C-60[CpRu(CO)(2)](2) is only one transition-metal fullerene complex with pure eta(1)-coordinated bonds, which was recently synthesized through the reaction between dinuclear Ru complex [CpRu(CO)(2)](2) and C60. Though new properties can be expected in the eta(1)-coordinated metal-fullerene complex, its characteristic features are unclear, and the [2 + 2]-type formation reaction is very slow with a very small yield. A density functional theory study discloses that the eta(1)-coordinated bond is formed by a large overlap between the Ru ds orbital and C ps one involved in the lowest unoccupied molecular orbital (LUMO) (p*) of C60 unlike the well-known eta(2)-coordinated metal-fullerene complex which has a p-type coordinate bond with metal dp orbital. The binding energy per one Ru-C bond is much smaller than those of eta(2)-coordinated Pt(PMe3)(2)(C-60) and IrH(CO)(PH3)2(C60) because the Ru d orbital exists at low energy. The formation reaction occurs via Ru-Ru bond cleavage on the C60 surface followed by a direction change of CpRu(CO)(2) to afford C-60[CpRu(CO)(2)](2) in a stepwise manner via two asymmetrical transition states to avoid a symmetry-forbidden character. The calculated Gibbs activation energy (Delta G degrees(double dagger)) is very large and the Gibbs reaction energy (Delta G degrees) is moderately negative, which are consistent with a very slow reaction rate and very small yield. The charge transfer from CpRu(CO)2 to fullerene CT(Ru ? C60) is important in the reaction, but it is small due to the presence of the Ru d orbital at low energy, which is the reason for the large Delta G degrees(double dagger) and moderately negative Delta G degrees. The use of Li+@C-60 is theoretically predicted to accelerate the reaction and increase the yield of Li+@C-60[CpRu(CO)(2)](2), because the CT(Ru -> C-60) is enhanced by the low energy LUMO of Li+@C60. It is also predicted that Li+@C-60[Re(CO)(4)(PMe3)](2) is a next promising target for the synthesis of the ?1-coordinated metal-fullerene complex, but syntheses of C-60[Co(CO)(4)](2), C-60[Re(CO)5]2, Li+@C-60[Co(CO)(4)](2), and Li+@C-60[Re(CO)(5)](2) are difficult. The use of nonpolar solvent is another important factor for the synthesis of the eta(1)-coordinated metal complex with Li+@C60.