Energy Level Structure and Multiple 4f125d1 Emission Bands for

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Article 12

1

Energy Level Structure and Multiple 4f 5d Emission Bands for Tm in Halide Perovskites: Theory and Experiment 2+

Mathijs de Jong, Andries Meijerink, Luis Seijo, and Zoila Barandiaran J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 28 Apr 2017 Downloaded from http://pubs.acs.org on April 29, 2017

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The Journal of Physical Chemistry

Energy Level Structure and Multiple 4f12 5d1 Emission Bands for Tm2+ in Halide Perovskites: Theory and Experiment Mathijs de Jong,1 Andries Meijerink,1 Luis Seijo,2 and Zoila Barandiarán2, ∗ 1

Condensed Matter and Interfaces, Debye Institute of Nanomaterials Science, Utrecht University, P.O. Box 80000, 3508TA Utrecht, The Netherlands 2

Departamento de Qu´ımica, Instituto Universitario de Ciencia de Materiales Nicolás Cabrera,

and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid, Spain (Dated: April 26, 2017)

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT

Rapid non-radiative relaxation from high-excited electronic states to lower-excited electronic states in luminescent materials leads to radiative transitions only from the lowest excited state. This behavior is observed in most luminescent materials. One notable exception is Tm2+ , which is known to show luminescence from up to three 4f 12 5d1 excited states. Here we report a study that explains the deviant behavior of Tm2+ . Using ab initio wavefunction-based embedded-cluster calculations in Tm2+ -doped CsCaBr3 and CsCaCl3 , we show that the manifold of 4f 12 5d1 excited states shows various energy gaps for states with parallel potential energy surfaces. This strongly limits non-radiative relaxation, enabling emission from highly excited states in case of a large energy gap to the next lower state. We also compared calculated and measured absorption and emission spectra and radiative decay times of the emitting states, which show a remarkably good agreement between theory and experiment. Based on the new insights in the Tm2+ excited states we predict that luminescence from highly excited 4f n−1 5d1 states is only expected in the heavy divalent lanthanides.


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I.

INTRODUCTION

Lanthanide ions are widely applied as activators in luminescent materials for lighting, displays, medical imaging, lasers and more.1–6 Rearrangements within the partially filled 4f electron shell, the f–f intraconfigurational transitions, are responsible for the sharp-line luminescence of the lanthanides. These transitions are well-understood. Upon excitation with high-energy photons, most lanthanides show emission from not only the lowest 4f n excited state, as predicted by Kasha’s rule,7 but also from higher 4f n excited states.8 This feature is due to slow non-radiative relaxation from high to low-excited states and provides the basis for lanthanide-based upconversion and quantum cutting materials.9 The broadband luminescence arising from the interconfigurational 4f n ↔ 4f n−1 5d1 (f–d) transitions is however not as well-understood. In particular, questions regarding non-radiative decay processes remain open. Excitation to high 4f n−1 5d1 excited states normally leads to rapid non-radiative relaxation to the lowest 4f n−1 5d1 state, such that only emission from the lowest excited 4f n−1 5d1 state is observed. Only among the heavy (n > 7) lanthanides luminescence from higher-excited states has been observed. Emissions from two excited 4f n−1 5d1 states have been reported for Er3+ and Tm3+ doped in fluoride hosts10 and for Yb2+ doped in SrCl2 11,12 and various perovskites.13 Preliminary studies suggest that in Dy2+ luminescence takes place from multiple excited 4f 9 5d1 states.14 The two emissions in all these cases were interpreted as spin-forbidden and spin-allowed emissions originating from high-spin and low-spin states. This interpretation was questioned by Pan et al.12 based on crystal field theory calculations. An ab initio calculation for Yb2+ -doped CsCaBr3 showed the limitations of this interpretation associated with extensive mixing of high-spin and low-spin states and interpreted the two emissions as spin-forbidden and spin-enabled.15 It has been reported that Tm2+ -doped CsCaBr3 , CsCaCl3 , CsCaI3 , RbCaI3 , CaCl2 , SrCl2 and CaBr2 show luminescence from up to three 4f 12 5d1 excited states with a separation of ∼7 000 cm−1 .14,16–19 Tm2+ is the only lanthanide dopant for which emission from three 4f n−1 5d1 states has been observed. The purpose of this article is to explain the deviant behavior of Tm2+ . To this end, we investigate whether the manifold of excited states in Tm2+ fulfills the requirements of large energy separation between excited states, to understand the multiple luminescing excited states. We also explain why the light divalent lanthanides (n ≤ 7) do not show emission from multiple 4f n−1 5d1 states. ACS Paragon 3Plus Environment


