VIBRATIONS OF A C-60 MOLECULE

The vibrations of a C60 molecule with the symmetry I(h) of a regular icosahedron are analysed. A frequency calculation is discussed for the two totally symmetrical (A(g)) vibrations, which involve only the stretching of the two types of carbon-carbon bonds of the molecule. It is proved that the experimental frequencies assigned to these modes cannot be accounted for by neglecting any interaction between the 90 stretching coordinates. This result explains some discrepancies currently displayed in the literature. It is shown that the interaction force constant between the two sets of bonds is positive. The force constants F(r) = 5.5 aJ angstrom-2 for the bonds within a five-member ring, F(r') = 6.7 aJ angstrom-2 for the bonds connecting two five-member rings and the interactions f(rr) = 0 and f(rr') = 0.5 aJ angstrom-2 are proposed. The last value involves an increase of the double bond characters in two five-member rings when the bond between them is stretched. This calculation appears as an attractive training example of molecular symmetry application.