Fig. 13.11. The real part of the complex molecular polarizability for solid C^ obtained from the data of Fig. 13.10 using the Clausius-Mossotti relation [Eq. (13.10)] [13.24],

The features in the infrared spectrum (see Fig. 13.10) below ~0.3 eV are due to molecular vibrations, including the four strong first-order Flu intramolecular modes at 526, 576, 1183, and 1428 cm-1, together with two strong combination (<ox + a>2) modes at 1539 cm-1 and 2328 cm-1 (see §11.5). Transmission experiments carried out on thicker (~2-3 ¿¿m) films reveal numerous (>100) additional weaker features attributed to other intramolecular combination modes [13.15], as discussed in §11.5.3 and §11.5.4.

Values for e^w) aiiJ *•>(«) in the IR {hu> < 0.5 eV) in Fig. 13.10 were calculated by a fit of the expc. '-nental reflectivity and transmission data according to the Lorentz model, in which the complex dielectric function e(w) is given by the sum of contributions from a background core (real) constant e^ and a phonon term ephonon(w) approximated as a sum of Lorentz oscillators whose parameters were adjusted to best fit the data:

For the ;'th phonon contribution, /•, o)j, and Ty are the oscillator strength, frequency, and damping, respectively, for each IR mode. Values of the firstorder IR mode Lorentz oscillator parameters are listed in Table 11.7.

e(o>) = e^w) + ie2(co) = e«, + ephonon(a)) (13.11)


As discussed in Chapter 11, there are also two first-order IR-active intermolecular modes with Tlu symmetry, which contribute at low frequencies. They correspond approximately to an out-of-phase displacement of "rigid" C60 molecules and are observed in the far IR at 40.9 cm-1 and 54.7 cm-1 [13.83],

13.3.2. Optical Absorption in C60 Films

Contributions to the dielectric function of solid C60 above ~1.7 eV come from electronic transitions from filled states, i.e., states derived from the HOMO-) orbitals, to empty states derived from the LUMO+j' orbitals, where j,j' = 0,1,2,____If C60 were an ideal molecular crystal, then the optical properties of the solid might be calculated directly from the Clausius-Mossotti relation [Eq. (13.10)]. In this limit, the solid state, or intermolecular interaction, does not significantly affect the electronic molecular wave functions, but rather the molecules interact with each other via an electric dipole-dipole interaction which introduces a local electric field correction. Higher-order, quadrupole or octapole terms can be added to describe the intermolecular interaction, if necessary. However, the interaction between next-neighbor molecules in the real crystalline solid will broaden the molecular orbitals into electronic energy bands, and these effects have been calculated by several groups [13.84,85] (see §12.1.2). Although using different computational techniques, these calculations arrive at qualitatively the same result, namely, that the intermolecular interaction broadens the molecular orbitals into bands with widths on the order of 0.5 to 1.0 eV. As calculated by Gelfand and Lu [13.86,87], the molecular orientational disorder in the high temperature solid state (T> T0l = 261 K) does not seriously affect the bandwidth of the electronic energy levels, but rather rounds off the sharp features in the electronic density of states.

In Fig. 13.12 we display experimental data showing the threshold for optical absorption at 1.7 eV associated with electronic transitions in C60 films [13.15]. Shown in Fig. 13.12 are e2(w) data for two thin solid C60 films of distinctly different thicknesses. The dielectric function data were obtained by fitting simultaneously the transmission and reflectance for samples of C60 films on quartz substrates to values for e\(a>) and e2(w), and the contributions to the observed spectra from the quartz (Suprasil) substrate were taken into account in the analysis.

More detailed information is obtained by comparing the optical absorption (OA) and photoluminescence (PL) spectra for pristine C60 films and in further comparing each of these film spectra with their corresponding solution spectra in the vicinity of the absorption edge (see Fig. 13.6). Structures observed in both the OA and PL thin-film spectra near the absorption

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