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Fig. 11.2. Schematic diagram of normal mode displacements for a consistent set of partners of each of the (a) eight Hg Raman-active and (b) four Fu infrared-active modes in C6IJ. The eigenvectors are a function of the model and force constants, but the general trend is that modes with primarily radial displacements have low vibrational frequencies, and those modes with predominantly tangential displacements correspond to higher frequencies. The plots are a courtesy of M. Grabow at AT&T Bell Laboratories [11.26],

For the actual C60 molecule, the eigenvalues and eigenvectors for the intramolecular vibrational problem depend on the solutions to the 180 x 180 dynamical matrix. All 180 degrees of freedom must be considered in the dynamical matrix, since the translational and vibrational degrees of freedom result in modes with finite frequencies away from the zone center. The high symmetry of the molecule allows us to bring the dynamical matrix into block diagonal form at the high-symmetry points in the Brillouin zone using a unitary transformation which brings the coordinates into the correct symmetrized form, each block corresponding to a particular sym-

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