Strength of spin coupling in high-spin organic molecules

The effective valence bond (EVB) model proposed by Malrieu and Maynau is exactly solved to calculate the strength of spin coupling in a large number of high-spin conjugated di- and polyradicals with up to 22 pi-electrons. In terms of simple concepts such as spin-coupling unit, spin-coupling path, etc., we carefully analyze the topological dependence of the calculated coupling constants in these high-spin molecules. For diradicals, our calculations indicate that the strong ferromagnetic coupling often requires short topological distance, numerous spin-coupling paths, and large delocalization interaction provided by spin coupling units. Besides this, the connectivity of two radical sites also plays a significant role in determining the coupling strength in diradicals. When extending diradicals to their homologous higher polyradicals, the coupling constant through vinylidene is found to decrease appreciably from the diradical to the ''linear'' and ''circular'' triradicals and to approach the corresponding value in related one-dimension infinite spin system at different rates; the spin coupling through m-phenylene in the diradical is predicted to be reduced by about 2 and 4 times in linear and ''star-branched'' macroscopic-size systems, respectively, while the 2,3'-connected biphenyl coupling unit has a stronger coupling ability in the linear triradical than in the diradical.