The Modulation of Jahn–Teller Coupling by Elastic and Binding Strain Perturbations—A Novel View on an Old Phenomenon and Examples from Solid-State Chemistry

Red Shift in Optical Excitations on Layered Copper Perovskites under Pressure: Role of the Orthorhombic Instability

The red shift under pressure in optical transitions of layered compounds with CuCl6 4- units is explored through first-principles calculations and the analysis of available experimental data. The results on Cu2+ -doped (C2 H5 NH3 )2 CdCl4 , that is taken as a guide, show the existence of a highly anisotropic response to pressure related to a structural instability, driven by a negative force constant, that leads to an orthorhombic geometry of CuCl6 4- units but with a hole displaying a dominant 3z2 -r2 character (z being the direction perpendicular to the layer plane). As a result of such an instability, a pressure of only 3 GPa reduces by 0.21 Å the longest Cu2+ -Cl- distance, lying in the layer plane, while leaving unmodified the two other metal-ligand distances. Owing to this fact, it is shown that the lowest d-d transition would experience a red shift of 0.34 eV while the first allowed charge transfer transition is also found to be red shifted but only by 0.11 eV that reasonably concurs with the experimental value. The parallel study on Jahn-Teller systems CdCl2 :Cu2+ and NaCl:Cu2+ involving tetragonal elongated CuCl6 4- units shows that the reduction of the long axis by a pressure of 3 GPa is three times smaller than that for the layered (C2 H5 NH3 )2 CdCl4 :Cu2+ compound. Accordingly, the optical transitions of such systems, which involve a positive force constant, are much less sensitive to pressure than in layered compounds. The origin of the red shift under pressure undergone by the lowest d-d and charge transfer transitions of (C2 H5 NH3 )2 CdCl4 :Cu2+ is discussed in detail.

New Ideas for Understanding the Structure and Magnetism in AgF2 : Prediction of Ferroelasticity

In the search for new high-temperature superconductors, it has been proposed that there are strong similarities between the fluoroargentate AgF2 and the cuprate La2 CuO4 . We explored the origin of the possible layered structure of AgF2 by studying its parent high-symmetry phase and comparing these results with those of a seemingly analogous cuprate, CuF2 . Our findings first stress the large differences between CuF2 and AgF2 . Indeed, the parent structure of AgF2 is found to be cubic, naturally devoid of any layering, even though Ag2+ ions occupy trigonal sites that, nevertheless, allow the existence of a Jahn-Teller effect. The observed Pbca orthorhombic phase is found when the system is cooperatively distorted by a local E⊗e trigonal Jahn-Teller effect around the silver sites that creates both geometrical and magnetic layering. While the distortion implies that two Ag2+ -F- bonds increase their distance by 15 % and become softer, our simulations indicate that covalent bonding and interlayer electron hopping is strong, unlike the situation in cuprate superconductors, and that, in fact, exfoliation of individual planes might be a harder task than previously suggested. As a salient feature, these results prove that the actual magnetic structure in AgF2 is a direct consequence of vibronic contributions involved in the Jahn-Teller effect. Finally, our findings show that, due to the multiple minima intrinsic to the Jahn-Teller energy surface, the system is ferroelastic, a property that is strongly coupled to magnetism in this argentate.

Key Role of Deep Orbitals in the dx2-y2-d3z2-r2 Gap in Tetragonal Complexes and 10Dq

Using first-principles calculations, we show that the origin of the intrinsic a_1g(∼3z² – r²)–b_1g(∼x² – y²) splitting, Δ_int, in tetragonal transition-metal complexes and the variations of the cubic field splitting, 10Dq, with the metal–ligand distance, R, are much more subtle than commonly thought. As a main novelty, the key role played by covalent bonding with deep valence ligand levels and thus the inadequacy of too simple models often used for the present goal is stressed. Taking as a guide the isolated D_4h CuF₆^4– complex, it is proved that Δ_int essentially arises from bonding with deep 2s(F) orbitals despite them lying ∼23 eV below 2p(F) orbitals. This conclusion, although surprising, is also supported by results on octahedral fluoride complexes where the contribution to 10Dq splitting from bonding with 2s(F) orbitals is behind its strong R dependence, stressing that explanations based on the crystal-field approach are simply meaningless.

Ground State and Optical Excitations in Compounds with Tetragonal CuF64- Units: Insight into KAlCuF6 and CuFAsF6

