Valence bond/broken symmetry analysis of the exchange coupling constant in copper(II) dimers. Ferromagnetic contribution exalted through combined ligand topology and (singlet) covalent-ionic mixing

In this paper we aim at presenting a full-VB (valence-bond) analysis of the DFT broken symmetry (BS) exchange coupling constant JBS. We extend Kahn and Briats "two sites-two electrons" VB original formalism (Kahn, O.; Briat, B. J. Chem. Soc. Farady Trans. II, 1976, 72, 268) by taking into account the covalent-ionic singlet state mixing, here translated into intersite magnetic orbital delocalization. In this way, two explicit contributions to the magnetic orbital overlap appear, one from the purely covalent state, and the other one from the covalent-ionic mixing. This scheme allows us to relax the strict orthogonality constraint of Kahn and Briats chemically heuristic model resulting into ferromagnetism. Moreover, we show how DFT-BS calculations applied to various copper(II) dimers yield effective parameters that can be injected into the full-VB model, allowing for a breaking down of JBS into various contributions, one of which being either ferromagnetic or antiferromagnetic depending on the bridging ligand topology. Two classes of systems emerge from this analysis and the exceptional ferromagnetic coupling property of the "end-on" azido-bridged copper dimer is especially emphasized.