Rotational spectra symmetric rotors

Figure 9.24 shows part of the laser Stark spectrum of the bent triatomic molecule FNO obtained with a CO infrared laser operating at 1837.430 cm All the transitions shown are Stark components of the rotational line of the Ig vibrational transition, where Vj is the N-F stretching vibration. The rotational symbolism is that for a symmetric rotor (to which FNO approximates) for which q implies that AA = 0, P implies that A/ = — 1 and the numbers indicate that K" = 7 and J" = 8 (see Section 6.2.4.2). In an electric field each J level is split into (J + 1) components (see Section 5.2.3), each specified by its value of Mj. The selection mle when the radiation is polarized perpendicular to the field (as here) is AMj = 1. Eight of the resulting Stark components are shown. 

Examples of prolate near-symmetric rotors are the s-trans and s-cis isomers of crotonic acid, shown in Figure 5.8, the a axis straddling a chain of the heavier atoms in both species. The rotational term values for both isomers are given approximately by Equation (5.37) but, because A and B are different for each of them, their rotational transitions are not quite coincident. Figure 5.9 shows a part of a low-resolution microwave spectrum of crotonic acid in which the weaker series of lines is due to the less abundant s-cis isomer and the stronger series is due to the more abundant s-trans isomer. 

For a symmetric rotor molecule the selection rules for the rotational Raman spectrum are... 

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 former feature is demonstrated by a part of the fs DFWM spectrum of benzene as depicted in Fig. 3. The data displayed is an extension to the published spectra in Ref. [5]. The experimental trace in Fig. 3a shows regions around the J-type recurrences at a total time delay of ca. 1.5 ns. In Fig. 3b a simulated spectrum is given, computed on the basis of a symmetric oblate rotor with the rotational constant B" = 5689 MHz and the CDs Dj- 1.1 kHz and Djk = -1.4 kHz. For comparison in Fig. 3c the same recurrences are calculated with all CDs set to zero. It can be seen that the CDs cause a strong modulation, splitting and time shift in the recurrences. Even recurrences are differently affected than odd ones. One can conclude that high temperatures do not prevent the occurrence of rotational recurrences and thus, the application of RCS. On the contrary, they enable the determination of CDs by analysis of spectral features at long time delay and hence, reflect the non-rigidity of molecules. 

By way of introduction let us note that the depolarized spectrum Ivh(co) calculated in Section 7.5 for independent rotors consists of a superposition of Lorentzian bands all centered at zero frequency. In the simplest case of symmetric top rotors the spectrum consists of a single band with a width [q2D + 6<9] which depends only on the translational self-diffusion coefficient D and on the rotational diffusion coefficient 0. This should be compared and contrasted with the depolarized spectrum Ivh(co) of certain pure liquids (e.g., aniline, nitrobenzene, quinoline, hexafluorobenzene) shown schematically in Fig. 12.1.1. The spectrum appears to be split. This entirely novel fea-... 

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]. 

The big surprise came in 1995 when high resolution infra-red spectroscopy revealed for embedded SFe molecules a spectrum with fully resolved rotational lines of the P, Q and R branches. FVom the relative intensities of the individual rotational lines the temperatures were measured to be 0.37K in remarkable agreement with earlier theoretical predictions. Subsequent IR-spectroscopy on linear and symmetric top molecules confirmed that the same rotational Hamiltonian as in the gas phase could explain all the spectral features in droplets. Greatly increased moments of inertia were observed for slow rotor molecules (B < lcm ) while fast rotors were not affected. Evidence that the free rotations are related to superfluidity came from an experiment in which the spectrum of OCS in non-superffuid He droplets showed a broad unresolved band structure as expected for a classical fluid. 

This suggests that we can determine littie more about the structure of symmetric tops other than a single rotational constant, even though symmetric tops have two distinct rotational constants. If molecules acted like perfect rigid rotors, this would be the case. But they re not perfect, and that does allow us to obtain additional information from a real spectrum. We will get to this in the next section. 

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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