Insights into the complexity of the excited states of Eu-doped luminescent materials

Jonas J. Joos *a, Philippe F. Smet a, Luis Seijo b and Zoila Barandiarán b
aLumiLab, Department of Solid State Sciences and Center for Nano- and Biophotonics (NB-Photonics), Ghent University, 9000 Ghent, Belgium. E-mail: jonas.joos@UGent.be
bDepartamento de Química, Instituto Universitario de Ciencia de Materiales Nicolás Cabrera, and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid, Spain

Received 8th November 2019 , Accepted 17th December 2019

First published on 17th December 2019


It has always been a spectroscopist's dream to correlate a material's luminescence properties with its microscopic structure, based on reliable structure–property relationships. Electronic structure methods are promising to achieve this goal; yet they are especially challenging in the case of Eu-based materials which are known to feature exceptionally high density of excited states, large spins and severe electron correlation. In this work, state-of-the-art multiconfigurational ab initio embedded-cluster methods are applied to gain a deeper insight into the luminescence mechanisms of Eu2+ and Eu3+-doped phosphors. Regardless of the difficulties, very accurate excitation energies are achieved, reaching 68% prediction intervals of 300 cm−1, corresponding to an accuracy of 5–10 nm in the visible wavelength range. Complete configurational coordinate curves are obtained, yielding breathing mode vibrational frequencies and equilibrium bond lengths for all excited states. Moreover, electric dipole transition moments and oscillator strengths are used to calculate absorption spectra. Excellent agreement with experiment is found. The ab initio calculations give an unprecedented detailed view of the Eu2+ excited state landscape, allowing for an improved understanding of its structure, including the origin of the so-called ‘staircase structure’ and the role of ligand covalency in the ligand field and exchange splitting. It is found that more covalent host compounds feature higher exchange splittings due to an increased stabilization of high-spin states by the interaction with virtual LMCT states. It is verified that the equilibrium Eu–ligand bond length contracts upon 4f–5d excitation towards the lowest 5d submanifold and that the bond lengths are directly related to the configurational character of the electronic eigenstate. Moreover, comparing ab initio calculations with crystal field calculations proves that a decoupled model for the Eu2+ excited states is inadequate, making the use of an intermediate coupling scheme compulsory. With this approach, computational design of luminescent materials is getting within reach.


1. Introduction

Europium is the most studied luminescent activator among the lanthanide elements. It can adopt two possible oxidation states when it is incorporated into inorganic crystals or coordination compounds, Eu3+ and Eu2+, having a 4f6 and 4f7 ground state configuration, respectively. Both oxidation states are of huge relevance for different lighting and display technologies,1,2 as well as for storage phosphors or scintillators, e.g. in medical imaging.3,4 Especially in fluorescent lamps, Eu3+ has a very rich history thanks to its saturated red emission color, dominated by the 5D07F2 emission line that can be invariably found around 611–616 nm and the presence of low-lying ligand-to-metal charge-transfer (LMCT) states, allowing efficient excitation with mercury UV emission (254 nm).

For more modern applications, based on white light-emitting diodes (LEDs), Eu2+ gets into the picture thanks to its low-lying 4f65d1 configuration, enabling efficient, while yet spectrally relatively narrow, emission across the visible and near-infrared spectral range upon excitation with blue or near-UV light.1,5–9 The energy difference between the 4f7 and 4f65d1 configurations is highly dependent on the chemical environment of the Eu2+ ion. Some coarse systematic behavior is known since a long time, e.g. that this energy difference scales roughly with the covalency of the chemical bond.10–12 The empirical approach is exploited for instance in color point tuning, i.e. provoking subtle color changes upon small chemical substitutions of anions or cations in the host compound.13,14 In contrast to their simplicity and accessibility, these empirical structure–property relationships are however not sufficiently accurate to design new functional materials where the requirements are typically very strict, not only in terms of the emission color, but also in terms of the thermal stability of the luminescence properties.15 As an example, the Rec. 2020 standard for a red-emitting phosphor for display applications requires an emission maximum of exactly 630 nm.16 Deviations from this value should be small, preferably less than 5 nm, otherwise overall energy losses will strongly increase due to color filtering. This deviation corresponds to a tolerance of only 250 cm−1 on computed excited state energies, which is beyond the abilities of empirical models.15

The important optical properties of europium derive from its electronic structure, which creates a particularly complex manifold of excited states. These are numerous, highly correlated, and dense sets of states of different nature. It is then not surprising that different – often contradictory – analyses of experimental 4f7 → 4f65d spectra exist17–27 and it is not clear which model correctly grasps the nature of the electronic levels underlying the broad absorption or excitation bands. Furthermore, emission bands are often present in photoluminescence spectra that seem to be related to the presence of Eu, but do not correspond to the expected 4f7 → 4f7 or 4f65d1 → 4f7 emissions.28–32 Because no convincing systematic behavior is found in terms of its occurrence or properties (such as lifetime, thermal behavior, etc.), the origin of these so-called anomalous emissions is typically not explained, or only hypothesized, without valid experimental or theoretical justification. Also, there is a long-standing question about the mechanism causing the persistent luminescence (afterglow) in many Eu-based phosphors, where it is very difficult to probe the exact charge-carrier dynamics or the presence and role of intrinsic and extrinsic crystal defects by existing experimental techniques.33–35

The importance and complexity of the excited states of europium in solids justify the present demand for accurate computational techniques that are able to explain and predict the luminescence properties of Eu based phosphors. This requires the ability to perform reliable calculations of not only the energies of excited states of different types, but also their structural properties, i.e, their configuration coordinate diagrams in general, and transition probabilities.

We show in this work that embedded cluster multiconfigurational ab initio methods give a detailed account of the complex excited states and spectra of Eu2+ and Eu3+ in the ionic fluorides CaF2, SrF2, and BaF2, and in the more covalent sulfides CaS, SrS, and BaS. Quantitative accuracies in a range of 300 cm−1 are achieved, opening the door for designing luminescent materials based on ab initio calculations.

The development and tuning of the used methods are attributed to the efforts that, apart from empirical rules, have been made to offer computational techniques that can describe the excited states of europium. Previous efforts have provided energies at fixed structures rather than configuration coordinate diagrams. Besides, their scope is limited to ligand-field states. On the empirical side, crystal field theory is hard to apply to Eu2+ spectra due to the large density of energy levels involved, complicating the optimization of parameters from experimental spectra.19,22,27,36–39 To avoid this, crystal field parameters can be calculated within some theoretical framework, such as the exchange-charge model. This has however not led to convincing results as the 4f–4f and 4f–5d Coulomb integrals cannot be calculated in the latter model.40–42 On the first-principles side, several methods have resulted in the calculation of crystal field parameters.43–46 For Eu2+, ligand-field density functional theory (LFDFT) has been successful in reproducing Eu2+ spectra for various compounds.45,46 In this approach, spin-restricted density functional theory (DFT) Kohn–Sham orbitals are used, with average of configuration (AOC) occupations, to obtain crystal field parameters. These are subsequently used for a conventional crystal field calculation.47 This theory, besides being limited to the use of ground state geometries, is focused on studying ligand-field excited states that can be described by the parametrization of the crystal field Hamiltonian, but emissions and more complex phenomena such as charge transfers or interactions of excited states with defects are by definition out of its scope.

Multiconfigurational ab initio methods have overcome these difficulties and can study configuration coordinate diagrams of ligand-field states48 and also states of other nature, such as ligand-to-metal charge transfer,49 inter-valence charge transfer,50 dopant-to-host charge transfer,51 or compensator-to-dopant charge transfer.52

The multiconfigurational wave function methodology captures very accurately the effect of electron correlation, which is exceptionally strong for f elements.53 This, together with the use of state-of-the-art relativistic Hamiltonians and quantum mechanical embedding techniques that provide a reliable description of the interactions between an optically active cluster and the rest of the host,54 makes the calculations sufficiently accurate to achieve good qualitative and quantitative agreement with experiments.

