The analysis of a molecule depends on the question that we wish to address. If we are interested in molecular orbital theory then our basis will be similar to a basis set that would be used in a quantum chemical calculation. It will consist of the s, p and d orbitals that are appropriate to each atom in the structure. If we are interested in molecular motions then our basis will be the Cartesian coordinate system on each atom. This 3N dimensional basis can be used to determine the irreducibe representations of translation (3), rotation (3) and vibrational (3N - 6) degrees of freedom. Finally, if we know the irreducible representations of either the MOs or the normal modes we can use those irreps as projection operators to generate linear combinations by symmetry that correspond to either the MOs or normal coordinates.
Generating reducible reprsentations
The first step in any such analysis is to determine the reducible represenation in the basis. For this we need to consider how the basis transforms under each symmestry oprations of th group.
Decomposing the reducible representation
XXX
- XXX
- XXX
|
