Stability and Teller’s theorem: Fullerenes in the March model

We study C${}_{60}$ with the use of the March model [N. H. March, Proc. Camb. Philos. Soc. 48, 665 (1952)]. A spherical shell model is invoked to treat the nuclear potential, where the nuclear and core charges are smeared out into a shell of constant surface charge density. The valence electron distribution and the electrostatic potential are efficiently computed by integration of the Thomas-Fermi equation, subject to the shell boundary conditions. Total energy is numerically calculated over a range of shell radii, and the mechanical stability of the model is explored with attention to the constraints of Teller’s theorem [E. Teller, Rev. Mod. Phys. 34, 627 (1962)]. The calculated equilibrium radius of the shell is in fair agreement with experiment.