The angular overlap model extended for two-open-shell f and d electrons

We discuss the applicability of the Angular Overlap Model (AOM) to evaluate the electronic structure of lanthanide compounds, which are currently the subject of incredible interest in the field of luminescent materials. The functioning of phosphors is well established by the f–d transitions, which requires the investigation of both the ground 4fn and excited 4fn−15d1 electron configurations of the lanthanides. The computational approach to the problem is based on the effective Hamiltonian adjusted from ligand field theory, but not restricted to it. The AOM parameterization implies the chemical bonding concept. Focusing our interest on this interaction, we take the advantages offered by modern computational tools to extract AOM parameters, which ensure the transparency of the theoretical determination and convey chemical intuitiveness of the non-empirical results. The given model contributes to the understanding of lanthanides in modern phosphors with high or low site symmetry and presents a non-empirical approach using a less sophisticated computational procedure for the rather complex problem of the ligand field of both 4f and 5d open she

Ligand field density functional theory calculation of the 4f2 → 4f15d1 transitions in the quantum cutter Cs 2KYF6:Pr3+

Herein we present a Ligand Field Density Functional Theory (LFDFT) based methodology for the analysis of the 4fn → 4f n-15d1 transitions in rare earth compounds and apply it for the characterization of the 4f2 → 4f15d 1 transitions in the quantum cutter Cs2KYF 6:Pr3+ with the elpasolite structure type. The methodological advances are relevant for the analysis and prospection of materials acting as phosphors in light-emitting diodes. The positions of the zero-phonon energy corresponding to the states of the electron configurations 4f2 and 4f15d1 are calculated, where the praseodymium ion may occupy either the Cs+-, K+- or the Y3+-site, and are compared with available experimental data. The theoretical results show that the occupation of the three undistorted sites allows a quantum-cutting process. However size effects due to the difference between the ionic radii of Pr3+ and K+ as well as Cs + lead to the distortion of the K+- and the Cs +-site, which finally exclude these sites for quantum-cutting. A detailed discussion about the origin of this distortion is also described. © 2013 The Owner Societies

Ligand field density functional theory calculation of the 4f2 → 4f15d1 transitions in the quantum cutter Cs 2KYF6:Pr3+

Herein we present a Ligand Field Density Functional Theory (LFDFT) based methodology for the analysis of the 4fn → 4f n-15d1 transitions in rare earth compounds and apply it for the characterization of the 4f2 → 4f15d 1 transitions in the quantum cutter Cs2KYF 6:Pr3+ with the elpasolite structure type. The methodological advances are relevant for the analysis and prospection of materials acting as phosphors in light-emitting diodes. The positions of the zero-phonon energy corresponding to the states of the electron configurations 4f2 and 4f15d1 are calculated, where the praseodymium ion may occupy either the Cs+-, K+- or the Y3+-site, and are compared with available experimental data. The theoretical results show that the occupation of the three undistorted sites allows a quantum-cutting process. However size effects due to the difference between the ionic radii of Pr3+ and K+ as well as Cs + lead to the distortion of the K+- and the Cs +-site, which finally exclude these sites for quantum-cutting. A detailed discussion about the origin of this distortion is also described. © 2013 The Owner Societies

Tailoring the optical properties of lanthanide phosphors: prediction and characterization of the luminescence of Pr3+-doped LiYF4

We present a theoretical work detailing the electronic structure and the optical properties of (PrF₈)⁵⁻ embedded in LiYF₄, complementing the insight with data that are not available by experimental line. The local distortions due to the embedding of the lanthanide ion in the sites occupied in the periodic lattice by smaller yttrium centres, not detectable in regular X-ray analyses, are reproduced with the help of geometry optimization. Then, based on the local coordination environment, the relation structure–optical properties is constructed by Density Functional Theory computations in conjunction with the ligand field theory analyses (LFDFT) determining the [Xe]4f² → [Xe]4f¹5d¹ transitions. In previous instances we analysed rather symmetric systems, here facing the complexity of low symmetry cases, treated in the Wybourne ligand field parameterization and in the Angular Overlap Model (AOM) frame. A very important improvement at the AOM level is the consideration of the f–d mixing that brings coupling term of odd–even nature, essential for the realistic description of the asymmetric coordination centres. Furthermore, we introduce now a principle for modelling the emission intensity. The results are in agreement with available experimental findings. The relevance of the modelling has a practical face in the rational design of optimal luminescent materials needed in domestic lightening and also an academic side, revisiting with modern computational tools areas incompletely explored by the standard ligand field theories

Development and applications of the LFDFT: the non-empirical account of ligand field and the simulation of the f–d transitions by density functional theory