This methodology has previously shown its value in interpreting and understanding absorption and luminescence spectra of lanthanide ions with simpler (although not simple) excited state manifolds, such as Ce3+, Pr3+, Tb3+, Tm2+ and Yb2+.48,54–58

Also, some calculations of this type exist on 4f65d1 states of Eu2+ in CaF2[thin space (1/6-em)]59 and SrAl2O4,60 which focused on the energies of the lowest states at fixed experimental or DFT optimized structures and omitted the study of configuration coordinate diagrams and detailed assignments and analyses of a large number of states.

In this paper, the multiconfigurational ab initio methodology is used to calculate the energies and wave functions, in order to identify and analyze a very large manifold of excited states of Eu2+ and Eu3+ in the Ca, Sr, and Ba series of ionic fluorides and covalent sulfides. This includes (i) the calculation of potential energy surfaces, resulting in configuration coordinate diagrams, bond lengths and breathing mode vibrational frequencies and (ii) the calculation of electric dipole transition moments and oscillator strengths, resulting in spectral profiles from first principles. This means that the methodology faces here its highest level of complexity so far.

The paper is organized as follows: in section 2 the method and details of the calculations are summarized. The results on the 4f7 and 4f65d1 configurations of Eu2+ are shown and discussed in section 3, with emphasis on their substructures, ligand field and exchange splittings, excited state bond lengths, and 4f7 → 4f65d1 spectra; in this section, also the 4f6 configuration of Eu3+ is discussed. Finally, conclusions are given in section 4.

2. Theoretical methods

The theoretical methods used in this work to study the excited states of europium in fluoride and sulfide crystals are well rooted in the ab initio quantum chemical methodology. Most of them are expressed in terms of complete (infinite) expansions that become feasible by wise, sensible, and systematic truncations. Hence they lead to systematic accuracies. We comment next on various truncations accepted in this work; some are quite standard, and others stem from the complexity of europium. Details of the calculations are given in the ESI.

At low concentrations, europium dopant ions form point defects in the solids we study, creating local (non-periodic) electronic states that induce local distortions. Hence the ab initio model potential embedded-cluster approximation (AIMP)61 should be a good alternative demanding that boundaries are set for the Eu-containing defect cluster and for the infinite embedding host. From left to right, Fig. 1 zooms in on a piece of crystal until the dopant is reached and shows three regions where the methodological efforts are dramatically increased, meaning that quantum-mechanical rigor, hence expansions, cannot be sacrificed. So, in the distant surrounding region (left) the ions can be treated classically;62 in the intermediate region (middle) quantum-mechanical Pauli antisymmetry related terms that correspond to ascribing single-reference (Hartree–Fock-like) frozen wave functions to the ions are needed. Finally, in the point-defect cluster (right), state-of-the-art molecular quantum chemical methodology must be used.


image file: c9qi01455a-f1.tif
Fig. 1 Graphical representation of the simulated system in the case of the alkaline earth fluorides and how it is divided in the (EuF8M12)2+ (M = Ca, Sr, Ba) cluster which is treated at the highest level of theory (right), a large shell represented by an embedding potential which is composed of full-ion AIMPs located at crystal lattice sites (middle) and a thick layer of point charges that terminates the system (left). The indicated distances pertain to CaF2 and are slightly larger for SrF2 and BaF2. A similar partition scheme is used for the sulfides (see the text). The interstices in the [100] directions are denoted by Int and indicated by black dots.

Europium is a genuine multivalent open-shell and heavy element. Therefore, correlated methods63,64 and spin-dependent Hamiltonians65,66 must be used to study its electronic structure. In the 90's it was recognized that the multiconfigurational space needed to tackle electron correlation is much larger than that necessary to deal with spin–orbit coupling and, on these grounds, two-step decoupling methods were proposed to address electron correlation in a first step, with a spin-free Hamiltonian, transporting the correlation corrections to the energy spectrum onto a second-step calculation over a smaller multiconfigurational space, through an effective spin–orbit Hamiltonian with reasonable approximations for other spin-dependent interactions.67,68

But, in spite of the evident benefits of such two-step decoupling, Eu poses a tremendous challenge: the number of excited states is too large, reaching 104, and they describe a dense spectrum with basically no energy gaps, which suggests that a dangerous energy-based criterion for truncation might be the only possible way towards feasibility. Yet, the two-step strategy serves the purpose in different ways as we comment next.

The total spin (S) remains a good quantum number of the wave functions in the first-step calculations since a spin-free Hamiltonian is used. This enables reasonable spin-based truncations, supported by exploratory calculations, revealing that states with lower than maximal spin occur at increasingly higher energies, meaning that their spin–orbit coupling effects will be increasingly weaker. Hence, we applied the following spin-based restrictions: only states with 2S + 1 ≥ 6 for Eu2+ and 2S + 1 ≥ 5 for Eu3+ were calculated in the first step. Therefore, only states with such spin multiplicities were coupled in the second-step spin–orbit calculations. Analyses of the multiconfigurational wave functions corroborate that the ground and many excited states of Eu can be labeled as 4f7 (Eu2+) and 4f6 (Eu3+), where 4f is the main atomic character of the molecular natural orbitals of the clusters. The 4f7 states do not interact with others describable as single excitation to higher 5d- or 6s-like shells, 4f65d1 or 4f66s1, due to the inversion center of the Eu Oh site symmetry in the fluorite and sulfide hosts (MF2 and MS, M = Ca, Sr, Ba). Thanks to this high symmetry, we could calculate all Oh-adapted electronic states of the 4fN (N = 7, 6) configurations (subject to the spin-based restrictions mentioned above) up to the final spin–orbit second-step. However, the number of Eu2+gerade states resulting from the 4f6 × 5d and 4f6 × 6s couplings is too large, even within the spin restrictions imposed. So, the results of the 4f6 manifold of Eu3+ were used to establish a reasonable 4f6-sub-shell-based truncation criterion. In particular, the energy gap above the lowest Eu3+ 4f6 term 7F (cf. Table S9) suggested restricting the number of roots to those resulting from the following couplings: 4f6(7F) × 5d, 4f6(7F) × 6s; however, this does not preclude intercalation of states of other configurations such as 4f6(5D) × 5d (cf. section 2). All we have just mentioned results in limiting the number of roots to be calculated. We focus next on truncations for multiconfigurational expansions. These are inherent in the used electron correlation methods and determine directly the accuracy and stability of the results.

The methods we use for electron correlation in the first-step, with a spin-free Hamiltonian, start by calculating a variational, multiconfigurational multistate reference63,69–72 upon which second order perturbation methods are applied.64,73–76 In the former calculations, the definition of an active orbital set over which a complete CI space is ideally built is instrumental (CI, Configuration Interaction). Typically, the open-shells and some unoccupied orbitals77–79 are meaningful and are used, such as those of the dominant Eu 4f, 5d, 6s, and 5f character, in this case. However, the complete active space generated by these meaningful active orbitals is too large and needs to be truncated. So, we performed 7- or 6-electron (for Eu2+ or Eu3+) state-average restricted active space self-consistent field calculations (SA-RASSCF) where all occupations of the 4f shell were allowed, whereas only single, double, triple, and quadruple excitation processes from the 4f to 5d, 6s, and 5f shells were permitted, compatible with the total spin and site symmetry of the Eu clusters. This truncation should be very close to the complete active space limit. Analyses of the SA-RASSCF wave functions and energy curves of the gerade excited states of Eu2+ revealed the occurrence of expected impurity-states ascribable to intraconfigurational excitation of Eu: 4f65deg1, 4f65dt2g1, and 4f66s1 configurations, but they also showed the presence of more delocalized states, so-called impurity-trapped-excitons (ITE), because the excited electron density spreads close but beyond first neighbors:80 4f6ϕITE1. These ITE states (of a1g symmetry) were found in the studied energy range for the fluoride hosts, while 4f66s1 states were obtained in the sulfides. States of different configurations show significant differences in bond lengths, as discussed in section 3.3.5. Here again, the very high density of states of Eu poses further difficulties that (only) affect some spin-sextet Eu2+ excited states that lie high in energy, in the middle of a continuum of other states. So, interactions between some impurity and ITE spin-sextet states resulted in deformations of their potential energy surfaces, including, in some cases, sharp avoided crossings. As mentioned above, the SA-RASSCF states obtained are allowed to interact in a larger space in the so-called multistate second order perturbational calculations (MS-RASPT2), which brings necessary dynamic correlation corrections after time-consuming and resource-demanding MS-RASPT2 calculations. Even though this multistate-reference method is prepared to deal with avoided crossings, and it generally does, we found irregular shapes in the potential energy surfaces in the form of small spikes and/or bumps close to the sharp avoided crossings of their parent SA-RASSCF states. The irregularities are smoothed slightly when the number of states allowed to interact was increased, but they did not disappear. Therefore, we decided to simply omit those spin-sextet states showing irregular potential energy surfaces or lying above them in the final second-step spin–orbit calculations. High energy sextets were also omitted from the spin–orbit calculation for the BaS host due to difficulties in their assignment to irreducible representations of the octahedral point group.

