According to geometrical considerations, a method is devised to show a geometric relationship between the tetrahedron and the small heterofullerenes below C/sub 60/: C/sub 24/N/sub 4/, C/sub 36/N/sub 4/ and C/sub 52/N/sub 4/, all of which belong to the T/sub d/ point group. These simple geometric relationships also allow us to predict the possible structures of heterofullerenes consisting of more than sixty carbons with the T/sub d/ symmetry. The number of hexagonal faces (besides the 12 pentagonal faces), vertices and edges of these heterofullerenes are obtained by applying Euler's theorem. Calculated by means of molecular mechanics MM2(87), the minimum energy structure, the bond lengths, the bond angles and the torsion angles for such heterofullerenes were generated. The simple Huckel MO calculations are used to determine the HOMO, LUMO and the energy gap between HOMO and LUMO of C/sub 24/N/sub 4/ and C/sub 36/N/sub 4/ heterofullerenes. The heats of formation of C/sub 28/ and C/sub 40/, C/sub 24/N/sub 4/ and C/sub 36/ N/sub 4/ were calculated according to the MNDO method. The ionization energies, the .DELTA..epsilon. (LUMO-HOMO) and the resonance energies were investigated with semiempirical MNDO methods for comparison with the stabilities of C/sub 28/, C/sub 24/N/sub 4/ and C/sub 28/H/sub 4/. The kinetic and thermodynamic stabilities of such tetrahedral derivatives of heterofullerenes were predicted based on the energy gaps and heats of formation.
Journal of the Chinese Chemical Society=中國化學會會誌 40(6), pp.497-502