Analytical application of the recursion and moments methods to the electronic structure of C-60: Exact solution for the pi and sigma states

The recursion and moments methods are applied analytically to study the electronic structure of a neutral C-60 molecule. We employ a tight-binding Hamiltonian which considers both the s and p valence electrons of carbon. From the recursion method, we obtain exact results for the pi and sigma eigenvalues and eigenfunctions, including the highest occupied molecular orbital and the lowest unoccupied molecular orbital states. We also compute the Green's function in analytic closed form and obtain the local density of states around several ring clusters, which can be probed experimentally by using, for instance, a scanning tunneling microscope. From the method of moments, identical results for the energy spectrum are also derived. In addition, the local density of states on one carbon atom is obtained; from this we can derive the degree of degeneracy of the energy levels.