Theoretical studies on Co₂(CO)₆(PX)₂ derivatives (X = H, Cl, OH, OMe, NH₂, NMe₂) predict the lowest energy structures to be butterfly structures containing five two-electron two-center bonds in the central Co₂P₂ unit. Among these butterfly structures the energy increases as the unique bond forming the “body” of the butterfly changes from Co–Co to Co–P and then P–P. Higher energy rhombus structures are also found for Co₂(CO)₆(PX)₂ with only Co–P bonds in the Co₂P₂ framework without any Co–Co or P–P bonds. In addition, for Co₂(CO)₆(POR)₂ (R = H, Me) still higher energy “diphosphine” structures are also found containing only three rather than four Co–P bonds, one P–P bond, and no Co⋯Co bond. For the isoelectronic Co₂(CO)₆S₂ a rhombus structure is competitive in energy with the butterfly structures with five structures lying within ∼4 kcal/mol thereby predicting a fluxional system. A tetrahedrane structure was not found for Co₂(CO)₆S₂ in contrast to the tetrahedrane structure known experimentally for the related Fe₂(CO)₆S₂ with one less electron per metal atom.