Pair states and orbital exchange coupling parameters of the dimeric diol complexes [Cr(ox) 2(OH)] 24− and [Cr(gly) 2(OH)] 2

Abstract

A method for calculating exchange-induced energy-level splittings in polynuclear transition-metal complexes when orbitally unquenched single-ion states are involved is described. The method refers to Dirac's permutation operator in the spin space. Using symmetry-adapted wavefunctions, the pair energies are readily derived, often directly from the diagonal matrix elements of the bilinear exchange hamiltonian ▪ The theoretical results have been applied to absorption and emission spectra from pure spin-flip transitions of two di-μ-hydroxo bridged chromium(III) complexes containing oxalate and glycine chelate ligands. Low-temperature measurements down to 1.9 K yielded highly resolved spectra, in particular in the region of the 4A 2g 4A 2g → 4A 2g 2E g transitions. Pair lines due to inequivalent molecules in the crystal lattice of Na 4[Cr(ox) 2(OH)] 2 were distinguished by site-selective emission spectroscopy. Complete assignments were derived using spin and symmetry selection rules, and pair energies were calculated in terms of orbital exchange coupling constants J ij , which strictly obey the Goodenough-Kanamori rules. The following parameter values were obtained for the binuclear oxalate (glycinate) complex (in cm −1): j 11 = 4 (55), j 12 = − 29 (−150), j 13 = 13 (30), j 33 = −6 (−10). These data show that super-exchange via the bridging OH − ligands dominates direct exchange, resulting m a relatively weak antiferromagnetic coupling for the 4A 2g 4A 2g ground state: J gr ab = −0.3 (−4.2) cm −1. Magneto-structural correlations are found to arise predominantly from the position of the hydrogen atoms within the bridging unit.