Info

"Since C140 lacks inversion symmetry, entries in the table are made only for the classes that are pertinent to point group I.

"Since C140 lacks inversion symmetry, entries in the table are made only for the classes that are pertinent to point group I.

4.2. Symmetry of Vibrational Modes

In this section we review the symmetries and degeneracies of the vibrational modes for the C60 molecule. There are 180 degrees of freedom (3 x 60) for each C60 molecule. Three of these degrees of freedom correspond to translations and three to rotation, leaving 174 vibrational degrees of freedom. Since icosahedral symmetry gives rise to a large number of degenerate modes, only 46 distinct mode frequencies are expected for the C60 molecule. The number of distinct modes Na for C60 and other icosahedral configurations is given in Table 4.6. The results given in Table 4.6 follow directly from group theoretical arguments, using the entries given in Table 4.4 for the characters for the equivalence transformation A'as (Qo) f°r the 60 equivalent carbon atoms in C60. Taking the direct product of ^-S-(C60) with the characters for the vector Xt\u (which transforms according to the irreducible representation F[u), as given in Table 4.1, and subtracting off the irreducible representations for pure rotations (Flg) and pure translations (Flu) yields the irreducible representations for the vibrational modes of C60. The symmetries of the resulting vibrational modes are listed in Table 4.6, where the multiplicities for each symmetry type are given. For example, X12 in Ih symmetry has N0} = 8 distinct modes, and the symmetry types that are

Irreducible representations for various atomic sites in the icosahedral group Ih. The characters for the corresponding equivalence transformations are given in Table 4.4.

Cluster

Was this article helpful?

0 0

Post a comment