Critical Role of Energy Transfer Between Terbium Ions for Suppression of Back Energy Transfer in Nonanuclear Terbium Clusters

Lanthanide (Ln(III)) complexes form an important class of highly efficient luminescent materials showing characteristic line emission after efficient light absorption by the surrounding ligands. The efficiency is however lowered by back energy transfer from Ln(III) ion to the ligands, especially at higher temperatures. Here we report a new strategy to reduce back energy transfer losses. Nonanuclear lanthanide clusters containing terbium and gadolinium ions, TbnGd9−n clusters ([TbnGd9−n(μ-OH)10(butylsalicylate)16]+NO3−, n = 0, 1, 2, 5, 8, 9), were synthesized to investigate the effect of energy transfer between Tb(III) ions on back energy transfer. The photophysical properties of TbnGd9−n clusters were studied by steady-state and time-resolved spectroscopic techniques and revealed a longer emission lifetime with increasing number of Tb(III) ions in TbnGd9−n clusters. A kinetic analysis of temperature dependence of the emission lifetime show that the energy transfer between Tb(III) ions competes with back energy transfer. The experimental results are in agreement with a theoretical rate equation model that confirms the role of energy transfer between Tb(III) ions in reducing back energy transfer losses. The results provide a new strategy in molecular design for improving the luminescence efficiency in lanthanide complexes which is important for potential applications as luminescent materials.


Results and Discussion
Theoretical Background. The theoretical background of the concept that back energy transfer (BET) can be suppressed using energy transfer between Tb(III) ions (TbET) in a nonanuclear Tb(III) cluster is provided in this section by using rate equations. The kinetic energy transfer processes in Tb 9 clusters 50 is depicted in Fig. 1b-h. The energy transfer processes in the cluster include photosensitized energy transfer (PSET), BET, and TbET. Although the closest Tb(III)-Tb(III) pair is less than 4 Å where multipolar and exchange interactions may contribute to the energy transfer rate 52 , calculation of this contribution does not significantly affect the results and conclusion of this section (see Supplementary Information S2 and Table S1). Therefore for the sake of discussion, the energy transfer rate constant between the closest pair of Tb(III) ions was defined as k TbET and the transfer rates for the other pairs were calculated relative to k TbET based on the simplest R −6 distance dependence of the dipole-dipole Förster mechanism. Tb(III) ions in the outer unit (Tbm, m = 1, 2, … , 8) are involved in PSET and BET with their coordinated butylsalicylate ligands. On the other hand, the center Tb(III) ion (Tb9) is coordinated only by oxygen atoms and is isolated from PSET and BET. The population density of Tb9 is solely dependent on the cycle of repetitive TbET to and from Tb(III) ions in the outer unit Tbm (energy migration). Based on these considerations, a system of differential equation in matrix form (Equation (1)) models the excited state dynamics of Tb 9 clusters: where X(t) is the vector of population density of an excited singlet state (S1(t)), excited triplet state (T1(t)), excited Tb(III) ions in the outer unit (Tbm(t), m = 1, 2, … , 8), and the center Tb(III) ion (Tb9(t)) as shown in Equation ( A is the matrix of constants that characterizes the relationship between dynamics of each species and other species in Tb 9 cluster and is given in the following equation:    isc  T1   BET  B ET  BET  B ET  BET  B ET  BET  B ET   PSET  Tb   TbET  TbET  TbET  TbET  TbET  TbET  TbET  TbET   PSET  TbET  Tb   TbET  TbET  TbET  TbET  TbET  TbET  TbET   PSET  TbET  TbET  Tb   TbET  TbET  TbET  TbET  TbET  TbET   PSET  TbET  TbET  TbET  Tb   TbET  TbET  TbET  TbET  TbET   PSET  TbET  TbET  TbET  TbET  Tb   TbET  TbET  TbET  TbET   PSET  TbET  TbET  TbET  TbET  TbET  TbET  TbET  TbET  TbET   PSET  TbET  TbET  TbET  TbET  TbET  Tb  Tb   TbET  TbET   PSET  TbET  TbET  TbET  TbET  TbET  TbET  TbET  Tb   TbET   TbET  TbET  TbET  TbET  TbET  