We discuss the collective resonances of the C60 molecule described by a spherical shell. Detailed results are given for the π and π + σ plasmons of C60, the polarisability and the dielectric function. We present results in good quantitative agreement with recent experiments. Some new features in the spectrum, like a monopole mode of oscillation, are predicted for a doped C60 molecule.

Abstract.We calculate the nonlinear optical properties of small metallic spheres using electromagnetic theory and assuming that the local response of the conduction electrons is the same as for a plane surface. Electromagnetic Mie-resonances cause a strong increase of the second and higher harmonics in the reflected light. Detailed results are given for the second and third harmonic generation, its dependence on the frequency and polarization of the incident light, and on the cluster size. An enhancement of the second harmonic generation by a factor of about 5000 is obtained for small spherical metallic clusters. This is in good agreement with experiments on artificially roughened metal surfaces.

We determine the electronic structure of single-wall, multiwall, and filled carbon nanotubes using the local-density-functional formalism. In order to handle these extremely inhomogeneous systems of nested graphene cylinders with 10 3 -10 4 valence electrons, we adopt a technique that discretizes the eigenvalue problem on a grid and yields simultaneously all occupied and unoccupied states. We apply this formalism to nanotubes, where the ionic background can be described by infinitely thin structureless cylindrical walls, and the electron distribution is subsequently obtained in a self-consistent manner. Comparison with parametrized calculations, which consider explicitly the atomic positions, proves that the essential features of the electronic structure in these systems do not depend on the exact atomic positions.

Previously, we discussed a purely classical model for analysing surface plasmons of the C 60 molecule. The molecule was described as an abrupt spherical shell containing an effective number of π or π + σ electrons. This simple model was found to be quite applicable for analysis of electron energy loss spectra (EELS), describing the main features of the experimentally observed collective resonances of electrons. In this study we have extended our earlier classical model using spherically averaged radial charge distributions of C 60 constructed using different numbers of valence electrons. These charge distributions have been obtained from a self-consistent local density calculation, based on a molecular-orbital linear combination of atomic orbitals (MO-LCAO) approach. Use of this type of smooth charge distribution introduces, together with causality, a natural broadening of the collective resonances.

Molecular cluster calculations within the local density approximation have been performed in a study of the electronic structure of the C60 molecule - “Buckminsterfullerene” doped with K, B and N. Calculations for the KC60 molecule, with the K atom located at the centre of the cage as well as at different positions inside or outside the cage, show how the valence 4s electron is transferred to the LUMO state of the bare C60 molecule. Doping with a B or N atom located at the centre of the cage creates a molecule with a partly occupied level of 2p character in the HOMO and LUMO gap, similar to donor and acceptor levels in the band gap of traditionally doped semiconductors. Doping by substitution of one or two of the carbon atoms in the cage with X = B or N, as modelled with the C59 X1 or C58X2 clusters, gives a different structure with a splitting of the HOMO and LUMO levels in the pure C60 molecule and with the creation of acceptor and donor levels with the substitution of B and N, respectively.