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 Delta P-2(Cu), the difference of copper squared spin populations as calculated for the high-spin (i.e. triplet) and broken-symmetry spin states, through JAF approximate to -U Delta P-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 atl alternative quantifier of the exchange phenomenon to that usually used, i.e. Delta(2), the square of the singly occupied molecular orbital splitting in the tripler state. Moreover? and quite interestingly, the quantity Delta P-2(Cu) can became negative (i.e. induce ferromagnetism) without apparently affecting the proportionality relation.