Does a benzene ring continue to oscillate at absolute zero? The carbon bonds in a benzene molecule oscillate between single and double bonds. As they do so, the distances between the carbon atoms changes (as the attached animated GIF illustrates). At absolute zero all molecular motion ceases; that is, the molecules stop bouncing into each other, but does that mean that molecules like benzene also cease their internal molecular motion?
"At absolute zero all molecular motion ceases; that is, the molecules stop bouncing into each other"

This statement is a common misconception about absolute zero and is totally false. At absolute zero, we are simply in the lowest possible energy state. That does not mean that molecular motion ceases. That would violate the uncertainty principle.