Origin of the Exotic Blue Color of Copper-Containing Historical Pigments

The study of chemical factors that influence pigment coloring is a field of fundamental interest that is still dominated by many uncertainties. In this Article, we investigate, by means of ab initio calculations, the origin of the unusual bright blue color displayed by historical Egyptian Blue (CaCuSi₄O₁₀) and Han Blue (BaCuSi₄O₁₀) pigments that is surprisingly not found in other compounds like BaCuSi₂O₆ or CaCuO₂ containing the same CuO₄^6– chromophore. We show that the differences in hue between these systems are controlled by a large red-shift (up to 7100 cm^–1) produced by an electrostatic field created by a lattice over the CuO₄^6– chromophore from the energy of the 3<i>z</i>²-<i>r</i>² → <i>x</i>²-<i>y</i>² transition, a nonlocal phenomenon widely ignored in the realm of transition metal chemistry and strongly dependent upon the crystal structure. Along this line, we demonstrate that, although SiO₄^4– units are not involved in the chromophore itself, the introduction of sand to create CaCuSi₄O₁₀ plays a key role in obtaining the characteristic hue of the Egyptian Blue pigment. The results presented here demonstrate the opportunity for tuning the properties of a given chromophore by modifying the structure of the insulating lattice where it is located

Electrostatic Control of Orbital Ordering in Noncubic Crystals

In noncubic insulating crystals where active orbitals are not degenerate the usual models to describe orbital ordering, Kugel–Khomskii and Jahn–Teller, are, in principle, not valid. For these materials we show, by means of first-principles calculations, that a key driving force behind orbital ordering is the electrostatic potential, <i>V</i>_R(<b>r</b>), created by the rest of lattice ions over the magnetic complex where active electrons are localized. In order to illustrate the key influence of <i>V</i>_R(<b>r</b>), often ignored in a true microscopic approach, we focus on K₂CuF₄ and La₂CuO₄ as model crystals since they have very similar electronic structure but, surprisingly, contrasting orbital orderings, antiferrodistortive and ferrodistortive, respectively. Considering the parent K₂NiF₄ structure (tetragonal space group <i>I</i>4/<i>mmm</i>) of both lattices, it is shown that in K₂CuF₄ the hole in a CuF₆^4– complex is forced by the anisotropy of <i>V</i>_R(<b>r</b>) to be in a 3<i>z</i>² – <i>r</i>² orbital, while for La₂CuO₄ the shape of <i>V</i>_R(<b>r</b>) forces the hole to be placed in the planar <i>x</i>² – <i>y</i>² orbital. As a salient feature, it is found that in the parent structure the orbitals of K₂CuF₄ are ferrodistortively ordered in contrast to the Kugel–Khomskii prediction. At the same time, it is also shown that in K₂CuF₄ this state is unstable and distorts to the experimental antiferrodistortive state where, despite the significant in-plane distortion, the hole is still found to be in a mainly 3<i>z</i>² – <i>r</i>² orbital, a fact in agreement with experimental magnetic resonance data. For this compound, it is found that <i>V</i>_R(<b>r</b>) induces changes on the energy of 3d levels, which are 2 orders of magnitude higher than those due to superexchange interactions. The present results stress that in insulating transition metal compounds with electrons localized on complexes the rest of the lattice ions play a key role for understanding the electronic and structural properties that is, in many cases, overlooked. The present ideas are also shown to account for the orbital ordering in other noncubic materials, like Na₃MnF₆, NaCrF₄, or Sr₂La₂CuTi₃O₁₂, and thus open a window in the design of magnetic materials

Strain-Induced Ferromagnetic to Antiferromagnetic Crossover in d⁹‑Ion (Cu²⁺ and Ag²⁺)‑Layered Perovskites

A characteristic aspect of undoped high-temperature layered copper oxide superconductors is their strong in-plane antiferromagnetic coupling. This state is markedly different from that found in other chemically similar copper- or silver-layered fluorides, which display a ferromagnetic ground state. The latter has been connected in the literature with the presence of an orthorhombic deformation of the lattice that shifts the intermediate ligand between two metal ions to be closer to one and further from the other. This distortion is completely absent in the oxides, which are essentially tetragonal. However, no quantitative information exists about how this distortion influences the antiferromagnetic state and its relative stability with respect to the ferromagnetic state. Here, we carry out first-principles simulations to show that the fluorides in the parent tetragonal phase are also antiferromagnetic and that the antiferromagnetic-to-ferromagnetic transition is only triggered for a large enough distortion, with a typical ligand shift of 0.1 Å. Moreover, we employ a valence-bond model and second-principles simulations to show that the factor in superexchange that favors the antiferromagnetic state reduces as the ligand moves away from the symmetric metal–metal position. Importantly, we find that this distortion is sensitive to the application of an epitaxial strain which, in turn, allows controlling the difference of energy between ferromagnetic and antiferromagnetic states and thus the Curie or Néel temperatures. In fact, for compressive strains larger than 5.1%, this piezomagnetic effect makes K2CuF4 and Cs2AgF4 antiferromagnetic, making these two lattices close chemical analogs of oxide superconductors

A Practical Computational Approach to Study Molecular Instability Using the Pseudo-Jahn–Teller Effect

Vibronic coupling theory shows that the cause for spontaneous instability in systems presenting a nondegenerate ground state is the so-called pseudo-Jahn–Teller effect, and thus its study can be extremely helpful to understand the structure of many molecules. While this theory, based on the mixing of the ground and excited states with a distortion, has been long studied, there are two obscure points that we try to clarify in the present work. First, the operators involved in both the vibronic and nonvibronic parts of the force constant take only into account electron–nuclear and nuclear–nuclear interactions, apparently leaving electron–electron repulsions and the electron’s kinetic energy out of the chemical picture. Second, a fully quantitative computational appraisal of this effect has been up to now problematic. Here, we present a reformulation of the pseudo-Jahn–Teller theory that explicitly shows the contributions of all operators in the molecular Hamiltonian and allows connecting the results obtained with this model to other chemical theories relating electron distribution and geometry. Moreover, we develop a practical approach based on Hartree–Fock and density functional theory that allows quantification of the pseudo-Jahn–Teller effect. We demonstrate the usefulness of our method studying the pyramidal distortion in ammonia and its absence in borane, revealing the strong importance of the kinetic energy of the electrons in the lowest <i>a</i>₂″ orbital to trigger this instability. The present tool opens a window for exploring in detail the actual microscopic origin of structural instabilities in molecules and solids