Solving Vibrational Problems… So easy!! …right? How to model the potential? 9x9 matrix. Don’t screw up your partials!

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Presentation transcript:

Solving Vibrational Problems… So easy!!

…right? How to model the potential? 9x9 matrix. Don’t screw up your partials!

Model needs Simplicity, Complexity, Symmetry, Accuracy. Forget it! What can SYMMETRY ALONE tell us?

Deduce Vibrations of H 2 0 with Group Theory 1)Find H 2 0 symmetry group. 2)What rep acts on our coord space? 3)Find which irreps correspond to a normal mode. 4)Get degeneracies and eigenvectors.

Can’t change the frequency!

Aside: Notation

OK, back to it…

Rep on coordinate space is equivalent to rep in normal mode space. Each frequency eigenspace is an invariant subspace of the representation!! Thus each frequency eigenspace corresponds to some irrep of G such that: Use characters to deduce which irreps are present. Then eliminate translations and rotations and identify eigenvectors using symmetry.

How many reps?

Internal Vibrations: B1 Mode

B1 Mode