Rotational spectra asymmetric rotors

This general behaviour is characteristic of type A, B and C bands and is further illustrated in Figure 6.34. This shows part of the infrared spectrum of fluorobenzene, a prolate asymmetric rotor. The bands at about 1156 cm, 1067 cm and 893 cm are type A, B and C bands, respectively. They show less resolved rotational stmcture than those of ethylene. The reason for this is that the molecule is much larger, resulting in far greater congestion of rotational transitions. Nevertheless, it is clear that observation of such rotational contours, and the consequent identification of the direction of the vibrational transition moment, is very useful in fhe assignmenf of vibrational modes. 

Table 4.7 shows the rotational constants for the complex and the monomers. The distances between the hydrogen-bonded heavy atoms are presented in Table 4.8. It is evident that the OH H202 complex is an asymmetric rotor. Because this hydrogen bond has a permanent dipole moment that is somewhat larger than those of the monomers, it should be active in the microwave region of the spectrum.

The carboxylic acid dimers are quite heavy, with rotational constants typically around 1 GHz, and the microwave absorption experiments are conducted at high temperatures of 200-300 K. The resulting large number of rotation-vibration states populated, coupled with low dimer number densities, on the order of 5 x 1014 mole-cules/cm3, makes complete resolution of the rotational spectrum not feasible. However, virtually all dimers are prolate rotors with only moderate asymmetry. Thus, AJ = 1 transitions (a-type) with the same initial and final quantum numbers, but otherwise of different asymmetric rotor state or different vibrational state, will have the same frequency within about 50 MHz for moderate J values e.g. for J < 5 and for transition frequencies less than 50 GHz. At this level of resolution, isotope shifts are not discernible, and the resulting spectra (Fig. 1) yield one rotational constant, (B + C)/2, with an accuracy of about 0.5 %. 

Figure 16. A 0.5 cm resolution spectrum of the (5,0,0) band. The top spectrum is calculated from an asymmetric rotor program with a Boltzmann rotational temperature of 30 K. The bottom spectrum is from an experiment with expansion conditions of 3% OCIO in 1.5 atm of helium.

E.E.Nikitin and M.Ya.Ovchinnikova, Asymmetric rotor model in the description of rotational structure of overtones bands in NH3 spectrum, Optika i Spekt. 67, 47 (1989)... 

A variety of different methods have been used to measure V, V, and (LS59, OM07) only a few of the more important will be discussed here. For asymmetric rotors, both the pure rotational spectrum and its torsion-rotation counterpart are electric dipole allowed and are affected in lowest order by the leading terms in the torsional Hamiltonian. Both types of spectra have been used extensively to determine (LS59). For symmetric tops with a single torsional degree of freedom, either the permanent electric dipole moment vanishes, as in CH CH, or the normal rotational spectrum is independent of 17 in lowest order, as in CH SiH. In... 

The microwave spectrum exhibits a tunnelling splitting due to a large amplitude internal rotation of the H2S subunit. The internal rotor states are labelled with the asymmetric rotor quantum number for the rotational levels... 

The microwave spectrum exhibits a tuimelling splitting due to a large amplitude internal rotation of the H2O subunit that exchanges bonded and non-bonded atoms. The internal rotor states are labelled with the asymmetric rotor quantum number for the rotational levels of free water (/tafc) and are designated as EOoo and Eloi 2 represents K=0 where K is the projection of the angular momentum of the water subunit onto the intermolecular axis. 

For the V3 band about 270 absorption lines were recorded between 920 and 967 cm The V3 band is an a-type band of a near-prolate asymmetric rotor, and at large Kg it should resemble the parallel band of a prolate symmetric top, i.e., AN = 0, 1, AKg ( AK) = 0. In the V3 band the symmetric top characteristics are not as obvious as in the band, however, a number of Pk and °Qk branches with N up to 28 and Rk branches with N up to 42 could be identified (for the band center, see p. 247). The assignment was supported by the results from a Fourier transform spectrum of NF2 at 890 to 980 cm The spin-rotation splitting is relatively small and unresolved in transitions with low Kg values. The asymmetry splitting is apparent in lines with low Kg and high N values, which was demonstrated with the (N=19 to 21) branch [9]. 

Transitions between the rotational states of a polyatomic molecules can produce a microwave spectrum. We will not discuss the details of the microwave spectra of polyatomic molecules, but make some elementary comments. As with diatomic molecules, we apply the rigid-rotor approximation, assuming that a rotating polyatomic molecule is locked in its equilibrium conformation. Any molecule in its equilibrium conformation must belong to one of four classes linear molecules, spherical top molecules, symmetric top molecules, and asymmetric top molecules. 

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