Solving Vibrational Problems… So easy!! …right? How to model the potential? 9x9 matrix. Don’t...
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Transcript of Solving Vibrational Problems… So easy!! …right? How to model the potential? 9x9 matrix. Don’t...
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Solving Vibrational Problems… So easy!!
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Solving Vibrational Problems… So easy!!
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Solving Vibrational Problems… So easy!!
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Solving Vibrational Problems… So easy!!
…right?
• How to model the potential?• 9x9 matrix.• Don’t screw up your partials!
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Model needs Simplicity, Complexity, Symmetry, Accuracy.
Forget it! ---------- What can SYMMETRY ALONE tell us?
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Deduce Vibrations of H20 with Group Theory
1) Find H20 symmetry group.2) What rep acts on our coord space?3) Find which irreps correspond to a normal mode. 4) Get degeneracies and eigenvectors.
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Can’t change the frequency!
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Aside: Notation
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Aside: Notation
OK, back to it…
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• 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.
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How many reps?
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How many reps?
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Internal Vibrations: B1 Mode
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Internal Vibrations: B1 Mode
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B1 Mode
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