Infrared absorption spectra of polyatomic molecules
المؤلف:
Peter Atkins، Julio de Paula
المصدر:
ATKINS PHYSICAL CHEMISTRY
الجزء والصفحة:
ص461-464
2025-12-06
37
Infrared absorption spectra of polyatomic molecules
The gross selection rule for infrared activity is that the motion corresponding to a normal mode should be accompanied by a change of dipole moment. Deciding whether this is so can sometimes be done by inspection. For example, the symmetric stretch of CO2 leaves the dipole moment unchanged (at zero, see Fig. 13.40), so this mode is infrared inactive. The antisymmetric stretch, however, changes the dipole moment because the molecule becomes unsymmetrical as it vibrates, so this mode is infrared active. Because the dipole moment change is parallel to the principal axis, the transitions arising from this mode are classified as parallel bands in the spectrum. Both bending modes are infrared active: they are accompanied by a changing dipole perpendicular to the principal axis, so transitions involving them lead to a perpendicular bandin the spectrum. The latter bands eliminate the linearity of the molecule, and as a result a Q branch is observed; a parallel band does not have a Q branch.
The active modes are subject to the specific selection rule ∆vq=±1 in the harmonic approximation, so the wavenumber of the fundamental transition (the ‘first harmonic’) of each active mode is #q. From the analysis of the spectrum, a picture may be con-structed of the stiffness of various parts of the molecule, that is, we can establish its force field, the set of force constants corresponding to all the displacements of the atoms. The force field may also be estimated by using the semi-empirical, ab initio, and DFT computational techniques described in Section 11.7. Superimposed on the simple force field scheme are the complications arising from anharmonicities and the effects of molecular rotation. Very often the sample is a liquid or a solid, and the molecules are unable to rotate freely. In a liquid, for example, a molecule may be able to rotate through only a few degrees before it is struck by another, so it changes its rotational state frequently. This random changing of orientation is called tumbling. The lifetimes of rotational states in liquids are very short, so in most cases the rotational energies are ill-defined. Collisions occur at a rate of about 1013 s−1 and, even allowing for only a 10 per cent success rate in knocking the molecule into another rotational state, a lifetime broadening (eqn 13.19) of more than 1 cm−1 can easily result. The rotational structure of the vibrational spectrum is blurred by this effect, so the infrared spectra of molecules in condensed phases usually consist of broad lines spanning the entire range of the resolved gas-phase spectrum, and showing no branch structure. One very important application of infrared spectroscopy to condensed phase samples, and for which the blurring of the rotational structure by random collisions is a welcome simplification, is to chemical analysis. The vibrational spectra of different groups in a molecule give rise to absorptions at characteristic frequencies because a normal mode of even a very large molecule is often dominated by the motion of a small group of atoms. The intensities of the vibrational bands that can be identified with the motions of small groups are also transferable between molecules. Consequently, the molecules in a sample can often be identified by examining its infrared spectrum and referring to a table of characteristic frequencies and intensities (Table 13.3).
Solar energy strikes the top of the Earth’s atmosphere at a rate of 343 W m−2. About 30 per cent of this energy is reflected back into space by the Earth or the atmosphere. The Earth–atmosphere system absorbs the remaining energy and re-emits it into space as black-body radiation, with most of the intensity being carried by infrared radiation in the range 200–2500 cm−1(4–50µm). The Earth’s average temperature is maintained by an energy balance between solar radiation absorbed by the Earth and black-body radiation emitted by the Earth. The trapping of infrared radiation by certain gases in the atmosphere is known as the greenhouse effect, so called because it warms the Earth as if the planet were enclosed in a huge greenhouse. The result is that the natural greenhouse effect raises the average surface temperature well above the freezing point of water and creates an environment in which life is possible. The major constituents to the Earth’s atmosphere, O2 and N2, do not contribute to the greenhouse effect because homonuclear diatomic molecules cannot absorb infrared radiation. However, the minor atmospheric gases, water vapour and CO2, do absorb infrared radiation and hence are responsible for the Solar energy strikes the top of the Earth’s atmosphere at a rate of 343 W m−2. About 30 per cent of this energy is reflected back into space by the Earth or the atmosphere. The Earth–atmosphere system absorbs the remaining energy and re-emits it into space as black-body radiation, with most of the intensity being carried by infrared radiation in the range 200–2500 cm−1(4–50µm). The Earth’s average temperature is maintained by an energy balance between solar radiation absorbed by the Earth and black-body radiation emitted by the Earth. The trapping of infrared radiation by certain gases in the atmosphere is known as the greenhouse effect, so called because it warms the Earth as if the planet were enclosed in a huge greenhouse. The result is that the natural greenhouse effect raises the average surface temperature well above the freezing point of water and creates an environment in which life is possible. The major constituents to the Earth’s atmosphere, O2 and N2, do not contribute to the greenhouse effect because homonuclear diatomic molecules cannot absorb infrared radiation. However, the minor atmospheric gases, water vapour and CO2, do absorb infrared radiation and hence are responsible for the
environment caused by a temperature increase of 3 K is a rise in sea level by about 0.5 m, which is sufficient to alter weather patterns and submerge currently coastal ecosystems. Computer projections for the next 200 years predict further increases in atmospheric CO2 levels and suggest that, to maintain CO2 at its current concentration, we would have to reduce hydrocarbon fuel consumption immediately by about 50 per cent. Clearly, in order to reverse global warming trends, we need to develop alternatives to fossil fuels, such as hydrogen (which can be used in fuel cells, Impact I25.3) and solar energy technologies.
Fig. 13.42The intensity of infrared radiation that would be lost from Earth in the absence of greenhouse gases is shown by the blue line. The purple line is the intensity of the radiation actually emitted. The maximum wavelength of radiation absorbed by each greenhouse gas is indicated.
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