  We study the structural, electronic, vibrational and magnetic properties of a
novel ${\rm C}_{48}{\rm N}_{12}$ aza-fullerene using density functional theory
and restricted Hartree-Fock theory. Optimized geometries and total energy of
this fullerene have been calculated. We find that for ${\rm C}_{48}{\rm
N}_{12}$ the total ground state energy is about -67617 eV, the HOMO-LUMO gap is
about 1.9 eV, five strong IR spectral lines are located at the vibrational
frequencies, 461.5 ${\rm cm}^{-1}$, 568.4 ${\rm cm}^{-1}$, 579.3 ${\rm
cm}^{-1}$, 1236.1 ${\rm cm}^{-1}$, 1338.9 ${\rm cm}^{-1}$, the Raman scattering
activities and depolarization ratios are zero, and 10 NMR spectral signals are
predicted. Calculations of diamagnetic shielding factor, static dipole
polarizabilities and hyperpolarizabilities of ${\rm C}_{48}{\rm N}_{12}$ are
performed and discussed.
