Deciphering and quantifying linear light upconversion in molecular erbium complexes

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Deciphering and quantifying linear light upconversion in molecular erbium complexes

GOLESORKHI, Bahman, et al.

Abstract

Single-center light upconversion corresponds to the pilling up of low-energy photons via successive linear absorptions: a phenomenon commonly observed in lanthanide-doped low-phonon ionic solids or nanoparticles. Its ultimate miniaturization in molecular complexes opens challenging perspectives in term of improved reproducibility, chemical control and optical programming. However, highenergy vibrations inherent to coordination complexes severely limit the efficiency of successive excited-state absorptions (ESA) responsible for the gain in photon energy. By carefully wrapping three polyaromatic ligand strands around trivalent erbium, we managed to induce low-power room temperature near infrared (exc = 801 nm or 966 nm) to visible green (em = 522 nm and 545 nm) light upconversion within mononuclear coordination complexes [Er(Lk)3]3+ operating either in the solid state or in non-deuterated solution. The calculated upconversion quantum yields set the zero-level of an elemental erbium-centered molecular ESA mechanism, a values which favorably compares with cooperative upconversion (CU) previously implemented in [...]

GOLESORKHI, Bahman, et al. Deciphering and quantifying linear light upconversion in molecular erbium complexes. Chemical Science, 2019, vol. 10, no. 28, p. 6876-6885

DOI : 10.1039/C9SC02068C

Available at:

http://archive-ouverte.unige.ch/unige:121588

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Publication: Chem. Sci. 2019, 10, 6871-6885. DOI: 10.1039/c9sc02068c

Deciphering and quantifying linear light upconversion in molecular erbium complexes

Bahman Golesorkhi, Alexandre Fürstenberg, Homayoun Nozary and Claude Piguet*

Department of Inorganic and Analytical Chemistry, University of Geneva, 30 quai E. Ansermet, CH- 1211 Geneva 4, Switzerland. Email: [email protected]

† Electronic supplementary information (ESI) available. For ESI see DOI xxx.

Abstract

Single-center light upconversion corresponds to the pilling up of low-energy photons via successive linear absorptions: a phenomenon commonly observed in lanthanide-doped low-phonon ionic solids or nanoparticles. Its ultimate miniaturization in molecular complexes opens challenging perspectives in term of improved reproducibility, chemical control and optical programming. However, high- energy vibrations inherent to coordination complexes severely limit the efficiency of successive excited-state absorptions (ESA) responsible for the gain in photon energy. By carefully wrapping three polyaromatic ligand strands around trivalent erbium, we managed to induce low-power room temperature near infrared (exc = 801 nm or 966 nm) to visible green (em = 522 nm and 545 nm) light upconversion within mononuclear coordination complexes [Er(Lk)3]³⁺ operating either in the solid state or in non-deuterated solution. The calculated upconversion quantum yields set the zero-level of an elemental erbium-centered molecular ESA mechanism, a values which favorably compares with cooperative upconversion (CU) previously implemented in sophisticated multisite Yb2Tb supramolecular assemblies. The various dependences of the upconverted emission on the incident excitation power imply different mechanisms, which can be tuned by molecular design.

