On the Mechanism for the Extremely Efficient Sensitization of Yb3+

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

On the Mechanism for the Extremely Efficient Sensitization of Yb3+ Luminescence in CsPbCl3 Nanocrystals Xiyu Li, Sai Duan, Haichun Liu, Guanying Chen, Yi Luo, and Hans Ågren J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b03406 • Publication Date (Web): 14 Jan 2019 Downloaded from http://pubs.acs.org on January 15, 2019

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The Journal of Physical Chemistry Letters

On the Mechanism for the Extremely Efficient Sensitization of Yb3+ Luminescence in CsPbCl3 Nanocrystals Xiyu Li,1 Sai Duan,1Haichun Liu,1 Guanying Chen,2 Yi Luo,1 Hans Ågren1,2,3* 1Department

of Theoretical Chemistry and Biology School of Engineering Sciences in Chemistry,

Biotechnology and Health, Royal Institute of Technology. Stockholm 10691, Sweden 2School

of Chemical Engineering and Technology, Harbin Institute of Technology, Harbin,

Heilongjiang 150001, China 3Federal

Siberian Research Clinical Centre under FMBA of Russia, 660037, Kolomenskaya,

26 Krasnoyarsk, Russia.

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

ABSTRACT: Rare earth ion (RE3+) doped inorganic CsPbX3 (X=Cl or Cl/Br) nanocrystals have been presented as promising materials for applications in solar-energy-conversion technology.

30 KEYWORDS: Quantum cutting, density function 31 theory (DFT), Ytterbium-Doped inorganic 32 perovskite.

An extremely efficient sensitization of Yb3+ luminescence in CsPbCl3 nanoparticles (NCs) was very recently demonstrated where quantum cutting is

responsible

for

the

performance

33 TOC image:

of

photoluminescence quantum yields over 100% (T. J. Milstein, et al., Nano Letters 2018, 18, 3792). In the present work, based on cubic phase of inorganic perovskite, we seek to obtain an atom-level-insight into the basic mechanisms behind these observations in order to boost the further development of RE3+ doped CsPbX3 NCs for optoelectronics. In our calculations of cubic crystal structure, we do not find any energy level formed in the middle of the band gap, which disfavors a mechanism of step-wise energy transfer from the perovskite host to two Yb3+ ions. Our work

indicates

that

the

configuration

with

“right-angle” Yb3+-VPb-Yb3+ couple are most likely to form in Yb3+-doped CsPbCl3. Associated with this “right-angle” couple, the “right-angle” Pb atom with trapped excited states would localize the photogenerated electrons and could act as the energy donor in a quantum cutting process, which achieves

simultaneous

neighboring Yb3+ ions.

sensitization

of

two

34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Perovskite is a remarkable calcium titanium oxide mineral discovered already in 1839.1,2 Its versatile crystal structure makes it possible to accommodate a wide variety of cations, which has evoked promising new opportunities to optimize the performance of photonic devices of solar cells, displays, lasers and photodetectors.3 For instance, organic-inorganic hybrid perovskite-based solar cells have achieved power conversion efficiencies over 20%.4-6 Especially, inorganic metal-halide perovskite

CsPbX3

(X=Cl/Br/I)

nanocrystals

possess high photoluminescence quantum yields (QY), broadband absorption, and narrow emission

1

ACS Paragon Plus Environment

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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

bandwidths,

which

can

be

used

in

optoelectronics.7-10 The incorporation of transition-metal or rare-earth

(RE3+)

ions into CsPbX3 NCs has been

proven to be an efficient strategy for extending the .11-15

optical properties of inorganic CsPbX3

Pb2+

instance, inorganic perovskites with replaced by

Mn2+

For ions

ions have exhibited sensitization

of inter Mn2+ d-d emission through the interaction between the host material and the dopant.11-13 Very recently, inorganic CsPbX3 NCs doped with RE3+ ions have been experimentally implemented and showed excellent