Detailed results can be found in the ESI: spin–orbit-free results (SA-RASSCF and MS-RASPT2) are presented in Tables S1–S6 and Fig. S1, S2, and those of the final spin–orbit calculations are given in Tables S9–S14, Fig. S3 and below. The calculations of this work have been performed using the MOLCAS programs.81 Relativistic basis sets from ref. 82 and 83 have been used to expand the molecular orbitals from the cluster.

From the comments in this section, pertaining to all the different truncations assumed in this work, it can be expected that the final spin–orbit results are robust and reveal systematic errors, increasing with energy, when confronted with direct experimental results. Accordingly, we compared theoretical and available experimental excited state energies (Fig. 2 and Table S15) and found a systematic overestimation, which is in consonance with the systematic methodological truncations discussed above. The deviation increases linearly with energy and suggests a 90% scaling of the theoretical values: EexpEsccalc = 0.9Ecalc. In the following, the results will be discussed based on these scaled energies; the corresponding raw calculated data are available in the ESI.


image file: c9qi01455a-f2.tif
Fig. 2 Comparison of calculated (this work) and experimental29,84–89 excited state energies of Eu2+ and Eu3+ in fluorides and sulfides. The dashed line represents perfect match between theory and experiment; the solid black line corresponds to Eexp = 0.9Ecalc. See Table S15 for detailed data.

Statistical analysis of the data shows a 68% prediction interval of only 300 cm−1 (40 meV). This is a figure of merit for which the computational design of luminescent materials for high-end applications, as described above, comes in reach. The achieved precision outperforms prevailing empirical rules based on inter- and extrapolation of known experimental data, e.g. to predict the 4f–5d transition energy of a lanthanide ion when this quantity is known for another ion in the same host. Typical 68% prediction intervals for empirical rules amount to 800–4000 cm−1 (100–500 meV).15

3. Results and discussion

3.1. Eu2+ excited states

The computed configuration coordinate diagrams of the Eu2+ active center in the six host crystals CaF2, SrF2, BaF2, CaS, SrS, and BaS, are shown in Fig. 3. These are potential energy curves along the breathing mode that include spin–orbit coupling effects (detailed analyses of the spin-free results can be found in the ESI). A summary of results is presented in Table 1. We will use them in the next sections, where we discuss the 4f7 and 4f65d1 manifolds of Eu2+ and the 4f6 manifold of Eu3+, as well as the systematic variations originating from cation substitution (from Ca to Sr to Ba) and by altering the covalency of the chemical bonds and the ligand coordination (from F to S).
image file: c9qi01455a-f3.tif
Fig. 3 Potential energy curves for the Eu2+ impurity in the alkaline earth fluorides CaF2, SrF2 and BaF2 and sulfides CaS, SrS and BaS. The black curves show the levels that correspond to the 4f7 configuration, while colored curves originate from the excited 4f6(5d,6s)1 configurations. Their color represents the spin-character of the eigenstates, ranging from green for pure spin-octets to red for pure spin-sextets.
Table 1 Spectroscopic constants of Eu2+-doped alkaline earth difluorides and sulfides. Experimental values for the lowest 4f–5d transition have been accurately determined from zero-phonon lines in CaF2 (ref. 88), SrF2 (ref. 85), CaS (ref. 86), and SrS (ref. 87); they are estimated from band shapes in BaF2 (ref. 85) and BaS (ref. 29), and are shown in italics. The ligand field splitting parameter εHSlfs is defined in eqn (1). Exchange splitting parameters image file: c9qi01455a-t13.tif are given for fluorides and image file: c9qi01455a-t14.tif for sulfides (eqn (2)). Energies are given in cm−1 and distances in Å
  CaF2 SrF2 BaF2 CaS SrS BaS
Eu–F/Eu–S equilibrium distances
 4f7(8S) 2.388 2.470 2.558 2.876 2.975 3.087
 4f65d1(1Γ8g) 2.373 2.451 2.535 2.849 2.945 3.037
EuF8/EuS6 breathing mode vibrational frequencies
 4f7(8S) 423 370 321 286 273 203
 4f65d1(1Γ8g) 428 370 328 283 263 196
Energy differences
Esc,fdcalc 23[thin space (1/6-em)]150 24[thin space (1/6-em)]145 25[thin space (1/6-em)]240 15[thin space (1/6-em)]580 17[thin space (1/6-em)]080 18[thin space (1/6-em)]320
Efdexp 24[thin space (1/6-em)]215 24[thin space (1/6-em)]925 25[thin space (1/6-em)]636 15[thin space (1/6-em)]995 17[thin space (1/6-em)]191 18[thin space (1/6-em)]729
Esc,fdcalcEfdexp −1065 −780 −396 −415 −110 −410
εHSlfs 18[thin space (1/6-em)]790 16[thin space (1/6-em)]220 14[thin space (1/6-em)]460 22[thin space (1/6-em)]370 20[thin space (1/6-em)]170 16[thin space (1/6-em)]070
εHSlfs,exp 16[thin space (1/6-em)]480 14[thin space (1/6-em)]150 12[thin space (1/6-em)]670
εHSlfsεHSlfs,exp 2310 2070 1790
image file: c9qi01455a-t15.tif or image file: c9qi01455a-t16.tif 4360 4410 5210 7090 7090 7820


3.2. The Eu2+ 4f7 configuration

The 4f7 configuration yields the ground state of the Eu2+ ion, more specifically the 8S term, which is composed of only one configuration where all seven f electrons have their spin parallel. In Oh symmetry, spin–orbit coupling splits this level into a quartet, Γ8u, and two Kramers doublets, Γ6u and Γ7u; however, the splitting of at most 0.2 cm−1 has no measurable influence on the optical and luminescence properties.

Eu–Ligand equilibrium distances (cf.Table 1) increase for crystals with larger alkaline earth ions. Sulfides feature larger bond lengths than the fluorides, irrespective of their smaller coordination number (6 vs. 8). In all cases, the ground state bond length is slightly smaller than the bond lengths for the higher-lying spin-sextets: about 0.002 Å and 0.006 Å for the fluorides and sulfides, respectively. Few experimental data exist on the exact geometries and bond lengths of dopants or defects, yet the Eu–F distance for CaF2:Eu2+ was found to be 2.413 Å ± 0.027 Å from the extended X-ray absorption fine structure (EXAFS),90 which agrees with the calculated value of 2.388 Å.