Introduction

In optics, the common degradation of energy considers the conversion of high-energy photons into photons of lower energy (downshifting) together with heat dissipation. The reverse situation, in which low-energy photons are transformed into higher energy ones (up-conversion) was early envisioned as a consequence of the non-linear dependence of the refractive index on the applied electric field,¹ and theoretically predicted by Goeppert-Mayer in 1931.² However, the so-called non-linear optical (NLO) response of matter is so inefficient that its experimental illustration for second-harmonic generation (in quartz)³ and for two-photon excitation fluorescence (in Eu²⁺-doped materials)⁴ was delayed until the first ruby laser providing strong and coherent incident beam became available in 1960.⁵ Beyond symmetry rules, there is no specific limitation for implementing NLO responses in matter and both macroscopic solids or (bio)molecules are prone to work as non-linear optical activators as long as huge incident power intensities in the 10⁵-10¹⁰ Wcm^-2 range are used.⁶ In parallel with NLO investigations, Bloembergen,⁷ rapidly followed by Auzel⁸ realized that open-shell centers possessing ladder-like series of intermediate excited states with small radiative rate constants (kr), as found for trivalent lanthanides, Ln³⁺, could be used as relays for successive linear excitations. When such ions are dispersed into low-phonon solids, the non-radiative relaxation pathways (knr) are also minimized to such an extent that linear excitation (kexc) becomes competitive with relaxation (krelax = kr + knr) and intermediate excited states can absorb efficiently additional photons to reach higher-energy excited levels. The latter sequential pilling up of several photons on a single activator (Excited-State Absorption = ESA) exploits linear optics and results in the conversion of low energy infra-red into visible photons, a phenomenon referred to as upconversion (Scheme 1).⁹ The use of more efficient linear optics combined with the sequential, rather than simultaneous (in NLO), nature of the excitation, negates the need for excessively high incident intensities and upconversion can be achieved using excitation powers that are 5-10 orders of magnitude lower than those required for NLO. A further gain in efficiency of up to two orders of magnitude^9a can be generated by the use of optimized peripheral sensitizers for absorbing photons prior to the stepwise transfer of the

accumulated energy onto the activator (energy transfer upconversion = ETU). In these conditions, upconversion quantum yields as large as 4-12% have been implemented in multi-centered mixed lanthanide-doped oxides or fluorides.¹⁰ These encouraging achievements make a multitude of challenging applications possible which intend at (i) reducing the spectral mismatch for solar cell technology,⁹ (ii) designing near-infrared addressable luminescent bioprobes where the biological tissues are transparent¹¹ and (iii) optimizing wave guides,¹² security inks¹³ lasers and display devices,¹⁴ and this despite the weak absorption cross sections of f-f transitions in lanthanides (on the order of   10^-20 cm²)¹⁵ or of d-d transitions in transition metals (on the order of   10^-19 cm²).¹⁶

Scheme 1 (a) Kinetic scheme for the modeling of the linear single-ion ESA process occurring upon off-resonance irradiation into the activator-centered absorption band and (b) associated first-order kinetic equations. k_exc^ij, k_r^ij, k_nr^ij are the first-order rate constants for excitation, radiative decay and non-radiative decay, respectively and k_relax^ijk_r^ijk_nr^ij.

Attempts to reduce the size of upconverting solids toward the nanometric scale for being compatible with high-technology hybrid materials and with their incorporation into biological organisms drastically suffer from surface quenching and difficult reproducibilities.^11,17 Maximum upconversion quantum yields within the 0.1-0.5% range have been obtained for optimized nanoparticles after

0 1 1 0 2 0

0 exc relax relax 0

A 1 2 A

exc

1 0 1 2 1 1

A exc 1 0 relax A

relax

2 2

A 2 0 A

relax 1 2

exc 2 1

relax

0

k k k

dN dt N

dN dt k k k N

dN dt k N

k k

k

  



 









 

 

 

     

       

     

       

   

      

b)

A A^*

0 1 A^** 2

a)

Energy

1 2

kexc^

0 1

kexc^ k_r^{1 0}

2 1

kr^ k_nr^{2 1}

1 0

knr^ 2 0

kr^ k_nr^{2 0}

surface passivation¹⁸ and/or coupling to a surface plasmon for increasing both absorption cross sections and radiative decays.¹⁹ Because the intensity of the upconverted light Iupconversion kr^{2 0} N² reflects the population density of the second excited state N² , its magnitude drastically depends on the lifetime of the intermediate excited state ¹ 1





