C-Cu orbital interactions between a two-layer Cu-10 or three-layer Cu-34 cluster model of a Cu(111) surface and an adsorbed single C-60 molecule have been theoretically investigated, so as to elucidate the nature of the C-60-Cu(111) bonding and orientational configuration of the C-60 molecule on a Cu surface. Geometry optimizations and single-point calculations at the B3LYP/LanL2MB level of theory and fragment molecular orbital (FMO) analyses, coupled with a paired-interaction-orbital (PIO) scheme at the extended Hackel level of theory, have been performed for five symmetric adsorption models, in which a C-60 molecule is attached to the Cu-10 or Cu-34 cluster respectively by a six-membered ring (6-ring), by a five-membered ring (5-ring), by a C-C bond belonging to two 6-rings (6-6 bond), by a C-C bond belonging to a 6-ring and a 5-ring (5-6 bond), and by an edge carbon atom that is located at the center of two 6-rings and a 5-ring. Large stabilization is obtained for adsorption by an edge carbon atom or a 6-6 bond, whereas the other coordination types are not favored. Our result differs from an XPD experimental result for a C-60 monolayer on Cu(111), in which adsorption by a 6-ring is most favored. The discrepancy strongly suggests that C-60-C-60 interactions contribute significantly to the determination of C-60 orientations in C-60/Cu(111) monolayer systems.