Overlapping with the dense 4f65d1 manifold (see section 3.3), excited terms of the 4f7 configuration can be found at energies above 25[thin space (1/6-em)]000 cm−1 (Fig. 3, in black), of which 6P, 6I and 6D are the first in energy (Table 2). Unless in some exceptional cases, such as sulfates or ternary fluorides,91 this part of the 4f7 manifold cannot be straightforwardly studied using luminescence spectroscopy due to the overlapping 4f65d1 manifold.92 An exception is when the so-called Fano antiresonances are present in the excitation spectrum; however this is rarely observed.21 A more practical approach to study higher excited states of the 4f7 configuration is by two-photon absorption spectroscopy, a technique where 4f–4f transitions are allowed.93,94 CaF2:Eu2+ and SrF2:Eu2+ happen to be the earliest test cases for this technique, proving the existence of higher-lying 4f7 levels in accordance with the iso-electronic Gd3+ ion.95,96 Later, Downer et al. carried out a meticulous study on the same crystals, resulting in the accurate determination of the levels of the 4f7 manifold of Eu2+ in these compounds up to 35[thin space (1/6-em)]000 cm−1.84 The average term energies that were experimentally found are compared with our ab initio results in Table 2. The 6G and 6F terms around 45[thin space (1/6-em)]000 cm−1 are almost degenerate, making it impossible to separate them. Table 2 also compares the energies of the individual lines that originate from the 6P term with the computed levels. From this analysis, it is clear that the multiplet splittings due to the interaction with the chemical environment and spin–orbit coupling can be reproduced by the calculation, showing deviations in the order of 100 cm−1 with a maximum of 337 cm−1.

Table 2 Average energies for the lowest terms of the 4f7 manifold of Eu2+ in CaF2 and SrF2. Experimental values obtained by two-photon absorption spectroscopy from ref. 84. All values are in cm−1
  CaF2:Eu2+ SrF2:Eu2+ BaF2:Eu2+
  E sccalc E exp Diff. E sccalc E exp Diff. E sccalc E exp Diff.
8S 0 0 0 0 0 0 0
6P 27[thin space (1/6-em)]726 27[thin space (1/6-em)]804 −78 27[thin space (1/6-em)]849 27[thin space (1/6-em)]901 −52 28[thin space (1/6-em)]057
 2Γ8u 27[thin space (1/6-em)]398 27[thin space (1/6-em)]558 −160 27[thin space (1/6-em)]519 27[thin space (1/6-em)]654 −135 27[thin space (1/6-em)]728 27[thin space (1/6-em)]727 1
 2Γ7u 27[thin space (1/6-em)]408 27[thin space (1/6-em)]564 −156 27[thin space (1/6-em)]527 27[thin space (1/6-em)]658 −132 27[thin space (1/6-em)]734 27[thin space (1/6-em)]729 5
 3Γ8u 27[thin space (1/6-em)]743 27[thin space (1/6-em)]588 155 27[thin space (1/6-em)]866 27[thin space (1/6-em)]672 194 28[thin space (1/6-em)]075 27[thin space (1/6-em)]738 337
 2Γ6u 27[thin space (1/6-em)]948 27[thin space (1/6-em)]959 −11 28[thin space (1/6-em)]075 28[thin space (1/6-em)]066 9 28[thin space (1/6-em)]285
 4Γ8u 27[thin space (1/6-em)]959 27[thin space (1/6-em)]999 −41 28[thin space (1/6-em)]085 28[thin space (1/6-em)]098 −14 28[thin space (1/6-em)]292
 3Γ7u 27[thin space (1/6-em)]978 28[thin space (1/6-em)]100 28[thin space (1/6-em)]304
6I 31[thin space (1/6-em)]631 31[thin space (1/6-em)]382 249 31[thin space (1/6-em)]767 31[thin space (1/6-em)]491 276 31[thin space (1/6-em)]981
6D 34[thin space (1/6-em)]290 34[thin space (1/6-em)]474 −184 34[thin space (1/6-em)]435 34[thin space (1/6-em)]496 −61 34[thin space (1/6-em)]667
6G + 6F 45[thin space (1/6-em)]249 45[thin space (1/6-em)]437 45[thin space (1/6-em)]693
6H 50[thin space (1/6-em)]602 50[thin space (1/6-em)]790 51[thin space (1/6-em)]043


3.3. The Eu2+ 4f65d1 configuration

4fN−15d1 configurations of lanthanide ions have in general a very complicated structure due to the large number of states (e.g. 30[thin space (1/6-em)]030 in Eu2+). They are more difficult to study than 4fN configurations because 4f–5d spectra feature relatively broad bands, whereas 4f–4f spectra show atom-like sharp lines. Parametrized (semi-)empirical approaches are hence impossible or at best impractical to study the details of these configurations.97 Yet, especially in the case of the Eu2+ ion, a good understanding of the 4f65d1 configuration is essential because many modern technologies rely on it.

It is empirically known that the onset of the Eu2+ 4f65d1 manifold with respect to the 4f7 ground state, and hence the emission color of the Eu2+ luminescence, depends strongly on the chemical nature of the ligands. Ligands that form ionic bonds, such as fluorides, typically give rise to a relatively high-lying 4f65d1 manifold corresponding to violet or near-UV emission. Ligands that form more covalent bonds redshift the 4f65d1 manifold, allowing a color tuning across the visible spectral range. E.g. the binary sulfides CaS:Eu2+ and SrS:Eu2+ give rise to a red and orange emission, respectively,87 which in turn illustrates that cations also play a role. However, knowledge of the systematic behavior of Eu2+ luminescence is only qualitative, which limits its practical use. This is specially so when industry requirements are very strict.1,2,98,99

In this section we aim at providing a quantitative understanding of the 4f65d1 configuration of Eu2+. Fig. 3 shows the calculated potential energy surfaces for the Eu2+ 4f65d1 states of the studied materials up to around 50[thin space (1/6-em)]000 cm−1. The host effect on the 4f65d1 manifold onset is presented in Table 1 with the zero-phonon line energies of the lowest 4f65d1 state: the calculated Esc,fdcalc and the experimental Efdexp. It is clear that the calculated host effect is qualitatively as expected, i.e. a red shift from fluorides to sulfides, which is attributed to the increase in the covalence of the chemical bond.100 But it is also quantitatively correct, with differences between the computed and experimental zero-phonon lines of the order of 1000 cm−1 or less, which evidences the quality of the computed wave functions and their ability to reproduce the host effects.

3.3.1. Impurity trapped excitons. Before the submanifolds of 4f65dt2g1, 4f65deg1 and high- or low-spin characters are discussed, the double-well structure found in the higher energy ranges of the fluoride hosts is examined. Similar electronic structures have been found earlier in other lanthanide and actinide doped materials80,101 and they result from the interaction between levels with a dominant 4f65d1 configurational character and impurity-trapped-exciton (ITE) levels. The latter have a dominant 4f6ϕITE1 configurational character, where the molecular orbital ϕITE describes an electron delocalized towards the nearby interstitial sites of the fluorite structure, almost ionized but trapped outside the EuF6 moiety. This results in ITE potential energy curves having very small Eu–F equilibrium distances as compared with regular Eu2+ states, only slightly larger than that in Eu3+ 4f6 states. The interaction between 4f65d1 and ITE states of equal symmetry and the avoided crossing according to the Wigner–Von Neumann rule explains the double well.
3.3.2. Structure of the 4f65d1 manifold. The structure of the Eu2+ 4f65d1 manifold in the six doped materials under study results from four crowded submanifolds. The lowest two show clear configurational and spin characters whereas the highest two overlap and interact significantly. We will discuss this for CaS for the sake of simplicity; similar descriptions hold for the other hosts, with obvious 5dt2g/5deg changes in the fluorides.

In CaS:Eu2+, the lowest two submanifolds have a common configurational character 4f6(7F)5dt2g1 and, associated with it, common local structure parameters (bond lengths and vibrational frequencies; see section 3.3.5). These submanifolds are made of all states resulting from the coupling between the well shielded 4f6 inner electronic shell in all its states derived from the 7F atomic term (strongly split by spin–orbit coupling and weakly split by the crystal field) and the outer 5dt2g electron. The first submanifold includes the states with high-spin coupling (HS, 2S + 1 = 8) and the second the higher energy states with low-spin coupling (LS, 2S + 1 = 6), shown respectively in green and red in Fig. 3. The spin–orbit coupling between the two submanifolds turns out to be very small.

