Tanczos theory for polyatomic molecules

Tanczos35 has extended the theory (for V-T and V-V transfer) to polyatomic molecules, and a detailed comparison with experiment was recently given by Stretton33. Considering each surface atom, energy transfer depends on how the intermolecular potential varies with the oscillation of the atom. In deriving the result for the diatomic molecule from the harmonic-oscillator wave functions, we substituted 

It could not be considered appropriate to give a full description of the Tanczos theory here. However, it should be useful to outline its application with some simple examples. For a diatomic molecule 

The amplitude of vibration is proportional to a , and therefore the squared amplitude depends on 

Thus for a given vibrational frequency, the squared amplitude is proportional to the term mc/mB(mB+mc) and the mean square amplitude is proportional to 

Evidently the squared matrix element is proportional to the mean square amplitude, and for polyatomic molecules Tanczos formalises 

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