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

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Creation of an unexpected plane of enhanced covalency in cerium(III) and berkelium(III) terpyridyl complexes

Controlling the properties of heavy element complexes, such as those containing berkelium, is challenging because relativistic effects, spin-orbit and ligand-field splitting, and complex metal-ligand bonding, all dictate the final electronic states of the molecules. While the first two of these are currently beyond experimental control, covalent M‒L interactions could theoretically be boosted through the employment of chelators with large polarizabilities that substantially shift the electron density in the molecules. This theory is tested by ligating BkIII with 4'-(4-nitrophenyl)-2,2':6',2"-terpyridine (terpy*), a ligand with a large dipole. The resultant complex, Bk(terpy*)(NO3)3(H2O)·THF, is benchmarked with its closest electrochemical analog, Ce(terpy*)(NO3)3(H2O)·THF. Here, we show that enhanced Bk‒N interactions with terpy* are observed as predicted. Unexpectedly, induced polarization by terpy* also creates a plane in the molecules wherein the M‒L bonds trans to terpy* are shorter than anticipated. Moreover, these molecules are highly anisotropic and rhombic EPR spectra for the CeIII complex are reported.

Structure and Characterization of an Americium Bis(O,O'-diethyl)dithiophosphate Complex

A facile synthesis of an americium complex with a sulfur-donor ligand has been developed, allowing characterization of americium bonding from multiple perspectives via several techniques. Reaction of ²⁴³Am with S₂P(OEt)₂^- yields the tetrakis complex [Am(S₂P(OEt)₂)₄]^- that can be crystallized as the tetraphenylarsonium salt. Structures obtained from single crystal X-ray diffraction show bond length discrepancies from the neodymium analogue consistent with the soft-donor bond enhancement common to actinides. Solid state optical spectroscopy confirms interaction of the ligand with 5f orbitals. ³¹P nuclear magnetic reflects the minor paramagnetism of Am(III). Computational investigations through CASSCF calculations, ligand-field density functional theory, and quantum chemical topological analysis allow a quantification of covalency or orbital interaction effects via total energy density and nephelauxetic parameters, both of which indicate greater covalency in the americium species than in the neodymium analogue or the americium aquo complex.

Probing a variation of the inverse-trans-influence in americium and lanthanide tribromide tris(tricyclohexylphosphine oxide) complexes

The synthesis, characterization, and theoretical analysis of meridional americium tribromide tris(tricyclohexylphosphine oxide), mer-AmBr3(OPcy3)3, has been achieved and is compared with its early lanthanide (La to Nd) analogs. The data show that homo trans ligands display significantly shorter bonds than the cis or hetero trans ligands. This is particularly pronounced in the americium compound. DFT along with multiconfigurational CASSCF calculations show that the contraction of the bonds relates qualitatively with overall covalency, i.e. americium shows the most covalent interactions compared to lanthanides. However, the involvement of the 5p and 6p shells in bonding follows a different order, namely cerium > neodymium ∼ americium. This study provides further insight into the mechanisms by which ITI operates in low-valent f-block complexes.

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.

Non-empirical calculation of X-ray magnetic circular dichroism in lanthanide compounds

Affordable calculations of X-ray magnetic circular dichroism and X-ray linear dichroism spectra of lanthanide ions purely based on structural input are difficult to achieve. Here we report on the successful application of ligand-field density-functional theory to obtain an exquisite reproduction of experimental spectra. As a testbed we use TbPc2 single-molecule magnets on a flat substrate.

Optical and nonlinear optical properties of Ln(Tp)2, where Ln = La,…,Lu and Tp = tris(pyrazolyl)borate: a DFT+TD-DFT study

DFT calculations of electronic, structural, thermodynamic properties, magnetic moment, static and dynamic polarizability and hyperpolarizability of Ln(Tp)₂ (Ln = rare earths, Tp = ring-unsubstituted tris(pyrazolyl)borate) complexes.

