Infrared spectra of linear molecules

Linear molecules belong to either the (with an inversion centre) or the (without an inversion centre) point group. Using the vibrational selection rule in Equation (6.56) and the (Table A. 3 7 in Appendix A) or (Table A. 16 in Appendix A) character table we can 

For all types of 2i vibrational levels the stack of rotational levels associated with them is given by 

The separation of individual lines within the Q branch is small, causing the branch to stand out as more intense than the rest of the band. This appearance is typical of all Q branches in infrared spectra because of the similarity of the rotational constants in the upper and lower states of the transition. 

The effective value of B, for the lower components of the doubled levels, can be obtained from the P and R branches by the same method of combination differences used for a type of band and, for the upper components, from the Q branch. From these two quantities and may be calculated. 

Flowever, unless is unusually large or the spectrometer is of fairly high resolution, the doubling of levels is relatively small and can be neglected. 

8 The symbols and indicate allowed and forbidden transitions, respectively, whichever is the upper state. 

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