In agreement with the experimental results of the groups of Rassat and Iwamura on respectively m-phenylene bis(tert-butyl nitroxides) 2 and 3, ab initio calculations on m-benzoquinodimethane (1a) and m-phenylene bis(nitroxide) (1d) find that near dihedral angles of phi = 90 degrees between the benzene ring and the radical-bearing groups, the singlet falls below the triplet in energy. The change in m-phenylene from a ferromagnetic coupler at angles around phi = 0 degrees to an antiferromagnetic coupler around phi = 90 degrees is found to be largely due to selective destabilization of the antisymmetric (A) combination of the singly-occupied orbitals on each of the radical centers by a sigma orbital of this symmetry on the m-phenylene coupler. The asymmetry about phi = 90 degrees in the singlet-triplet energy difference that is calculated for Id is shown to be due to additional interactions of the oxygens of the singly-occupied nitroxyl orbitals with p-pi AOs of the benzene ring.