Stimulated by recent preparation and characterization of the first C58F18 fullerene derivative, with a heptagon in the framework (Science, 2005, 309, 278), we have performed systematic density functional studies on the stabilities and electronic properties of two different structures C58X18 (A) and C58X18 (B), where X = H, F, and Cl. The large energy gaps between the highest occupied molecular orbitals and the lowest unoccupied molecular orbitals (between 2.64 and 3.45 eV) and the aromatic character (with nucleus independent chemical shifts from -10.0 to -13.9 ppm) of C58X18 (A) and C58X18 (B) indicate that they possess high stabilities. Further investigations show that the heats of formation of C58X18 fullerene derivatives are highly exothermic, suggesting that adding nine X-2's releases much of the strain of pure C-58 fullerene and leads to stabilities of the derivatives. Lower in energy and stronger in aromatic character than C58F18 (B), which has been experimentally characterized, C58F18 (A) should also be isolated. In addition, C58F18 and C58Cl18 are predicted to possess large electron affinities, especially for C58F18 (B) and C58Cl18 (B) with values of 3.00 and 3.06 eV, respectively, even larger than that (2.50 eV) of C60F18. Hence, C58F18 and C58Cl18 can serve as good electron-acceptors with possible photonic/photovoltaic application. The IR spectra of C58X18 are simulated to facilitate identification of different isomers experimentally. In addition, the electronic spectra and second-order hyperpolarizabilities of C58X18 are predicted by ZINDO and sum-over-states model. With the addition of 9X(2), both the static and frequency-dependent second-order hyperopolarizabilities of C58X18 greatly decrease compared to those of C-58.