danandam [7.48]. The site symmetries for the Fm3 group are given in Table 7.2, where it is seen that the C60 molecules are located on a sites having m3 or Th symmetry. The character table for the Th point group, showing the symmetry classes and irreducible representations, is given in Table 7.3 [7.50,51], while the corresponding basis functions are given in Table 7.4. The transformation properties of the various sites in Table 7.2 are given in Table 7.5 in terms of the irreducible representations of group Th that are contained in the equivalence transformation for the various atom sites (a,b,..., i).

The compatibility relations between the Ih, Th, and T groups are given in Table 4.15. These compatibility relations are used to obtain the crystal field splittings associated with the symmetry lowering that occurs when an icosahedral Cm molecule is placed in a cubic field. To have the full Th point group symmetry, all the C60 molecules must be similarly oriented in the cubic field with their x, y, z molecular twofold axes along the same x, y, z

Table 7.4

Basis functions for the point group Th.

Table 7.4

Basis functions for the point group Th.

S? Basis functions | |

A, |
x2 + y2 + z2 |

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