1 = 3.7 ms in Gd²O²S) under steady-state excitation using reasonable incident pump power (1-10 Wcm^-2) predicts mole fractions of 210^-3 ≤ N ² ≤ 510^-3 for the double excited state A^**.²⁰ Similar calculations performed for typical short-lived molecular erbium-based complexes possessing high- energy C-H, C-C and C-N oscillators (for instance ¹ = 2.8 s in a [GaErL³] helix) do not exceed

N 2 ≤ 10^-11.²⁰ It is thus no so surprising that single-centered linear upconversion was originally thought to be undetectable in molecular lanthanide complexes,²¹ and huge incident power intensities around 10⁹ Wcm^-2 produced by modern pulsed femto-lasers were required to induce faint upconverted signals for [Ln(2,6-dipicolinate)³]^3-, [Ln(EDTA)]^- (Ln = Nd, Tm, Er),²² and [Tm(DMSO)x]³⁺ in solution.²³ These discouraging results, combined with the approximate 0.1 Wcm^-

2 power density of the terrestrial solar irradiance,^9c,d paved the way for the exclusive consideration of non-coherent upconversion based on triplet-triplet annihilation (TTA) as the only viable route for performing reliable and workable linear upconversion in molecules.²⁴ However, if the latter annihilation process occurs between two discrete triplet-state entities, their formation requires energy diffusion through multiple chromophores and cannot be really considered as a (uni)molecular process.²⁵ Let’s therefore return to the challenge of implementing single-centered upconversion in a molecule where (i) the strong coupling with undesirable high-energy oscillators (mainly O-H, C-H vibrations) limits intermediate excited-state lifetimes and (ii) the small lanthanide absorption cross section ^ij provide minor excitation rate constants k_exc^ij (eq. 1; P is the pump wavelength, P is the incident pump intensity, h is the Planck constant and c is the speed of light in vacuum).²⁶

p exc

i j i j

k P

hc

 

   ⁽¹⁾

Fig. 1 Erbium-based coordination complexes exhibiting linear upconversion processes following the ETU mechanism. The X-ray crystal structure is shown for a) [CrErCr(L)³](CF³SO³)^928a and chemical structures deduced from spectroscopic data recorded in solution are depicted for b) [IR- 806][Er(L)4],²⁹ c) [(LEr)F(LEr)]⁺³⁰ and d),e) [Tb(YbL)2].³¹

The decorrelation between light absorption, performed by specific sensitizers, and light-upconversion occurring on an optimized lanthanide activator in multicenter molecular aggregates using the ETU

mechanism proved to be less challenging and some protected Er(III)-activators combined with optimized peripheral Yb(III)-sensitizers in multi-doped metal-organic frameworks or coordination polymers displayed weak upconverted green (Er(⁴S^3/2⁴I1^5/2) and red (Er(⁴F^9/2⁴I1^5/2) signals upon intense Yb(²F5/2²F5/2) excitation.²⁷ Encouraged by these preliminary data collected on infinite macroscopic solids, an Er(III) activator was flanked by a couple of Cr(III) sensitizers in the molecular triple helix [CrErCrL3]⁹⁺ to give the first molecular-based green upconversion process induced by reasonable power pump intensities (Fig. 1a).²⁸ This success was rapidly confirmed for two other molecular sensitizer/activator pairs obtained by host-guest associations in organic solvents ([IR- 806][Er(L)4] in Fig. 1b)²⁹ or in water ([(LEr)F(LEr)]⁺ in Fig. 1c).³⁰ None of these ETU processes were characterized by quantum yield measurements because of the very faint upconverted signals. In two recent publications,³¹ Charbonnière and coworkers reported on two novel aqueous-phase assemblies made of a central Tb(III) activator surrounded by two or more Yb(III) sensitizers ([Tb(YbL)2] in Figs 1d-e). Surprisingly, these (supra)molecular entities exhibit detectable near- infrared to green upconversion, for which only cooperative energy transfers may explain the feeding of the high-energy Tb(⁵D4) level (Figs 1d-e). Though some aspects of the theoretical modeling of the latter cooperative upconversion mechanism (CU) are rather analogous to ETU, its efficiency is usually much weaker because it involves quasi-virtual pairs levels between which transitions have to be described by higher-order perturbations.^9a Despite this limitation, Charbonnière and coworkers were able to estimate a quantum yield of up= 1.410^-8 for the complex depicted in Fig. 2e (deuterated water, room temperature).^31b Boosted by these remarkable results, we reasoned that ultimate miniaturization using single-site excited state mechanism (ESA) implemented in a trivalent erbium complex should become an obvious target for setting a zero-level for the quantification of molecular upconversion. Taking advantage of the rare dual visible (Er(⁴S3/2⁴I15/2) at 542 nm, green) and near- infrared (Er(⁴I13/2⁴I15/2) at 1520 nm) downshifted emissions observed upon UV excitation of the triple-helical [Er(L1)3]³⁺ complex (Fig. 2a), a chromophore which closely mirrors the activator unit in the triple helix [CrErCrL3]⁹⁺ (Fig. 1a),³² we recently discovered that some weak upconverted green