The rate of non-radiative relaxation between two states depends on the overlap of the vibrational parts of resonant wavefunctions.20–24 The non-radiative transition rate between two states increases for (1) an increasing offset between the potential energy surfaces and (2) a decreasing energy gap between the states in units of vibrational quanta. This means that hosts with low maximum local phonon energies are more likely to show luminescence from multiple excited states than hosts with high maximum local phonon energies. The maximum local phonon energy is determined by the type of ligand and the coordination number of the host. Thus for a given coordination, hosts with heavy coordinating ions like bromides give lower maximum phonon energies (typically 200–250 cm−1 ) than hosts with lighter coordinating ions like chlorides (typically 300–350 cm−1 ), fluorides and oxides (typically 400–500 cm−1 ). The 4f n−1 5d1 excited state manifold usually contains a large number of excited states (e.g. 910 in Tm2+ and even 30 030 in Eu2+ ), creating a dense manifold of excited states usually without large energy gaps between 4f n−1 5d1 states, which is required to observe emission from a high-energy 4f n−1 5d1 state. However, Grimm et al. explained the presence of multiple emitting states in Tm2+ by the presence of energy gaps in the 4f 12 5d1 manifold.18 We have started a combined experimental and theoretical investigation of radiative and non-radiative relaxation in Tm2+ focusing on two main research goals. The first is to take advantage of the known fact that Tm2+ has two stable emitting 4f 12 5d1 states to significantly expand the experimental information for this complex dopant. The second is to investigate why radiative decay can compete with non-radiative decay for those two states, and in some hosts also for a third even higher 4f 12 5d1 excited state. The first objective was addressed in a previous work,25 where the stability of two states emitting in the red and in the blue was used to probe the electronic structure of higher levels through two-color two-photon excited state excitation (ESE) experiments. The results of the ESE experiments, combined with some of the results of the ab initio calculations we present here, allowed to conclude that the emitting states are immersed in a dense set of parallel potential energy surfaces. The second objective is the goal of the present paper. The calculations reveal the magnitude and physical origin of the energy gaps that hamper non-radiative relaxation from the emitting states. The theoretical results explain the observation of three emission bands for Tm2+ in CsCaBr3 and explain why non-radiative decay is faster in the CsCaCl3 host where only two 4f 12 5d1 emitting states have been found experimentally. The validity of conclusions based ACS Paragon 4Plus Environment

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on theoretical investigation depends on the accuracy of the methods that have been used to calculate the electronic states of the Tm2+ dopant. This accuracy has been investigated through direct comparisons of ab initio calculated spectra and low-temperature experimental spectra and show a remarkably good agreement between the calculated and experimentally observed energy level structure.

II.

METHODS

The calculations that we use in this work are ab initio wavefunction-based embedded4+ cluster calculations. In this approach we define a molecular cluster TmBr6 Cs4+ 8 or TmCl6 Cs8

(see Fig. 1a) of which all electrons, except those of the [Cd] core of Cs, are included in a multi-reference multi-configurational calculation. Relativistic effects (including spin–orbit coupling) are taken into account. To incorporate the influence of the host lattice, the ab initio model potential embedded-cluster method (AIMP)26,27 is used (see Fig. 1b). In the Supporting Information we describe the methods used and the details of the calculations. Briefly, the calculations consist of three steps: first, restricted active space self-consistent field (RASSCF)28–30 calculations are performed to calculate the wavefunctions and energies of the embedded clusters under the influence of non-dynamic correlation of thirteen active electrons within the active space, using a scalar relativistic second order Douglas-Kroll-Hess Hamiltonian.31,32 In a second step, dynamic correlation is included for all valence electrons of the clusters, performing multi-state restricted active space second order perturbation theory (MS-RASPT2) calculations,30,33–37 see Tables S1 and S3 in the Supporting Information. In the third and last step, spin–orbit coupling is included in restricted active space state interaction (RASSI) calculations.38,39 The resulting states and their corresponding potential energy surfaces are listed in Tables S2 and S4 in the Supporting Information.

