The electron distribution and orbital interactions of C60 with metals coordinated at different sites on the outside of the fullerene are evaluated. These sites include the position of a metal atom directly above a carbon atom (eta1 site), the metal atom centered above two carbons of a pentagon or above two carbons between two pentagons (both eta2 sites), the metal atom centered above a pentagon (eta5 site), and the metal atom centered above a hexagon (eta6 site). The frontier orbitals of C60 are illustrated first with three-dimensional orbital contour plots. A palladium atom is then used to probe the bonding at the different sites on the C60 surface. The results with Pd0 are compared to our earlier study with the harder Ag+ ion in order to examine the effects of metal electron richness and size. In addition, these results are compared with the bonding to more traditional ligands that represent the hapticity of these sites, such as methyl (eta1), ethylene (eta2), cyclopentadienyl (eta5), and benzene (eta6). The strength of the metal-C60 interaction and the amount of charge delocalized from the metal to C60 is sensitive to the site of coordination, the electron richness of the metal, and distortions in the geometry of C60. As discussed in our previous work, the frontier orbitals of C60 are well-suited for synergistic bonding of a metal atom to a carbon-carbon pair in an alkene-like fashion, in which the HOMO of C60 donates carbon-carbon pi bonding electron density to the metal, and the LUMO of C60 accepts electron density from the metal into a carbon-carbon pi* antibonding orbital. Although the HOMO and LUMO of C60 describe the basic interaction, many frontier orbitals are involved. The site above the C-C bond between two pentagons is favored over the site above the C-C bond within a pentagon, and the interaction above the other sites is indicated to be net repulsive by these calculations. The differentiation between these sites increases with the electron richness of the metal center. The bonding of the metal to C60 is generally weaker than to the small ligands, except for very electron rich metal centers where the bonding to the eta2 site between pentagons apparently becomes stronger than the bonding to ethylene.