Page 189 - Academic Press Encyclopedia of Physical Science and Technology 3rd Analytical Chemistry

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Encyclopedia of Physical Science and Technology EN007C-340 July 10, 2001 14:45

800 Infrared Spectroscopy

K. Molecular Rotation
Pure rotation of molecules in the gaseous state causes ab-
sorption of radiation in the microwave region and to some
extent in the far-IR region. In order for a pure rotation to
absorb radiation, the rotating molecule must have a per-
manent dipole moment. Imagine that the dipole moment
is oriented perpendicularly to the radiation electric field
FIGURE 8 Infrared spectra of gas-phase bands for linear
direction. The field exerts forces in opposite directions on molecules and asymmetric top molecules. Unresolved contours
the negative and positive ends of the dipole. This gener- are shown for different types of bands. Asymmetric top molecules
ates a torque, which tends to rotate the dipole moment have different contours for different ratios of the moments of iner-
tia. The parallel band of linear molecules and the B-type band of
and therefore tends to increase the rotational frequency
the asymmetric top have no central peak.
of the molecule. If the rotational frequency increases, the
rotational energy increases at the expense of the radiation
energy. The rotational energy, like the vibrational energy,
caused by the vibration. In polyatomic linear molecules
is not continuously variable but is quantized. Imagine a
such as CO 2 and acetylene, IR-active stretching and bend-
rotating linear molecule such as HCl in a certain rota-
ing vibrations cause dipole moment changes parallel and
tional energy state with a quantum number J, which has
perpendicular to the molecular axis, respectively. For par-
an integer value (1, 2, 3, ... ). The selection rule for pure
allel vibrations, the gas-phase band contour is a broad
rotation states that photon energy absorption can increase
doublet (Fig. 8). In the low-frequency and high-frequency
the quantum number by only 1 to the state J + 1. The
wings of the band, the rotational quantum numbers for
photon that has the right energy to cause this transition
each of the various energy states have decreased and in-
has a frequency intermediate between the classical rota-
creased by 1, respectively, during the vibrational transi-
tional frequencies for the initial (J) and the final (J + 1)
tion. Perpendicular bands have the same broad doublet
states. Unlike the classical vibrational frequency, the clas-
seen in the parallel bands, but a perpendicular band has
sical rotational frequency of the molecule increases dur-
an additional central peak not seen in the parallel band,
ing the transition, and the oscillating electric field of the
where the rotational energy remains unchanged during the
photon with this intermediate frequency can stay nearly
vibrational transition.
synchronized with the rotating dipole moment throughout
Tetrahedral or octahedral molecules such as CH 4 and
the transition. An analysis of the rotational fine structure
SF 4 arecalledsphericaltopsandhavethreeequalmoments
in the spectrum may yield information about the moments
of inertia for rotation about three mutually perpendicular
of inertia of the molecule.
axes. The gas-phase contour is similar to the perpendicular
band of the linear molecule, with two broad wings and a
central peak for all the IR-active vibrations.
L. Gas-Phase Band Contours
Molecules with one threefold or higher axis of symme-
In the vibrational spectrum the molecule usually changes try such as CHCl 3 ,BF 3 , and C 2 H 6 are called symmetric
from the ground vibrational state (v = 0) to the first excited tops. Two moments of inertia are equal and differ from the
vibrationalstate(v = 1).Whenthesampleisinthegaseous third unique moment of inertia for rotation about the axis
state, the molecule may change its rotational state at the of threefold or higher symmetry. When a vibration causes
same time it changes its vibrational state. The molecule a dipole moment change parallel to the major symme-
in the ground vibrational state is rotating with a certain try axis, the unresolved gas-phase contour is similar to the
angular momentum. When the molecule ends up at the perpendicular band of the linear molecule, a broad doublet
first excited vibrational state, it may be rotating with an with a central peak. When the dipole moment change is
increased or decreased angular momentum. As a result perpendicular to the major symmetry axis, the band struc-
of the rotational energy changes, rotational structure is ture is more complex and the unresolved contour depends
superimposed on the vibrational band, which is referred on the relative magnitudes of the moments of inertia.
to as a vibration–rotation band. In molecules with less symmetry, the three moments
If the molecular moments of inertia are sufficiently low of inertia are different. These are called asymmetric tops.
and the spectrometer has adequate resolution, rotational The axes with minimum and maximum moments of in-
fine structure can be resolved in the vibration–rotation ertia are called the a and c axes, respectively, and the
band. For larger molecules, the fine structure is usually axis with intermediate moment of inertia is called the b
unresolved, resulting in a broad band. The contour of the axis. Vibrations with dipole moment changes parallel to
bandmayrevealthedirectionofthedipolemomentchange these axes are called A, B, and C bands. The unresolved