  We carry out large scale {\sl ab initio} calculations of Raman scattering
activities and Raman-active frequencies (RAFs) in ${\rm C}_{48}{\rm N}_{12}$
aza-fullerene. The results are compared with those of ${\rm C}_{60}$.
Twenty-nine non-degenerate polarized and 29 doubly-degenerate unpolarized RAFs
are predicted for ${\rm C}_{48}{\rm N}_{12}$. The RAF of the strongest Raman
signal in the low- and high-frequency regions and the lowest and highest RAFs
for ${\rm C}_{48}{\rm N}_{12}$ are almost the same as those of ${\rm C}_{60}$.
The study of ${\rm C}_{60}$ reveals the importance of electron correlations and
the choice of basis sets in the {\sl ab initio} calculations. Our best
calculated results for ${\rm C}_{60}$ with the B3LYP hybrid density functional
theory are in excellent agreement with experiment and demonstrate the desirable
efficiency and accuracy of this theory for obtaining quantitative information
on the vibrational properties of these molecules.