On The Density Functional Theory Treatment of Lanthanide Coordination Compounds: A Comparative Study in a Series of Cu-Ln (Ln = Gd, Tb, Lu) Binuclear Complexes

The nontrivial aspects of electron structure in lanthanide complexes, considering ligand field (LF) and exchange coupling effects, have been investigated by means of density functional theory (DFT) calculations, taking as a prototypic case study a series of binuclear complexes [LCu(O₂COMe)Ln(thd)₂], where L^2- = N,N'-2,2-dimethyl-propylene-di(3-methoxy-salicylidene-iminato) and Ln = Tb, Lu, and Gd. Particular attention has been devoted to the Cu-Tb complex, which shows a quasi-degenerate nonrelativistic ground state. Challenging the limits of density functional theory (DFT), we devised a practical route to obtain different convergent solutions, permuting the starting guess orbitals in a manner resembling the run of the β electron formally originating from the f⁸ configuration of the Tb(III) over seven molecular orbitals (MOs) with predominant f-type character. Although the obtained states cannot be claimed as the DFT computed split of the ⁷F multiplet, the results are yet interesting numeric experiments, relevant for the ligand field effects. We also performed broken symmetry (BS) DFT estimation of exchange coupling in the Cu-Gd system, using different settings, with Gaussian-type and plane-wave bases, finding a good match with the coupling parameter from experimental data. We also caught BS-type states for each of the mentioned series of different states emulated for the Cu-Tb complex, finding almost equal exchange coupling parameters throughout the seven LF-like configurations, the magnitude of the J parameter being comparable with those of the Cu-Gd system.

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  → 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)

It is shown that LFDFT can be used to simulate the optical spectrum of 2p core-electron excitation in compounds with 3d transition metal ions.

On the calculation of multiplet energies of three-open-shell 4f135fn6d1electron configuration by LFDFT: modeling the optical spectra of 4f core-electron excitation in actinide compounds

My presentation relates the modeling of X-ray absorption spectra of actinides, exemplified here by the study of U⁴⁺ion with configuration 4f¹³5f²6d¹.

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.

Optical contrast and cycling of bistable luminescence properties in Rb2KIn(1-x)CexF6 compounds

Irradiation cycling was performed to evaluate the ageing of the redox process observed on cerium-doped Rb2KInF6 compounds. An on-off switch of monovalent indium luminescence is observed for the lowest cerium doped material, whereas a nice colourimetric contrast between a bluish-green and orange emission is generated for the material with the highest cerium content. Photoluminescent properties combined with X-ray diffraction, chemical analysis and magnetism measurements allowed an accurate characterization of the system. A complete explanation of the optical behaviour is therefore proposed. Finally, printing tests were performed to illustrate the good functionality of the prepared materials for UV sensitivity.

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 Eu(2+)-based systems: this lanthanide ion undergoes many dipole-allowed transitions from the initial 4f(7)((8)S7/2) state to the final 4f(6)5d(1) ones, considering the free ion and doped materials. The relativistic calculations showed a good agreement with experimental data for a gaseous Eu(2+) ion, producing reliable Slater-Condon and spin-orbit coupling parameters. The Eu(2+) ion-doped fluorite-type lattices, CaF2:Eu(2+) and SrCl2:Eu(2+), 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 4f(7)-4f(6)5d(1) transitions, rendering a realistic convoluted spectrum.

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.

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 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.

Discussion on the structure stability and the luminescence switch under irradiation of a Ce-doped elpasolite compound

Ce-doped Rb2 KInF6 elpasolite has the potential for tunable luminescence due to an unusual reversible redox process between the cerium and indium cations. Coupled with a deep understanding of the luminescence properties, XRD analysis and DFT calculations are used to locate the doping elements in the host lattice. The origin explanation of the charge-transfer mechanism that causes a decrease or increase in the blue-green cerium emission in opposition to the red indium emission is discussed regarding the crystallographic structure, the connection of the metallic cations and their equilibrium valence. Still detectable after nineteen years, the optical contrast created under irradiation makes this material a good candidate as photosensor for data storage.

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.

Energy level modeling of lanthanide materials: review and uncertainty analysis

Empirical energy level models for describing lanthanide materials are reviewed and situated in a broader theoretical framework. The accuracy of determining experimental quantities through modeling is assessed.

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

Methodological advances for the treatment of electron structure and properties of the f-type ions embedded in fullerenes are presented.