III.

RESULTS AND DISCUSSION

In the first step of the calculations, spin–orbit interaction is not included. The spin–orbit free results presented in Tables S1 and S3 of the Supporting Information show extensive interaction between the expected excited configurations 4f 12 5d1 (t2g ), 4f 12 5d1 (eg ) and 4f 12 6s1 ,

E 43 with the latter being of impurity-trapped exciton (ITE) type 4f 12 6s1 aIT . This is due to 1g



a

b

FIG. 1. (a) Molecular cluster comprising one unit cell of the cubic perovskite structure of CsCaBr3 or CsCaCl3 .40,41 In the center is the Ca2+ cation (red), which is in our calculations replaced by Tm2+ . The cation is octahedrally coordinated by six Br− /Cl− ions (green); eight Cs+ ions (blue) are located at the corners of the unit cell. (b) Cross section illustrating the molecular cluster (purple) surrounded by 7×7×7 unit cells consisting of total ion AIMPs (cyan), and an additional volume of point charge ions (yellow).42 See Supporting Information for details.

the fact that the small ligand field splitting for the halide ligands results in a small energy separation between states originating from the coupling of the 4f 12 subshell with the 5d(t2g ),

E shells. Once spin–orbit coupling is considered (see Tables S2 and S4 5d(eg ) and 6s aIT 1g

in the Supporting Information), the configurational mixings are amplified by an extensive spin–orbit mixing which, with few exceptions, overrides the possibility to clearly assign the spin–orbit states to pure configurations or free-ion spin–orbit terms. This can be observed in Figs. 2a,b where we plot the calculated configuration coordinate diagrams of the states of CsCaBr3 :Tm2+ and CsCaCl3 :Tm2+ lying below 50 000 cm−1 , with the corresponding equilibrium distances in Figs. 2c,d. In addition to the states with 4f 13 electron configuration (plotted in black), only the states below 35 000 cm−1 show a pure configurational character: 4f 12 5d1 (t2g ) (blue). Above 35 000 cm−1 , the states have mixed

E configurational character (purple) and the strong mixing of 4f 12 5d1 (t2g /eg ) /4f 12 6s1 aIT 1g

states leads to a variation in offset of the excited state equilibrium distances. The configuration coordinate diagrams in Fig. 2 show that upon excitation from the 4f 13 ground state to a 4f 12 5d1 (t2g ) excited state there is a contraction in Tm–Br/Cl bond length, resulting in broad 4f 13 → 4f 12 5d1 bands in the absorption spectra of Tm2+ , which is in line with previous observations.44 Fig. 2 also shows that all 4f 12 5d1 (t2g ) states shown have parallel potential energy surfaces with a common bond length. This is due to the fact that these states arise from variations in the inner shell configuration of the 4f 12 shell, whose participation in bonding is very small. As a result, all transitions within the 4f 12 5d1 (t2g ) manifold are expected to show sharp line absorption spectra, in agreement with the ESE ACS Paragon 6Plus Environment

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a

b

50

c

d

40 Energy (103 cm−1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


30 20

2616

2597

1460 3821

1454 4264

10 0 2.6

2.7 RTm–Br (Å)

2.8

2.5

2.6 RTm–Cl (Å)

2.7

2.65 RTm–Br,e (Å)

2.70 2.50

2.55 RTm–Cl,e (Å)

FIG. 2. (a) CsCaBr3 :Tm2+ and (b) CsCaCl3 :Tm2+ calculated configuration coordinate diagrams of the fully symmetric breathing mode vibration, obtained by performing calculations in 4+ TmBr6 Cs4+ 8 and TmBr6 Cs8 embedded clusters with various Tm–Br/Cl distances. The dominant E character of the states is 4f13 (black), 4f 12 5d1 (t2g ) (blue) or mixed 4f 12 5d1 (t2g /eg ) /4f 12 6s1 aIT 1g (purple). Significant energy gaps are indicated. (c) CsCaBr3 :Tm2+ and (d) CsCaCl3 :Tm2+ potential energy surface equilibrium distances of the configuration coordinate diagrams in a,b.

