Excitations, optical absorption spectra, and optical excitonic gaps of heterofullerenes. I. C60, C59N+, and C48N12: Theory and experiment

Low-energy excitations and optical absorption spectrum of ${\mathrm{C}}_{60}$ are computed by using time-dependent (TD) Hartree–Fock, TD-density functional theory (TD-DFT), TD DFT-based tight-binding (TD-DFT-TB), and a semiempirical Zerner intermediate neglect of diatomic differential overlap method. A detailed comparison of experiment and theory for the excitation energies, optical gap, and absorption spectrum of ${\mathrm{C}}_{60}$ is presented. It is found that electron correlations and correlation of excitations play important roles in accurately assigning the spectral features of ${\mathrm{C}}_{60},$ and that the TD-DFT method with nonhybrid functionals or a local spin density approximation leads to more accurate excitation energies than with hybrid functionals. The level of agreement between theory and experiment for ${\mathrm{C}}_{60}$ justifies similar calculations of the excitations and optical absorption spectrum of a monomeric azafullerene cation ${\mathrm{C}}_{59}{\mathrm{N}}^{+},$ to serve as a spectroscopy reference for the characterization of carborane anion salts. Although it is an isoelectronic analogue to ${\mathrm{C}}_{60},$ ${\mathrm{C}}_{59}{\mathrm{N}}^{+}$ exhibits distinguishing spectral features different from ${\mathrm{C}}_{60}:$ (1) the first singlet is dipole-allowed and the optical gap is redshifted by 1.44 eV; (2) several weaker absorption maxima occur in the visible region; (3) the transient triplet–triplet absorption at 1.60 eV (775 nm) is much broader and the decay of the triplet state is much faster. The calculated spectra of ${\mathrm{C}}_{59}{\mathrm{N}}^{+}$ characterize and explain well the measured ultraviolet–visible (UV–vis) and transient absorption spectra of the carborane anion salt $[{\mathrm{C}}_{59}{\mathrm{N][Ag(CB}}_{11}{\mathrm{H}}_6{\mathrm{Cl}}_6{)}_2]$ [Kim et al., J. Am. Chem. Soc. 125, 4024 (2003)]. For the most stable isomer of ${\mathrm{C}}_{48}{\mathrm{N}}_{12},$ we predict that the first singlet is dipole-allowed, the optical gap is redshifted by 1.22 eV relative to that of ${\mathrm{C}}_{60},$ and optical absorption maxima occur at 585, 528, 443, 363, 340, 314, and 303 nm. We point out that the characterization of the UV–vis and transient absorption spectra of ${\mathrm{C}}_{48}{\mathrm{N}}_{12}$ isomers is helpful in distinguishing the isomer structures required for applications in molecular electronics. For ${\mathrm{C}}_{59}{\mathrm{N}}^{+}$ and ${\mathrm{C}}_{48}{\mathrm{N}}_{12}$ as well as ${\mathrm{C}}_{60},$ TD-DFT-TB yields reasonable agreement with TD-DFT calculations at a highly reduced cost. Our study suggests that ${\mathrm{C}}_{60},$ ${\mathrm{C}}_{59}{\mathrm{N}}^{+},$ and ${\mathrm{C}}_{48}{\mathrm{N}}_{12},$ which differ in their optical gaps, have potential applications in polymer science, biology, and medicine as single-molecule fluorescent probes, in photovoltaics as the n-type emitter and/or p-type base of a $\mathrm{p–n}$ junction solar cell, and in nanoelectronics as fluorescence-based sensors and switches.