signals could be generated upon direct near-infrared excitation of the erbium center in this system.³³ Building on these preliminary data, we report here on the quantification and detailed mechanism rationalizing the rare single-site upconversion occurring in [Er(L1)³]³⁺. Comparison with related optical processes implemented in analogous, but stepwise deprotected [Er(Lk)3]³⁺ (Lk =2-4) mononuclear triple helices offers an opportunity for establishing some preliminary rules for implementing single-center erbium upconversion in molecular complexes (Fig. 2).

Fig. 2 Erbium-based coordination complexes exhibiting linear upconversion processes following the ESA mechanism discussed in this work. The X-ray crystal structures are shown for [Er(L1)3](ClO4)31.5CH3CN, [Er(L2)3](ClO4)3, [Er(L3)3](ClO4)3 and [Er(L4)3](ClO4)31.5CH3CN.

The counter-anions, solvent molecules and H atoms are omitted for clarity. Color code: C = grey, blue = N, green = Er.³²

Results and Discussions

Preparation and structural characteristics of the triple-helical complexes. The four tridentate ligands L1-L4 (Fig. 2) have been shown to react with Er(ClO4)3 in acetonitrile to give highly stable triple helical complexes [Er(Lk)3]³⁺ (<0.1% dissociated at 10 mM total concentration), which can be crystallized by slow evaporation.³² In the crystal structures of [Er(Lk)3](ClO4)3 (Fig. 2), the Er cations are well-protected from external metallic perturbations (i.e. no cross-relaxation process) since the shortest intermolecular ErEr distances amount to 1.03-1.21 nm. Furthermore, the closest intramolecular ErH contact distance (C-H oscillators) reaches 3.86 Ǟ for [Er(L1)³]³⁺ (L1 is a 2,6- bis(benzimidazol-2-yl)pyridine ligand), but slightly shrinks to 3.42-3.46 Ǟ for [Er(Lk)3]³⁺ (Lk = L2- L4, terpyridine-based ligands). Compared with ErH contact distances of 2.85 Å found for the aquo ion [Er(H2O)9](CH3CH2SO3)3 (O-H oscillators),³⁴ the situation of trivalent erbium in the [Er(Lk)3]³⁺

complexes is compatible with limited multiphonon relaxation due to coupling with remote high- energy oscillators³⁵ as ascertained by the 2-6 s characteristic room-temperature lifetimes reported for the emissive Er(⁴I13/2) levels.³² Whereas intramolecular ErH distances are not significantly modified in solution for these rigid triple-stranded helicates,³⁶ the average intermolecular ErEr distance extends to approximately 6.8 nm at 10 mM concentration, which makes these metallic centers completely isolated in solution.

