Symmetry violations in partially oxidized one-dimensional (1D) transition metal polymers. The Ni(CN)2−4 system

Abstract

The band structure of tetracyanonickelate (II), Ni(CN)2−4 1 has been studied in the unoxidized state and in a partially oxidized form with one electron removed per two Ni(CN)2−4 sites. Computational tool for this investigation is a semiempirical INDO (intermediate neglect of differential overlap) crystal orbital (CO) model based on the tight-binding formalism and combined with the grand canonical (GC) averaging procedure. This approximation allows for the formation of average values over certain manifolds of one- (or many-electron) states and thus makes possible the investigation of violations of the spatial symmetry separated from metal–insulator transitions and spin-dependent phenomena. The oxidation process in 1 is metal centered (3dz2 states) and leads to a broken symmetry CDW (charge density wave) solution with trapped valences at the Ni sites within the allowed variational space in the Hartree–Fock (HF) CO formalism. The charge separation between the transition metal centers ΔqNi amounts to ∼0.87e. The band structure shows some analogies to the dispersion curves encountered in semiconductor superlattices. The physical origin for this valence trapping is analyzed and compared with violations of spatial symmetries in finite transition metal complexes, clusters as well as simple solids. The title compound belongs to a class of organometallic polymers in the 3d series where the covalent metal–metal interaction (kinetic energy operator) is negligibly small in comparison to the strongly repulsive two-electron part. The symmetry adapted HF state of the partially oxidized backbone with averaged populations at the Ni sites is thus unstable against a condensation into an arrangement with alternating oxidation states (trapped valences).