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f\u, f2u, g„, hu

hu

flg, flg, gg, hg

"Note that "u" vibrational modes couple with "g" excitonic states (and vice versa) in order to achieve an excited vibronic state with "u" parity. Vibronic states with "u" parity couple via an electric dipole transition to the "g" ground state ('Ag), subject to the selection rules given in this table.

"Note that "u" vibrational modes couple with "g" excitonic states (and vice versa) in order to achieve an excited vibronic state with "u" parity. Vibronic states with "u" parity couple via an electric dipole transition to the "g" ground state ('Ag), subject to the selection rules given in this table.

lated all the vibrational modes which lead to a vibronic state containing the Flu irreducible representation for excitonic states of every possible symmetry. It should be noted that many of the intramolecular mode frequencies in the fullerenes are quite high, and therefore they can make a significant contribution to the energy of the vibronic state. For Cjq, the highest firstorder normal mode frequency is 1577 cm-1, which corresponds to ~0.2 eV (see Table 11.1).

13.2. Optical Studies of Cm in Solution

To obtain an adequate signal-to-noise ratio, the study of the electronic levels of the "free" molecule is most conveniently carried out in solution or by using matrix isolation techniques [13.16,18]. A summary of results obtained from absorption, luminescence and time-resolved measurements on C60 molecules in solution is presented in this section. Features near the absorption edge and at higher photon energies are both considered. The weak absorption at the absorption edge has a number of special features associated with excitonic states which are activated into electronic transitions through a vibronic Herzberg-Teller (H-T) coupling mechanism (as discussed in §13.2.1). The absorption at higher photon energies is, however, dominated by dipole-allowed transitions which are described by more conventional treatments.

13.2.1. Absorption of C60 in Solution

In Fig. 13.5(c), we show experimental results from Leach et al. [13.17] for the optical density as a function of wavelength for Qo dissolved in rc-hexane in the UV-visible region of the spectrum. Since C60 in other organic solvents yields almost the same spectrum, the structure in the figure is not identified with solvent-related absorption bands, but rather with the intrinsic spectrum for C60. The optical density (OD) is defined as Iog10(l/5r), where ST is the optical transmission coefficient. Neglecting corrections for reflection loss at the optical cell walls, the optical density is proportional to the optical absorption coefficient. As can be seen in Fig. 13.5(c), a region of weak rr-ir* absorption extends from ~ 640 nm (1.9 eV) to 440 nm (2.8 eV), where tt and tt* refer to /^-function-derived occupied and empty levels (or bands), respectively. Since the threshold for this tt-tt* absorption (640 nm) is close to the values for the HOMO-LUMO gap EH_L (1.9 eV) calculated on the basis of a one-electron approach ([13.19]), a number of authors have attempted to describe the optical properties of CM over a wide range of photon energies in terms of a one-electron treatment. However, as discussed above, the tt-tt* transitions at the absorption edge should be s

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