Raman scattering in ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{48}{\mathrm{N}}_{12}$ aza-fullerene:  First-principles study

We carry out large-scale ab initio calculations of Raman scattering activities and Raman-active frequencies (RAF’s) in ${\mathrm{C}}_{48}{\mathrm{N}}_{12}$ aza-fullerene. The results are compared with those of ${\mathrm{C}}_{60}.$ Twenty-nine nondegenerate polarized and 29 doubly degenerate unpolarized RAF’s are predicted for ${\mathrm{C}}_{48}{\mathrm{N}}_{12}.$ The RAF of the strongest Raman signal in the low- and high-frequency regions and the lowest and highest RAF’s for ${\mathrm{C}}_{48}{\mathrm{N}}_{12}$ are almost the same as those of ${\mathrm{C}}_{60}.$ The study of ${\mathrm{C}}_{60}$ reveals the importance of electron correlations and the choice of basis sets in the ab initio calculations. Our best calculated results for ${\mathrm{C}}_{60}$ 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.