Isotropic non-Heisenberg behavior in M3(dpa)4Cl2 extended metal atom chains

Isotropic deviations to the standard Heisenberg Hamiltonian have been extracted for a series of trinuclear extended metal atom chain complexes, namely, [Ni(3)(dpa)(4)Cl(2)], and the hypothetical [NiPdNi(dpa)(4)Cl(2)] and [Pd(3)(dpa)(4)Cl(2)], following a scheme recently proposed by Labéguerie and co-workers (J. Chem. Phys 2008, 129, 154110) within the density functional theory framework. Energy calculations of broken symmetry monodeterminantal solutions of intermediate M(s,tot.) values can provide an estimate of the magnitude of the biquadratic exchange interaction (λ) that accounts for these deviations in systems with S = 1 magnetic sites. With the B3LYP functional, we obtain λ = 1.37, 13.8, and 498 cm(-1) for the three molecules, respectively, meaning that a simple Heisenberg Hamiltonian is enough for describing the magnetic behavior of the Ni(3) complex but definitely not for Pd(3). In the latter case, the origin of such extreme deviation arises from (i) an energetically affordable local non-Hund state (small intrasite exchange integral, K ∼ 1960 cm(-1)) and (ii) a very effective overlap between Pd-4d orbitals and a large J. Furthermore, this procedure enables us to determine the relative weights of the two types of magnetic interactions, σ- and δ-like, that contribute to the total magnetic exchange (J = J(σ) + J(δ)). In all of the systems, J is governed by the σ interaction by 95-98%.