetry,

those normal modes not seen in the infrared spectrum will be seen in the Raman

spectrum, and those seen in the infrared spectrum will not be seen in the Raman

spectrum.