The rototranslational spectra

If molecular gases are considered, infrared spectra richer than those seen in the rare gases occur. Besides the translational spectra shown above, various rotational and rotovibrational spectral components may be expected even if the molecules are non-polar. Besides overlap, other induction mechanisms become important, most notably multipole-induced dipoles. Dipole components may be thought of as being modulated by the vibration and rotation of the interacting molecules so that induced supermolecular bands appear at the rotovibrational frequencies. In other words, besides the translational induced spectra studied above, we may expect rotational induced bands in the infrared (and rotovibrational and electronic bands at higher frequencies as this was suggested above, Eq. 1.7 and Fig. 1.3). Lines at sums and differences of such frequencies also occur and are common in the fundamental and overtone bands. We will discuss the rotational pair and triplet spectra first. 

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Isotope spectra. Rotovibrational spectra of deuterium, and of deuterium-rare gas mixtures, have also been recorded over a wide range of temperatures and densities [342]. The differences between the H2-X and D2-X spectra (with X = H2 or D2, respectively, or a rare gas atom) are much like what has been seen above for the rototranslational spectra. 

Later studies showed the same phenomena in deuterium and deuterium-rare gas mixtures [335, 338, 305], and also in nitrogen and nitrogen-helium mixtures [336] in nitrogen-argon mixtures the feature is, however, not well developed. The intercollisional dip (as the feature is now commonly called) in the rototranslational spectra was identified many years later see Fig. 3.5 and related discussions. The phenomenon was explained by van Kranendonk [404] as a many-body process, in terms of the correlations of induced dipoles in consecutive collisions. In other words, at low densities, the dipole autocorrelation function has a significant negative tail of a characteristic decay time equal to the mean time between collisions see the theoretical developments in Chapter 5 for details. 

For the rototranslational spectra, within the framework of the isotropic interaction approximation, the expressions for the zeroth and first moments, Eqs. 6.13 and 6.16, are exact provided the quantal pair distribution function (Eq. 5.36) is used [314]. A similar expression for the binary second translational moment has been reported [291],... 

While for an accurate (+1%) treatment of the rototranslational spectra (v = v = 0) the matrix elements (vj (9 v f) of the lower rotational states do not much depend on the rotational transitions (j,f), for the vibrational bands (v > 0), for v f v, relatively strong j,f dependences are usually observed (9 designates the multipole and polarizability operator. Similar j dependences are also obtained for the dipole components Bc that are significant for line shape computations [63]. The accounting for the j dependences is relatively easy because the main effect of the j dependence is on the integrated intensity, but not so much on the shape of the profile. The main effect of neglecting the j dependence in the low-temperature spectra is an excess intensity of the Sj(l) lines. 

The rototranslational profiles of molecular systems are surprisingly closely approximated by certain model profiles, which are functions of frequency, temperature, and three parameters, see Eqs. 5.105ff. The BC profiles have been found to approximate most closely, and for a maximal peak-towing intensity ratio, the multipole-induced profiles of low order while the overlap-induced components are best represented by the K0 model [69]. Analytical models of the rototranslational spectra of H2-He pairs have... 

Other systems like H2-H2 feature a small number of bound states. Whenever molecular pairs form bound dimers, spectroscopic structures appear. First and usually most importantly, the continuum of the purely rotational band appears, but various other structures associated with bound-to-free transition usually show up that are harder to model closely. As a rule, the rototranslational absorption spectra of most molecular systems are not as easily modeled as that of H2-He, because of the dimer structures. Of course, in the typical high-pressure laboratory measurements, dimer structures may be broadened to the point where these are hardly discernible. In such a case, the BC and KO model profiles may become adequate again. In any case, the rototranslational spectra of a number of binary systems have been modeled closely over a broad range of temperatures [58], including the (coarse) dimer structures. 

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