spectra of Tm2+ -doped CsCaBr3 and CsCaCl3 .25 In the configuration coordinate diagram of Fig. 2 we observe a number of energy gaps within the 4f 12 5d1 (t2g ) set of excited states, as predicted by Grimm et al.18 The states surrounding the gaps are summarized in Table 1. CsCaBr3 :Tm2+ shows luminescence from three states in the 4f 12 5d1 manifold. We assign the luminescent 4f 12 5d1 states to the 1 Γ8g , 3 Γ8g and 8 Γ6g excited states based on our calculations. All these states are separated from the next lower 4f 12 5d1 energy level by an energy gap. The energy gaps under the three luminescent states are 3 821 cm−1 , 1 460 cm−1 and 2 617 cm−1 (Fig. 2a), which equals respectively 17.4, 6.6 and 11.9 vibrational quanta of 220 cm−1 in the bromide. The observation of luminescence from these states is thus in line with the limited non-radiative relaxation rate because of the large energy gaps in terms of vibrational quanta. For CsCaCl3 :Tm2+ , the picture is similar, with the difference that luminescence was only observed experimentally from two states, which we associate with the 1 Γ8g and 8 Γ6g excited states based on our calculations. The energy gaps below the 1 Γ8g , 3 Γ8g and 8 Γ6g states are 4 264 cm−1 , 1 454 cm−1 and 2 597 cm−1 (Fig. 2b), which equals respectively 12.2, 4.1 and 7.4 vibrational quanta of 350 cm−1 in the chloride. With an energy gap smaller than 5 vibrational quanta, it is indeed expected that the 3 Γ8g state in the chloride will not show luminescence and ACS Paragon 7Plus Environment


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non-radiative relaxation to the next lower state will dominate. The gaps in the manifold of excited states thus explain all observed emission bands and the absence of more sufficiently large energy gaps explains why there are not more emission bands in Tm2+ -doped CsCaBr3 and CsCaCl3 . To gain insight in the states involved in the energy gaps that are responsible for the observation of multiple Tm2+ emission bands, we now consider the full energy level diagram of Tm2+ in CsCaBr3 and CsCaCl3 (Fig. 2 and Table 1). When going from low to high energies, three gaps can be observed. The first energy gap of ∼4 000 cm−1 in the configuration coordinate diagram of Fig. 2 separates the higher-energy 4f 13 and lowest-energy 4f 12 5d1 states. This large f–d gap allows for the observation of luminescence from the lowest 4f 12 5d1 state. Accurate calculation of the interconfigurational transitions and the size of this gap depends on how well electron correlation differences between these two configurations are taken into account.45,46 The second energy gap of ∼1 500 cm−1 is best explained by analyzing the results without spin–orbit coupling, where total spin S is a good quantum number (see Tables S1 and S3 in the Supporting Information, and Figs. 3a,c). In the configuration coordinate diagrams of the spin–orbit free states in Figs. 3a,c, there is a small energy gap of ∼850 cm−1 that separates the three lowest 4f 12 (3 H) 5d1 (t2g ) states from higher states. The lowest doublet states (green in Fig. 3) appear ∼3 000 cm−1 above the lowest quartet states (red in Fig. 3). Spin–orbit coupling causes extensive and strong mixing between the quartets and doublets and only the lowest quartet states remain largely unaffected by the interaction. Figs. 3b,d show that after including spin–orbit coupling, the gap remains (blue arrow) and is slightly increased from 850 cm−1 to 1 500 cm−1 . The three lowest-energy states show more than 80% S =

3 2

character (red), while above the gap most states are a mixture with varying contributions of S =

3 2

and S =

1 2

(orange).

