Group Representation Theory, Molecular Dynamics, and Vibrations of the Bucky Ball
Smyrnios, Troy C.
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The Bucky Ball, i.e. C60, shaped like a soccer ball, has a great number of symmetries. As it turns out, the symmetries of a structure are intimately linked with its normal modes. After finding these symmetries, we can then apply representation and character theory to bypass solving the numerous and complicated differential equations involved with the physics model of the motion of the molecule and get straight to the normal modes. Then, by accounting for our limitations on how we can stimulate the molecule to make it vibrate, we can single out the vibrational normal modes that actually manifest themselves in nature.