In the recently synthesized rare earth transition metal carbide $La_7O_{s4}C_9$ one finds one-dimensional organometallic $[O_{s4}C_9]^{21-}$ polymers embedded in a $La^{3+}$ ionic matrix. The electronic structure of the polymeric $[O_{s4}C_9]^{21-}$ chain was investigated by density of states (DOS) and crystal orbital overlap population (COOP), using the extended Huckel algorithm. A fragment molecular orbital analysis is used to study the bonding characteristics of the $C_2$ units in $La_7O_{s4}C_9$ containing $C_2$ units and single C atoms as well. The title compound contains partially filled Os and carbon bands leading to metallic conductivity. As the observed distances already indicated, the calculations show extensive Os-C interactions. The C-C bond distance in the diatomic $C_2$ units ($d_{C-C}$=131 pm) in the solid is significantly increased relative to $${C_2}^{2-}$$</TEX> or acetylene, because antibonding $1{pi}_g$ orbitals are partially filled by the Os-$C_2(1;{pi}_g)$ bonding contribution found at and below the Fermi level.