Cu²⁺ in Layered Compounds: Origin of the Compressed Geometry in the Model System K₂ZnF₄:Cu²⁺

Abstract

Many relevant properties (including superconductivity and colossal magnetoresistance) of layered materials containing Cu(2+), Ag(2+), or Mn(3+) ions are commonly related to the Jahn-Teller instability. Along this line, the properties of the CuF6(4-) complex in the K2ZnF4 layered perovskite have recently been analyzed using a parametrized Jahn-Teller model with an imposed strain [Reinen, D. Inorg. Chem.2012, 51, 4458]. Here, we present results of ab initio periodic supercell and cluster calculations on K2ZnF4:Cu(2+), showing unequivocally that the actual origin of the unusual compressed geometry of the CuF6(4-) complex along the crystal c axis in that tetragonal lattice is due to the presence of an electric field due to the crystal surrounding the impurity. Our calculations closely reproduce the experimental optical spectrum. The calculated values of the equilibrium equatorial and axial Cu(2+)-F(-) distances are, respectively, R(ax) = 193 pm and R(eq) = 204 pm, and so the calculated distortion R(ax) - R(eq) = 11 pm is three times smaller than the estimated through the parametrized Jahn-Teller model. As a salient feature, we find that if the CuF6(4-) complex would assume a perfect octahedral geometry (R(ax) = R(eq) = 203 pm) the antibonding a(1g)*(∼3z(2) - r(2)) orbital is placed above b(1g)*(∼x(2) - y(2)) with a transition energy E((2)A(1g) → (2)B(1g)) = 0.34 eV. This surprising fact stresses that about half the experimental value E((2)A(1g) → (2)B(1g)) = 0.70 eV is not due to the small shortening of the axial Cu(2+)-F(-) distance, but it comes from the electric field, E(R)(r), created by the rest of the lattice ions on the CuF6(4-) complex. This internal field, displaying tetragonal symmetry, is thus responsible for the compressed geometry in K2ZnF4:Cu(2+) and the lack of symmetry breaking behind the ligand relaxation. Moreover, we show that the electronic energy gain in this process comes from bonding orbitals and not from antibonding ones. The present results underline the key role played by ab initio calculations for unveiling all the complexity behind the properties of the model system K2ZnF4:Cu(2+), opening at the same time a window for improving our knowledge on d(9), d(7), or d(4) ions in other layered compounds.

Compounds Containing Tetragonal Cu2+ Complexes: Is the dx2–y2–d3z2–r2 Gap a Direct Reflection of the Distortion?

“…31 This result thus strongly supports that the distortions and Δ gaps in layered copper and silver complexes are not necessarily associated with the Jahn−Teller effect as was suggested by Pickett. 2 Obviously, this effect is much reduced in cubic lattices where the tetragonal distortion of the complex induces a weak quadrupolar field.…”

“…24,25 As a salient feature, the present calculations reproduce that the CuF 6 4− complexes are elongated in K 2 CuF 4 , KCuF 3 , and KZnF 3 / Cu 2+15,17,18,24,25 but compressed in K 2 ZnF 4 /Cu 2+ , a fact that is also in agreement with experimental findings 16 and results from ab initio calculations. 31 According to Table 1, the experimental u value for K 2 CuF 4 (28.7 pm) is 16% smaller than that for KCuF 3 (33.3 pm). Therefore, if the observed splitting Δ depends only on the distortion of the fluorine octahedron, it is hard to understand why Δ for K 2 CuF 4 (1.03 eV) 15 is higher than that for KCuF 3 (0.95 eV).…”

“…As active electrons are conf ined in the CuF 6 4− unit, calculations have been performed on a simple CuF 6 4− complex but are subject to the electrostatic potential V R (r) created by the rest of the lattice ions. 31 In these calculations, we have used the popular B3LYP hybrid functional 32 in the spin-unrestricted Kohn−Sham formalism of the DFT and high-quality all-electron basis sets of triple-ζ plus polarization (TZP) type.…”

“…The role of this internal field is often discarded in the traditional ligand field theory. 31 Let us now discuss the possible influence of E R (r) upon the optical excitations of CuF 6 4− in the four considered systems. To clarify this matter, we have first calculated the value of the d−d transitions for an isolated CuF 6 4− complex at the equilibrium geometry determined for KZnF 3 /Cu 2+ , K 2 ZnF 4 /Cu 2+ , K 2 CuF 4 , and KCuF 3 (Table 1).…”

A comprehensive local structure analysis of Cr3+ centers in K2ZnF4 crystals: A semi-empirical approach

“…Several experimental and theoretical investigations have been devoted to transition metal ions, such as Fe 3+ , Cr 3+ , Co 2+ , Ni 2+ and Mn 2+ , doped K 2 ZnF 4 crystal. For example, K 2 ZnF 4 :Fe 2+ system was studied experimentally by Bousseksou et al [1] and theoretically by Rudowicz et al [2]; and a couple of experimental [3][4][5] and theoretical [6] studies were carried out for K 2 ZnF 4 :Cu 2+ system. Besides, numerous theoretical studies focused on some other systems K 2 ZnF 4 :Ni 2+ [7], K 2 ZnF 4 :Mn 2+ [8,9], and K 2 ZnF 4 :Co 2+ [10].…”