TbET  TbET  TbET  Tb9 where S1 S1 S1 isc Tb9 Tb Tb TbET k isc , kr, knr, k PSET , k BET , and k TbET are defined as intersystem-crossing, radiative, nonradiative, PSET, BET, and TbET rate constants, respectively. The subscript indicates a species in a Tb 9 cluster. Finally, vector J(t) represents the input function of each species in Tb 9 cluster: The excited state decay dynamics after short-pulse excitation were solved using Dirac's delta function, and the quantum yield (steady-state excitation) was determined by using constants (Supplementary Information S3). In this calculation, the ground state population density is approximated as always being constant, and doubly excited Tb 9 clusters are ignored because excitation with reasonably low pump intensity (under 20 W mm −2 ) is being considered 41 . The population density of S1(t) (excited singlet state) after excitation is normalized to unity. Figure 2 shows the calculated decay curve of the population density of Tb 9 cluster following a short-pulse excitation for k TbET = 0 s −1 (absence of TbET: blue line) or k TbET = 50000 s −1 (presence of TbET: red line) in the presence of BET. The other rates kr S1 + knr S1 = 3.4 × 10 8 s −1 , kisc s1 = 7.5 × 10 8 s −1 , kr T1 + knr T1 = 15000 s −1 , and kr Tb = knr Tb = 400 s −1 were chosen from previous reports 53,54 . The values of k PSET and k BET are arbitrary and do not affect the qualitative result. For clarity of the results, k PSET = 6000 s −1 and k BET = 3000 s −1 were chosen. The lifetime of collective Tb(III) ions (Tb1(t) + Tb2(t) + … + Tb9(t)) is extended to τ calc = 720 μ s in the presence of TbET compared to τ calc = 685 μ s in the absence of TbET. The decay curves of the T 1 state in Fig. 2 contain short (0-0.1 ms region) and long components (0.1 ms and onward). The short component corresponds to the relaxation process of the T 1 state following intersystem crossing from the S 1 state. The time of this process matches that of the rise in population density of Tb(III) ions. The longer component corresponds to the repopulation of the T 1 state by BET from Tb(III) ions and as a result the decay rate is the same as for the Tb(III) ions. Population density of Scientific RepoRts | 6:37008 | DOI: 10.1038/srep37008 the longer component of the T 1 state in the presence of TbET is lower than that in the absence of TbET, indicating suppression of BET. Table 1 summarizes the emission quantum yield Φ ππ*,calc and BET efficiency η BET,calc obtained by the calculation for steady-state excitation. BET efficiency η BET,calc is defined as the difference in yield of excited Tb(III) ions with BET (k BET = 3000 s −1 ) and without BET (k BET = 0 s −1 ). An approximately 3% decrease in BET efficiency η BET,calc is observed in the Tb 9 cluster in the presence of TbET compared to that in the absence of TbET. We also calculated the population density for a hypothetical cluster where all Tb(III) ions are in an identical environment to confirm the importance of Tb9 being isolated from BET (Supplementary Information S5 and  Table S3). In this case, no change was observed in the emission lifetime, quantum yield, or BET efficiency regardless of the rate of TbET. These calculations clearly show that the combination of fast TbET and Tb9 plays a role in the suppression of BET in Tb 9 cluster. Structure and Identification. X-ray single-crystal analysis of Gd 9 cluster was performed in order to understand the molecular structure and coordination geometry of the nine Ln(III) ions in Tb n Gd 9−n clusters. The analysis showed that Gd(III) ions in the nonanuclear cluster take the form of an "hour-glass" structure in which the upper four and lower four Gd(III) ions are connected to the center Gd(III) ion via oxygen-bridging as shown in Fig. 3a. All Gd (III) ions take the form of an 8-coordination structure. The center Gd(III) ion is coordinated only by eight oxygen atoms. Each of the Gd(III) ions in the upper four and lower four sites (outer unit) are coordinated by both butylsalicylate ligands and oxygen atoms. The distances between two Gd(III) ions for all combinations are summarized in Table S4.
