Azido-, hydroxo-, and oxo-bridged copper(II) dimers: spin population analysis within broken-symmetry, density functional methods

Within the general context of homometallic spin-coupled Cu(II) dimers, we propose to relate the antiferromagnetic part of the exchange coupling constant, J _AF, to the quantity ΔP ²(Cu), the difference of copper squared spin populations as calculated for the high-spin (i.e. triplet) and broken-symmetry spin states, through J _AF≈−UΔP ²(Cu), where U is interpreted as the covalent–ionic term. This proportionality is illustrated for three “bare” Cu(II) dimers (i.e. without peripheral ligation, so as to enhance the antiferromagnetic contribution) bridged by azido, hydroxo, or oxo groups. This provides an alternative quantifier of the exchange phenomenon to that usually used, i.e. Δ², the square of the singly occupied molecular orbital splitting in the triplet state. Moreover, and quite interestingly, the quantity ΔP ²(Cu) can become negative (i.e. induce ferromagnetism) without apparently affecting the proportionality relation. Received: 17 September 1999 / Accepted: 9 March 2000 / Published online: 21 June 2000