Light-downshifting operating in the mononuclear triple-helical complexes. With these structural characteristics in mind, it is not so surprising that ligand-centered excitation at 401 nm of these trivalent erbium complexes [Er(Lk)3]³⁺ in the solid state and in solution systematically showed dual downshifted visible Er(⁴S^3/2⁴I^15/2) and near-infrared Er(⁴I^13/2⁴I^15/2) luminescence at 542 nm and 1515 nm, respectively (Fig. 3).³² The log-log plots of the intensity of the emitted light with respect to the incident power return slopes around 1.0 (Fig. 3),²⁶ which are the signatures of single-photon ligand-centered excitation processes followed by energy migration according to the antenna effect (Fig. 4a).³² Please notice in Fig. 3a the superimposition of the visible Er(²H11/2⁴I15/2) and

Er(⁴S3/2⁴I15/2) emission bands with the tails of the residual broad ligand-centered ^1^*¹ bands, which is typical for an incomplete metal sensitization via the antenna mechanism.

Fig. 3 Downshifted a) visible and b) near-infrared emissions and corresponding log-log plots of downshifted intensities I as a function of incident pump intensities P (in mW/cm²) observed for [Er(L1)₃](ClO₄)₃ (solid state, 298 K) upon ligand-centered laser excitation at 401 nm (24938 cm^-1) and for different incident pump intensities focused on a spot size of ≈ 0.05 cm².

Alternatively, the low-energy downshifted near-infrared Er(⁴I13/2⁴I15/2) luminescence at 1515 nm can be sensitized via direct Er-centered excitation at exc = 801 nm into the Er(⁴I9/2⁴I15/2) transition (molar absorption coefficients 0.20 ≤ 801 ≤ 0.24 M^-1cm^-1, Table S1) of the [Er(Lk)3]³⁺ complexes in acetonitrile solution (Fig. 5a) or in the solid state (Figs S1-S3 in the ESI). The slopes of log(I)-log(P) plots are systematically close to 1.0 (Fig. 5b), a trend in line with single-photon excitations according to the standard mechanism depicted in Fig. 4b (left).

0.0 1.3 2.63.9 5.26.5 7.8 9.1 10.411.7 13.0 14.315.6 16.918.2 19.5 20.8 22.123.4 24.7 26.0 27.328.6 29.931.2 32.5 33.8 35.136.4 37.7 39.040.3 41.642.9 44.2 45.5 46.848.1 49.450.7 52.0 53.3 54.655.9 57.2 58.559.8 61.162.4 63.7 65.0 66.367.6 68.9 70.2 71.572.8 74.175.4 76.7 78.0 79.380.6 81.9 83.2 84.5 85.887.1 88.4 89.7 91.092.3 93.694.9 96.2 97.5 100.198.8 101.4 102.7 104.0 105.3 106.6 107.9 109.2 110.5 111.8 113.1 114.4 115.7 117.0 118.3 119.6 120.9 122.2 123.5 124.8 126.1 127.4 128.7 130.0 131.3 132.6 133.9 135.2 136.5 137.8 139.1 140.4 141.7 143.0 144.3 145.6 146.9 148.2 149.5 150.8 152.1 153.4 154.7 156.0 157.3 158.6 159.9 161.2 162.5 163.8 165.1 166.4 167.7 169.0 170.3 171.6 172.9 174.2 175.5 176.8 178.1 179.4 180.7 182.0 183.3 184.6 185.9 187.2 188.5 189.8 191.1 192.4 193.7 195.0 196.3 197.6 198.9 200.2 201.5 202.8 0.0 400.0 800.0 1 200.0 1 600.0 2 000.0 2 400.0 2 800.0 3 200.0 3 600.0 4 000.0 4 400.0 4 800.0 5 200.0 5 600.0 6 000.0 6 400.0 6 800.0 7 200.0 7 600.0 8 000.0 8 400.0 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17.0 17.5 18.0 18.5 19.0 19.5 20.0 22 mW

20 mW 18 mW 16 mW 13 mW 10 mW 7 mW 4 mW

5.2 5.4 5.6 5.8

1.8 2.0 2.2 2.4 2.6

540 520

5.0 5.2 5.4 5.6

3.8 4.0 4.2 4.4

570 555

Wavenumber / 10³ cm^-1

Intensity /a.u.