Ligand field density functional theory (LFDFT) is a methodology consisting of non-standard handling of DFT calculations and post-computation analysis, emulating the ligand field parameters in a non-empirical way. Recently, the procedure was extended for two-open-shell systems, with relevance for inter-shell transitions in lanthanides, of utmost importance in understanding the optical and magnetic properties of rare-earth materials. Here, we expand the model to the calculation of intensities of f → d transitions, enabling the simulation of spectral profiles. We focus on Eu²⁺-based systems: this lanthanide ion undergoes many dipole-allowed transitions from the initial 4f⁷(⁸S7/2) state to the final 4f⁶5d¹ ones, considering the free ion and doped materials. The relativistic calculations showed a good agreement with experimental data for a gaseous Eu²⁺ ion, producing reliable Slater–Condon and spin–orbit coupling parameters. The Eu²⁺ ion-doped fluorite-type lattices, CaF₂:Eu²⁺ and SrCl₂:Eu²⁺, in sites with octahedral symmetry, are studied in detail. The related Slater–Condon and spin–orbit coupling parameters from the doped materials are compared to those for the free ion, revealing small changes for the 4f shell side and relatively important shifts for those associated with the 5d shell. The ligand field scheme, in Wybourne parameterization, shows a good agreement with the phenomenological interpretation of the experiment. The non-empirical computed parameters are used to calculate the energy and intensity of the 4f⁷–4f⁶5d¹ transitions, rendering a realistic convoluted spectrum

Ligand field density functional theory for the prediction of future domestic lighting

We deal with the computational determination of the electronic structure and properties of lanthanide ions in complexes and extended structures having open-shell f and d configurations. Particularly, we present conceptual and methodological issues based on Density Functional Theory (DFT) enabling the reliable calculation and description of the f → d transitions in lanthanide doped phosphors. We consider here the optical properties of the Pr³⁺ ion embedded into various solid state fluoride host lattices, for the prospection and understanding of the so-called quantum cutting process, being important in the further quest of warm-white light source in light emitting diodes (LED). We use the conceptual formulation of the revisited ligand field (LF) theory, fully compatibilized with the quantum chemistry tools: LFDFT. We present methodological advances for the calculations of the Slater–Condon parameters, the ligand field interaction and the spin–orbit coupling constants, important in the non-empirical parameterization of the effective Hamiltonian adjusted from the ligand field theory. The model shows simple procedure using less sophisticated computational tools, which is intended to contribute to the design of modern phosphors and to help to complement the understanding of the 4fⁿ → 4fⁿ⁻¹5d¹ transitions in any lanthanide system

The theoretical account of the ligand field bonding regime and magnetic anisotropy in the DySc₂N@C₈₀ single ion magnet endohedral fullerene

Considering the DySc₂N@C₈₀ system as a prototype for Single Ion Magnets (SIMs) based on endohedral fullerenes, we present methodological advances and state-of-the art computations analysing the electronic structure and its relationship with the magnetic properties due to the Dy(III) ion. The results of the quantum chemical calculations are quantitatively decrypted in the framework of ligand field (LF) theory, extracting the full parametric sets and interpreting in heuristic key the outcome. An important result is the characterization of the magnetic anisotropy in the ground and excited states, drawing the polar maps of the state-specific magnetization functions that offer a clear visual image of the easy axes and account for the pattern of response to perturbations by the magnetic field applied from different space directions. The state-specific magnetization functions are derivatives with respect to the magnetic field, taken for a given eigenvalue of the computed spectrum. The methodology is based on the exploitation of the data from the black box of the ab initio spin–orbit (SO) calculations. The ground state is characterized by the Jz = ±15/2 quantum numbers with easy axis along the Dy–N bond. The implemented dependence on the magnetic field allowed the first-principles simulation of the magnetic properties. The computational approach to the properties of endohedral fullerenes is an important goal, helping to complement the scarcity of the experimental data on such systems, determined by the limited amount of sample

On exchange coupling and bonding in the Gd2@C80 and Gd2@C79N endohedral dimetallo-fullerenes

A series of computational experiments performed with various methods belonging to wave-function and density functional theories approaches the issue of bonding regime and exchange coupling in the title compounds. Gd₂@C₈₀ is computed with a very weak exchange coupling, the sign depending on the method, while Gd₂@C₇₉N has resulted with a strong coupling and ferromagnetic ground state, irrespective of the computational approach. The multi-configuration calculation and broken symmetry estimation are yielding closely coincident coupling constants, of about J ∼ 400 cm⁻¹. No experimental estimation exists, but the ferromagnetic ground state of Gd₂@C₇₉N is confirmed from paramagnetic resonance data. The different behaviour is due to particularities of electron accommodation in the orbital scheme. The exchange effects localised on atom lead to preference for parallel alignment of the electrons placed in the 4f and 5d lanthanide shells, determining also a ferromagnetic inter-centre coupling. The structural insight is completed with a ligand field analysis of the density functional theory results in the context of frozen density embedding. The energy decomposition analysis of bonding effects is also discussed. Finally, with the help of home-made codes (named Xatom+Xsphere), a model for the atom encapsulated in a cage is designed, the exemplified numeric experiments showing relevance for the considered endohedral metallo-fullerene issues

A ligand field theory-based methodology for the characterization of the Eu²⁺ [Xe]4f⁶5d¹ excited states in solid state compounds

The theoretical rationalization of the open-shell 4f and 5d configuration of Eu²⁺ is by far not trivial because it involves a non-standard version of ligand field theory, based on a two-shell Hamiltonian. Here we present our methodology based on ligand field theory, taking the system CsCaBr₃:Eu²⁺ as a case study with an octahedral coordination sphere of Eu²⁺. The ligand field, interelectronic and spin-orbit coupling parameters are deduced from experimental data. The assignment of the transitions to the corresponding irreducible representations of the double group was performed together with the intensity modelling resulting in an excellent match to the experimental spectra