Electronic Structure and Photoluminescence Properties of Eu(η9-C9H9)2.

The electronic structure of Eu2+ compounds results from a complex combination of strongly correlated electrons and relativistic effects as well as weak ligand-field interaction. There is tremendous interest in calculating the electronic structure as nowadays the Eu2+ ion is becoming more and more crucial, for instance, in lighting technologies. Recently, interest in semiempirical methods to qualitatively evaluate the electronic structure and to model the optical spectra has gained popularity, although the theoretical methods strongly rely upon empirical inputs, hindering their prediction capabilities. Besides, ab initio multireference models are computationally heavy and demand very elaborative theoretical background. Herein, application of the ligand-field density functional theory (LFDFT) method that is recently available in the Amsterdam Modeling Suite is shown: (i) to elucidate the electronic structure properties on the basis of the multiplet energy levels of Eu configurations 4f7 and 4f65d1 and (ii) to model the optical spectra quite accurately if compared to the conventional time-dependent density functional theory tool. We present a theoretical study of the molecular Eu(η9-C9H9)2 complex and its underlying photoluminescence properties with respect to the Eu 4f-5d electron transitions. We model the excitation and emission spectra with good agreement with the experiments, opening up the possibility of modeling lanthanides in complex environment like nanomaterials by means of LFDFT at much-reduced computational resources and cost.

Electronic fine structure calculation of metal complexes with three-open-shell s, d, and p configurations.

The ligand field density functional theory (LFDFT) algorithm is extended to treat the electronic structure and properties of systems with three-open-shell electron configurations, exemplified in this work by the calculation of the core and semi-core 1s, 2s, and 3s one-electron excitations in compounds containing transition metal ions. The work presents a model to non-empirically resolve the multiplet energy levels arising from the three-open-shell systems of non-equivalent ns, 3d, and 4p electrons and to calculate the oscillator strengths corresponding to the electric-dipole 3d m  â†’ ns 13d m 4p 1 transitions, with n = 1, 2, 3 and m = 0, 1, 2, …, 10 involved in the s electron excitation process. Using the concept of ligand field, the Slater-Condon integrals, the spin-orbit coupling constants, and the parameters of the ligand field potential are determined from density functional theory (DFT). Therefore, a theoretical procedure using LFDFT is established illustrating the spectroscopic details at the atomic scale that can be valuable in the analysis and characterization of the electronic spectra obtained from X-ray absorption fine structure or electron energy loss spectroscopies.

A non-empirical calculation of 2p core-electron excitation in compounds with 3d transition metal ions using ligand-field and density functional theory (LFDFT).

Methodological advents for the calculation of the multiplet energy levels arising from multiple-open-shell 2p53dn+1 electron configurations, with n = 0, 1, 2,… and 9, are presented. We use the Ligand-Field Density Functional Theory (LFDFT) program, which has been recently implemented in the Amsterdam Density Functional (ADF) program package. The methodology consists of calculating the electronic structure of a central metal ion together with its ligand coordination by means of the Density Functional Theory code. Besides, the core-hole effects are treated by incorporating many body effects and corrections via the configuration interaction algorithm within the active space of Kohn-Sham orbitals with dominant 2p and 3d characters of the transition metal ions, using an effective ligand-field Hamiltonian. The Slater-Condon integrals (F2(3d,3d), F4(3d,3d), G1(2p,3d), G3(2p,3d) and F2(2p,3d)), spin-orbit coupling constants (ζ2p and ζ3d) and parameters of the ligand-field potential (represented within the Wybourne formalism) are therefore determined giving rise to the multiplet structures of systems with 3dn and 2p53dn+1 configurations. The oscillator strengths of the electric-dipole allowed 3dn → 2p53dn+1 transitions are also calculated allowing the theoretical simulation of the absorption spectra of the 2p core-electron excitation. This methodology is applied to transition metal ions in the series Sc2+, Ti2+,…, Ni2+ and Cu2+ but also to selective compounds, namely SrTiO3 and MnF2. The comparison with available experimental data is good. Therefore, a non-empirical ligand-field treatment of the 2p53dn+1 configurations is established and available in the ADF program package illustrating the spectroscopic details of the 2p core-electron excitation that can be valuable in the further understanding and interpretation of the transition metal L2,3-edge X-ray absorption spectra.

