Translational band interaction

The simplest systems of interest consist of two interacting, non-reactive atoms, such as He-Ar. In such cases (if electronic transitions are ignored), there is only the translational band to be considered. Line shape computations are straightforward but will in general require the use of digital computers if realistic intermolecular potentials are employed. 

Figure 2 The absorption coefficient a, normalized by the helium and hydrogen gas densities, pi and P2, respectively, as function of frequency in the H2 roto-translational band, at the temperature of 296 K (upper trace) and 196 (lower trace, shifted downward one step for clarity). Solid and dashed curves represent calculations with and without accounting for the anisotropy of the intermolecu-lar interactions, respectively. Also shown are measurements (as in Fig. 3.12, p. 85) from Ref. [17]...

V. I. Bukhtoyarova and M. V. Tonkov. Intermolecular interactions in compressed gases from translational absorption spectra I Spectral moments of translation bands. Opt. Spectrosc., 43 27, 1977. 

Besides, the review could conditionally be divided in accord with another criterion, (a) In Sections III-V and VII we discuss so-called unspecific interactions, which take place in a local-order structure of various polar liquids, (b) In Sections VI-IX we also consider specific interactions [16]. These are directly determined by the hydrogen bonds in water, are reflected in the band centered at 200 cm-1, which is termed here the R-band, and is characterized by some spectral features in the submillimeter wavelength range (from 10 to 100 cm-1). Note that sometimes in the literature the R-band is termed the translational band, since the peak frequency of this band does not depend on the moment of inertia I of a water molecule. 

Collision-induced absorption from free pairs of molecules appear as broad lines or bands located at the wavenumbers of the pure-rotation or vibration-rotation transitions in the participating individual molecules. Figure 3.3.6 shows the spectrum for H2-H2 collisions (Bachet et al., 1983) [see also Courtin (1988)]. In the far infrared (below 200 cm ) a weak translational band is also present. In H2 the prominent features in planetary atmospheres occur at the pure-rotation / = 0 -> 2 and 1 3 transitions located at 354 and 587 cm . The widths of collision-induced features are extremely large, about 100 cm or more, because the time during the collision in which the partners are interacting is very short ( 10 seconds or less). The width of a spectral line is related to the reciprocal of the collision duration. 

The SCF method for molecules has been extended into the Crystal Orbital (CO) method for systems with ID- or 3D- translational periodicityiMi). The CO method is in fact the band theory method of solid state theory applied in the spirit of molecular orbital methods. It is used to obtain the band structure as a means to explain the conductivity in these materials, and we have done so in our study of polyacetylene. There are however some difficulties associated with the use of the CO method to describe impurities or defects in polymers. The periodicity assumed in the CO formalism implies that impurities have the same periodicity. Thus the unit cell on which the translational periodicity is applied must be chosen carefully in such a way that the repeating impurities do not interact. In general this requirement implies that the unit cell be very large, a feature which results in extremely demanding computations and thus hinders the use of the CO method for the study of impurities. 

The preceding suggests that the structure of the density of vibrational states in the hindered translation region is primarily sensitive to local topology, and not to other details of either structure or interaction. This is indeed the case. Weare and Alben 35) have shown that the density of vibrational states of an exactly tetrahedral solid with zero bond-bending force constant is particularly simple. The theorem states that the density of vibrational states expressed as a function of M (o2 (in our case M is the mass of a water molecule) consists of three parts, each of which contains one state per molecule. These arb a delta function at zero, a delta function at 8 a, where a is the bond stretching force constant, and a continuous band which has the same density of states as the "one band Hamiltonian... 

Table 3.1 lists measured spectral moments of rare gas mixtures at various temperatures. (We note that absorption in helium-neon mixtures has been measured recently [253]. This mixture absorbs very weakly so that pressures of 1500 bar had to be used. Under these conditions, one would expect significant many-body interactions the measurement almost certainly does not represent binary spectra.) For easy reference below, we note that the precision of the data quoted in the Table is not at all uniform. Accurate values of the moments require good absorption measurements over the whole translational frequency band, from zero to the highest frequencies where radiation is absorbed. Such data are, however, difficult to obtain. Good measurements of the absorption coefficient a(v) require ratios of transmitted to incident intensities, /(v)//o, that are significantly smaller than unity and, at the same time, of the order of unity, i.e., not too small. Since in the far infrared the lengths of absorption paths are limited to a few meters and gas densities are limited to obtain purely... 

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. 

In Chapter 5 the absorption spectra of complexes of interacting atoms were considered. If some or all of the interacting members of a complex are molecular, additional degrees of freedom exist and may be excited in the presence of radiation. As a result, besides the translational profiles discussed in Chapter 5, new spectral bands appear at the rotovibrational transition frequencies of the molecules involved, and at sums and differences of such frequencies - even if the non-interacting molecules are infrared inactive. The theory of absorption by small complexes involving molecules is considered in the present Chapter. 

Table 6.2. The zeroth, first, and second translational moments of the fundamental band of Fh-He, of the three main induced dipole components, at four temperatures. The M are the uncorrected values of the nth moment, obtained with the assumption Kg (/ ) = J/0l/ (R), and the M 1 are values corrected for the vibrational dependences of the interaction potential the M are obtained from line shape calculations which account for the v dependence of the interaction.

We have not attempted to exhibit in great detail the effects of the rotational excitations on the induced dipole components B and those of vibrational excitation on the interaction potential because this was done elsewhere for similar systems [151, 63,295,294], The significance of the j,f corrections is readily seen in the Tables and need not be displayed beyond that. The vibrational influence is displayed in Fig. 6.20 first and second spectral moments are strongly affected, especially at high temperatures, similar to that which was seen earlier for H2-He [294], Fig. 6.23. The close agreement of the measurements of the rotovibrational collision-induced absorption bands of hydrogen with the fundamental theory shown above certainly depends on proper accounting for the rotational dependences of the induced dipole moment, and of the vibrational dependences of the final translational states of the molecular pair. 

Physically, the Brillouin spectrum arises from the inelastic interaction between a photon and the hydrodynamics modes of the fluid. The doublets can be regarded as the Stokes and anti-Stokes translational Raman spectrum of the liquid. These lines arise due to the inelastic collision between the photon and the fluid, in which the photon gains or loses energy to the phonons (the propagating sound modes in the fluid) and thus suffer a frequency shift. The width of the band gives the lifetime ( 2r)-1 of a classical phonon of wavenumber q. The Rayleigh band, on the other hand, represents the... 

Landau (26) proposed that an additive electron in a dielectric can be trapped by polarization of the dielectric medium induced by the electron itself. Applying the model to electrons in the conduction band of an ionic crystal is rather complicated since the translational symmetry of the solid must be considered and the interaction of the excess electron with the lattice vibrations must be treated properly (I, 13, 14). 

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