Wavelength / nm a)

b)

log (I)

log (P/ mWꞏcm^-2)

4S_3/2⁴I_15/2

2H11/24I15/2

Wavenumber / cm^-1

Intensity /a.u.

Wavelength / nm 1515 1484 1565 1540

4I13/2⁴I15/2

log (I)

log (P/ mWꞏcm^-2) Slope = 0.77(4)

Slope = 0.94(7) 464.1

465.4 466.7 468.0 469.3 470.6 471.9 473.2 474.5 475.8 477.1 478.4 479.7 481.0 482.3 483.6 484.9 486.2 487.5 488.8 490.1 491.4 492.7 494.0 495.3 496.6 497.9 499.2 500.5 501.8 503.1 504.4 505.7 507.0 508.3 509.6 510.9 512.2 513.5 514.8 516.1 517.4 518.7 520.0 521.3 522.6 523.9 525.2 526.5 527.8 529.1 530.4 531.7 533.0 534.3 535.6 536.9 538.2 539.5 540.8 542.1 543.4 544.7 546.0 547.3 548.6 549.9 551.2 552.5 553.8 555.1 556.4 557.7 559.0 560.3 561.6 562.9 564.2 565.5 566.8 568.1 569.4 570.7 572.0 573.3 574.6 575.9 577.2 578.5 579.8 581.1 582.4 583.7 585.0 586.3 587.6 588.9 590.2 591.5 592.8 594.1 595.4 596.7 598.0 599.3 600.6 601.9 603.2 604.5 605.8 607.1 608.4 609.7 611.0 612.3 613.6 614.9 616.2 617.5 618.8 620.1 621.4 622.7 624.0 625.3 626.6 627.9 629.2 630.5 631.8 633.1 634.4 635.7 637.0 638.3 639.6 640.9 642.2 643.5 644.8 646.1 647.4 648.7 650.0

6290 6490 6690 6890

80 mW 70 mW 65 mW 60 mW 55 mW 50 mW 40 mW 30 mW 20 mW

Fig. 4 Jablonski diagram summarizing the downshifting processes following a) ligand-centered or b) erbium-centered excitation (dashed upward arrows), energy transfers (dotted horizontal arrows), non-radiative multiphonon relaxation (undulating arrows) and radiative emission processes (straight downward arrows) operating in the complexes [Er(Lk)3]³⁺ (Lk = 1-4).

Interestingly, the dependence of the emitted downshifted intensity I_down^exc:801 on the temperature T is completely different for the terpyridine derivatives [Er(Lk)³]³⁺ (Lk = L2-L4) and for the extended 2,6-bis(benzimidazol-2-yl)pyridine analogue [Er(L1)³]³⁺ (Fig. 5c and Fig. S4). A reasonable explanation considers that the non-radiative Er(⁴I^9/2)  Er(⁴I^13/2) relaxation pathway (E  5900 cm^-

1, Fig. 4b), requested for feeding the emissive Er(⁴I13/2) level following 801 nm excitation, is strongly phonon-activated (harmonics and/or combination bands) with terpyridine ligands. This mechanism disappears at low temperature, which overcomes the expected increase in intensity due to the minimizing of the non-radiative quenching of the Er(⁴I13/2⁴I15/2) luminescence at 1515 nm. For the extended 2,6-bis(benzimidazol-2-yl)pyridine binding units in [Er(L1)3]³⁺, the larger density of available vibrations detected in the fingerprint region of the IR spectrum (Fig. S5) provides some better adapted combination of vibration modes for filling the pertinent energy gap E = E(Er(⁴I9/2))- E(Er(⁴I13/2)  5900 cm^-1 and the downshifted luminescence is retained at low temperature (Fig. 5c).

