Band Contours for Linear Molecules

A linear molecule can be assumed to be a rigid rotor, and the rotational term values (energies// c) can be described by an equation similar to that used for diatomic molecules. The equation will be of the form 

However, the moment of inertia associated with the rotational constant B will, of course, be different from that used for diatomic molecules. 

For a symmetric molecule, such as CO2, this formula reduces to Ib = 2mrl (4-38) 

The vibration of a linear molecule can be considered similar to that of a harmonic oscillator, so that the vibrational energy levels can be described by a formula analogous to that used for diatomic molecules. However, the energy equation must be written in a more general form  

It is also difficult to introduce simple expressions in the harmonic oscillator equations to account for the anharmonic character of polyatomic molecules. Because of the complexity of this type of calculation, and the relatively small number of simple linear molecules to which the analogy can be reasonably applied, this method is of only limited usefulness and will therefore not be discussed here. 

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