Infrared Absorption and the Greenhouse Gases

We can now show that the three main greenhouse gases are IR active as a result of their molecular symmetry. Eor the case of water, we have already found in Section 5.6 that the irreducible representations are 

The two Ai modes are the symmetric stretch and bending motions and the vibration is the asymmetric stretch. By reference to the standard character table in Appendix 12 for C2V, we find that all three modes are IR active, because Z belongs to Ai and y to B - 

Application of the reduction formula to the groups of infinite order (Dooh and Coov) is problematic because the order of these groups h = oo. In this book we have used an approach based on the equation from which the reduction formula was obtained in Section 5.5  

Six basis vectors can only give 6 cos(0) if we only have If reps. These are the doubly degenerate reps, so we have three irreducible reps to find 

By this elimination procedure, the reducible representations are found to be  

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