The third gap of ∼2 500 cm−1 is already present in the spin–orbit free calculations shown in Figs. 3a,c as the gap between the highest-energy 4f 12 (3 H) 5d1 (t2g ) and the lowest-energy 4f 12 (3 F) 5d1 (t2g ) states (see Tables S1 and S3 in the Supporting Information, and Fig. 3a,c). Upon including spin–orbit coupling in Figs. 3b,d, the gap remains as the gap between the 4f 12 (3 H6 ) 5d1 (t2g ) and 4f 12 (3 F4 ) 5d1 (t2g ) manifolds, although it is slightly reduced in energy from 2 800 cm−1 to 2 500 cm−1 (see Tables S2 and S4 in the Supporting Information, and Fig. 3b,d). This gap originates from the different states of the 4f 12 core in the 4f 12 5d1 ACS Paragon 8Plus Environment

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a Energy (103 cm−1)

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b 25

3

F

S=

Mixed 3

1 2

F4

20

c 25

d 3

F

3

F4

20 3

H

15 2.6

S=

3

3 2

2.7

3

H6

2.6

2.7

RTm–Br (Å)

RTm–Br (Å)

15

H

3

H6

2.5

2.6 RTm–Cl (Å)

2.5

2.6 RTm–Cl (Å)

FIG. 3. Origin of the energy gaps in the manifold of 4f12 5d1 excited states in Tm2+ . Part of the configuration coordinate diagrams of the results (b,d) with and (a,c) without including spin–orbit coupling for (a,b) CsCaBr3 :Tm2+ and (c,d) CsCaCl3 :Tm2+ . All states are labelled according to their spin character: states with >80% S = 23 in red, states with >80% S = 12 in green and states with neither >80% S = 32 nor >80% S = 21 in orange. Blue and purple arrows indicate change of the second and third energy gap upon applying spin–orbit coupling. The term symbols refer to the free ion states of the 4f12 core of the 4f 12 5d1 (t2g ) excited states.

exicted Tm2+ ion, which can be approximated as those observed for the Tm3+ ion. For the excited states below the gap the Tm3+ core is in the 3 H6 ground level, above the gap in the first excited level 3 F4 . The width of the third gap is thus related to the energy difference between the ground and first excited levels in the corresponding 4f n−1 trivalent lanthanide core of the 4f n−1 5d1 configuration. Using the results of the spin–orbit calculations (Tables S2 and S4 in the Supporting Information), we calculated the envelope of the emission and absorption spectra by imposing a fixed spectral width (175 cm−1 for CsCaBr3 :Tm2+ and 200 cm−1 for CsCaCl3 :Tm2+ in broad-band spectra, 5 cm−1 in narrow-line spectra) on each of the vibronic progressions of the calculated 4f 13 ↔ 4f 12 5d1 /4f 12 6s1 transitions. The Huang–Rhys parameters for the vibronic progressions were calculated from the theoretical potential energy surface equilibrium differences (Tables S2 and S4 in the Supporting Information). For example, the 4f13 ↔ 4f 12 5d1 (t2g ) transitions have Huang-Rhys parameters of ∼0.7 in CsCaBr3 :Tm2+ and ∼0.3 in CsCaCl3 :Tm2+ . Comparison of the calculated spectra with experimental data provides a useful assessment of the accuracy of the calculations. In Fig. 4 we compare the calculated emission and absorption spectra of CsCaBr3 :Tm2+ and CsCaCl3 :Tm2+ with experimental spectra.47 For both materials the calculated and measured absorption spectra show three peaks between 14 000 cm−1 and 18 500 cm−1 with intensities low–low–high, corresponding to transitions to various 4f 12 (3 H6 ) 5d1 (t2g ) states. Transitions to the lowest-energy states with ACS Paragon 9Plus Environment


CsCaBr3:Tm2+

( ) ( )

CsCaCl3:Tm2+

( / ) ( )

4f12 3H6 5d1 t2g 4f12 3F4 3H5 5d1 t2g a

( ) ( )

( / ) ( )

4f12 3H6 5d1 t2g 4f12 3F4 3H5 5d1 t2g b Calculations

Transition strength

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c

d Experiments

15 000

20 000

25 000

15 000

−1

Energy (cm )

20 000

25 000 −1

Energy (cm )

