The density functional theory in the PBE approximation was used to explore the geometry and electronic structure of sumanene C21H12 and its five derivatives C21H12R6 (R = H, F, Cl, Br, and CN). The R groups in C21H12R6 molecules are attached to carbon atoms in α positions with respect to the central six-membered ring. The possibility of the formation of C21H12R6η 6-π complexes with Cr(C6H6), Cr(CO)3, Mo(C6H6), and Mo(CO)3 was discussed. The relative stability of these complexes was evaluated. The attachment of M(C6H6) and M(CO)3 (M = Cr, Mo) to sumanene C21H12 with the formation of η6-π bonds is energetically less favorable than their attachment to sumanene derivatives C21H12R6. The complexes of sumanene derivatives with Cr(C6H6), Cr(CO)3, Mo(C6H6), and Mo(CO)3 were found to be the most promising objects for synthesis. The C60 and η6-(C6H6)M-C60 and η6-(CO)3M-C60 (M = Cr, Mo) fullerene complexes were predicted to be much less stable than the η6-(CO)3M-C60R6 and η6-(C6H6)M-C60R6 complexes (M = Cr, Mo; R = H, Hal, CN), where R groups bordered one of the fullerene C60 six-membered rings comprising the atoms to which metal atoms were coordinated.