"Calculated mode frequencies of Ref. [11.9], ^Calculated mode frequencies of Ref. [11.7]. c Calculated mode frequencies of Ref. [11.5]. ''Calculated mode frequencies of Ref. [11.38]. 'Calculated mode frequencies of Ref. [11.6]. ^Calculated mode frequencies of Ref. [11.22], ^Calculated mode frequencies of Ref. [11.23]. ''Calculated mode frequencies of Ref. [11.24].
Quong et al. [11.23] (first principles local density approximation, LDA), and Feldman et al. [11.24] (adjustable force constants)]. It should be noted that the phonon mode calculations in Table 11.2 represent only a subset of the various vibrational mode calculations that have thus far been reported.
11.3.2. Theoretical Crystal Field Perturbation of the Intramolecular Modes ofCm
The intermolecular interactions between C60 molecules in the solid state are weak, and therefore the crystal field resulting from the C60 crystal lattice may be treated as a perturbation on the molecular modes [11.44-46]. Since the observed splittings and frequency shifts of vibrational modes related to solid state effects are very small in fullerene solids, most of these observations do not require crystal field symmetry-lowering effects for their explanation. In fact, most of the experimentally observed splittings that have been attributed to crystal field symmetry-lowering effects in the literature are theoretically inconsistent with such an explanation. A detailed treatment of the symmetry of crystal field effects is given in §7.1.2.
For temperatures above the orientational ordering transition T01 (see §7.1.3), the Qo molecules are rotating rapidly, at a frequency comparable to the librational frequencies (10-40 cm-1) observed below r01. Since the rotational frequencies are low compared with the intramolecular vibrational frequencies, the C60 molecules in the solid above r01 are orientationally disordered. The effect of the crystal field is to make all the vibrational modes in the solid phase weakly Raman and infrared-active, with a large linewidth due to the molecular orientational disorder; this effect would be observable in terms of a background Raman scattering or infrared absorption. The reported Breit-Wigner-Fano Raman lineshapes (see Fig. 11.23) would represent a signature of this broad Raman background.
For temperatures below Tm, the crystal field would be expected to exhibit two effects, if all the C60 molecules were to align orientationally with respect to the Th site symmetry of the crystal field. The first effect is associated with the splitting of the icosahedral Ih modes as the symmetry is lowered from Ih to cubic Th symmetry. From §7.1.2 and Table 7.10, we have the result that in the cubic crystal field (where the irreducible representations have A, E, and T symmetries), the icosahedral modes exhibit the following splitting pattern:
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