Stability and Teller's Theorem: A Thomas-Fermi Theory of Fullerenes

We study {{\rm C}${}_{60}$} with the use of Thomas-Fermi theory. 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. The calculated equilibrium radius of the shell is in good agreement with experiment.