## 3: "Ferromagnetism" in Solid Free Radicals (CIT)

In odd alternate aromatic radicals the spin density alternates in sign as one moves from one atom to the next. It occurred to me that if a 3D array of these radicals were stacked on top of one another with a geometry so that each negative spin was paired with a neighboring molecular positive spin, the spins would arrange in such a way that the state of lowest energy would have the largest spin — a potential state of molecular “ferromagnetism.” (89) Years later this concept was elegantly verified ^{[3,} ^{4]} by Japanese workers who synthesized molecules with S = 1 ground states from suitably stacked odd alternate radicals each with S = ½. In fact this little paper stimulated a great deal of experimental work but unfortunately no significant practical applications. For a confirmatory theoretical analysis of the problem and many references, see M. Deumal et al.,^{[5]} and Yoshizawa et. al.^{[6]}

Odd alternate radicals have many interesting properties. For example I predicted that the triplet ground state of the biradical trimethylene methyl would be one in which the spin on the central carbon atom would be negative. Assuming D_{3h} symmetry for the radical, I predicted that the fine structure splitting for the radical would be small due to a cancellation of positive contributions of spin-spin repulsions on the CH_{2} groups, and negative contributions due to the negative spin density on the central carbon atom (76).

A small fine structure splitting was indeed found to be the case in the work of Claesson et al.^{[7]} Unfortunately, in my paper on the subject I failed to mention the importance of the proton hyperfine splittings on the CH_{2} groups. Claesson et al., report isotropic proton hyperfine splittings of -26 MHz for these protons, leading to an estimated spin density of -26/Q = -26/-63 = 0.41 for the spin density on each these three atoms. (Valence bond theory predicts 0.416 for these spin densities.) Thus there is 3(0.41) spin density on the methylene protons, which implies 2-(3)(0.41)=0.77 missing spin density, corresponding to a negative spin density of -0.77 on the central carbon atom. (My manuscript erroneously gives this negative spin density as -0.25, which should instead be -0.75.). Strangely, I have not found any discussion of these spin densities in this interesting radical since my 1961 paper (76).

Chapter 4: Tripet Excitons (CIT)