Stabilization of mixed valence states in partly oxidized one-dimensional transition metal systems

Abstract

The spatial hole-state properties of partly oxidized one-dimensional (1D) organometallic solids with weak metal-metal interactions (either due to large separations between the corresponding building blocks or due to bridging organic ligand functions) have been studied in the crystal orbital (CO) formalism based on the tight-binding technique. The numerical analysis is restricted to insulating band states. The employed computational model is a semiempirical self-consistent-field (SCF) Hartree-Fock (HF) CO variant derived within the INDO (intermediate neglect of differential overlap) approximation. We have adopted a simple averaging procedure for the “open shell” systems which is based on a density operator that has its origin in the grand canonical (GC) ensemble in order to avoid the numerical difficulties of restricted or unrestricted tight-binding calculations on the oxidized 1D chains. The present method, however, is not related to temperature-dependent equilibria in statistical mechanics but is only a formal, highly efficient approach for the formation of average-states in the mean-field approximation. As one-dimensional models we have adopted the infinite tetracyanatonickelate(II), Ni(CN) ²⁻₄ 1, and the cyclopentadienylmanganese(I), MnCp2, systems. The electron removal processes in both 1D materials are more (1) or less (2) metal-centered ($3d_{z^2 }$ states). The mean-field ground states of both oxidized modifications correspond to broken symmetry CDW (charge density wave) solutions that lead to mixed valence states with inequivalent numbers of electrons at adjacent transition metal centers. This symmetry breaking guarantees that important left-right correlations between the 3d atoms are taken into account even in the SCF HF approximation. The valence trapping in1 is strong, i.e. the mutual charge separation between the Ni centers amounts to 0.87e. The bridging organic π ligands in2 prevent such pronounced differences of the net charges at the Mn centers and cause a reduction of the charge separation to 0.09e–0.14e.