Er(III)

4I

15/2 13/2 11/2 9/2

4F9/2 4S_3/2

2H11/2 7/25/2 2H_9/2

3/2 4F S₁

L1-L4 T₁

4G

11/29/2 7/2

401 nm 542 nm

E×103 cm-1

0 4 8 12 16 20 24 28 32

1515 nm

I.S.C

4F9/2 4S3/2 2H_11/2

4I_13/2

4I15/2 4I11/2 4I_9/2

801nm 1515 nm 966nm

b) Erbium-excitation

Er(III) a) Ligand-excitation

Fig. 5 a) Near-infrared downshifted Er(⁴I13/2⁴I15/2) emission observed for [Er(L1)3](ClO4)3 in acetonitrile (10 mM, 298 K) upon laser excitation of the Er(⁴I9/2⁴I15/2) transition at ^exc = 801 nm (

= 12284 cm^-1) and for different incident pump intensities focused on a spot size of ≈ 0.07 cm² and b) corresponding log-log plots of downshifted intensities I as a function of incident pump intensities P (in Wcm^-2) for [Er(Lk)3]³⁺ in acetonitrile (The straight lines correspond to extrapolated linear fits) and c) dependences of downshifted intensities I as a function of temperature (solid state, P = 10 Wꞏcm^-2, the dashed lines are only guides for the eyes).

Excitation at exc = 966 nm into the Er(⁴I11/2⁴I15/2) transition (molar absorption coefficients 0.54 ≤

⁹⁶⁶ ≤ 0.66 M^-1cm^-1, Table S1) surprisingly gives log(I)-log(P) plots with slopes larger than 2.0 for all complexes (Figs S6-S8), which suggests the sequential absorption of at least two photons prior to relaxation into the Er(⁴I13/2) level followed by ultimate Er(⁴I13/2⁴I15/2) emission. These unexpected

0.0 0.2 0.4 0.6 0.8 1.0

0 60 120 180 240 300

Normalized Intensity

T/ K

[Er(L1)₃]³⁺

[Er(L4)₃]³⁺

[Er(L3)₃]³⁺

[Er(L2)₃]³⁺

3.7 3.9 4.1 4.3 4.5

0.4 0.6 0.8 1.0 1.2

log (I)

[Er(L1)₃]³⁺ 1.14(3)

[Er(L4)₃]³⁺ 1.18(3) [Er(L3)₃]³⁺ 1.15(3) [Er(L2)₃]³⁺ 1.15(1) Slopes

log (P/ Wꞏcm^-2) a)

