Near-symmetric rotor

At a simple level, the rotational transitions of near-symmetric rotors (see Equations 5.8 and 5.9) are easier to understand. For a prolate or oblate near-symmetric rotor the rotational term values are given, approximately, by... 

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 spectmm 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 the same reason, the radial coordinate cannot be obtained from symmetrical substitution of symmetric rotors. One way to overcome this problem is to use single isotopic substitution of an off-axis atom making the substituted molecule a slightly asymmetric near-prolate or -oblate rotor. For many of these near symmetric rotors it is difficult to determine 4 precisely. An alternate method described by Li et al. 

The vibrations of species can have distinct band contours. The Q-branch is generally fairly strong in these bands. The type A band for asymmetric rotors that have moments of inertia such that they are nearly symmetric rotors can be considered to be an a 1 vibration. 

SPECTRAL ANALYSIS OF FORMALDEHYDE [ ] (NEAR-SYMMETRIC ROTOR)... 

Surin et al. [05Sur] have measured new mm-wave transitions for C 0 °Ne, C 0 and analyzed them together with previous literature data in terms of a near-symmetric-rotor Hamiltonian [see No. 107, CN2O], with the following results ... 

The reorientation of partially deuterated rotors, as discussed in Section IV.A.5, is an example of proton displacements between positions that are distinguishable. Even when these positions are equivalent in the isolated molecule, the interaction with an environment of lower symmetry usually makes the positions inequivalent so that the PES becomes asymmetric. This situation applies also for proton translations in intra- and intermolecular PT processes, examples of which are discussed below (Sections IV.B.l and IV.B.2). Prototype examples for intramolecular transfers are the tautomer-ization of free base porphyrines and phthalocyanines and the PT in malonaldehyde, tropolone, 9-hydroxyphenalone, and so on. The tautomer-ization of carboxylic dimers is the best studied example of intermolecular transfer in a (near) symmetric PES. 

For a prolate symmetric top, k = -1, and for an oblate top, K = -l-l. If B = C, /c = -1, the asymmetric top may be classified as a near-prolate rotor. If A = B, k = +, we have a near-oblate asymmetric rotor. The case k = 0 corresponds to the most asymmetric top possible. Most molecules are prolatelike asymmetric tops. Illustrative examples of rotational constants for some asymmetric tops are given in Table V. 

The two bands appear very different. Their rotational structure is quite symmetrical but that of aniline shows a pronounced gap near the band centre whereas that of aniline Ar shows a grouping of intense lines. The reason for the difference is that the band of aniline is a type B band of a prolate asymmetric rotor (see Section 6.2.4.4) whereas that of aniline Ar is a type C band of an oblate asymmetric rotor. The electronic transition moment in aniline itself is directed along the b axis which is in the plane of the benzene ring and perpendicular to the C—N axis (which is the a axis). In the aniline Ar molecule, the argon atom sits on the benzene ring, attracted by the n electrons. The fact that the argon atom is relatively heavy causes a rotation of the principal axes on inertia ... 

Fi om Table XVI-3, several statements about the rotational fine structure in the Raman effect may be made immediately. The polarized, totally symmetric band of a linear rigid rotor will resemble a perpendicular (.L) infrared band of the same type of rotor, except that the line spacing is twice as great ( AJ1 = 2 instead of jA./j = 1). The degenerate Raman band, on the other hand, will more nearly resemble a parallel (j ) infrared... 

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]. 

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