Asymmetric molecules rotational spectra

Of the visible spectroscopic techniques, CD spectroscopy has seen the most rapid and dramatic growth. The far-UV circular dichroism spectrum of a protein is a direct reflection of its secondary structure [71]. An asymmetrical molecule, such as a protein macromolecule, exhibits circular dichroism because it absorbs circularly polarized light of one rotation differently from circularly polarized light of the other rotation. Therefore, the technique is useful in determining changes in secondary structure as a function of stability, thermal treatment, or freeze-thaw. 

Silicon dicarbide has been identified by Thaddeus et al. (1984) as a circumstellar molecule on the basis of 9 hitherto unassigned millimeter wave lines observed in the late type star IRC + 10216. The molecule is the first ring molecule detected in space, and its rotational spectrum is that of a near prolate asymmetric top with C2v symmetry. The molecule had been detected in the laboratory prior to the interstellar detection by optical laser spectroscopy (Michalopoulous et al. 1984). 

If we look at the N2O vibration-rotation spectrum, instead of two bands in the infrared, we find three. This is immediate evidence that the molecule does not have a center of symmetry. The frequencies are = 1285.0 cm (symmetrical stretch), V2 = 588.8 cm (degenerate bending vibration), and V3 = 2223.5 cm (asymmetrical stretch). 

In favorable cases the analysis of the rotational spectrum of asymmetric molecules in the vibrational state Uj t j ajN 6 eillows the determination of the constants listed in this table. The vibration-rotation interaction constants must be determined by the analysis of at least two vibrational states of the same normal yibration. 

Since the rotational spectrum of a symmetric top molecule generally gives only one rotational constant and therefore provides only one information concerning the molecular structure, the rotational spectrum of isotopic forms of this molecule must also be investigated. In many cases the symmetric top molecule becomes an asymmetric top molecule due to isotope substitution. These asymmetric top molecules appear in this table. For explanation of the parameters see section 2.5.1, subvol. II/19b. 

The pure rotation spectrum of an asymmetric top is very complex, and cannot be reduced to a formula giving line positions. Instead, it has to be dealt with by calculation of the appropriate upper and lower state energies (Section 7.2.2). The basic selection rule, A7 = 0, 1, applies to absorption/emission spectra, and there are other selection rules. These depend on the symmetry of the inertial ellipsoid, which is always Dan, but the orientations of the dipole moment components depend on the symmetry of the molecule itself. For the rotational Raman effect A7= 2 transitions are allowed as well. The selection rules for pure rotational spectra are described in more detail in the on-line supplement for Chapter 7. 

GW Hills, WJ Jones. Raman spectra of asymmetric top molecules. Part 1. The pure rotational spectrum of ethylene. Trans Faraday Soc II 71 812-842, 1975. 

In section 2.2 through 2.5 the molecules (radicals are included with references to chapter 4) are ordered according to the type of their respective rotational spectrum as follows Diatomic molecules (2.2), linear molecules (2.3) symmetric top molecules (2.4), and asymmetric top molecules (2.5). Molecules which are asymmetric only due to isotopic substitution are listed together with their parent species in 2.4. The tables include rotational constants, centrifugal distortion constants, rotation-vibration interaction constants, and /-type doubling constants. Some additional molecular constants obtained by microwave type methods have been listed as well. References to publications concerning the molecular structure are cited separately. 

The analysis of the rotational spectrum of an asymmetric molecule in the vibrational state ui,... vj,... v u-6 normally allows the determination of the constants listed in this table. All rotating molecules show the influence of molecular deformation (centrifugal distortion, c.d.) in their spectra. The theory of centrifugal distortion was first developed by Kivelson and Wilson [52Kiv]. The rotational Hamiltonian in cylindrical tensor form has been given by Watson [77 Wat] in terms of the angular momentum operators J, J/and as follows ... 

