Summary of Selection Rules

Equation (A6.44) will also apply to the particular case of transitions from the ground state, and so together with Equation (A6.39) forms the basis of the selection rules for IR absorptions within the harmonic oscillator approximation. In general, we can now say that an IR absorption will be observed if  

The photon energy matches the spacing between harmonic oscillator energy levels, i.e. the photon frequency equals the classical frequency of vibration. This gives a transition involving only a unit change of quantum number m = n l. 

The dipole moment of the molecule changes during the course of a transition between the states in such a way that its derivative with respect to the atomic displacements is not zero. 

The excited vibrational state has the same symmetry as x, y or z in the molecular point group. 

The mathematics of the IR selection rules and the use of the time-dependent Schrddinger equation to discuss the actual transition event between the stationary states is covered in McQuarrie DA (2008) Quantum Chemistry, 2nd edn. University Science Books, Sausalito, CA (ISBN 978-1-891389-50 ). 

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A summary of selection rules based on Huckel and Mobius topologies is given below ... 

TABLE III. Summary of selection rules for vibronic effects (related to e-mv coupling). 

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