FIG. 4. (a,b) Calculated absorption and emission spectra of Tm2+ in CsCaBr3 and CsCaCl3 based on the results of the spin–orbit calculations. Absorption spectra (blue) are calculated with the 1 Γ6u ground state as the initial state, emission spectra are calculated with the 1 Γ8g (red), 3 Γ8g (orange) and 8 Γ6g (green) excited states as initial states. The narrow-line spectra in gray are equal to the colored spectra, except for the smaller linewidth, and indicate the positions and relative intensities for zero-phonon and vibronic lines. (c,d) Experimental absorption (reproduced with permission from Ref. 47) and emission spectra of Tm2+ in CsCaBr3 and CsCaCl3 .

strong S =

3 2

character are too weak to be visible in the experimental and calculated ab-

sorption spectra of Fig. 4, confirming the low oscillator strengths of these spin-forbidden transitions (Tables S2 and S4 in the Supporting Information). Following the trio of peaks, there is a gap between 18 500 and 20 000 cm−1 in the absorption spectrum. Next, absorption bands corresponding to transitions to a set of mixed 4f 12 (3 F4 /3 H5 ) 5d1 (t2g ) excited states are observed. The profiles of these, which are a combination of four peaks with intensities low–high–high–low between 20 000 cm−1 and 26 000 cm−1 , show a very good match between calculations and experiments. In Supporting Information Fig. S4 we make a comparison over a larger spectral range and in Supporting Information Fig. S3 we assign the peaks in detail to transitions to the calculated electronic states. Overall there is a discrepancy of only a few hundred wavenumbers between the energies of the calculated and measured spectra. This confirms the high accuracy of the calculations and their validity for explaining the origin of the multiple emitting 4f12 5d1 states in Tm2+ . Grimm et al. assigned bands in the absorption spectrum from 26 281 cm−1 and 29 266 cm−1 respectively in the bromide and chloride as excitations to 4f 12 5d1 (eg ) states.47 In the configACS Paragon10 Plus Environment

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uration coordinate diagram of Fig. 2, the states with (partial) 4f 12 5d1 (eg ) character (green) are shifted in equilibrium distance with respect to states with 4f 12 5d1 (t2g ) character (blue) and have an onset at 34 901 cm−1 and 35 433 cm−1 respectively in the bromide and chloride, i.e. these absorption bands are at much higher energy than assigned by Grimm et al. In the experimental emission spectrum of CsCaBr3 :Tm2+ , three emission bands with peak energies 12 280 cm−1 , 13 720 cm−1 and 19 140 cm−1 are observed, of which the energies in the calculations are 12 740 cm−1 , 14 500 cm−1 and 20 420 cm−1 . For CsCaCl3 :Tm2+ , two emission bands with energies 12 500 cm−1 and 19 470 cm−1 were observed, of which the energies in the calculations are 13 240 cm−1 and 21 000 cm−1 . The theoretical calculations systematically overestimate the energies of the emission band but the differences with the experimentally observed emission band energies are small (between 4% and 8%). Grimm et al. assigned the three emitting 4f 12 5d1 states of Tm2+ in CsCaBr3 as (1) (2)

3

3

H6 , t2g ; 23 ,

H6 , t2g ; 21 and (3) (3 F4 , t2g ), in which the first term is the free-ion term symbol for

the state of the 4f 12 core, the second term the state of the 5d-electron and the third term the total spin of the 4f 12 5d1 state. This should be compared to our assignment of (1) 1 Γ8g , (2) 3 Γ8g and (3) 8 Γ6g . The configurational character of these three states (see Table 1) in the calculations agrees with the assignment of Grimm et al. Also the spin character of the emitting states in the calculations is in agreement with the assignments of Grimm et al., with the exception of the spin character of state 2 (see Tables S2 and S4 in the Supporting Information). In the calculations this state has a mixed spin character with a strong S = component. Excitation from the S =

1 2

3 2

ground state to this state is therefore not spin-

allowed, but spin-enabled.15 Grimm et al. suggested that spin–orbit coupling is so strong for the (3 F4 , t2g ) states that there is no clear distinction between S =

