End-On Azido-Bridged Copper Dimers: Spin Population Analysis and Spin Polarization Effect as Exhibited by Valence-Bond/Broken Symmetry, Density Functional Methods

Abstract

Within the general context of homometallic spin-coupled copper(II) dimers, we define the quantity ΔP2(Cu), the difference of copper squared spin populations as calculated for the high-spin (i.e., triplet) and broken symmetry spin states. In the specific case of an azido-bridged copper(II) dimer, the antiferromagnetic part of the exchange coupling constant is then shown, using density functional (DF), valence bond−broken symmetry (VB−BS) techniques, to be proportional to this quantity. This provides a quantifier of the exchange phenomenon alternative to that usually used, that is, Δ2, squared of the singly occupied molecular orbital splitting in the triplet state. Moreover, spin polarization, through the spin population being delocalized from one copper ion onto the other one, offers the possibility of changing the sign of ΔP2(Cu), thus resulting in a ferromagnetic contribution, for weak magnetic orbital overlap, here found at the VB ground-state level. Phenomenologically, this last effect can be formulated in terms of McConnell's mechanism I for ferromagnetic interaction in solid free radicals (McConnell, H. M. J. Chem. Phys. 1963, 39, 1910). We finally show that the standard copper basis sets commonly used for inorganic chemistry computations may be deficient. This leads to exaggerated spin delocalization and to bad agreement between DF computed (Mulliken) spin populations and those recently measured by polarized neutron experiments (Aebersold, M. A. et al.: J. Am. Chem. Soc. 1998, 120, 5238).