Vibrational, electronic, and vibronic excitations of polar ${\text{C}}_{60}{\text{F}}_{18}$ molecules: Experimental and theoretical study

Polarized optical conductivity spectra in the IR and visible range and variable-temperature photoluminescence spectra of the ${\text{C}}_{60}{\text{F}}_{18}$ single crystals in the 4–300 K temperature range are reported. Density-functional theory (DFT) calculations of vibrational spectra and time-dependent DFT calculations of the excitation energies of the ${\text{C}}_{60}{\text{F}}_{18}$ molecule are performed to interpret experimentally observed phenomena. Orientation of the $C_{3v}$-symmetric ${\text{C}}_{60}{\text{F}}_{18}$ molecules in the single crystal is revealed by comparison of the experimental polarized IR spectra and vibrational DFT calculations. $A_2$ symmetry is assigned to the lowest energy singlet excited state of ${\text{C}}_{60}{\text{F}}_{18}$, and hence pure electronic $S_0\to S_1$ excitation is found to be dipole forbidden. Fine vibronic structure found at low temperature is interpreted in terms of Herzberg-Teller and Franck-Condon mechanisms. Considerable similarity with vibronic spectra of ${\text{C}}_{60}$ is found and explained by presumable localization of the lowest energy electronic excitation of ${\text{C}}_{60}{\text{F}}_{18}$ on the fullerenelike part of the molecule.

Figure 1

(Color online) (a) Molecule of ${\text{C}}_{60}{\text{F}}_{18}$ showing direction of the dipolar moment; (b) photo of the crystal face used in the polarized spectroscopic measurements; one of the possible orientations of individual ${\text{C}}_{60}{\text{F}}_{18}$ molecules with respect to the crystal face is shown in (b) (opposite direction of dipolar moment is also possible; these two direction are indistinguishable with current experimental data).

Figure 2

(a) IR and (b) Raman spectra of ${\text{C}}_{60}{\text{F}}_{18}$ powder: experimental (upper curves) and computed (lower curves).

Figure 3

(Color online) Experimental polarized conductivity spectra measured in (a) perpendicular and (b) parallel orientations of the polarization plane of the incident light with respect to the longer side of the crystal face as compared to the DFT-calculated IR spectra [(a) only $E$ modes and (b) only $A_1$ modes].

Figure 4

(a) Optical conductivity in parallel orientation; calculated spectrum shows only $S_0\to n{{}^{1}A}_1$ excitations. (b) Optical conductivity in perpendicular orientation; calculated spectrum shows only $S_0\to n{}^{1}E$ excitations. (c) Superposition of optical conductivity in parallel and perpendicular orientations with the weight factor 2 for the latter (dotted line) and the spectrum of ${\text{C}}_{60}{\text{F}}_{18}$ measured in toluene solution (solid line). Calculated spectrum (dashed line) and $S_0\to n{{}^{1}A}_1$ contributions (thin dashed-dotted line) are shown for comparison. For the sake of comparison, calculated spectra in (a)–(c) are broadened with Gaussian peaks (half with 0.2 eV) and shifted in the energy scale by 0.36 eV.

Figure 5

(Color online) Photoluminescence spectra of toluene solution (300 K, dotted line) and variable-temperature spectra of single crystal.

Figure 6

MO energy levels and orbital symmetries in ${\text{C}}_{60}{\text{F}}_{18}$ molecule in the range of frontier orbitals as predicted by DFT.

Figure 7

(Color online) Difference electronic densities for the excitations: (a) $S_0\to 1{{}^{1}A}_2$, (b) $S_0\to 1{{}^{1}A}_1$, (c) $S_0\to 6{}^{1}E$, and (c) $S_0\to 7{}^{1}E$. Blue (dark) lobes correspond to the positive value of difference density, green (light) lobes—to the negative difference density.

Figure 8

Schlegel diagram of ${\text{C}}_{60}{\text{F}}_{18}$ with notation of the bonds. The bonds labeled by the same letter with different number of primes (e.g., $c$, $c^{\prime }$, and $c^{″}$) are equivalent in the ground state ($C_{3v}$ symmetry) but become different in the first excited state ($C_s$ symmetry).

Figure 9

(a) Experimental PL spectrum of crystalline ${\text{C}}_{60}$ at 4 K from Ref. 39 and of ${\text{C}}_{60}$ in Ne matrix at 4 K from Ref. 33 and TD-DFT calculated spectrum. In calculated PL spectra of ${\text{C}}_{60}$, zero corresponds to the energy of $1{{}^{1}G}_g$ state, while 0-0 origins of $1{{}^{1}T}_g$ and $1{{}^{1}T}_{2g}$ are assumed to be 10 and $40{\text{cm}}^{-1}$ lower in energy (Ref. 30). (b) Experimental (single crystal, 4 K) and calculated PL spectra of ${\text{C}}_{60}{\text{F}}_{18}$. Broadband background in the experimental spectrum is subtracted for clarity. Calculated spectra are broadened with Gaussian peaks (half with 0.2 eV).