Translational band

Many common dimers possess just a few rotovibrational levels, but some, like Xe2, possess thousands of rotovibrational states. Molecular transition frequencies vary from just a few wavenumbers to tens of wavenumbers. Besides these rotovibrational bands, dissociation continua exist, see Chapters 5 and 6 for details. Experimentally, very little is known about these dimer signatures in the translational band, presumably because high-resolution work in the far infrared is difficult. Furthermore, because of the feebleness of induced dipoles, high pressures are commonly necessary for a recording of the absorption spectra. This fact tends to pressure-broaden dimer lines to a point where their observation may be impossible. 

According to Eq. 3.5, yi may be considered the total absorption in the translational band. We, however, prefer to consider Mq the total intensity, Eq. 3.4 with n = 0, because the spectral function g(v) is more closely related to the emission (absorption) process than a(v). For rare gas mixtures, we have the relationships of Eqs. 3.7. In other words, yo may be considered a total intensity of the spectral function, g(v), and the ratio yi /yo is a mean width of the spectral function (in units of cm-1). Both moments increase with temperature as Table 3.1 shows. With increasing temperature closer encounters occur, which leads to increased induced dipole moments and thus greater intensities. 

Table 3.2. Ternary integrated absorption coefficients of the translational band. Measurement from [95] calculation [296],...

It is interesting to note the near-absence of absorption in the translational band of pure para-hydrogen. At the temperature of the measurement (20.8 K), all para-H2 molecules are in the rotational ground state (J = 0) which is optically isotropic. The optical properties of these molecules are thus much like those of He atoms. No translational ab-... 

We note that similar conclusions were drawn from the data obtained in the rototranslational bands, and the purely translational bands, pp. 75ff. and 104ff. In all cases considered, the moments calculated with the assumption of pairwise-additivity are smaller than the measurements. 

Table 4.1. Empirical induced dipole models for the translational band Eq. 4.30, with n = 1 where B(n) 0.

Attempts have been made to construct translational band shapes from more or less sophisticated dynamical models. When such computations... 

We note that in the definition of moments, we have used frequency v in units of cm-1. Other units of frequency are sometimes chosen instead of the experimentalist s standard use of frequency in wavenumber units (cm-1), angular frequencies co = 2ncv are the most likely choice of theorists, which leads to different dimensions of the moments, and to the appearence of factors like powers of 2nc. We note, moreover, that in the early days of collisional induction studies the zeroth moment yo was defined without the hyperbolic cotangens function, Eqs. 5.6. For the vibrational bands (hco 3> kT), the old and new definitions are practically identical. However, for the ro to translational band substantial differences exist. The old definition of yo was never intended to be used for the far infrared [314] only Eq. 5.6 gives total intensity in that case. 

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. 

U. Buontempo, S. Cunsolo, P. Dore, and P. Maselli. Analysis of translational band observed in gaseous and liquid Kr-Ar mixtures. J. Chem. Phys., 66 1278, 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. 

Figure 65. Frequency dependence of dielectric loss in ice Ih. (a) Recorded [171] spectrum in the translational band, T = 100 K. (b) The main part of the loss line shown in Fig. (a), calculated for the constant field (solid line) and for the cosine-squared potential (dashed line) points represent experimental data from Ref. 171.

First it should be noted that most of the experimental work on infrared absorption of gas mixtures has been restricted to cases where the constituent molecules themselves are not infrared active, Much work has for instance been done on mixtures of noble gases and noble gases with H2 . Noble gas mixtures show a broad band centered around 100 cm . This is due to absorption by the translational motion of two unlike atoms relative to their joint center of mass. The same kind of translational band has also been measured in Hj-noble gas mixtures and pure H2 . ... 

This system of charges is spectroscopically active. It contributes to the complex permittivity and absorption in the THz region.4 In water the relevant absorption peak is located at 200 cm-1. Our estimate shows that in the VIB state the concentration Vvib of water molecules is commensurable5 with their total concentration N (estimation gives Avib = Afrvib with rvib 35-45%). The b mechanism is responsible for the translational band (T-band) located in the vicinity of 180 cm-1 and the c mechanism is responsible for the band that we term the V-band, with the center placed in the vicinity of 150 cm-1. 

Thus, in the case of heavy water the librational-band maximum is shifted to low frequencies due to increase of the moment of inertia 7or, while the translational-band maximum is located at approximately the same frequency vq 200 cm-1 though doubling of the moment of inertia 7vib (see the note in Table II). The calculated microwave/THz spectra of OW and HW are also rather close (cf. Figs. 4 and 5, Figs. 6 and 7). This result corresponds to the experiment by Zelsmann [21]. 

Thus, action(ice) is about six times the limiting action (equal to h). Therefore, ice behaves more as a classical fluid than does water, since for water Eq. (AlOa) holds instead of Eq. (AlOb). Correspondingly, in the translational band the absorption curve a(v) becomes less damped for ice than for water. 

Let us touch now the opposite case of a rather narrow translational band. By a physical reasoning, the absorption bandwidth Av cannot become extremely narrow, whatever the lifetime t. We relate with v the period Tmd of electromagnetic radiation Tmd = (cv), where c is the speed of light in vacuum. We have ATrad Av(cv2)-1, where min(Arrad) is meant to be positive and v is an average of v value in the frequency interval under investigation. 

For the translational-band center we set here v 200 cm-1. Then we obtain from... 

A variety of mixed models of water is widely available. We use a variant of such models for calculation of wideband spectra in liquid water. In terms of our analytical approach important arguments concerning the mixed model are provided by the different origins of the librational and translational bands. As was demonstrated in Section III, the center of the first is sensitive to the change of H20 or D20, while the center of the second is insensitive. 

Our calculation of the absorption coefficient a in the translational-band region (Fig. 15a) agrees with recent experimental data by Vij et al. [32] depicted in Fig. 15b. The absorption maximum amax is reached in both cases at 30°C. It is interesting that at higher temperature the amax value substantially decreases. 

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