Core electron excitations in U(4+): modelling of the nd(10)5f(2)→nd(9)5f(3) transitions with n = 3, 4 and 5 by ligand field tools and density functional theory.

Ligand field density functional theory (LFDFT) calculations have been used to model the uranium M4,5, N4,5 and O4,5-edge X-ray absorption near edge structure (XANES) in UO2, characterized by the promotion of one electron from the core and the semi-core 3d, 4d and 5d orbitals of U(4+) to the valence 5f. The model describes the procedure to resolve non-empirically the multiplet energy levels originating from the two-open-shell system with d and f electrons and to calculate the oscillator strengths corresponding to the dipole allowed d(10)f(2)→ d(9)f(3) transitions appropriate to represent the d electron excitation process. In the first step, the energy and UO2 unit-cell volume corresponding to the minimum structures are determined using the Hubbard model (DFT+U) approach. The model of the optical properties due to the uranium nd(10)5f(2)→nd(9)5f(3) transitions, with n = 3, 4 and 5, has been tackled by means of electronic structure calculations based on the ligand field concept emulating the Slater-Condon integrals, the spin-orbit coupling constants and the parameters of the ligand field potential needed by the ligand field Hamiltonian from Density Functional Theory. A deep-rooted theoretical procedure using the LFDFT approach has been established for actinide-bearing systems that can be valuable to compute targeted results, such as spectroscopic details at the electronic scale. As a case study, uranium dioxide has been considered because it is a nuclear fuel material, and both atomic and electronic structure calculations are indispensable for a deeper understanding of irradiation driven microstructural changes occurring in this material.

Photoluminescence properties of Yb(2+) ions doped in the perovskites CsCaX3 and CsSrX3 (X = Cl, Br, and I) - a comparative study.

The Yb(2+)-doped perovskite derivatives CsMX3 (M = Ca and Sr; X = Cl, Br, and I) are ideal systems for obtaining a detailed insight into the structure-luminescence relationship of divalent lanthanides. The investigation of the respective photoluminescence properties yielded two emission bands in the violet and blue spectral range for all compounds, which are assigned to the spin-allowed and spin-forbidden 5d-4f transitions, respectively. The impact on their energetic positions is dependent on both the covalency of the Yb(2+)-halide bond and the corresponding bond length in agreement with expectations. The excitation spectra provide a detailed fine structure at low temperatures and can be partly interpreted separating the 4f(13) core from the 5d electron in the excited state. The local crystal field in CsSrI3:Yb(2+) provides a special case due to the trigonal distortion induced by the crystal structure that is clearly evident in the luminescence features of Yb(2+). The structure-property relationship of several spectroscopic key quantities of Yb(2+) in this series of halides is analyzed in detail and parallels the properties of Eu(2+) ions doped in the given perovskites.

Effect of Ca(2+) codoping on the Eu(2+) luminescence properties in the Sr2Si5N8 host lattice: a theoretical approach.

Here we report a theoretical analysis of the luminescence properties of Sr2Si5N8 host lattices codoped with Ca(2+) and Eu(2+). These systems have been first synthesized by Li et al. [J. Solid State Chem., 2008, 181, 515], who have found that Ca(2+) doping provokes a red-shifting of the emission peak of Eu(2+), from 620 nm to 643 nm. However, the mechanism that drives this shift is still unclear from experimental data. Based on density functional theory and ligand field analysis, we study the structure, stability, and emission properties of Eu(2+) embedded in the (Sr1-xCax)2Si5N8 host lattice. Our results provide a full explanation of the experimental data and the methodology could constitute a valuable tool for the design of phosphors with tunable emission spectra.

