400 600

Wavelength (nm)

Fig. 13.5. (a) Calculated free response oscillator strength of C^, [13.7]. (b) Calculated screened response oscillator strength [13.7], (c) Experimental absorption spectra for C60 in n-hexane solution [13.17]. The three experimental spectra to the right are magnified with respect to the first as discussed in Ref. [13.17].

400 600

Wavelength (nm)

Fig. 13.5. (a) Calculated free response oscillator strength of C^, [13.7]. (b) Calculated screened response oscillator strength [13.7], (c) Experimental absorption spectra for C60 in n-hexane solution [13.17]. The three experimental spectra to the right are magnified with respect to the first as discussed in Ref. [13.17].

forbidden by symmetry considerations, and a more detailed treatment including strong electron-electron and electron-phonon effects is therefore needed.

As discussed in §13.1.3, the weak absorption band between 440 and 640 nm can be explained in terms of vibronic transitions from the HOMO-derived, Ag symmetry ground state to excitonic states, as shown schematically by the upward arrows in Fig. 13.4. Negri et al. [13.9] have calculated the oscillator strengths for various electric dipole transitions involving important vibronic states using the "complete neglect of differential overlap for spectroscopy" or the CNDO/S method [13.20]. Accordingly, they have used their results to assign the structure in the weak optical absorption (OA) band spanning the 440-640 nm range to transitions between the lAg (S0) level and the vibronic manifold associated with the zero vibration 'Flg

(5j) state (Fig. 13.4). Consistent with Table 13.1, the H-T active vibrational modes were shown to be the Flu(4), Hu(7), and Au(l) symmetry vibrational modes, where the number of mode frequencies of each symmetry type is indicated in parentheses (see Table 11.1). Of course, numerous combination and overtone modes (see §11.5.3 and §11.5.4) also have the Fiu, Hu, and Au symmetries and they too give rise to higher-order H-T active excitations. The relation between the optical absorption spectra and the photoluminescence spectra is discussed in §13.2.2.

We next turn our attention to the much stronger optical absorption observed experimentally for C60 in n-hexane [Fig. 13.5(c)] at wavelengths in the UV for A < 440 nm. As can be seen in Fig. 13.5(c), three, reasonably sharp, bands are observed, with absorption maxima at 3.7 eV (335 nm), 4.6 eV (270 nm), and 5.8 eV (215 nm) [13.17]. Electron impact studies on free C60 have been interpreted to show allowed dipole transitions at 3.78 and 4.84 eV and a collective tt-tt* state at 6.1 eV [13.21], The origin of these absorption bands can be understood using the approximation of one-electron orbitals (see Fig. 12.1). Theoretical calculations of the excited one-electron state energies have been carried out by several authors [13.7,19,22,23] and these are summarized in Table 13.2. Electric dipole absorption is allowed between these states as long as the initial (occupied) and final (empty) states have different parity and are coupled by the electric dipole matrix element which transforms as Tu (Flu), using the notation of Table 13.1. Of course, depending on the nature of the wave functions for the ground and excited states, the calculated oscillator strengths for

Transition frequencies (in eV), oscillator strengths, and proposed assignments of interband transitions in solid CM. Results for the transition frequencies and oscillator strengths are given for both the free molecules and the screened (scr) response [13.2.4]. Here h and I denote abbreviations for the HOMO and LUMO levels, respectively [13.7],

Transition frequencies (in eV), oscillator strengths, and proposed assignments of interband transitions in solid CM. Results for the transition frequencies and oscillator strengths are given for both the free molecules and the screened (scr) response [13.2.4]. Here h and I denote abbreviations for the HOMO and LUMO levels, respectively [13.7],

Transition Unscreened Screened

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