Reduction of 1,4-dimethylenecyclohexane-2,3,5,6-tetron forms the title dianion 1(2-), which may also be formulated as the 1,4-dimethide of deprotonated rhodizonic acid, Substituted versions of this species, designed as a charged electronic analogue of dimethylenecyclobutadiene, are proposed as building blocks for assembly of molecule-based magnets. A possible mode of self-organization of their metal salts into 2-D structures with intermolecular ferromagnetic coupling is outlined, Full pi space CAS(14,12)/6-31+G*//CAS(14,12)/ 6-31G* calculations were performed to probe the ground spin state (singlet vs tripler) of 1(2-) as a function of substituent variations. This study has found that a triplet ground state preference as high as 4.5 kcal/mol may be achieved for the symmetrically coordinated dianion.