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Abstract
A critical review is presented of results obtained with different computational methods (mainly ab initio) on C60, C70, and specific fullerene derivatives, also in comparison with experimental data. From the discussion of diverse systems, the (often underestimated) complexity of their physical and chemical behavior emerges, and hence the importance of an accurate description and the need for a careful inspection of the experimental data, with which comparison is often intrinsically difficult. The ambition of this review is to help establish a basis not only for a nonsuperficial reading of the existing literature, but also for a constructive approach with computations to the challenge posed by recent promising applications of fullerenes in nanotechnology, optoelectronics, and biology.