Energetics of transition-metal ions in low-coordination environments

The energetics of the interaction of transition-metal ions with low-coordination, non-close-packed neighbor shells are studied by ab initio total-energy calculations using plane-wave and other basis sets. Total energies are calculated for small clusters containing 3d transition-metal ions in simple, low-coordination environments. The clusters are obtained by placing four molecules of NH₃, H₂O, or H₂S at the vertices of a square or tetrahedron, with the N, O, or S facing the ion. The energy differences between square and tetrahedral structures are found to be ≈ 1 eV in several cases. Such a large magnitude is expected for open d-shell systems because of ligand-field-splitting effects, but similar energy differences are also found in closed-shell systems. We use the results to show that the main factors determining the structural energetics of the ions, in addition to direct ligand-ligand interactions, are the ligand-field splitting of the transition-metal d shell, and a contribution from the interaction of the ligand orbitals with the transition metal charge and sp orbitals. The results are used to parametrize a classical force field for Cu²⁺ and evaluate its accuracy.