Dependence of the π-electron eigenvalue sum on the number of atoms in almost spherical C cages -: art. no. 013210

A free-electron-like model is first shown to lead to the eigenvalue sum of the pi electrons in almost spherical C cages, being proportional to N, where N is the number of C atoms. The model is also closely related to a tight-binding model, stemming from the Huckel theory of pi electrons. The equilibrium radius R-e of the C cages is assumed to be determined by the "rule" of constant surface area per C atom, and hence R(e)proportional toN(1/2). We then compare these models with a series of Hartree-Fock calculations on the fullerenes C-50, C-60, C-70, and C-84, from which more accurate energy scaling relations are obtained. Finally, the relation between the total energy of the four C cages at equilibrium and the all-electron eigenvalue sum is confirmed by the Hartree-Fock studies.