optical properties, including

high photoluminescence QY, good stability and emission color tunability, benefitting various optoelectronic Yb3+-doped

applications.16,17

Intriguingly,

CsPbCl3 NCs were reported to be able

to generate NIR photoluminescence with QY well over 100%.16,18 Two different mechanisms have been proposed to explain the extremely efficient sensitization of Yb3+ luminescence in CsPbX3 NCs. Firstly, a mechanism of step-wise energy transfer (depicted in Figure 1a) was

proposed.16

Energy

levels in the middle of the band gap of pristine CsPbCl3, associated with the defects of NCs host, were suggested to play a key role in the step-wise energy quantum

transfer cutting

mechanism. (QC)

Subsequently,

mechanism

at

a the

picosecond scale was proposed, as depicted in

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

Page 2 of 11

charge-neutral couple of Yb3+-VPb-Yb3+ (VPb: Pb2+ ion vacancy), due to charge compensation, is critical for the facilitation of the QC mechanism. This Yb3+-VPb-Yb3+ couple induced shallow defect energy levels below the conduction-band-edge, which could compete with native defects of host NCs for a picosecond nonradiative energy-transfer from the conduction band, followed by nearly resonant energy transfer to two Yb3+ ions in a single QC step. The proposed QC process, with the Yb3+-induced defect state acted as the energy donor, is different from conventional QC process. The QC process is referred to the division of each ultraviolet/visible

photon

absorbed

into

two

simultaneous photons emitted. Usually, inorganic host materials are selected to accommodate the RE3+ ions to serve QC in terms of energy level alignment and energy transfer efficiency. For instance, the incorporation of RE3+-Yb3+ (RE: Tb/Tm/Pr/Ce/Nd) ions into the host lattice of LiGdF4/LaF3/SrF2 has been explored for the optimization

of

optical

performance

and

investigation of the QC mechanism, with RE3+ acting as energy donors and Yb3+ as energy acceptors.19-21

In perovskite NCs, the system of

CsPbCl1.5Br1.5 co-doped with Ce3+ and Yb3+ ions, was reported as an example of conventional QC,22 where Ce3+ ions act as energy donors and Yb3+ ions as energy acceptors, as shown in Figure 1c.

Figure 1b.18 It implies that the formation of

Figure 1 Scheme of (a) step-wise energy transfer mechanism and (b) QC mechanism for Yb3+-doped CsPbCl3, (c) and the conventional QC mechanism with RE3+-Yb3+ incorporated into inorganic CsPbX3.

60 Overall, two different mechanisms of energy 61 transfer were proposed to explain the optical

62 properties for the systems of Yb3+-doped CsPbCl3 63 in the two experimental works.16,18 This is a 2


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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

fundamental

issue

RE3+-doped

for

CsPbX3

the

NCs

development for

of

optoelectronic

applications, which calls for understanding and further scrutiny. The cubic phase was the mostly often observed in studies of inorganic perovskite nanocrystals.16,22-25

In this work, using density

function theory (DFT), we selected the cubic phase to investigate the properties of the system of Yb3+-doped CsPbCl3 and explore the optical mechanism at an atomic scale. Our calculated results

reveal

that

the

configuration

with

Yb3+-V

-Yb3+

charge-neutral right-angle (RA)

Pb

couple is most likely formed in the crystal matrix which, however, lacks defect energy level in the middle of the band gap and thus is not in favor of the previously proposed step-wise energy transfer mechanism.16

Our calculations basically support

the quantum cutting mechanism proposed in Ref. 18, but provide further atomic-level insight. Particularly, we find that lanthanide doping causes variation in the valence band of pristine CsPbCl3 NCs rather than inducing a shallow defect level below the conduction band, and that the unique Pb (RA) atom with trapped excited states, associated with the RA

Yb3+-V

Pb

-Yb3+

couple, would localize

the photogenerated electron for the quantum cutting mechanism. All calculations were carried out at the spin-polarized density functional theory (DFT) level using the VASP package.26 The Kohn–Sham equations of the valence electrons were expanded using plane-wave basis sets. The Perdew, Burke,