0.0 1.2 2.43.6 4.8 6.0 7.28.4 10.89.6 12.0 13.214.4 15.6 16.8 18.019.2 20.421.6 22.8 24.0 25.226.4 27.6 28.8 30.031.2 32.4 33.634.8 36.037.2 38.4 39.6 40.842.0 43.2 44.4 45.646.8 48.049.2 50.4 51.6 52.854.0 55.2 56.457.6 58.8 60.0 61.262.4 63.664.8 66.0 67.2 68.469.6 70.8 72.0 73.274.4 75.6 76.878.0 79.280.4 81.6 82.8 84.085.2 86.4 87.6 88.890.0 91.292.4 93.6 94.8 96.097.2 98.4 100.899.6 102.0 103.2 104.4 105.6 106.8 108.0 109.2 110.4 111.6 112.8 114.0 115.2 116.4 117.6 118.8 120.0 121.2 122.4 123.6 124.8 126.0 127.2 128.4 129.6 130.8 132.0 133.2 134.4 135.6 136.8 138.0 139.2 140.4 141.6 142.8 144.0 145.2 146.4 147.6 148.8 150.0 151.2 152.4 153.6 154.8 156.0 157.2 158.4 159.6 160.8 162.0 163.2 164.4 165.6 166.8 168.0 169.2 170.4 171.6 172.8 174.0 175.2 176.4 177.6 178.8 180.0 181.2 182.4 183.6 184.8 186.0 187.2 188.4 189.6 190.8 192.0 193.2 194.4 195.6 196.8 198.0 199.2 200.4 201.6 202.8 204.0 205.2 206.4 207.6 208.8 210.0 211.2 212.4 213.6 214.8 216.0 217.2 218.4 219.6 220.8 222.0 223.2 224.4 225.6 226.8 228.0 229.2 230.4 231.6 232.8 234.0 235.2 236.4 237.6 238.8 240.0 241.2 242.4 243.6 244.8 246.0 247.2 248.4 249.6 250.8 252.0 253.2 254.4 255.6 256.8 258.0 259.2 260.4 261.6 262.8 264.0 265.2 266.4 267.6 268.8 270.0 271.2 272.4 273.6 274.8 276.0 277.2 278.4 279.6 280.8 282.0 283.2 284.4 285.6 286.8 288.0 289.2 290.4 291.6 292.8 294.0 295.2 296.4 297.6 298.8 300.0 301.2 302.4 303.6 304.8 306.0 307.2 308.4 309.6 310.8 312.0 313.2 314.4 315.6 316.8 318.0 319.2 320.4 321.6 322.8 324.0 325.2 326.4 327.6 328.8 330.0 331.2 332.4 333.6 334.8 336.0 337.2 338.4 339.6 340.8 342.0 343.2 344.4 345.6 346.8 348.0 349.2 350.4 351.6 352.8 354.0 355.2 356.4 357.6 358.8 360.0 361.2 362.4 363.6 364.8 366.0 367.2 368.4 369.6 370.8 372.0 373.2 374.4 375.6 376.8 378.0 379.2 380.4 381.6 382.8 384.0 385.2 386.4 387.6 388.8 390.0 391.2 392.4 393.6 394.8 396.0 397.2 398.4 399.6 400.8 402.0 403.2 404.4 405.6 406.8 408.0 409.2 410.4 411.6 412.8 414.0 415.2 416.4 417.6 418.8 420.0 421.2 422.4 423.6 424.8 426.0 427.2 428.4 429.6 430.8 432.0 433.2 434.4 435.6 436.8 438.0 439.2 440.4 441.6 442.8 444.0 445.2 446.4 447.6 448.8 450.0 451.2 452.4 453.6 454.8 456.0 457.2 458.4 459.6 460.8 462.0 463.2 464.4 465.6 466.8 468.0 469.2 470.4 471.6 472.8 474.0 475.2 476.4 477.6 478.8 480.0 481.2 482.4 483.6 484.8 486.0 487.2 488.4 489.6 490.8 492.0 493.2 494.4 495.6 496.8 498.0 499.2 500.4 501.6 502.8 504.0 505.2 506.4 507.6 508.8 510.0 511.2 512.4 513.6 514.8 516.0 517.2 518.4 519.6 520.8 522.0 523.2 524.4 525.6 526.8 528.0 529.2 530.4 531.6 532.8 534.0 535.2 536.4 537.6 538.8 540.0 541.2 542.4 543.6 544.8 546.0 547.2 548.4 549.6 550.8 552.0 553.2 554.4 555.6 556.8 558.0 559.2 560.4 561.6 562.8 564.0 565.2 566.4 567.6 568.8 570.0 571.2 572.4 573.6 574.8 576.0 577.2 578.4 579.6 580.8 582.0 583.2 584.4 585.6 586.8 588.0 589.2 590.4 591.6 592.8 594.0 595.2 596.4 597.6 598.8 600.0

6290 6490 6690 6890

725 mW 700 mW 660 mW 620 mW 570 mW 520 mW 470 mW 420 mW 350 mW 250 mW

Wavenumber / 10³ cm^-1

Intensity /a.u.

Wavelength / nm 1515 1484 1565 1540

4I_13/2⁴I_15/2

b)

c)