Prospecting Lighting Applications with Ligand Field Tools and Density Functional Theory: A First-Principles Account of the 4f(7)-4f(6)5d(1) Luminescence of CsMgBr3:Eu(2+).

The most efficient way to provide domestic lighting nowadays is by light-emitting diodes (LEDs) technology combined with phosphors shifting the blue and UV emission toward a desirable sunlight spectrum. A route in the quest for warm-white light goes toward the discovery and tuning of the lanthanide-based phosphors, a difficult task, in experimental and technical respects. A proper theoretical approach, which is also complicated at the conceptual level and in computing efforts, is however a profitable complement, offering valuable structure-property rationale as a guideline in the search of the best materials. The Eu(2+)-based systems are the prototypes for ideal phosphors, exhibiting a wide range of visible light emission. Using the ligand field concepts in conjunction with density functional theory (DFT), conducted in nonroutine manner, we develop a nonempirical procedure to investigate the 4f(7)-4f(6)5d(1) luminescence of Eu(2+) in the environment of arbitrary ligands, applied here on the CsMgBr3:Eu(2+)-doped material. Providing a salient methodology for the extraction of the relevant ligand field and related parameters from DFT calculations and encompassing the bottleneck of handling large matrices in a model Hamiltonian based on the whole set of 33,462 states, we obtained an excellent match with the experimental spectrum, from first-principles, without any fit or adjustment. This proves that the ligand field density functional theory methodology can be used in the assessment of new materials and rational property design.

Tailoring the optical properties of lanthanide phosphors: prediction and characterization of the luminescence of Pr(3+)-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]4f(2)→ [Xe]4f(1)5d(1) 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.

Magnetic anisotropy in "scorpionate" first-row transition-metal complexes: a theoretical investigation.

In this work we have analyzed in detail the magnetic anisotropy in a series of hydrotris(pyrazolyl)borate (Tp(-)) metal complexes, namely [VTpCl](+), [CrTpCl](+), [MnTpCl](+), [FeTpCl], [CoTpCl], and [NiTpCl], and their substituted methyl and tert-butyl analogues with the goal of observing the effect of the ligand field on the magnetic properties. In the [VTpCl](+), [CrTpCl](+), [CoTpCl], and [NiTpCl] complexes, the magnetic anisotropy arises as a consequence of out-of-state spin-orbit coupling, and covalent changes induced by the substitution of hydrogen atoms on the pyrazolyl rings does not lead to drastic changes in the magnetic anisotropy. On the other hand, much larger magnetic anisotropies were predicted in complexes displaying a degenerate ground state, namely [MnTpCl](+) and [FeTpCl], due to in-state spin-orbit coupling. The anisotropy in these systems was shown to be very sensitive to perturbations, for example, chemical substitution and distortions due to the Jahn-Teller effect. We found that by substituting the hydrogen atoms in [MnTpCl](+) and [FeTpCl] by methyl and tert-butyl groups, certain covalent contributions to the magnetic anisotropy energy (MAE) could be controlled, thereby achieving higher values. Moreover, we showed that the selection of ion has important consequences for the symmetry of the ground spin-orbit term, opening the possibility of achieving zero magnetic tunneling even in non-Kramers ions. We have also shown that substitution may also contribute to a quenching of the Jahn-Teller effect, which could significantly reduce the magnetic anisotropy of the complexes studied.

Non-empirical Prediction of the Photophysical and Magnetic Properties of Systems with Open d- and f-Shells Based on Combined Ligand Field and Density Functional Theory (LFDFT).

