N. Laouini, O.K. Andersen, and O. Gunnarsson
Max-Planck-Institut für Festkörperforschung, Stuttgart
Assuming icosahedral symmetry of the C60 molecule, we give analytical expressions for the hu highest occupied and the t1u and t1g lowest unoccupied molecular orbitals (HOMO's and LUMO's). These are used for solid C60 to derive analytical one-electron Hamiltonians of minimal size, 5N*5N, 3N*3N, and 3N*3N, for respectively the hu, t1u, and t1g subbands. Here, N is the number of C60 molecules per primitive cell. We use the nearest-molecule neighbor orthogonal tight-binding and single-MO approximations, both of which have been shown to work well for solid C60. We explicitly consider structures with the C60 molecules at the sites of an fcc lattice: The uni, bi, and quadridirectional crystal structures with N=1, 2, and 4, respectively. The quadridirectional structure is that of pure and Na-doped C60 at low temperature. The bidirectional structure is usually considered a good approximation to the (unknown) structure of K and Rb-doped C60. All nine subband Hamiltonians can be expressed in such a way that they have the same functional dependence of the Bloch vector. The number of inter-molecular transfer integrals is small, because we choose the MO's to transform in accordance with the common symmetry of the molecules. For each of the three structures and each of the three subbands, explicit expressions are given for the bandwidths and for the energies and wavefunctions at high-symmetry k-points. For the quadridirectional structure, this is done for a general angle of rotation phi.
Phys. Rev. B 51, 17446 (1995).