Evaluation of coordination geometry of Gd(III) ions was done through continuous shape measures (CShM) calculation using SHAPE [55][56][57] . The CShM criterion S, summarized in Table S5, represents the degree of deviation from ideal coordination geometry. We have chosen CShM over another method called "shape measure" (ShM) 58 because it takes account of the distortion of center metal ion from the center of mass. The principle and comparison of the calculation method in CShM and ShM is described in Supplementary Information S7. The S value for the center Gd(III) ion (Fig. 3b) was 0.082 when calculated for 8-coordinated square antiprism (8-SAP) geometry and it was 2.481 for 8-coordinated trigonal dodecahedron (8-TDH) geometry. Therefore, the coordination geometry of the center Gd(III) ion is attributed to the 8-SAP structure. The upper four and lower four Gd(III) ionns (Fig. 3c) take an 8-TDH structure since the S values calculated for 8-TDH are smaller than those for 8-SAP. This structural result is similar to that of our previously reported Tb 9 cluster 50 .
The structures of the other Tb n Gd 9−n clusters (n = 1, 2, 5, 8) were determined by the combination of powder XRD ( Figure S2a) and FAB-MS ( Figure S2b). In the XRD results, the diffraction angle is corrected on the Si peak at 2θ = 28.43 degrees for accurate comparison of the peaks derived from the Tb n Gd 9−n clusters. Three distinguished peaks (2θ 1 = 11.3 degrees, 2θ 2 = 15.6 degrees, and 2θ 3 = 19.8 degrees) were observed for all of the clusters indicating that the mixed Tb/Gd clusters have the same structure as those of Tb 9 and Gd 9 clusters. This is further supported by FAB-MS spectroscopy which showed m/z value of the Tb n Gd 9−n clusters corresponding to their calculated molecular weight without the NO 3 − counter-anion. The results presented above indicate that all Tb n Gd 9−n clusters were successfully synthesized with identical structures.  Optical Properties. Emission spectra of Tb n Gd 9−n clusters (n = 1, 2, 5, 8, 9) in 1.0 × 10 −4 M chloroform solution were measured and Fig. 4a shows the spectra, normalized at the peak intensity. The Tb n Gd 9−n clusters exhibit characteristic emission of the 4f-4f transition of the Tb(III) ion with each of the peaks corresponding to its 5 D 4 → 7 F J (J = 6 − 1) transitions 59 . The spectral shape of the emission was identical in all Tb n Gd 9−n clusters. Additionally, the emission spectral shape of Tb 9 cluster in powder form ( Figure S4) was the same as that in the solution form, indicating that the coordination structure is maintained in solution. The emission spectrum of Gd 9 cluster in 1.0 × 10 −4 M chloroform solution at 210 K ( Figure S5) was measured to estimate the excited triplet state (T 1 ) energy level of the ligand 38,60,61 . The emission peak was observed at 461 nm (21690 cm −1 ). Since the 5 D 4 level of a Tb(III) ion is 20620 cm −1 as observed in the emission spectra (485 nm), the energy gap ΔE between T 1 and 5 D 4 was estimated to be 1070 cm −1 . This is well within the range for BET in Tb(III) complexes (ΔE < 1850 cm −1 ) 33,34,38 , and thus BET is expected to take place in Tb n Gd 9−n clusters. The absolute emission quantum yield was determined by using an integration sphere (λ EX = 380 nm, ligand excitation) and emission lifetimes were determined by using a nanosecond pulse laser (λ EX = 355 nm, λ EM = 550 nm, ligand excitation) for clusters in a chloroform solution. The emission decay profiles were single-exponential (Fig. 4b) in all Tb n Gd 9−n clusters. As summarized in Table 2, the emission quantum yield Φ ππ* and lifetime τ obs increased with increasing numbers of Tb(III) ions in the Tb n Gd 9−n clusters. The emission quantum yield reflects the effect of all photophysical processes in Tb n Gd 9−n clusters. Of these processes, TbET, PSET, and BET are all likely to vary with n in the Tb n Gd 9−n clusters, and the effect purely based on TbET is indistinguishable. The effect of TbET with increasing number of Tb(III) ions in the clusters was investigated by measuring the temperature dependence of emission lifetimes (Fig. 5). A clear temperature dependence was observed above 270 K for Tb 1 Gd 8 and Tb 2 Gd 7 clusters, while lifetimes remained constant for Tb 5 Gd 4 , Tb 8 Gd 1 , and Tb 9 clusters. The rate constant of BET k BET can be estimated by the following equation 37,62 .
