Electronic structure of C₆₀: from the molecular to the solid state

Abstract

The electronic structure of fullerides is discussed in the theoretical framework of an INDO (intermediate neglect of differential overlap) Hamiltonian defined for molecules and, in the basis of Bloch orbitals, for crystalline solids. In the C₆₀ molecule the strength of the symmetry allowed π/σ and π*/σ* interaction is quantified by using localized molecular orbitals (MOs) as well as a so-called precanonical MO basis confined to decoupled π,π* and σ,σ* MO spaces. Consequences for the solid state electronic structure of C₆₀ are given. The theoretical determination of the electronic transition energies in the C₆₀ molecule in a CI (configuration interaction) calculation shows the importance of the two-electron interaction in this system. This behaviour is confirmed by Green's function calculations that are employed to derive the ionization potentials (IPs) and the electron affinity of the C₆₀ molecule. Pair-relaxation effects in the cationic hole-states lead to significant many-body corrections to calculated IPs. Calculated electronic transition energies as well as the IPs and the electron affinity are close to the experimental values. The Hubbard on-site (intramolecular) two-electron repulsion U is calculated for the isolated C₆₀ molecule. For the dimer the Hubbard nearest neighbour repulsion V is evaluated. Both values are compared with available experimental and theoretical estimates. The two integrals are quite large in magnitude. Sizeable two-electron repulsion also occurs in the solid state calculations. For the K _x C₆₀ fullerides (x = 1, 2, 3) the INDO crystal orbital (CO) formalism predicts, in agreement with experiment, a quasi-degeneracy between metallic configurations and Mott-like states with a maximum number of singly occupied CO microstates in the highest filled dispersion curves. A finite band gap is predicted for C₆₀, K₄C₆₀ and K₆C₆₀. The theoretical data are discussed in the light of available experimental findings. In K _x C₆₀ fullerides (x = 0, 1, 2, 3, 4, 6) changes in the solid state electronic structure as a function of the potassium doping are analysed. We discuss the induced modification of the CC bonds in the C₆₀ unit as well as the magnitude of the potassium-to-C₆₀ charge transfer.