The coupling between 4f6(7F) and the ligand-field excited 5deg electron leads, initially, to two similar sets of separated HS and LS states that start at around 40[thin space (1/6-em)]000 cm−1 above the ground state. But the internal excitation within the 4f6 shell into 4f6(5D) is similar in energy to the 5dt2g–5deg ligand-field splitting and, as a result, LS states of the 4f6(5D)5dt2g1 character lie in the same energy window as HS states of the 4f6(7F)5deg1 character, and their mixing is strong. All of this results in a third submanifold of states with strong HS–LS mixing and strong 4f6(5D)5dt2g1–4f6(7F)5deg1 configurational mixing and, associated with the latter, more complex bond lengths and vibrational frequencies (see section 3.3.5). The fourth submanifold has a more clear LS character.

This discussion also holds for SrS. For BaS and the fluorides, it holds as well, but the absence of high energy spin-sextets in the spin–orbit calculations (section 2) prevents the spin and configurational mixing of the third submanifold, hence the dominant green color in their high energy curves. However, as we will see below, the impact of these sextets in the absorption spectrum is negligible.

According to the crowded submanifolds resulting from combining main spin and configurational characters, namely HS and LS, 4f6(7F)5deg1 and 4f6(7F)5dt2g1, it is possible and convenient to introduce a few experimentally meaningful parameters. We will consider HS or LS states of those whose spin–orbit wave function shows a ≥90% spin octet or sextet character, respectively.

3.3.3. Ligand field splitting. Let us first define a high-spin ligand field splitting parameter εHSlfs, as the positive energy difference between the averages of the equilibrium energies of the HS 4f6(7F)5deg1 and 4f6(7F)5dt2g1 states:
 
image file: c9qi01455a-t1.tif(1)

This parameter reveals the ligand field strength on the 5d shell, but it should not be identified with traditional crystal field theory parameters such as 10 Dq, which is the splitting of one-electron levels, nor is it a configurational average parameter. Furthermore, we make averages only at HS levels because they have nonzero transition probability from the 4f7 ground state (see below). The computed values are given in Table 1.

Experimentally, the ligand field splitting as defined by eqn (1) can be approximated by the difference of the average values of both excitation bands. This is denoted as εHSlfs,exp in Table 1. This approach is very approximate because spectral shapes change as a function of temperature or doping concentration; therefore the empirical values are written in italic. Furthermore, this approach is not applicable to the sulfides because of low-lying excited states of the host compound (see below). On comparing the experimental values with the computed ligand field splittings, it is clear that a constant offset of approximately 2000 cm−1 is found between experimental and computed parameters. Regardless of this offset, which is believed to be the cumulative effect of systematic errors in the calculated energies and the difficulty to empirically obtain this parameter, the systematic trend is correctly reproduced.

From the εHSlfs values in Table 1, a drop can be observed in the increasing size of the alkaline earth cation, hence with the Eu–ligand bond length, both in the difluorides and the sulfides. This corresponds to the well-known qualitative trend.102 Quantitatively, εHSlfs drops from CaF2 to SrF2 (14%) to BaF2(11%) and from CaS to SrS (10%) to BaS (20%). It is lower in the difluorides than in the sulfides, in spite of the shorter Eu–ligand distances (16% lower in CaF2 than in CaS, 20% lower in SrF2 than in SrS, and 10% lower in BaF2 than in BaS), and results from the balance of several factors: Eu–ligand distance, coordination number, ligand oxidation state, and bond covalency.

3.3.4. Exchange splitting. It is also interesting to define exchange splitting parameters image file: c9qi01455a-t2.tif (for the fluorides) and image file: c9qi01455a-t3.tif (for the sulfides), as the differences between the averages of the equilibrium energies of the LS and HS 4f6(7F)5deg states, and the LS and HS 4f6(7F)5dt2g states, respectively:
 
image file: c9qi01455a-t4.tif(2)
with γ = eg, t2g. These parameters reveal the strength of the 4f–5deg and 4f–5dt2g interactions. Only states with high spin-purity (≥90%) are used in eqn (2). The definition of εγexch relies on S being a good (at least by approximation) quantum number. If this condition is not fulfilled, e.g. for the higher submanifolds of the 4f65d1 configuration of Eu2+, or in the 4fN−15d1 configurations of heavier lanthanides such as Tm2+ (ref. 58) or Yb2+,48 this parameter loses its meaning. The numerical values for Eu2+ are shown in Table 1.

The 4f–5d exchange splittings only slightly increase upon enlarging the unit cell, but they experience a significant increase from the difluorides (around 4500 cm−1) to the sulfides (around 7500 cm−1). This is opposite to the experimentally shown decrease of the 4f–5d exchange splitting with the covalency of the host in the 4f75d1 configuration of Tb3+.103,104

The opposite effect of increasing covalency on the exchange splitting of Eu2+ and Tb3+, hence of 4f65d1 and 4f75d1 configurations, can be understood by analyzing the role of virtual ligand-to-metal charge transfer (LMCT) excitation or valence bond (VB) configurations, which are more important in more covalent bonds. This mechanism is displayed in Fig. 4. In effect, in Eu2+-doped sulfides for instance, S 3p → Eu 4f virtual excitation creates LMCT configurations of the type Eu+(4f75d1) × S(3p5). In reality, the S-3p hole will distribute among the ligands according to the molecular orbital; hence the notation 4f75d1[L with combining low line] is used to denote the virtual LMCT configuration, where [L with combining low line] denotes the hole in a ligand molecular orbital. A state of the 4fN−15d1 configuration with total spin S will experience stabilization from the virtual LMCT states with the same total spin. States with different spins are hence affected differently by the virtual LMCT configuration. This results in the exchange splitting being effectively influenced by the location (related to the covalency of the ligand) and the nature of the LMCT states (which S values appear, related to N). In the following, this effect is elaborated for Eu2+ and Tb3+.


image file: c9qi01455a-f4.tif
Fig. 4 Schematic representation of how the configuration interaction (CI) with virtual ligand-to-metal charge transfer (LMCT) states increases or decreases the exchange splitting of the 4fN−15d1 configurations of Eu2+ (N = 7) and Tb3+ (N = 8), respectively. L/[L with combining low line] denote a ligand shell which is full/contains one hole.

In the case of Eu2+, the values of the total spin S of the virtual LMCT states result from the coupling S4f75d1 × SL, which can take the values 4, 3 (lower spins are not considered because of their higher energy and smaller interaction strength) and 1/2, respectively. The coupling image file: c9qi01455a-t5.tif produces image file: c9qi01455a-t6.tif, and the coupling image file: c9qi01455a-t7.tif produces image file: c9qi01455a-t8.tif. The splitting of the 4f75d1[L with combining low line] configuration according to S4f75d1 and, subsequently, S is shown in Fig. 4. The LMCT configuration results in a larger number of image file: c9qi01455a-t9.tif virtual excitation processes than image file: c9qi01455a-t10.tif ones, providing extra stabilization to the HS octet states (S = 7/2) with respect to the LS sextet states (S = 5/2). The virtual LMCT configuration appears at lower energy for more covalent ligands, and consequently its effect on the LS-HS energy difference is larger in sulfides than in fluorides. Eu2+ hence shows a larger exchange splitting in sulfides than in fluorides.

In the case of Tb3+, the opposite trend is found. Here, a 4f85d1[L with combining low line] configuration is formed following a S 3p → Tb 4f virtual excitation. Spin coupling according to S4f85d1 × SL leads to image file: c9qi01455a-t11.tif, which produces S = 4, 3, and image file: c9qi01455a-t12.tif, which produces S = 3, 2 (see Fig. 4). Then, there is a larger number of S = 3 virtual excitation processes than S = 4 ones, which results in extra stabilization of the LS (S = 3) states with respect to the HS (S = 4) states and a corresponding lowering of the exchange splitting. This effect, of course, is larger for more covalent ligands (see Fig. 4).

3.3.5. Excited state bond lengths. It is interesting to have a close look at how the bond length changes across the manifold of excited states and the insight it provides on their nature. Equilibrium bond lengths and energies obtained by fitting a third order polynomial to the potential energy curves are displayed in Fig. 5 for CaS:Eu2+ (see also Table 1 and ESI for more data).
image file: c9qi01455a-f5.tif
Fig. 5 Equilibrium bond lengths for all potential energy curves of CaS:Eu2+. This graph indicates the decrease (increase) in the bond length for 4f65dt2g1 (4f65deg1) levels with respect to the 4f7 manifold. 4f7 levels are shown in black crosses. 4f6(5d,6s)1 is shown in colored crosses that depend on its 2S + 1 character at dEu–S = 2.85: red(6)–yellow(mixed)–green(8) (see also Fig. 3).

