Spin–Spin interactions in polynuclear transition-metal complexes

Local properties, such as partial charges or local spins, are an important concept in chemistry. In this work, two alternative local decomposition schemes for molecular total spin expectation values 〈 S ^ 2 〉 are compared for Kohn–Sham density functional theory calculations on polynuclear transition-metal clusters. It is confirmed that the scheme proposed by Mayer resolves the problem of the non-zero local spins 〈 S ^ A 2 〉 which arise in the first approach of this kind suggested by Clark and Davidson. Furthermore, it is demonstrated that Mayer’s 〈 S ^ A 2 〉 expectation values can be interpreted as S A ( S A + 1 ) . The cross-terms, 〈 S ^ A · S ^ B 〉 A ≠ B , are very similar in both schemes when calculated for two metal atoms in polynuclear clusters, whereas they differ for small open-shell molecules such as NO. Overall, Mayer’s approach is more consistent for the local decomposition of 〈 S ^ 2 〉 .