Ab initio theoretical predictions of C28, C28H4, C28F4, (Ti@C28)H4, and M@C28 (M=Mg, Al, Si, S, Ca, Sc, Ti, Ge, Zr, and Sn)

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Abstract
Recent experiments have demonstrated that C28 is the smallest fullerene cage that successfully traps elements in its inside. In this work, we have studied the electronic structures, equilibrium geometries, and binding energies of the title molecules at the self-consistent field (SCF) Hartree–Fock level of theory employing basis sets of double-zeta quality. The empty C28 fullerene is found to have a 5A2 open-shell ground state and behaves as a sort of hollow superatom with an effective valence of 4, both toward the outside and inside of the carbon cage. The theoretical evidence suggests that C28H4 and C28F4 should be stable molecules. The possibility of simultaneous bonding from the inside and outside of the C28 shell, as in (Ti@C28)H4, is also explored. Our calculations show that the binding energy of the M@C28 species is a good indicator of the success in experimentally trapping the metal atoms (M) inside the fullerene cage. Based on these results, we propose that elements with electronegativities smaller than 1.54 should form endohedral fullerenes larger than a minimum size which depends on the ionic radius of the trapped atom. This qualitative model, correctly reproduces the available experimental evidence on endohedral fullerenes.