It is observed that the levels of the lowest 4f65d1 group, i.e. 4f6(7F)5dt2g1 in the sulfides and 4f6(7F)5deg1 in the fluorides, where the respective most stable 5d molecular orbital shell is occupied, have a shorter bond length than the 4f7 ground state. When the levels have the most unstable 5d shell occupied, their bond lengths are longer than those in the 4f7 ground state, e.g. 4f6(7F)5deg1 in sulfides and 4f6(7F)5dt2g1 in fluorides.

This result is in contrast to many intuitively constructed configurational coordinate models that can be found in the literature, where all levels of the Eu2+ 4f65d1 manifold are almost invariably drawn at longer equilibrium distances than the 4f7 levels, inspired by the fact that 5d orbitals have larger orbital radii than 4f orbitals and reach further. There is a misconception behind this which lies in the implicit assumption that 4f electrons play an important role in the Eu–ligand bond, hence determining the Eu–ligand bond length.

A detailed constrained space orbital variation (CSOV) quantum chemical analysis105 has shown that the bond length between an f-element ion in a 4fN configuration and ligands is realized by the interaction between the 5p6 shell and the ligand's valence electrons. When the ion is in a 4fN−15d configuration, additional covalent interactions appear (mostly electron transfer from the ligand to the inner 4f hole) that shorten the bond length; the shortening is enhanced by the 5d ligand field stabilization in 4fN−15dlowest1 configurations and opposed in 4fN−15dhighest1 configurations. The magnitudes of these effects result in a systematic bond length trend: 4fN−15dlowest1 < 4fN < 4fN−15dhighest1, the differences being smaller than those between 4f and 5d orbital radii.105 This observation was found in Ce3+, Pr3+, Sm2+, Tb3+, Tm2+, Yb3+, and Yb2+ as dopants in ionic solids and regarded as generally valid.54 Here we confirm the observation for Eu2+ in the difluorides, and also in the more covalent sulfides.

The prediction of a bond length shortening upon the lowest 4f → 5d excitation was shown to imply its redshift under pressure,106 which opened the door for its indirect experimental validation. This effect was in fact demonstrated by Valiente et al.107 from high-pressure spectroscopic experiments on Cs2NaLuCl6:Ce3+. Multiple similar experiments have been reported that show the same effect in Eu2+-doped MF2[thin space (1/6-em)]108,109 and CaS110 hosts, hence supporting our findings.

Fig. 5 shows that a pure t2g configurational character for the 5d electron brings about a 0.029 Å bond length shortening with respect to the ground state in CaS:Eu2+ and a pure eg character implies a 0.006 Å bond length elongation. However, above approximately 40[thin space (1/6-em)]000 cm−1 the pure configurational character is lost and the mixed t2g–eg character (and the 4f6(7F)–4f6(5D) character) in the eigenstates is translated into intermediate bond lengths. It is clear that the 5dt2g or 5deg characters of the wave function determine the excited state bond lengths and that the knowledge of the bond length evolution, e.g. from high-pressure spectroscopy, can be used to extract qualitative information about the nature of the wave function.

3.4. Eu2+ 4f7 → 4f65d1 spectra

Along with the calculation of the eigenenergies and wave functions of the studied systems, probabilities for electric dipole transitions are obtained in the form of oscillator strengths (Tables S9–S14). This enables a direct calculation of absorption or excitation spectra for the 4f7 → 4f65d1 transitions which can be compared to experimental results from luminescence and UV-VIS spectroscopy. The computed spectra are shown in Fig. 6 and 7 for the fluorides and sulfides, respectively, along with the available experimental spectra.23,28,29,85–88,111,112
image file: c9qi01455a-f6.tif
Fig. 6 Top: Computed 4f7 → 4f65d1 absorption spectrum for Eu2+ in the alkaline earth fluorides rendered with broadening parameters of 5, 100 and 300 cm−1 and scaled for improved visibility. Bottom: Experimental absorption (or excitation, indicated by ‘X’) spectra for the same transitions adapted from ref. 88 and 111 (CaF2), ref. 28 and 85 (SrF2) and ref. 28 and 85 (BaF2). The temperatures at which the experimental spectra were obtained are indicated.

image file: c9qi01455a-f7.tif
Fig. 7 Top: Computed 4f7 → 4f65d1 absorption spectrum for Eu2+ in the alkaline earth sulfides rendered with broadening parameters of 5, 100 and 300 cm−1. Bottom: Experimental excitation spectra for the same transitions adapted from ref. 86 and 87 (CaS), ref. 23 and 87 (SrS) and ref. 29 (BaS, here the anomalous emission was monitored). The host absorption is also added (dashed lines) to distinct between intrinsic and Eu2+ caused spectral features, adapted from ref. 112. The temperatures at which the experimental spectra were obtained are indicated.
3.4.1. Spectral assignments. The computed and experimental spectra are very similar, in terms of both energy ranges and the spectral shape (Fig. 6 and 7). Two broad bands are found in all cases. The first band originates from the spin-allowed transitions from the 4f7(8S) ground state to the HS 4f65dlowest1 submanifold. The second band originates from excitation towards the configurationally mixed third and fourth submanifolds. Regardless of the configurational mixing, the good agreement with experiment for the fluorides (where the contributions of LS 4f65dhighest1 was not accounted for; see section 2 and Fig. 3) shows that the second band is dominated by the HS contributions.

Excitation from the 4f7(8S) ground state towards the HS 4f65dlowest1 submanifold is spin-forbidden, yielding a gap between the two bands in the spectrum that is larger than the gap in the associated energy level schemes (Fig. 3). Even though they are spectroscopically invisible, the presence of the LS levels is important to understand the behavior of Eu2+ based luminescent materials. The LS levels provide an efficient nonradiative relaxation channel, precluding any radiative decay other than that from the lowest level of the 4f65d1 manifold.

The gap between the LS 4f65dlowest1 and HS 4f65dhighest1 submanifolds becomes smaller when going from the Ca-compounds to the Sr-compounds and almost disappears for the Ba-compounds (see Fig. 3). Therefore, spin–orbit interactions between both submanifolds become larger and the amount of spin-mixing is increased, with the average HS content ranging from 0.5% for CaF2 to 2% for BaS for the LS 4f65dlowest1 submanifold. This leads to so-called spin-enabled transitions towards these states, which feature a small but observable transition intensity (see Fig. 6 and 7). Similar spin-enabled transitions were assigned by Suta and Wickleder27 for an extraordinarily well-resolved low-temperature absorption spectrum of SrCl2:Eu2+ single crystals by Karbowiak and Rudowicz.97

Interpretation of the spectra of the Eu2+ doped sulfides poses an additional difficulty with respect to the fluorides. Due to their small band gaps, the sulfide hosts already absorb at energies where absorption or photoluminescence spectra are typically measured (see dashed lines in Fig. 7). As a result, the second band in the experimental absorption and excitation spectra of the Eu2+-doped sulfides is to be regarded as the added effect of Eu-centered and host-related excitation processes.

3.4.2. Origin of the fine structure. When measured at room temperature, Eu2+ absorption or excitation spectra look broad and featureless. Only when sufficiently cooled, some fine structure might be resolved. This effect is simulated in the calculated spectra by using a variable widening factor in Fig. 6 and 7. Experimentally, a well-resolved fine structure is found for the fluorides, while this is much less the case for the sulfides (e.g. the excitation spectra of CaF2 and CaS were both measured at 10 K). This can be attributed to the larger difference between the equilibrium bond lengths, dEu–X,e(4f65d1)–dEu–X,e(4f7(8S)), in the case of the sulfides (e.g. 0.027 Å for CaS:Eu2+), compared to the fluorides (e.g. 0.010 Å for CaF2:Eu2+).