Despite the important growth of ab initio and computational techniques, ligand field theory in molecular science or crystal field theory in condensed matter offers the most intuitive way to calculate multiplet energy levels arising from systems with open shells d and/or f electrons. Over the past decade we have developed a ligand field treatment of inorganic molecular modelling taking advantage of the dominant localization of the frontier orbitals within the metal-sphere. This feature, which is observed in any inorganic coordination compound, especially if treated by Density Functional Theory calculation, allows the determination of the electronic structure and properties with a surprising good accuracy. In ligand field theory, the theoretical concepts consider only a single atom center; and treat its interaction with the chemical environment essentially as a perturbation. Therefore success in the simple ligand field theory is no longer questionable, while the more accurate molecular orbital theory does in general over-estimate the metal-ligand covalence, thus yields wave functions that are too delocalized. Although LF theory has always been popular as a semi-empirical method when dealing with molecules of high symmetry e.g. cubic symmetry where the number of parameters needed is reasonably small (3 or 5), this is no more the case for molecules without symmetry and involving both an open d- and f-shell (# parameters ∼90). However, the combination of LF theory and Density Functional (DF) theory that we introduced twenty years ago can easily deal with complex molecules of any symmetry with two and more open shells. The accuracy of these predictions from 1(st) principles achieves quite a high accuracy (<5%) in terms of states energies. Hence, this approach is well suited to predict the magnetic and photo-physical properties arbitrary molecules and materials prior to their synthesis, which is the ultimate goal of each computational chemist. We will illustrate the performance of LFDFT for the design of phosphors that produces light similar to our sun and predict the magnetic anisotropy energy of single ion magnets.

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 4f(n) and excited 4f(n-1)5d(1) 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 shells.

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 Pr(3+) 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 4f(n) → 4f(n-1)5d(1) 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 samples.

Ligand field density functional theory calculation of the 4f2→ 4f15d1 transitions in the quantum cutter Cs2KYF6:Pr3+.

Herein we present a Ligand Field Density Functional Theory (LFDFT) based methodology for the analysis of the 4f(n)→ 4f(n-1)5d(1) transitions in rare earth compounds and apply it for the characterization of the 4f(2)→ 4f(1)5d(1) transitions in the quantum cutter Cs2KYF6:Pr(3+) 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 4f(2) and 4f(1)5d(1) are calculated, where the praseodymium ion may occupy either the Cs(+)-, K(+)- or the Y(3+)-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 Pr(3+) 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.

Jahn-Teller instability in cationic boron and carbon buckyballs B80+ and C60+: a comparative study.

This paper investigates the Jahn-Teller effect in the icosahedral cation B(80)(+) and compares the descent in symmetry with that in C(60)(+). For both cations the icosahedral ground state is a (2)H(u) state, which exhibits a H ⊗ (g ⊕ 2h) Jahn-Teller instability. A detailed construction of the potential energy surface of B(80)(+) using different DFT methods including B3LYP/6-31G(d), VWN/6-31G(d), PBE/TZP and PBE/6-31G(d) shows that, contrary to C(60)(+), which prefers D(5d) symmetry, the ground state of B(80)(+) adopts S(6) point group symmetry. A D(3d) structure is identified as a saddle point among the S(6) minima of B(80)(+). The distortion of D(3d) to S(6) in B(80)(+) is attributed to a superposition of Jahn-Teller and pseudo-Jahn-Teller effects. Imaginary modes, transforming as the g(g) representation, which are present in neutral icosahedral B(80), form the dominant symmetry breaking active modes. The pronounced difference between the JT effects in the boron and carbon buckyball cations is due to the plasticity of the boron caps. The calculated Jahn-Teller stabilization of B(80)(+) is nearly 1549 cm(-1) (PBE/TZP), which exceeds the stabilization of 596 cm(-1) computed for C(60)(+) at the same level.

General treatment of the multimode Jahn-Teller effect: study of fullerene cations.