It has been argued that AAlCuF₆ (A = K, Cs) and CuFAsF₆ are the only known crystals that exhibit compressed CuF₆^4- units due to the Jahn-Teller effect. However, no grounds for this singular behavior have yet been reported. By means of first-principles calculations on such compounds and the isomorphous compounds involving Zn²⁺ ions instead of Cu²⁺, we prove that neither the ground state nor the equilibrium geometry of CuF₆^4- complexes in KAlCuF₆ and CuFAsF₆ is the result of a Jahn-Teller effect. In contrast, it is shown that the internal electric field, E_R(r), created by the rest of the lattice ions upon the localized electrons in the complex, plays an important role in understanding this matter as well as the d-d transitions of these two compounds. The energy of an optical transition is shown to involve two contributions: the intrinsic contribution derived for the isolated CuF₆^4- unit at equilibrium and the extrinsic contribution coming from the E_R(r) field. Aside from reproduction of the experimental d-d transitions observed for KAlCuF₆, it is found that in CuFAsF₆ the b_1g(x² - y²) → a_1g(3z² - r²) transition is not the lowest one due to the stronger effects from the internal field. Interestingly, the intrinsic contribution corresponding to that transition can simply be written as β(R_eq - R_ax) where R_eq and R_ax are the equatorial and axial Cu²⁺-F^- distances and β = 2.7 eV/Å is the same for all systems involving tetragonal CuF₆^4- units and an average metal-ligand distance close to 2.03 Å. This shows the existence of a common point shared by the Jahn-Teller system KZnF₃:Cu²⁺ and other non-Jahn-Teller systems such as KAlCuF₆, CuFAsF₆, K₂ZnF₄:Cu²⁺, and Ba₂ZnF₆:Cu²⁺. Although most Jahn-Teller systems display an elongated geometry, there are however many Cu²⁺ compounds with a compressed geometry but hidden by an additional orthorhombic instability. The lack of that instability in KAlCuF₆ and CuFAsF₆ is also discussed.

Local structure and excitations in systems with CuF64− units: lack of Jahn–Teller effect in the low symmetry compound Na2CuF4

The lack of a Jahn–Teller effect in Na₂CuF₄ is illustrated by the anisotropy of the Na₂ZnF₄ parent lattice.

Understanding the Structure and Ground State of the Prototype CuF2 Compound Not Due to the Jahn-Teller Effect

Insulating CuF₂ is considered a prototype compound displaying a Jahn-Teller effect (JTE) which gives rise to elongated CuF₆^4- units. By means of first-principles calculations together with an analysis of experimental data of both CuF₂ and Cu²⁺-doped ZnF₂, we demonstrate that such an idea is not correct. For ZnF₂:Cu²⁺, we find that CuF₆^4- units are compressed always along the Z local axis with a hole essentially in a 3 z²- r² antibonding orbital, in agreement with experimental EPR data that already underline the absence of a JTE. The structure of the monoclinic CuF₂ crystal also comes from compressed CuF₆^4- complexes, although hidden by an additional orthorhombic instability due to a negative force constant of b_2g and b_3g local modes. The associated distortion, similar to that involved in K₂CuF₄ and other layered Cu²⁺ compounds, is also shown to be developed for ZnF₂:Cu²⁺ upon increasing the copper concentration. The origin of this cooperative effect is discussed together with the differences between non-Jahn-Teller systems like ZnF₂:Cu²⁺ and CuF₂ and true Jahn-Teller systems like KZnF₃:Cu²⁺. From present results and those on layered compounds, the usual assumption of a JTE for explaining the properties of d⁹ ions in low-symmetry lattices can hardly be right.

Crystal, electronic, and magnetic structures of M2AgF4 (M = Na–Cs) phases as viewed from the DFT+U method

Theoretical analysis of various polymorphic forms of a series of four alkali metal fluoroargentates(ii), M₂AgF₄ (M = Na–Cs), helped to establish clear trends of crystal structures and magnetic properties across the alkali metal series.

Transition metal complexes coupled to vacancies in oxides: origin of different properties of Cr3+ in MgO bounded to a <100> or <110> Mg2+ vacancy

Despite the importance of vacancies over the properties of insulating oxides its influence on neighboring transition metal ions is far from being understood. This work is devoted to find the origin of various up to now unexplained properties of chromium bounded either to a <100> or a <110> Mg(2+) vacancy in MgO. In these model systems particular attention is paid to understand, by means of ab initio calculations, why the cubic field splitting parameter, 10Dq, is surprisingly 1600 cm(-1) higher for a <100> than for a <110> vacancy, a fact behind the suppression of the sharp (2)E → (4)A2 luminescence in the latter case. Our calculations, which reproduce the main experimental facts, prove that the average Cr(3+)-O(2-) distance is the same within 0.8% for both systems, and thus, the low 10Dq value for a <110> vacancy is shown to be due mainly to the electrostatic potential from the missing Mg(2+) ion, which increases the energy of antibonding t(2g) (∼xy, xz, yz) levels. By contrast, for a <100> Mg(2+) vacancy that potential provides a supplementary increase of the e(g) (∼x(2) - y(2), 3z(2 )- r(2)) level energy and thus of 10Dq. The existence of the (2)E → (4)A2 luminescence for Cr(3+)-doped MgO under perfect cubic symmetry or with a <100> vacancy is shown to be greatly helped by the internal electric field created by the rest of the lattice ions on the CrO6(9-) unit, whose importance is usually ignored. The present results underline the role of ab initio calculations for unveiling the subtle effects induced by a close vacancy on the properties of transition metal ions in oxides. At the same time they stress the failure of the empirical superposition model for deriving the equilibrium geometry of C4v and C2v centers in MgO:Cr(3+).