Ab initio Hartree-Fock calculations were performed on the equilibrium geometries and electronic structures of a series of endohedral, exohedral and endohedral-exohedral complexes of C~4~0. The C~4~0(T~d) cage is found to have four unpaired electrons with a ^5A~2 open-shell ground state and have four dangling bonds. C~4~0(T~d) behaves as a sort of hollow superatom with an effective valence of 4, both toward the outside and inside of the carbon cage, so it is possible to form the endohedral metallofullerene Nb@C~4~0, exohedral complex C~4~0H~4 and endohedral-exohedral complex Nb@C~4~0H~4 from C~4~0. From the values of binding energies per atom, it's found that C~4~0(T~d) is more stable than C~4~0(C~3~v), while C~4~0^+ (C~3~v) is more stable than C~4~0^+(T~d). In networked metallofullerenes NbC~3~9^+, Nb is connected directly with three carbon atom, forming three Nb-C single bonds with the Nb atom protruding from the surface of the carbon cage. Our calculated results show that C~4~0 and C~4~0^+ are more stable than NbC~3~9^+, and NbC~3~9^+ is more stable than Nb@C~4~0^+. The results are consistent with the experimental results. Through the comparison of the C~4~0 series clusters with the C~2~8 and related compounds, we have found that there are many similarities between C~4~0 and C~2~8. Our calculated results may shed light on other endohedral and exhedral complexes of fullerenes and networked type metallofullerenes in general.

Key words: NIOBIUM COMPLEX, FULLERENES, CAGE STRUCTURE, ELECTRONIC STRUCTURE, CONFIGURATION, AB INITIO CALCULATION