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 61 62 63 64

and

Ernzerhof

functional

(PBE)

within

approximation

a

employed.27

generalized

(GGA)

augmented-wave

exchange-correlation and

(PAW)

gradient

the

projector

potential

were

Although the PBE functional could

underestimate the band gap due to its nature, it can provide an effective way to investigate the defect effect on the electronic structures of materials.28,29 The computational details are provided in the Supporting Information (Figure S1). It should be pointed

out

that

owing

to

the

pseudopotentials, the density of states for

Yb3+

used was

neglected in our simulations. The nanocrystal surface will modulate the optical properties of NCs, e.g., emission quenching, which results from some special characteristics of the surface, such as defects, dangling bonds and

adsorbed organic

groups. However, the basic optical properties of perovsikte NCs are found to be determined fundamentally by their intrinsic composition.18,30 For simplicity, without losing general physical significance, we investigated the optical properties of nanocrystals by calculating the atomic and electronic structures for bulk crystals. This theoretical approach is well accepted and widely used, and has been proven useful in investigating properties

of

nanocrystals.16,23 present work the

inorganic

prevoskites

It should be noted that in the assumption is made that

the

nanocrystal surface plays an unimportant role in the underlying optical mechanism, which is supported by a recent report.30

3



Page 4 of 11

Figure 2 (a) The atom structure of CsPCl3 with Pb vacancy, denoted VPb-CsPbCl3; the atom structure of Yb3+-doped CsPbCl3 with couple of Yb3+-VPb-Yb3+ in (b) right-angle and (c) line configuration. The atomic scheme of (d) PbCl6 octahedron in pure CsPbCl3 and (e) RA couple in Yb3+-doped CsPbCl3. The Cs atoms are omitted. Table 1 The calculated energies of Yb3+-doped CsPbCl3 structures with two Yb atoms and one VPb, including five Yb-concentrations and seven different atomic structures for each Yb3+-concentration

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Energies (eV)

Right-angle

Linear

Random1

Random2

Random3

Random4

Random5

433 (5.7%)

-640.52

-640.43

-640.18

-640.22

-640.23

-640.31

-640.22

443 (4.3%)

-852.11

-852.02

-851.94

-851.95

-851.93

-851.94

-851.87

444 (3.2%)

-1134.17

-1134.12

-1134.02

-1134.04

-1134.02

-1134.07

-1133.72

544 (2.5%)

-1415.51

-1415.46

-1415.27

-1415.28

-1415.42

-1415.44

-1415.31

555 (1.6%)

-2209.98

-2209.87

-2209.84

-2209.78

-2209.76

-2209.84

-2209.57

the

and

The native VPb defect can exist in perovskites because of its low formation energy (Figure 2a).18,31-33

For

Yb3+

doping, it is known that Pb2+

ions could occupy the site of the that the doping of two

Yb3+

calculated

the

ion, and

ions can generate one

Pb vacancy (VPb) due to charge We

Yb3+

compensation.18

energies

of

different

configurations to identify the atom structures of Yb3+-doped CsPbCl3 (details provided in the Supporting Information), including couples of Yb3+-V

Pb

-Yb3+

with right-angle (RA) and linear

configurations (Figure 2b and 2c). The calculated energies of all considered model systems are listed in

Table

1.

Yb3+-V

-Yb3+

Pb

most

stable

The

results

suggest

the

couple with RA configuration is the one,

followed

by

configuration, for all five different concentrations.

that

This

result

agrees

the

linear

Yb3+-doping with

the

proposed Yb3+-VPb-Yb3+ charge neutral complex in Ref 18. However, due to the small energy

