Electronic structures, chemical bonding, and defect formation in mixed cyanoferrates M2Cu[Fe(CN)6] (M = Na, K, Rb, and Cs)

Abstract

The effect of the alkali metal nature on the electronic structures and chemical bonding in mixed cyanoferrates M2Cu[Fe(CN)6] (M = Na, K, Rb, and Cs) was studied by ab initio tight-binding linear muffin-tin orbital (TB-LMTO) method (in the spin-polarized implementation) and the extended Huckel molecular orbital (EHMO) method. It was found that the X-ray photoelectron spectra of the ferrimagnetic compounds Na2Cu[Fe(CN)6] (I), K2Cu[Fe(CN)6] (II), Rb2Cu[Fe(CN)6] (III), and Cs2Cu[Fe(CN)6] (IV) are similar. The magnetic moments on Cu2+ and iron ions remain virtually constant in compounds I–IV (μ(Cu) = 0.9 μB, μ(Fe) < −0.06 μB). Analyses of the electron density maps and the bond overlap populations showed that the cubic frameworks of cyanoferrates are built from stable fragments ⋯-Fe-C≡N-Cu-⋯. The bond strength in these fragments decreases substantially in the order C-N → Fe-C → Cu-N and only slight in the order IV → III → II → I. The calculated total energies of the cyanoferrates Cs2−x Cu[Fe(CN)6], CsHCu[Fe(CN)6], and NaHCu[Fe(CN)6] for different concentrations and configurations of defects (cesium vacanices and hydrogen substitution defects) suggest mutual repulsion of defects. This repulsion is responsible for the experimentally observed lowering of the ionic conductivity with an increase in the defect concentration in the mixed cyanoferrates.