Infrared spectra of spherical rotors

As we proceed to molecules of higher symmetry the vibrational selection rules become more restrictive. A glance at the character table for the point group (Table A.41 in Appendix A) together with Equation (6.56) shows that, for regular tetrahedral molecules such as CH4, the only type of allowed infrared vibrational transition is 

Neglecting centrifugal distortion, the rotational term values for a spherical rotor in an A j vibrational state are 

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 

For a spherical rotor belonging to the octahedral Of, point group, Table A.43 in Appendix A, in conjunction with the vibrational selection rules of Equation (6.56), show that the only allowed transitions are 

Such bands also obey the rotational selection rules in Equation (6.82) and appear similar to a U-I band of a linear molecule. 

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