21 22 23 24 25 26 27 28 29

difference

30 31 32 33 34 35 36 37 38 39 40

(Figure 2d).34 The doping of Yb3+ ions would

between

RA

linear

configurations, these two structures may co-exist at finite temperature. In order to assess which configuration is most likely to form, we further examined the symmetry of the micro-structure of the materials. Pure CsPbCl3 possesses ideal PbCl6 octahedrons with perfect symmetry (six uniform Pb-Cl bonds of 2.83 Å and uniform Pb-Cl bond angles of 90°), which is important to the stability distort some PbCl6 octahedrons, influencing the stability of this perovskite system. For the configuration with a linear Yb3+-VPb-Yb3+ couple, Yb-Cl bonds with length of ~2.63 Å can be formed as a result of the Yb-Cl interaction. These Yb-Cl bonds lead to the weakening of adjacent Pb-Cl interactions and stretched Pb-Cl bonds with length of 3.08 Å (denoted as Pb-Cl(Yb) bonds, shown in Figure S2a). Consequently, the Pb2+ ion related PbCl6 octahedrons would have non-uniform Pb-Cl

4


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1 2 3 4 5 6 7 8 9 10 11 12 13 14

bonds and Pb-Cl bond angles. In the linear configuration, there are five Yb-Cl bonds for one Yb3+

ion, which means that five PbCl6 octahedrons

would be distorted. Since there are two

Yb3+

ions

in the linear couple, the number of distorted octahedrons (NDO) of PbCl6 is 10 in this configuration (Figure S2a). Nevertheless, for the configuration with RA

Yb3+-V

Pb

-Yb3+

couple, one

PbCl6 octahedron is co-distorted by both Yb3+ ions with

two

Pb-Cl(Yb)

bonds

for

the

RA

characteristic, which leads to one less distorted octahedron of PbCl6 than for the linear structure and thus the NDO is 9 for the RA couple (Figure 2e and Figure S2b). The Pb-Cl bond lengths of this

15 16 17 18 19 20 21 22 23 24 25 26 27 28

distorted octahedron are 3.07, 3.06, 2.84, 2.83, 2.82, 2.79 Å, respectively. The smaller

PbCl6

NDO of the RA configuration should induce less restructuring of the perovskite structure than that of the linear configuration. For the configurations without Yb3+-VPb-Yb3+ couples (Figure S3), there are 9-12 distorted PbCl6 octahedrons. Higher total energies mean that these configurations have less probability to form (Table 1). Based on this analysis, we argue that the RA configuration is more likely to form than the linear or any of the other structures. We therefor focus on the most stable configuration with RA couple in the remaining.

Figure 3 (a) The energy alignment of pure CsPbCl3 (Pure), CsPbCl3 with native defect of VPb (VPb), 433-supercell with RA couple (RA), and 433-supercell with RA couple and VPb (RA+VPb), respectively. (b) The partial density state (PDOS) near the conduction band (CB) for the RA+VPb configuration. (c) The electronic wavefunction of the CB for RA+VPb configuration with an isosurface value of 0.0035 eÅ-3 (red). Cs atoms are not plotted.

29 30 31 32 33 34 35 36 37 38 39 40 41

The electronic structures of materials play a critical role in their optical properties. Herein, we are at a position to explore the electronic structures of

Yb3+-doped

CsPbCl3. The band structure of pure

CsPbCl3 was first calculated, as shown in Figure S4, suggesting that the direct band gap is located at the K-point of (0.5, 0.5, 0.5) in the Brillouin zone. The calculated value of the bandgap is 2.18 eV, in accordance with previous theoretical work.28 The main contribution to the conduction band (CB) is due to the Pb atoms, while the Cl atoms mainly contribute to the valence band (VB) (Figure S5). Because of symmetry, all Pb atoms are identical

42 43 44 45 46 47 48 49 50 51 52 53 54

and contribute equally to the conduction band of pure CsPbCl3 (Figure S6 and S7). We then investigated the band gaps of 433/443/444/544/555 configurations with RA couple (Figure S8). The 433-configuration incorporating the RA couple and VPb can be used to simulate the realistic Yb3+-doped CsPbCl3 with the co-existence of the neutral couple and the native defect VPb (Figure 3). The results suggest that all configurations with the direct band gap located at the K-point of (0.5, 0.5, 0.5) in Brillouin zone, the various Yb3+-doping concentrations cause only slight differences in the band gap from that of CsPbCl3 with VPb (less than

