This chapter employs spin-polarized density-functional theory (DFT) to investigate the structural build up of the different Ti8C12 metallocarbohedryne clusters. The calculations were performed using DFT with a plane wave basis set and the projector augmented-wave method as implemented in the Vienna Ab Initio Simulation Package. The orientation of the C2 units relative to the Ti atoms cube is used as the basis for structural classification. The C3v structure is found to be the most stable structure and is 0.6 eV less than the second lower energy isomer. The electronic structure of the clusters is used to rationalize their bonding properties. The preliminary results of the calculation of the vibrational spectra of the C3v and C2v structures are compared using MD simulations at finite temperatures with those obtained from the frozen-vibration method.
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