The application of zero-range potentials to the electronic properties of footballene, C 60

Abstract

We have used the experimental value of the first special transition from molecular beam studies of C 60 to determine the one parameter in a semi-empirical method that couples zero-range potentials with the free electron method. The method then allows the estimation of three other spectral transition energies and the relative spacing of five photoionization peaks. These results an excellent qualitative match and even a reasonable quantitative match of the nine transitions with the theoretical values. The one fitted parameter is the strength of the zero-range potential. All other semi-empirical quantities entering the calculation are geometric in nature. Because of the high sphericity of the molecule, two electron integrals are easily calculated within the model, and we obtain estimates of 0.83 eV for the 1T lu to 3T lu splitting, 1.9 eV for the electron affinity, and 11.2 eV for the second ionization potential. Variations in the charge distribution lead to the conclusion that, inclusing the σ electrons, there are 60 bonds with order 1.321 and 30 with order 1.359. The success of the treatment strongly suggests that simple geometry dominates much of the physics of C 60.