I was looking at this page:(adsbygoogle = window.adsbygoogle || []).push({});

http://en.wikipedia.org/wiki/Molecular_vibration

And saw that they have six different vibrational modes listed for the water molecule. Elsewhere on they page they discuss the "3N-6" rule for determining the number of vibrational modes of a polyatomic molecule. That seems contradictory to me. There seems to be clearly six possible modes.

I tried to check around the web for an answer to the contradiction, but everything else I find only lists the first three modes (the ones pictured on the wikipedia page as "symmetrical stretching," "asymmetrical stretching," and "scissoring.") And make no mention of the other three. If you only count these three, the 3N-6 rule works, of course. But I don't see how you can simply ignore the others, particularly since "scissoring" appears to be simply "asymmetrical rocking."

Is this just a disconnect between classical and quantum mechanics? Are some of those six "modes" not actually possible, or do they just not contribute to the heat capacity for some other reason?

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# Equipartition Theorem and Number of Modes

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