A general model for the analysis of the Adiabatic Potential Energy Surfaces (APES) of the molecules that are subject to the multimode Jahn-Teller effect is presented. The method utilizes the information obtained by DFT calculations on a distorted stationary point on the APES. The essence of the model is to express the distortion along a model minimal energy path called Intrinsic Distortion Path (IDP), projecting the geometry of the system on the normal modes of the either high-symmetry (HS) or low symmetry (LS) nuclear configuration. This allows us to determine the significance of all of the involved normal modes along a relevant particular path of distortion, and the direct calculation of the vibronic coupling constants. The IDP analysis is illustrated by the discussion of the multimode H ⊗ (g + 2h) JT effect in fullerene cations (C(60)(+)) giving a deep insight into the origin and the mechanism of vibronic coupling in fullerene based molecules.

Treatment of the multimode Jahn-Teller problem in small aromatic radicals.

The family of the Jahn-Teller (JT) active hydrocarbon rings, C(n)H(n) (n = 5-7), was analyzed by the means of multideterminantal density functional theory (DFT) approach. The multimode problem was addressed using the intrinsic distortion path (IDP) method, in which the JT distortion is expressed as a linear combination of all totally symmetric normal modes in the low symmetry minimum energy conformation. Partitioning of the stabilization energy into the various physically meaningful terms arising from Kohn-Sham DFT has been performed to get further chemical insight into the coupling of the nuclear movements and the electron distribution.

Density functional theory for the study of the multimode Jahn-Teller effect.

The Jahn-Teller (JT) theorem states that in a molecule with a degenerate electronic state, a structural distortion must occur that lowers the symmetry, removes the degeneracy and lowers the energy. The multideterminental-DFT method performed to calculate the JT parameters for JT active molecules is described. Within the harmonic approximation the JT distortion can be analyzed as a linear combination of all totally symmetric normal modes in any of the low symmetry minimum energy conformation, which allows the intrinsic distortion path (IDP) to be calculated, exactly from the high symmetry point to the low symmetry configuration. Results obtained by the approach described here give direct insight into the coupling of electronic structure and nuclear movements.

The giant magnetic anisotropy energy of Fe+ ions in SrCl2.

We show that values of the magnetic anisotropy energy (MAE), which are about two orders of magnitude larger than the usual ones for transition metal cations in insulators (approximately 0.01-1 cm(-1)), can be found for the less common ion Fe+. In SrCl2:Fe+, the MAE is 93 cm(-1) when calculated using second-order perturbation multi-configurational calculations (CASPT2) while a similar value is found using multi-reference density functional theory (MR-DFT). This result is even larger than other recently reported giant MAEs for atoms on surfaces or magnetic clusters. The microscopic origin of this giant MAE is discussed in detail.

Theoretical study of the geometrical and electronic structures and thermochemistry of spherophanes.

A set of supramolecular cage-structures--spherophanes--was studied at the density functional B3LYP level. Full geometrical structure optimisations were made with 6-31G and 6-31G(d) basis sets followed by frequency calculations, and electronic energies were evaluated at B3LYP/6-31++G(d,p). Three different symmetries were considered: C1, Ci, and Oh. It was found that the bonds between the benzene rings are very long to allow pi-electron delocalisation between them. These spherophanes show portal openings of 2.596 A in Spher1, 4.000 A in Meth2, 3.659 A in Oxa3, and 4.412 A in Thia4. From the point of view of potential host-guest interaction studies, it should also be noted that the atoms nearest to the centre of the cavities are carbons bonded to X groups. These supramolecules seem to exhibit relatively large gap HOMO-LUMO: 2.89 eV(Spher1), 5.26 eV(Meth2), 5.73 eV(Oxa3), and 4.82 eV(Thia4). The calculated Delta H degrees (f) (298.15 K) values at B3LYP/6-31G(d) are (in kcal mol(-1)) 750.98, 229.78, -10.97, and 482.49 for Spher1, Meth2, Oxa3, and Thia4, respectively. Using homodesmotic reactions, relative to Spher1, the spherophanes Meth2, Oxa3, and Thia4 are less strained by -399.13 kcal mol(-1), -390.40 kcal mol(-1), and -411.38 kcal mol(-1), respectively. Their infrared and (13)C NMR calculated spectra are reported.