1 2

and S =

3 2

states.18 The

configuration coordinate diagrams of Figs. 3b,d show that strong doublet–quartet mixing already starts for the higher-energy (3 H6 , t2g ) states. With the calculated wavefunctions for the ground and excited states, it is also possible to calculate the radiative lifetimes of the excited states (see Supporting Information for details). The calculated radiative lifetimes of the 1 Γ8g excited state in the bromide and chloride are 847 µs and 704 µs, which can be compared with experimental lifetimes of 296 µs and 278 µs.18 The calculated radiative lifetimes of the 8 Γ6g excited state in the bromide and chloride are 1.54 µs and 1.41 µs, which can be compared with experimental lifetimes of 1.90 µs and 1.17 µs.18 The radiative lifetimes of the two states differ by several orders ACS Paragon11 Plus Environment


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of magnitude. This reflects the different spin characters of the two emitting states: the high-energy emitting state 8 Γ6g has a much higher S =

1 2

character than the low-energy

emitting state 1 Γ8g , making the transition more spin-allowed, or spin-enabled. Note that the calculated lifetimes are in vacuum, because local field corrections require the refractive indices of the host materials,48 which have not been reported. Local field corrections will result in shorter calculated lifetimes.

The appearance of an energy gap in a region of the 4f n−1 5d1 manifold of states with parallel potential energy surfaces is a requirement for higher-energy 4f n−1 5d1 excited states to emit. Whether higher-energy emissions appear in a divalent lanthanide depends on many factors, including effects of the symmetry and the coordinating ligands of the host lattice, the possible overlap between the 4f n and 4f n−1 5d1 manifolds, the chemical stability of the lanthanide in the divalent oxidation state and possible quenching mechanisms through intervalence charge transfer states.49 Quantum chemical calculations are required when giving predictions regarding multiple emitting states. However, with the increased understanding of the origin of the gaps in the 4f 12 5d1 manifold of Tm2+ , we want to point out a relevant feature of the excited state manifolds of the divalent lanthanides. The large third energy gap in Tm2+ originates from a large energy gap between the 3 H6 and 3 F4 levels in Tm3+ . In the bottom of the Dieke diagram in Fig. 5, this gap is marked in purple. The 3 H6 –3 F4 energy gap of ∼5 500 cm−1 in Tm3+ results in a ∼2 500 cm−1 gap in the Tm2+ 4f 12 5d1 manifold, equal to 11.9 vibrational quanta in CsCaBr3 or 7.4 vibrational quanta in CsCaCl3 . For a divalent lanthanide to show luminescence from a higher 4f n−1 5d1 state, a large energy gap between the ground level and first excited level in its corresponding trivalent lanthanide is required. We can conclude from Fig. 5 that this energy gap increases for increasing n, as a result of stronger spin–orbit coupling for atoms with higher atomic numbers. Only among the heavy lanthanides (n > 7) suitable candidates can be found, e.g. Dy2+ , Ho2+ , Er2+ and Yb2+ . This is in agreement with the absence of luminescence from highly excited states in Eu2+ and Sm2+ . For Yb2+ , with a large energy gap between the 2 F7/2 and 2 F5/2 states for the Yb3+ core, emission from higher excited 4f13 5d1 states can be expected and calculations in Ref. 45 confirm the presence of a large energy gap of 4 600 cm−1 in CsCaBr3 :Yb2+ . To our knowledge, the emission from a 4f 13

2

F5/2 5d1 state in Yb2+ , though predicted theoretically,

has not been reported yet. ACS Paragon12 Plus Environment

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Energy (103 cm−1)

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10 3

F4

5 3

H6

0

Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb

FIG. 5. Energy level diagram of the 4fn ground and 4fn low excited levels of all trivalent lanthanides. The 3 H6 –3 F4 energy gap, responsible for the gap that enables emission from the 4f 12 3 F4 5d1 (t2g ) excited state in some Tm2+ -doped materials, is marked in purple. IV.