The electronic origin of this fine structure has been the topic of a long-standing debate in the literature, which has been largely confined to empirical and crystal-field theoretical approaches.17–26 We address now the origin of the fine structure with the help of crystal field theory calculations performed (with an in-house written Python code113) in the light of the ab initio electronic structure summarized in Fig. 3.

It is common to explain the fine structure in the lowest part of the Eu2+ excitation or absorption spectra with the decoupled scheme, a model described by Freiser, Methfessel and Holtzberg in 1968.17 According to it, in the first place, the lowest 4f65d1 states can be obtained from the multiplets of the 4f6(7F) core, reminiscent of the lowest 5000 cm−1 of the Dieke diagram for Eu3+, and the lowest crystal-field level of the single 5d electron, which acquires a well-defined t2g character in the sulfides (eg in the difluorides; for simplicity, the discussion is continued for sulfides). This point of view is supported by the multiconfigurational ab initio calculations, as we discussed in section 3.3.2. In the second place, the decoupled scheme assumes that the coupling between the 4f6(7F) core and the 5dt2g electron is of a mean-field type, i.e. that it does not lead to relevant splittings. Then, since the spin–orbit coupling is very small in the 5dt2g shell but strong within the 4f6(7F) core, and the 4f electrons are shielded from ligand field effects, the fine structure is entirely due to the 4f6(7F) internal spin–orbit coupling, i.e. the well-known 7FJ = 0–6 seven multiplets of Eu3+ (see the left panel of Fig. 8).


image file: c9qi01455a-f8.tif
Fig. 8 Crystal field calculation for the low energy part of the 4f65d1 configuration in an octahedral field, obtained in the 490 dimensional |4f6(7F)5d1〉 basis. The transition from the decoupled scheme (including only 4f spin–orbit coupling as an additional interaction) to a scheme with only the 4f–5d Coulomb interaction is shown. The colors of the curves represent the spin-characters of the eigenstates, ranging from green for pure spin-octets to red for pure spin-sextets. The shaded area indicates the energy range where configurational mixing can be expected (see section 3.3). The vertical bands, denoted by ‘F’ and ‘S’, denote the parameter ratio where the crystal field calculation resembles best the ab initio calculations for the fluorides and sulfides, respectively.

The decoupled scheme is usually justified by the occurrence of a so-called staircase structure that can be resolved in certain low temperature Eu2+ spectra17,20,21,23–26 and the seven most prominent maxima in the absorption or excitation spectra are labeled as J = 0–6. However, as we discussed above, the staircase is also found in the ab initio calculations, although the couplings between the 4f6(7F) core and the 5dt2g electron are included and nothing indicates that they are small.

In order to investigate the strength of the 4f6(7F) × 5dt2g coupling, hence the validity of the decoupled scheme, the Coulomb interaction between the 4f and 5d electrons can be taken into account on the crystal field theory level by tuning the value of the Slater–Condon integrals Fk(4f,5d) (k = 2, 4) and Gk(4f,5d) (k = 1, 3, 5). This was firstly done by Yanase and Kasuya in 1970 in order to study the optical and magnetic properties of EuF2 and subsequently studied in a more general approach by Weakliem in 1972 on a set of 4f6(7F)5deg levels.18,19 Here, we perform a similar simulation on the entire 4f6(7F)5d1 manifold and compare it to our ab initio excited state landscape. Fig. 8 shows how the eigenvalues of an intermediate coupling calculation for the 4f6(7F)5d1 manifold evolve with the coupling parameter G1(4f,5d)/ζ4f, from the decoupled scheme, where the states are labeled as 4f6(7FJ)5dγ1 (J = 0–6, γ = t2g, eg), towards the other limiting case, where only the term splitting due to the f–d Coulomb interaction and 5d crystal field are accounted for (right panel). Qualitative inspection of this diagram shows that a decoupled scheme can never provide a good representation of reality because it shows no overall exchange splitting, which is clearly present in the ab initio excited state landscapes (Fig. 3). The total angular momentum of the 4f6 subshell, J, is hence not a good quantum number, not even approximately in the cases of alkaline earth fluorides or sulfides. The 4f–5d coupling strengths, as measured with the G1(4f,5d)/ζ4f ratios, which show the best qualitative correspondence to the electronic structure of the Eu2+ doped fluorides and sulfides, are indicated in Fig. 8.

Rarely, the electronic structure of the 4f65d1 configuration is even more simplified by solely accounting for the 5d crystal field splitting, leading to a maximum of five levels for the lowest symmetries.42 It is then argued that the remaining splittings are negligible with respect to the 5d crystal field splitting and lead at most to a broadening of the spectral features. The above analysis shows however that this is a too severe simplification, overlooking the strong term- and multiplet splitting of the 4f6 subshell, the 4f–5d coupling and the configurational mixing of the 5d wavefunctions.

In summary, the simplified models have been and are still very useful to aid in the qualitative interpretation of Eu2+ spectra, even though they fall short for quantitative analysis. If information beyond the low-energy tail of the 4f7 → 4f65d1 absorption or excitation spectra is however required, also the qualitative similarity to reality will cease. From the experimental point of view, the limited window where these approximations are reasonable, together with the extremely high density of energy levels, prohibits the reliable determination of radial integrals such as crystal field parameters, Slater–Condon integrals or spin–orbit constants. Here, ab initio calculations are compulsory.

3.5. The Eu3+ 4f6 configuration

Trivalent europium, Eu3+, is a lanthanide ion with a rich history in scientific and technological applications. It features a characteristic red or orange emission, underlying its successful application in fluorescent lighting.114 Furthermore, the low J-values of the multiplets that take part in the luminescent transitions make this ion suited as a symmetry probe.115–119 Notwithstanding the success of Eu3+, a satisfactory analysis of its spectrum is not always possible, due to too small crystal field splittings, which are especially troublesome in the case of high coordination numbers, low transition strength, or the need for polarized spectra to distinguish between different point symmetries. In the last case, single crystals are required, which are in practice not always accessible. These shortcomings indicate that the empirical approach would serve well with the support of ab initio calculations.

Here, the spin-septet and spin-quintet states of Eu3+ were calculated upon doping it into the alkaline fluorides and sulfides. As an example, the resulting curves after spin–orbit splitting for CaF2:Eu3+ are shown in Fig. 9. In all cases, the Eu3+ ion is substituted on a divalent alkaline earth site, requiring the compensation of a singly positive charge. In these calculations, it is assumed that the compensation is non-local, maintaining the high Oh symmetry. Magnetic resonance studies on CaF2, doped with Eu3+ or other trivalent lanthanides, showed that this situation can be achieved by a rapid quenching of the crystal during the high-temperature synthesis.120–123 In the sulfides, Eu3+ is more easily reduced to Eu2+ and Eu3+ typically appears along with Eu2+, or not at all. Magnetic resonance studies on Ce3+ in the sulfides showed that approximately half of the ions are in a high-symmetry site (Oh), while the others show a lower site symmetry due to local charge compensation.124,125


image file: c9qi01455a-f9.tif
Fig. 9 Potential energy curves for the 4f6 configuration of the Eu3+ impurity in CaF2. (a) Result upon inclusion of spin–orbit coupling. (b) Resulting minimum energies of the spin-free calculation, colored according to their dominant 2S+1L character (see Fig. S2 for the corresponding curves).

Fig. 9 illustrates that the well-known structure of the 4f6 configuration is well-reproduced, showing the 6FJ (J = 0,…,6) multiplets at low energy, followed by a gap of approximately 12[thin space (1/6-em)]000 cm−1 after which the well-separated 5D0, 5D1, 5D2 and 5D3 multiplets are found. In this low-energy region J-mixing is limited, justifying the use of the atomic quantum numbers L, S and J. At higher energies, a dense set of levels is found, originating from 5D4, 5L, 5G and higher-excited terms. In this region, J-mixing is considerable, and the double group irrep labels are the only valid labels. Even though some gaps of 1000 cm−1 or more are found in the excited state landscape, no multiplet label can be attached to any set of levels (see also the ESI). As an insight into the spin-free result, the term splitting is also displayed in Fig. 9.