5



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

0.1 eV difference in the values of band gaps), which could be attributed to the high defect tolerance of perovskites. Importantly, all the electronic structures of 433-configurations show that there is no defect energy level formed in the middle of the band gap (Figure 3a and Figure S9). Thus, our calculated results are not in favor of the previously proposed step-wise energy transfer mechanism (Figure 1a), where such kind of defect energy level was indispensable. Besides, our results show that the native defect of VPb could induce variation in the VB, while the conduction band remained almost unchanged (Figure 3a and Figure S8). This is in accordance with the findings in many previous theoretical works on different types ),31,32,35-41

of perovskite materials (ABX3

where

the vacancy of B site (VPb) was found to mostly induce shallow levels in the region of the valence band. This kind of shallow levels cannot act as trap states but have rather a slight effect on the optical properties of CsPbX3, consistent with the fact that perovskites have the intrinsic tendency to keep its properties even with the existence of high concentration crystallographic high

defect

tolerance.3,42

defects,29 To

i.e., with a

explain

the

experimental results of over 100% quantum yield for

Yb3+-doped

CsPbCl3, Milstein et al. proposed a

QC mechanism (Figure

1b).18

In order to examine

the physical basis of the QC mechanism, the density of state (DOS) of CB (DOS-CB) of 433-configuration with RA couple and VPb defect was here explored, because the excited electrons would more likely populate on the location with DOS-CB. We find that the excited electrons in the currently studied system would be located on the Pb atoms due to the fact that the conduction band is mainly formed by the Pb atoms. This is exemplified by the partial density of states (PDOS) with three kinds of Pb atoms, with the 9 Pb atoms with distorted PbCl6 octahedrons (Pb(Dis.n)), with Pb atoms near VPb (denoted as Pbn(VPb)) and with the normal Pb atoms (Pb(Nor.n), as shown in Figure 3b. One can find that the intensities of the DOS-CB around the selected Pb atoms are not

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Page 6 of 11

equal, which indicates that the excited electrons would be located on different Pb atoms with different probabilities. Particularly, the higher DOS-CB intensities receive contributions by those Pb atoms with distorted PbCl6 octahedrons. Specially, the Pb (RA) atom with most distorted PbCl6 octahedrons possesses the highest intensity of DOS-CB, suggesting the highest probability of population of the excited electrons. Figure 3c shows the corresponding electronic wave function of the CBM. The highest density of the electronic wave function locates on the Pb (RA) atom, agreeing with the results shown in Figure 3b. Considering that the distances between the Pb (RA) atom and the two Yb atoms are the same, with the value of 5.68 Å, Pb (RA), with its trapped excited state, could act as the energy donor in the proposed QC mechanism. In summary, the association of the Yb3+-VPb-Yb3+ couple with the Pb (RA) atom could provide a channel to both the neighboring Yb3+ ions for efficient simultaneous excitation of both in a QC mechanism, as proposed in supporting Ref. 18. The electronic structure of configuration with the linear couple was also calculated. The results show that the photo-generated electrons would be localized on the Pb atoms close to the both Yb atoms (Figure S10). Nevertheless, no two Yb atoms with equal distance to each of these Pb atoms can be fund, which would not aid the quantum cutting process. The scheme in Figure 4 summarizes the mechanistic conclusions for Yb3+-doped CsPbCl3: A

quantum

cutting

performance of

Yb3+

is

responsible

for

the

photoluminescence quantum

yields over 100%; The charge-neutral RA couple of Yb3+-VPb-Yb3+ most likely exists in the crystal matrix, which is associated with the Pb (RA) atom; the Pb (RA) atom with trapped excited state can work as energy donor to excite two Yb3+ ions in a single quantum cutting step. Importantly, the natural proximity due to the association of Yb3+-VPb-Yb3+ couple with Pb (RA) atom benefits the energy transfer from the Pb (RA) atom to two neighboring Yb3+ ions for simultaneous excitation

6


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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

of both and aid the quantum cutting process. These findings basically support the proposal in Ref. 18. However,

further

in-depth

studies,

both

experimental and theoretical, are necessary to approve the functioning of the QC mechanism in the sensitization of

Yb3+

photoluminescence in

Yb3+-doped CsPbCl3 NCs, of different crystal phases.

