The recent accomplishment in the design of molecular nanowires characterized by increasing conductance with length has led to the origin of an extraordinary new family of molecular junctions referred to as “anti-ohmic” wires. Herein, this highly desirable, non-classical behavior, has been examined for molecules long-enough to exhibit pronounced diradical character in their ground state within the unrestricted DFT formalism with spin symmetry breaking. We demonstrate that highly conjugated acenes signal higher resistance in an open-shell singlet (OSS) configuration as compared to their closed-shell counterparts. This anomaly has been further proven for experimentally certified cumulene wires, which reveals phenomenal modulation in the transport characteristics such that an increasing conductance is observed in the closed-shell limit, while higher cumulenes in the OSS ground state yield regular decay of conductance.