Unless there is an accidental near-vibrational degeneracy, the rotational spectrum of an asymmetric top in an excited vibrational state is similar to that obtained in the ground state, except that the spectrum is characterized by a slightly different set of rotation and distortion constants. Other nonrigid effects are often more important for asymmetric tops, such as internal rotation, and these are considered in Section VII. Similar statements apply to linear and symmetric-top molecules in excited nondegenerate vibrational states. For example, the rotational frequencies for symmetric tops in nondegenerate vibrational states are given by Eq. (54) with the rotation and distortion constants replaced by effective constants B ,... 

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. 

The pure-rotational Raman spectrum of a polyatomic molecule provides information on the moments of inertia, hence allowing a structural determination. For a molecule to exhibit a pure-rotational Raman spectrum, the polarizability must be anisotropic that is, the polarizability ellipsoid must not be a sphere. As noted in Section 5.2, a spherical top has a spherical polarizability ellipsoid, and so gives no pure-rotational Raman spectrum. Symmetric and asymmetric tops have asymmetric polarizabilities. The structures of several nonpolar molecules (which cannot be studied by microwave spectroscopy) have been determined from their pure-rotational Raman spectra these include F2, C2H4, and C6H6. 

It is well known that the v, band of liquid acetonitrile is significantly asymmetric due to an overlap of hot band transitions in the low frequency side. A study of gas phase rotation-vibration spectrum [19] showed that the hot band transition from the first exited state of the degenerated C-C = N bending v8 mode, v hl = v + v8 - vs, has its center at 4.944 cm 1 lower than that of the fundamental transition, v,. Also the presence of v,h2 = v, + 2v8 - 2v8 transition is expected. The careful study on the v band of liquid acetonitrile by Hashimoto et al [20] provided the reorientational and vibrational relaxation times of liquid acetonitrile molecule. They corrected the contribution by the hot band transition using the Boltzmann population law and approximated the v , v,hl, 2h2, and v, + v4 bands by Lorentzian curves. 

Both the rotational fine structure and the contours of bands are helpful in assigning vibrations of gaseous compounds with a known structure. It is well known that vibrational transitions of diatomic AS molecules without changes in the rotational state ( -branch, AJ = 0) are not allowed in the IR spectrum. Likewise, selection rules exist for linear molecules, spherical tops, symmetric and asymmetric tops. With different irreducible representations, these lead to characteristic band contours, which are discussed in detail in another part of this book (Sec. 4.3). 

The results simplify considerably if the body-fixed axis system is a principal axis system for the polarizability tensor as well as for the rotational diffusion tensor. In this case Ag = At = A5 = 0 in Eq. (7.5.27). Then the spectrum consists of only two Lorentzians. Many asymmetric diffusors do have enough symmetry to rigorously satisfy this condition-for instance, planar molecules with at least one two fold rotation axis in the molecular plane. Others may have these axes so close together that Ag = A4 = A5 = 0 and the spectrum effectively consists of only two Lorentzians. In any particular application, it must be kept in mind that the spectrum might very well be the five-Lorentzian form given by the Fourier transform of Eq. (7.5.25). 

The infrared spectrum of gaseous CO2 has a vibration-rotation doublet at 4.23 and 4.28 ix. Physically adsorbed CO2 was expected to produce a single band between 4.23 and 4.28 y because the CO2 molecules would not be rotating freely. Physically adsorbed CO2 was studied to check this prediction and to insure that a band at 4.56, which is observed during the oxidation of CO, was not due to some unforseen factor which would shift the band position of the asymmetric carbon-oxygen stretching frequency in the physically adsorbed state. 

CO. The alternative assumption (i) did not lead to such a coincidence of calculated and measured isotopic separations. A comparison of the band profiles observed with CO on the calcium forms (asymmetric profile) and on sodium forms (symmetric profile) of the zeolites suggested that in the case of calcium-exchanged A- and X-type zeolites the rotation of the CO molecules is significantly hindered, which resulted in the observed one strong band and two shoulders on both sides. Thus, the three absorptions in the case of CO/Na-A were interpreted as indicating the R, Q and P branches, i.e., free rotation. The spectrum of... 

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