Symmetric rotor band types

Evidcintly the rotational structure of the band of a spherical rigid rotor is similar i,o that of a perpendicular (X) band of a lineal rigid rotor. The two types of bands of a. symmetric rotor are more complex. The paralhd ( ) typo of Itand, for which AK = 0, will, however, bo similar in structure to that of a spherical lotor or a perpendicular (X) band in a linear rotor. For a perpendicular (X) band, however, the position of the Q branch is dependent both upon the initial value of K in the transition and upon the sign of AK, as can be seen from the following expressions ... 

The symmetric rotor fine structure for a totally symmetric vibration (polarized) should be similar in the Raman effect to the parallel ( ) infrared band of the same type of molecule, except that 0 and S branches occur and that the Q branch is very strong. The nontotally symmetric and degenerate modes in the Raman spectrum should have a fine structure resembling that of a perpendicular ( L) infrared band, since changes in K occur. 

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. 

Combination differences of the observed wavenumbers of the lines in the absorption bands of symmetric, spherical, and asymmetric rotors can be obtained. However, the rotational constant B to be calculated will depend on the type of vibration the band represents. In considering a symmetric rotor, the rotational constant for one of the molecule s moments of inertia is obtained from a parallel vibration, while a second moment of inertia is determined from the perpendicular vibration. Thus, the spacing of lines in the bands of a symmetric rotor is dependent upon the type of vibration. Moreover the interlinear spaces are not equal, as they are for linear or symmetric triatomic molecules. The perturbations of the fine-line structure of bands that have been discussed in other sections must also be taken into account before a combination difference is formed and a rotational constant calculated. 

The fine-line structure of symmetric rotors may be subdivided For example, when AJ = 0, +1, — 1, the rotational lines associated with AX = 0 are termed Qq, Qr- and Qp-branches for AX = +1, the lines are Rq-, Rp-, and Rp-branches and for AX = — 1, they are Pq-, Pp-, and Pp-branches. These branches are known as subbands. Under medium or low resolution the subbands are not resolved from each other and the maxima observed for the total band will represent collections of the subbands. The subbands can be considered to have small interlinear spacings, which are given by equations similar to those developed for linear molecules. For example, the R-branch of a parallel vibration can be described by an equation of the type used to describe the R-branch of a perpendicular vibration of a... 

In the following section the spectra of such symmetric rotors as NH3, H2CO, etc., will be presented. An excellent summary of band contours found for e type vibrations of these rotors is given in the work of Rao and Polik p ]. 

An A band for a fairly symmetric molecule resembles (under medium dispersion) a parallel band of a symmetric rotor, that is, it shows somewhat symmetric P- and R-branches, with a medium to strong Q-branch. The V3 band for H2O at 3756 cm" is an example of this type of band. The band for H2CO at 1746 cm" is another example. The spectrum of H2CO is shown in Figures 4-36 and 4-37. Using the nomenclature introduced in Section 4.4, we can describe both A bands of H2CO as vibrations. 

The fundamental is also in the 3-4 /t region. It is overlapped by the lines of the fundamental V4, but it appears to be at 2766.39 cm" It is an A band and closely resembles a parallel band of a symmetric rotor. Such a band usually has a strong but unresolved Q-branch, and since the strong line at 2766.39 cm resembles a Q-branch of this type, it is assigned as the band center for the fundamental. 

Symmetric rotors have two types of bands, corresponding to AK = 0 and AK = 1. If each set of P-, Q-, and R-branches for a single value of K is called a sub-band, then all sub-bands in a AK = 0 type band are centered at the same location. These... 

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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