Page 188 - 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

Infrared Spectroscopy 799

results if the restoring force is not a linear function of a fundamental energy level (v 2 = 1) of a completely dif-
the mass displacement, in which case the potential energy ferent vibrational mode. This means that, if no pertur-
will have higher-order terms such as cubic and quartic bation occurred, an overtone absorption band would have
terms. Electrical anharmonicity results if the dipole mo- nearly the same frequency as that of the fundamental band
ment change is not a linear function of the mass displace- of a different vibration. If anharmonicity is present, the
ment. If either mechanical or electrical anharmonicity is higher-order terms in the potential energy may cause per-
present, transitions where the quantum number changes turbations between the fundamental and overtone types
by 2 or more will no longer be forbidden in the IR spec- involved, generating new mixed energy levels. The vibra-
trum. This allows overtones to appear in the spectrum. In tion types involved should be those that can be coupled by
a fundamental transition, the quantum number changes by the anharmonic potential function, which requires them
1 and the photon causing the transition has the same fre- to be of the same symmetry type. The perturbation can
quency as the classical dipole moment oscillation. In an become significant when the unperturbed energy level dif-
overtone transition, the quantum number changes by 2 or ference is small. Combination bands, as well as overtones,
more. The photon that has the right energy to change the can be involved in this interaction, which is called Fermi
quantum number by 2 has a frequency twice that of the resonance.
molecular dipole moment oscillation, and in a harmonic- Consider the case where the unperturbed overtone and
type vibration there will be no dipole moment component fundamental nearly coincide. When interaction occurs,
changing at this frequency. In an anharmonic vibration, two strong bands appear in the spectrum, above and below
the dipole moment change is complicated by the anhar- the expected position of the overtone and the fundamen-
monicity, and overtones are allowed in the spectrum. The tal before interaction. Both bands involve the fundamental
overtone intensity depends on the amount of anharmonic- and both involve the overtone. The strong intensity of both
ity. Overtones are usually fairly weak. bands comes from the fact that the fundamental is involved
In a harmonic oscillator, the spacing
E between the in both bands. The frequency spacing is a function of the
energy levels for v = 0, 1, 2 ... has a constant value hv. perturbation (Table II).
If mechanical anharmonicity is present, the spacing is If the expected frequencies of the unperturbed overtone
no longer exactly constant, which means that overtone and the interacting fundamental are not identical but are
frequencies will not be exactly 2, 3, or more times the still close to one another in frequency, interaction will not
frequency of the fundamental. For example, CHCl 3 has be as strong as before. Two bands of unequal intensity
a CH bending fundamental band at 1216 cm −1 and a will be seen at again somewhat wider spacing than that
−1
much weaker CH bending overtone band at 2400 cm . for the two unperturbed bands. The stronger band will
A ketone has a carbonyl stretching fundamental band be nearer the unperturbed fundamental and will involve
near 1715 cm −1 and a much weaker overtone band near more of the fundamental vibration. The weaker band will
−1
3410 cm . be nearer the unperturbed overtone and will involve more
In polyatomic molecules, combination and difference of the overtone vibration. The weaker band will still in-
bands are allowed when anharmonicity is present. In a volve some fundamental vibration, however, which will
combination-type transition one photon excites two differ- cause this “overtone” band to be more intense than an
ent vibrations at the same time to a new excited state where unperturbed overtone.
both vibrational modes have nonzero quantum numbers
(say, v 1 = 1 and v 2 = 1). If both quantum numbers are 1,
the combination band will appear in the spectrum near the TABLE II Examples of Fermi Resonance
frequency sum of the two fundamentals. In a difference-
Wave number
type transition, the molecule that is already vibrating in an −1
Molecule (cm ) Assignment
excited state for one vibration (say, v 1 = 1) absorbs a pho-
ton of the proper energy and changes to an excited state NaNCO 620 NCO bend
of a different vibration (say, v 2 = 1). The difference band 1216 a NCO in-phase stretch plus
appears at exactly the frequency difference of the two fun- 1305 overtone of NCO bend
damentals in this case. Combination and difference bands, 2220 NCO out-of-phase stretch
like overtones, are usually fairly weak. C 6 H 5 CHO 1392 Aldehyde CH in-plane bend
1700 Aldehyde C O stretch
a
2740 Aldehyde CH stretch plus

J. Fermi Resonance
2825 overtone of CH bend
In a polyatomic molecule it may happen that an over- a The two bands in parentheses have nearly equal intensities, and both
tone energy level (v 1 = 2) has nearly the same energy as involve a fundamental mixed with an overtone of another vibration.