Rotational state, pressure broadening

For liquids, the collision rate is close to 1030 collisions s 1. Microwave spectroscopy, which studies molecular rotation, only uses dilute gases to obtain pure rotational states of sufficient lifetime. Rotational transitions are broadened by molecular collisions, because the pressure is close to a few tenths of a bar, as shown in Fig. 1.6. 

Heijmen TGA, Moszynski R, Wormer PES, Van der Avoird A, Rudert AD, Halpern JB, Martin J, Gao WB, Zacharias H (1999) Rotational state-to-state rate constants and pressure broadening coefficients for He— C2H2 collisions Theory and experiment. J Chem Phys 111 2519—2531... 

In condensed phases it is well known there are energy transfers between rotational and vibrational states. Indeed, molecular rotation does not actually occur in liquids - rotational states turn into vibrational states because of an increase in collisions. For liquids, the collision rate is dose to 10 collisions per second. Micro-wave spectroscopic studies of molecular rotation only use dilute gases to obtain pure rotational states with a suflident lifetime. Broadening of rotational transitions induced by molecular collisions occurs because pressures are dose to a few tenths of a Bar as described for Fig. 1.10. 

Collisions between molecules are the greatest cause of line broadening at the pressures normally employed for MMW spectrometry. In the Lorentz theory (ref 2, p. 338) the lifetime of the rotational state involved in the transition is ended abruptly by collision with another molecule which stops the rotation. When the molecule starts to rotate again, its phase with respect to the other molecules is random. For an assembly of molecules this will give rise to an absorption line profile with a FWHM of Xjlm, where r is the mean time between collisions. This is the linear sum of two terms, one for the upper and one for the lower state, having the shape of the Lorentz function (Figure 1.4) when Av [Pg.12]

Molecular two-photon spectroscopy can also be applied in the infrared region to induce transitions between rotational-vibrational levels within the electronic ground state. One example is the Doppler-free spectroscopy of rotational lines in the V2 vibrational bands of NH3 [258]. This allows the study of the collisional properties of the V2 vibrational manifold from pressure broadening and shifts (Vol. 1, Sect. 3.3) and Stark shifts. 

Although UFg has a conveniently high vapor pressure at room temperature, its absorption spectrum is much more complex than that of the metal because of the large number of vibrational and rotational states superposed on each electronic state. Moreover, at room temperature these bands are broadened sufficiently to preclude selective absorption. 

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. 

Recently, this problem was treated by a rigorous quantum chemistry calculation by Bakalov et al. [28], First, the authors calculated ab initio the interatomic interaction V(R,r, ) between an atomcule pHe- and a He atom based on the Born-Oppenheimer approximation. Since the rotational frequency of the p (of order of 1015 s-1) is much higher than the collision frequency (of order of 1012 s-1), the angular dependence is smeared out, and typically, the Van der Waals minimum occurs around R 5.5 a.u., and the repulsive barrier starts around R 5 a.u. The potential V(R) depends on (n,l), and thus, a small difference AV(R) occurs between an initial state and a final state. It is this difference that causes pressure shifts and broadening in the resonance line. 

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