Magnetic coupling constants of self-assembled Cu(II) [3×3] grids: alternative spin model from theoretical calculations.

This paper reports a theoretical analysis of the electronic structure and magnetic properties of a ferromagnetic Cu(II) [3×3] grid. A two-step strategy, combining calculations on the whole grid and on binuclear fragments, has been employed to evaluate all the magnetic interactions in the grid. The calculations confirm an S = 7/2 ground state, which is in accordance with the magnetisation versus field curve and the thermal dependence of the magnetic moment data. Only the first-neighbour coupling terms present non-negligible amplitudes, all of them in agreement with the structure and arrangement of the Cu 3d magnetic orbitals. The results indicate that the dominant interaction in the system is the antiferromagnetic coupling between the ring and the central Cu sites (J3 = J4 ≈ -31 cm(-1)). In the ring two different interactions can be distinguished, J1 = 4.6 cm(-1) and J2 = -0.1 cm(-1), in contrast to the single J model employed in the magnetic data fit. The calculated J values have been used to determine the energy level distribution of the Heisenberg magnetic states. The effective magnetic moment versus temperature plot resulting from this ab initio energy profile is in good agreement with the experimental curve and the fitting obtained with the simplified spin model, despite the differences between these two spin models. This study underlines the role that the theoretical evaluations of the coupling constants can play on the rationalisation of the magnetic properties of these complex polynuclear systems.