Figure 4 The scheme of proposed quantum cutting mechanism for Yb3+-doped CsPbCl3 of cubic phase. In addition, we have performed calculations on lanthanum

(La3+)

and gadolinium

(Gd3+)

ions-doped CsPbCl3 of cubic phase with different doping concentrations. The calculated results show that the configurations with right-angle (RA) couple of

La3+/Gd3+-V

form in

La3+/Gd3+-doped

Pb

-La3+/Gd3+

also most likely

CsPbCl3 nanocrystals

(Tables S1 and S2 in the Supporting Information). The electronic structures of the RA configuration suggest that the photo-generated electron would be localized on the Pb atom associated with right-angle (RA) couple (Figure S11 in the Supporting

Information).

These

atomic

and

electronic structures of La3+/Gd3+-doped CsPbCl3 are in correspondence with those of Yb3+-doped CsPbCl3.

Since

lanthanum,

gadolinium

and

ytterbium are three representative rare earth elements, located at the left, middle and right side

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 61 62 63 64 65 66 67

of the lanthanide series in the periodic table, respectively, our conclusions should likely have generality. In conclusion, the present work is motivated by seeking underlying reasons for the observed extremely

efficient

sensitization

of

Yb3+

luminescence in CsPbX3 nanocrystals (NCs), where quantum cutting has been responsible

for

the

proposed to be

performance

of

photoluminescence quantum yields over 100%.18 Our computational work on the cubic phase of inorganic perovskite leads to a few general and detailed conclusions. Among the latter, we find that right-angular (RA) couples of Yb3+-VPb-Yb3+ in Yb3+-doped CsPbCl3 are most likely to form. However, there is no defect energy level formed in the middle of the band gap, which is not favorable for a step-wise energy transfer mechanism. Thus, quantum cutting is the most probable mechanism responsible

for

the

performance

with

photoluminescence quantum yields well over 100%. Different from the proposal in Ref. 18, where Yb3+-induced defect was assigned as the energy donor, we find that, for cubic phase, the Pb (RA) atom possess the highest intensity of DOS-CB, indicating its role as the energy donor in the quantum cutting process. This Pb (RA) atom is associated with the Yb3+-VPb-Yb3+ couple, leading not only to the quantum cutting but also to the Yb3+ sensitization. The general conclusion is that DFT investigations of the kind presented here can provide atom-level-insight into the fundamental issue

for

perovskite

the

development

nanocrystals

for

RE3+-doped

of

optoelectronic

applications and understanding of the underlying optical mechanisms.

68 ASSOCIATED CONTENT 69 Supporting Information 70 71 72 73 74

Additional

atomic

structures

and

electronic

structures of studied models as Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

7



1 AUTHOR INFORMATION 2 Corresponding Author 3 *E-mail: [email protected] 4 5 Notes 6 The authors declare no competing financial 7 interest. 8 9 ACKNOWLEDGMENT

10 11 12 13 14 15 16 17 18 19

Page 8 of 11

H.Å. and X.L. acknowledge the US Air Force of Scientific Research (contract FA-9550-18-1-0032) for support. H.L. acknowledges the financial support from a Starting Grant (2016-03804) from the Swedish Research Council (Vetenskapsrådet). The calculations were supported by the Swedish National Infrastructure for Computing (SNIC) and were performed within the project “Multiphysical Simulation 2017/12-49.

8


of

Molecular

Materials”

SNIC

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11


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On the Mechanism for the Extremely Efficient Sensitization of Yb3+

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