Ab initio calculations of electronic structures, polarizabilities, Raman and infrared spectra, optical gaps, and absorption spectra of $M@{\mathrm{Si}}_{16}$ $(M=\mathrm{Ti}$ and Zr) clusters

Ab initio calculations have been performed using density-functional theory with the B3PW91 hybrid exchange-correlation functional and the Gaussian method to obtain the electronic and vibrational properties of the fullerene (f) and Frank-Kasper (FK) isomers of the metal-encapsulated silicon clusters $M@{\mathrm{Si}}_{16},$ $M=\mathrm{Ti}$ and Zr. The electron affinities of the two isomers are found to differ significantly and our result for $\mathrm{FK}-\mathrm{Ti}@{\mathrm{Si}}_{16}$ is in good agreement with recent experiments. The Raman and infrared vibrational spectra of the f and FK isomers show marked differences, due to their distinct bonding natures and structural features, that can be used unambiguously to identify the structures of these clusters experimentally. The polarizabilities, however, have similar values and lie above the bulk limit of silicon. The optical gaps and absorption spectra have been calculated using time-dependent density-functional theory. The lowest electronic excitation for the FK isomer lies in the deep blue region, while the one for the f isomer lies in the red region, making them attractive for optoelectronic applications.