In earlier work, we previously established a formalism that allows to express the exchange energy J vs. fundamental molecular integrals without crystal field, for a fragment A–X–B, where A and B are 3d1 ions and X is a closed-shell diamagnetic ligand. In this article, we recall this formalism and give a physical interpretation: we may rigorously predict the ferromagnetic (J < 0) or antiferromagnetic (J > 0) character of the isotropic (Heisenberg) spin-spin exchange coupling. We generalize our results to ndm ions (3 £ n £ 5, 1 £ m £ 10). By introducing a crystal field we show that, starting from an isotropic (Heisenberg) exchange coupling when there is no crystal field, the appearance of a crystal field induces an anisotropy of exchange coupling, thus leading to a z-z (Ising-like) coupling or a x-y one. Finally, we discuss the effects of a weak crystal field magnitude (3d ions) compared to a stronger (4d ions) and even stronger one (5d ions). In the last step, we are then able to write the corresponding Hamiltonian exchange as a spin-spin one.
Spin Exchange Coupling in Dimethoxo-Bridged Dichromium(III) Complexes: A Density Functional Theory Study