CONCLUSIONS

We performed ab initio wavefunction-based embedded-cluster calculations on Tm2+ doped CsCaBr3 and CsCaCl3 with the aim to understand the occurrence of multiple emitting 4f 12 5d1 states in Tm2+ . The calculated configuration coordination diagrams revealed the presence of three relatively large energy gaps within the 4f 12 5d1 (t2g ) manifold of excited states with parallel potential energy surfaces. In this situation the non-radiative relaxation rate to lower excited states is reduced, resulting in the observation of emission from multiple 4f 12 5d1 (t2g ) excited states. All energy gaps are sufficiently large in terms of vibrational quanta to limit non-radiative relaxation for Tm2+ in CsCaBr3 and three 4f12 5d1 emissions are observed. The higher vibrational energy in the chloride results in fast relaxation for the smallest gap in CsCaCl3 :Tm2+ , which is in agreement with the experimental observation of two 4f12 5d1 emission bands in CsCaCl3 :Tm2+ . Next, we compared the calculated absorption and emission spectra and radiative lifetimes with experimental data. The good agreement between the overall appearance (positions and relative intensities) in absorption and emission spectra and between calculated and experimental luminescence decay times confirm the high accuracy of the present calculations.

ACKNOWLEDGMENTS

We are grateful to Judith Grimm, who measured the CsCaBr3 :Tm2+ and CsCaCl3 : Tm2+ absorption spectra and approved reprinting the spectra. The work in this article was partially supported by the EU Marie Curie Initial Training Network LUMINET (316906) and partially supported by Ministerio de Econom´ıa y Competitividad, Spain (Dirección General ACS Paragon13 Plus Environment


de Investigación y Gestión del Plan Nacional de I+D+i, MAT2014-54395-P).

∗

[email protected]

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Page 18 of 19

TABLE 1. Overview of the energy levels of Tm2+ doped into CsCaBr3 and CsCaCl3 , including spin–orbit coupling. Minimum-to-minimum energies relative to the 4f13 ground state in cm−1 , Tm–Br/Cl bond Re in ˚ A and vibrational energies of the totally symmetric breathing mode ωa1g in −1 cm . Luminescence has been observed experimentally from the states marked in blue.18

CsCaBr3 :Tm2+ State Energy Re

1 Γ6u 1 Γ8u 1 Γ7u

CsCaCl3 :Tm2+ ωa1g

State Energy Re

4f13 (2 F7/2 ) 0 2.692 218 128 2.692 218 248 2.692 218

1 Γ6u 1 Γ8u 1 Γ7u

ωa1g

4f13 (2 F7/2 ) 0 2.556 350 176 2.557 349 330 2.557 349

4f13 (2 F5/2 ) 2 Γ8u 9072 2.692 218 2 Γ7u 9241 2.692 218 Gap = 3822 cm−1

4f13 (2 F5/2 ) 2 Γ8u 9103 2.556 349 2 Γ7u 9318 2.557 349 Gap = 4264 cm−1

4f 12 (3 H6 ) 5d1 (t2g ) Γ8g 13063 2.672 221 Γ8g 13157 2.672 221 Γ6g 13219 2.672 221 Gap = 1460 cm−1 Γ8g 14679 2.670 221 Γ8g 14758 2.670 221 .. .

4f 12 (3 H6 ) 5d1 (t2g ) Γ8g 13582 2.540 354 Γ8g 13700 2.540 355 Γ6g 13786 2.540 353 Gap = 1454 cm−1 Γ8g 15240 2.538 351 Γ6g 15298 2.538 353 .. .

1 2 1 3 4

1 2 1 3 2

7 Γ6g 17998 2.669 221 Gap = 2617 cm−1

13 Γ8g 18578 2.537 351 Gap = 2597 cm−1

4f 12 (3 F4 /3 H5 ) 5d1 (t2g ) 8 Γ6g 20615 2.670 221 14 Γ8g 20673 2.670 221 .. .

4f 12 (3 F4 /3 H5 ) 5d1 (t2g ) 8 Γ6g 21175 2.538 352 14 Γ8g 21243 2.538 349 .. .

E 4f 12 5d1 (t2g /eg ) /6s1 aIT 1g 55 Γ8g 34901 2.680 158 28 Γ6g 35020 2.698 144 .. .

E 4f 12 5d1 (t2g /eg ) /6s1 aIT 1g 28 Γ6g 35433 2.520 309 55 Γ8g 35512 2.511 294 .. .


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Energy

Emission

#1 #2

1 2 3 4 5 6

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Tm–ligand distance

Energy

#3

Energy Level Structure and Multiple 4f125d1 Emission Bands for

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