Low-energy excitations and optical absorption spectrum of 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 C-60 is presented. It is found that electron correlations and correlation of excitations play important roles in accurately assigning the spectral features of 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 C-60 justifies similar calculations of the excitations and optical absorption spectrum of a monomeric azafullerene cation C59N+, to serve as a spectroscopy reference for the characterization of carborane anion salts. Although it is an isoelectronic analogue to C-60, C59N+ exhibits distinguishing spectral features different from 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 C59N+ characterize and explain well the measured ultraviolet-visible (UV-vis) and transient absorption spectra of the carborane anion salt [C59N][Ag(CB11H6Cl6)(2)] [Kim et al., J. Am. Chem. Soc. 125, 4024 (2003)]. For the most stable isomer of C48N12, we predict that the first singlet is dipole-allowed, the optical gap is redshifted by 1.22 eV relative to that of 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 C48N12 isomers is helpful in distinguishing the isomer structures required for applications in molecular electronics. For C59N+ and C48N12 as well as C-60, TD-DFT-TB yields reasonable agreement with TD-DFT calculations at a highly reduced cost. Our study suggests that C-60, C59N+, and C48N12, 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 p-n junction solar cell, and in nanoelectronics as fluorescence-based sensors and switches. (C) 2004 American Institute of Physics.