Rotational-vibrational bands in the mid-IR

Excepting when the temperature is 0 K, atoms within molecules are in perpetual motion and each one of them possesses three degrees of freedom, which refer to the three classic Cartesian coordinates. All of these movements confer upon each isolated molecule a combined mechanical energy. The theory is postulated 

The values of these energies are very different and according to the Born— Oppenheimer principle they can vary independently of each other. 

In the mid-IR, a source emitting a radiation of 1000 cm corresponds to a photon energy E= hcv = 0.125 eV. If such a photon is absorbed by a molecule its total energy will be increased by this energy. Theoretically the term E. will be modified but the term will not change because this energy is too weak to cause transition between two different electronic levels. 

In practice, as samples are usually in the form of condensed (liquid) or solid phases, pure or in solution and not in the form of isolated species, numerous dipole-dipole interactions are produced between the species present, which perturb both the energy levels and the absorption wavelengths. Thus a spectrum is always in the form of broadened signals called bands which extend over tens of cm , which common apparatus are unable to separate into individual transitions. 

It is noteworthy that the width of an absorption signal is inversely proportional to the lifetime of the excited state (Heisenberg s uncertainty principle). Hence, for gases, the lifetime is long and the absorption lines are sharp. This is why small di- or triatomic molecules sampled in the gas state and at low pressures can lead to spectra containing narrow regular bands whose positions enable the elucidation of the various energetic states predicted by the theory. 

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