In the case of CaF2, a detailed account of the energy levels of cubic Eu3+ impurities has been provided by Gastev et al.,89 elegantly exploiting the difference in lifetimes of the 5D0 and 5D1 emitting levels to separate both emissions, enabling a comparison between the calculated and experimental energies (see Table S15).

It is clear that, provided that the same scaling of computed energies, by 90%, is applied, a satisfactory correspondence between the experimental and computed levels is found, with deviations of the order of 100 cm−1 (see also red triangles in Fig. 2).

Table 3 summarizes the main results of the Eu3+ calculations in the different hosts, where the energies were averaged over the Stark components of the 7F0–6 and 5D0–3 multiplets. It is confirmed that these energies are insensitive to the chemical environment. Yet, an increase of 50–100 cm−1 of the 5D0 level is found when going from the Ca to Sr and Ba compounds, and a depression of the same order of magnitude is found when going from fluorides to sulfides. Translated to wavelengths, this corresponds to a shift of at most a few nanometers. Low temperatures and accurately (wavelength) calibrated detectors are hence indispensable to acquire spectroscopic data on the 4f6 configuration.

Table 3 Computed equilibrium Eu–F and Eu–S distances (in Å), ground state breathing mode vibrational frequencies (in cm−1), and average scaled energies for the lowest multiplets (in cm−1) of Eu3+ in MF2 and MS (M = Ca, Sr, Ba). X = F, S
  CaF2 SrF2 BaF2 CaS SrS BaS
d Eu–X,e 2.261 2.313 2.363 2.729 2.800 2.829
ν e 495 445 402 307 286 248
4f6(7FJ)
J = 0 0 0 0 0 0 0
1 311 323 327 335 336 338
2 940 949 954 957 961 963
3 1877 1850 1844 1831 1826 1825
4 2887 2849 2836 2803 2797 2796
5 3978 3932 3909 3839 3839 3839
6 5120 5068 5047 4991 4980 4976
4f6(5DJ)
J = 0 18[thin space (1/6-em)]021 18[thin space (1/6-em)]025 18[thin space (1/6-em)]075 17[thin space (1/6-em)]904 17[thin space (1/6-em)]976 18[thin space (1/6-em)]007
1 18[thin space (1/6-em)]745 18[thin space (1/6-em)]752 18[thin space (1/6-em)]804 18[thin space (1/6-em)]629 18[thin space (1/6-em)]703 18[thin space (1/6-em)]735
2 20[thin space (1/6-em)]255 20[thin space (1/6-em)]266 20[thin space (1/6-em)]322 20[thin space (1/6-em)]140 20[thin space (1/6-em)]219 20[thin space (1/6-em)]252
3 22[thin space (1/6-em)]646 22[thin space (1/6-em)]668 22[thin space (1/6-em)]732 22[thin space (1/6-em)]544 22[thin space (1/6-em)]626 22[thin space (1/6-em)]663


Systematic studies of Eu3+ spectra are often restricted to the energy of the 7F05D0 line which changes over maximally a few 100 cm−1 between different hosts.115,126–129 Its intensity is especially sensitive to the site symmetry and vanishes when Eu3+ occupies an inversion center.116 In that regard, the differences in calculated 7F05D0 energies along the series of Ca–Sr–Ba-compounds and F–S ligands (see Table 3) are significant. Three effects play a role: the difference in the Eu–ligand bond length along the series Ca–Sr–Ba causes a blueshift, while the decrease in the coordination number and the increased nephelauxetic effect when going from fluorides to sulfides cause a redshift.

Interestingly, the equilibrium Eu–X (X = F, S) distance difference between Eu2+ and Eu3+, Δde(Eu), increases when going from the Ca to the Ba compound, 0.13, 0.16 and 0.20 Å for MF2, while being 0.15, 0.18 and 0.26 Å for MS (M = Ca, Sr, Ba). This parameter is of major importance to appreciate the effect of charge-transfer states on the Eu-induced luminescence. It was shown that the larger Δde(Eu) for BaF2 is directly responsible for the complete quenching of the Eu2+ 4f65d1 → 4f6 emission by intervalence charge transfer, while this is not the case in CaF2 or SrF2.130

The above numbers also indicate that Δde(Eu) is larger for the sulfides than for the fluorides. The reason is that the sulfides are more elastic than the fluorides, and undergo a larger “strain”, characterized by Δde(Eu) upon the changing chemical “stress”, as quantified by the bulk moduli.131,132

4. Conclusions

Multiconfigurational ab initio embedded cluster calculations have been performed on the energies and wave functions of the crowded 4f7 and 4f65d1 manifolds of Eu2+ and the 4f6 manifold of Eu3+ doped into two types of chemically different host crystals, the alkaline earth difluorides MF2 and the more covalent alkaline earth sulfides MS (M = Ca, Sr, Ba). Handling the numerous, highly correlated and dense sets of excited states made the theoretical methodology face its highest level of complexity so far. The excited states have been identified and analyzed, and their configuration coordinate diagrams calculated, which allowed us to extract the excited state bond lengths and breathing mode vibrational frequencies. This, together with the calculation of electric dipole transition moments and oscillator strengths, allowed for the production of theoretical 4f → 5d spectral profiles directly comparable with experiments. The agreement is excellent.

All computed quantities were compared to experimental data when available. The calculated energy level locations show a systematic overestimation of 10% due to the used approximations and truncations that keep the calculation manageable. After correction for this systematic error, a quantitative agreement is found between computed and spectroscopically determined level locations with a 68% prediction interval of 300 cm−1.

The calculated Eu–F and Eu–S equilibrium distances for ground and excited states indicate that the lowest 4f → 5d excitation (4f → 5deg in difluorides and 4f → 5dt2g in sulfides) leads to a compression of the coordination polyhedron of Eu2+, which explains the red shift of these transitions under high pressure. Excitation to the highest 5d shell (5dt2g in difluorides and 5deg in sulfides) leads to an expansion, but this holds for a limited number of states only, because at the energies of these excitation processes severe configurational mixing exists that leads to intermediate bond lengths.

The 4f–5d exchange splittings in the 4f65d1 configurations of Eu2+ were found to be 150% larger in the sulfides than in the difluorides. This behavior, which is opposite to the 4f75d1 configurations of Tb3+, was explained on the basis of covalency, which enhances the role of ligand-to-4f virtual excitation processes, which overstabilize the high-spin states in Eu2+ and low-spin states in Tb3+.

The fine structure of the 4f → 5d absorption and excitation spectra, the so-called staircase structure, was well reproduced in the ab initio calculations. A detailed investigation of the strength of the 4f6(7F) × 5dt2g coupling in sulfides via crystal-field-theory calculations revealed that the popular “decoupled scheme”, which attributes the fine structure to the J = 0–6 levels of the 4f6(7FJ) subshell, is not justified. An intermediate coupling is compulsory and it is the interplay between the spin–orbit coupling within the 4f6(7FJ) subshell and the 4f–5d exchange splitting, i.e. the splitting into a high-spin and low-spin part, which dominates the fine structures of the 4f6(7F)5dt2g1 and 4f6(7F)5deg1 sets.

Overall, these multiconfigurational ab initio calculations offer a detailed view of the excited state landscape of Eu-doped solids which underlies their optical and luminescence properties. The ability to get an accurate description of very different host crystals opens new doors to use this approach to help in designing new functional materials for technological applications where requirements are very restrictive and to answer fundamental questions related to Eu-doped phosphors.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

J. J. J. acknowledges the UGent Special Research Fund (BOF/PDO/2017/002101) and the Fund for Scientific Research-Flanders (FWO) for a travel grant (V416818N). This work was partially supported by Ministerio de Economía y Competitividad, Spain (Dirección General de Investigación y Gestión del Plan Nacional de I+D+i, MAT2017-83553-P).

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Footnote

Electronic supplementary information (ESI) available: Computational method, tables and configurational coordinate curves of Eu2+ and Eu3+ in MF2 and MS (M = Ca, Sr, Ba) at the spin-free and spin-orbit levels. See DOI: 10.1039/C9QI01455A

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