Symmetric rotor molecules

For an oblate symmefric rotor, such as NFI3, fhe rofafional term values are given by 

This is the same as Equation (5.14) for a diatomic or linear polyatomic molecule and, again, the transitions show an equal spacing of 2B. The requirement that the molecule must have a permanent dipole moment applies to symmetric rotors also. 

When the effects of centrifugal distortion are included the term values of a prolate symmetric rotor are given by 

2 ROTATIONAL INFRARED, MILLIMETRE WAVE AND MICROWAVE SPECTRA 

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Stark effect in diatomic, linear and symmetric rotor molecules... 

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

For a symmetric rotor molecule such as methyl fluoride, a prolate symmetric rotor belonging to the C3 point group, in the zero-point level the vibrational selection mle in Equation (6.56) and the character table (Table A. 12 in Appendix A) show that only... 

Although, as in linear and symmetric rotor molecules, the term values are slightly modified by Coriolis forces in a degenerate (T2) state, the rotational selection rules... 

In Table 3 are listed some experimental values related to the torsional motion for a series of symmetric rotor molecules. The given examples are chosen to illustrate the points discussed in this section. 

An exact summation over the rotational components, in the case of a parallel band of a symmetric rotor molecule, leads to the expression on the right-hand side of (17) multiplied by the factor... 

The Coriolis interaction is found to be larger for degenerate vibrational states than for nondegenerate levels. Thus, for symmetric rotor molecules, the doubly degenerate vibrations may be split so that they differ slightly in energy. The fine-line structure of the absorption band will then show lines due to transitions to both of these levels. For spherical rotor molecules, the Coriolis interaction will cause the triply degenerate frequencies to split. 

For symmetric rotor molecules of C symmetry, the Coriolis perturbations occur between the following pairs of vibrations ( ic), a2e (flia2), ee). For the first two pairs, the perturbation increases with increasing J, while for the latter two it increases with increasing K. For molecules of C2t, symmetry, the following pairs of vibrational levels may perturb each other ( 1 2), ciib2% ( 2 iX ( 2 2)5... 

Symmetric rotor molecules can also show intensity alternation. For example, for CH3Br the fundamental shows this effect, the lines being strong, weak, strong, weak, and so on. The variation of the line intensity can become quite complex if the number of axes of symmetry increases. Intensity alternation can also occur for asymmetric rotors, but the complexity in such cases precludes any discussion here. 

By definition, of the three moments of inertia of symmetric rotor molecules, two are equal and differ from the third. For the equations above,... 

Inversion doubling imposes further restrictions on permitted energy transitions, but these cases will not be discussed here. Hybrid bands, i.e., bands of partly parallel and partly perpendicular character, are also possible for symmetric rotor molecules. 

Frequently no simple band contours are observed for either the parallel or the perpendicular bands of symmetric rotor molecules. The contours depend on many factors, including (1) the relative difference between the terms A and B (2) the value of (A — B) in the initial state (before the energy transition) compared to its value in the final state and (3) the extent of the Coriolis interaction between the rotational and vibrational levels. 

The ctmtribution of rotational quantization to the integrated absorption coefficient has been treated for symmetric rotor molecules [8]. Summation over rotational quantum numbers for parallel and perpendicular bands introduces a correction factor in the expression for the absorption... 

FIGURE 6 Rotational energy level diagram for CH3CN, a typical symmetric rotor molecule. The rotational quantum numbers J and K, along with the associated energy above the ground state, are indicated for each level. 

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