Electronic structure and magnetic properties of a trigonal prismatic CuII6cluster

Abstract

A combination of detailed magnetisation studies and electronic-structure analysis using broken-symmetry DFT is used to explore the electronic structure of a trigonal prismatic Cu^II₆ cluster. The presence of six paramagnetic metal centres with S = 1/2 gives rise to a maximum multiplicity of S = 3 and a total of 31 broken-symmetry states with M_S < 3. Computed differences in energy between the high-spin and broken-symmetry states are expressed in terms of the 15 distinct Heisenberg exchange coupling parameters, J_ij, and the equations are solved by a least-squares fitting procedure. By inspection of the errors introduced by progressive symmetrisation of the Hamiltonian to reduce the number of independent J_ij, we arrive at a minimal model containing only four distinct J_ij (three intra- and one inter-triangular). The computed values then guide the fitting of the magnetisation data. The computed trends in J_ij can only be reproduced when antisymmetric exchange is included in the model Hamiltonian. The use of this Hamiltonian provides a reasonable description of the magnetic behaviour at all temperatures and fields. If a simpler isotropic model Hamiltonian is used instead, the best fit values of J_ij are compromised by the need to fit the low-temperature region where antisymmetric exchange dominates the shape of the curve.