BET 210K BET where τ is measured emission lifetime at a given temperature, τ 210K is the emission lifetime at 210 K, A is frequency factor, Ea BET is activation energy for BET, R is gas constant, and T is temperature. Ea BET and k BET can be calculated for Tb 1 Gd 8 cluster by an Arrhenius plot within the range in which temperature dependency was    (9). A is frequency factor. d Analyzed from an Arrhenius plot of Equation (9) using lifetime temperature dependency results. k BET and E aBET could only be calculated for Tb 1 Gd 8 cluster since other Tb n Gd 9−n clusters (n = 2, 5, 8,9) involve TbET, which contributes to the temperature dependency of lifetimes. observed ( Figure S6). The BET rate constant k BET and activation energy Ea BET for Tb 1 Gd 8 cluster were calculated to be 167 s −1 and 38.7 kJ mol −1 , respectively ( Table 2). Emission lifetime and its temperature dependence are in qualitative agreement with theoretical results presented in the Theoretical Background section. The theoretical lifetime of Tb 9 cluster in the absence of BET is constant regardless of TbET rate k TbET (Supplementary Information S4 and Table S2). Experimentally, BET is absent in Tb n Gd 9−n clusters at 210 K, and the number of Tb(III) ions in the cluster is directly related to k TbET . Thus the emission lifetime at this temperature should be the same for all Tb n Gd 9−n clusters. The experimental emission lifetimes of Tb n Gd 9−n clusters at 210 K τ 210K are approximately 1.12 ms regardless of the number of Tb(III) ions in the clusters (Table 2 and Fig. 5). Meanwhile, the theoretical lifetime of Tb 9 clusters in the presence of BET shows that the lifetime is longer in the presence of TbET than in the absence of TbET. This comparison is analogous to experimental lifetimes of Tb 9 cluster (presence of TbET) and Tb 1 Gd 8 cluster (absence of TbET) at a temperature above 270 K, at which BET occurs. At a temperature above 270 K, the experimental lifetime is clearly longer for clusters with larger numbers of Tb(III) ions than for clusters with smaller numbers of Tb(III) ions. Such agreement between the theoretical and experimental results implies that the contribution of BET is indeed suppressed in Tb 9 cluster because of TbET and the existence of a center Tb(III) ion not in direct contact with ligands for which no BET occurs.

Summary and Conclusion.
The role of energy transfer between Tb(III) ions in luminescent Tb(III) complexes has been demonstrated to reduce BET losses both theoretically and experimentally using Tb n Gd 9−n clusters ([Tb n Gd 9−n (μ -OH) 10 (butylsalicylate) 16 ] + NO 3 − ) as model system. In the Theoretical Background section, we demonstrated that two features of Tb 9 cluster were important for suppressing BET: 1) TbET by closely assembled Tb(III) ions and 2) existence of Tb9 that is isolated from BET. Experimentally, we synthesized and investigated the photophysical properties of nonanuclear Tb n Gd 9−n clusters where n = 0, 1, 2, 5, 8, and 9. The combination of X-ray single-crystal analysis, powder XRD, and FAB-MS revealed that these clusters have nearly identical structures. Temperature dependency measurements of emission lifetime revealed that effect of BET becomes prominent in Tb n Gd 9−n clusters at temperatures above 270 K. Below this temperature, the emission lifetime is constant for all clusters. Above 270 K, the decrease in emission lifetime is mitigated for clusters with over five Tb(III) ions. By comparing the trends observed in experimental results to those of theoretical results, it was found that the contribution of BET is indeed suppressed in clusters with a large number of Tb(III) ions. These findings provide a new insight into the fundamental photophysics of Ln(III) complexes as well as indication of a novel strategy to achieve higher luminescence efficiency in Ln(III) complexes. Apparatus. FAB-MS spectra were measured on a JEOL JMS-700TZ. Elemental analyses were performed by Exter Analytical CE440. Infrared spectra were recorded on a JASCO FT/IR-4600 spectrometer. XRD spectra were characterized by a RIGAKU X-ray diffractometer RINT 2200. Single crystal X-ray diffractions were made on a RIGAKU RAXIS RAPID imaging plate area detector.

Materials.
Optical Measurements. Absorption spectra of Tb n Gd 9−n clusters were obtained by using a JASCO V-670 spectrometer. Emission spectra were measured using a Horiba/Jobin-Yvon FluoroLog-3 spectrofluorometer and a JASCO FP-6600 spectrometer. The combination of an integration sphere and a JASCO FP-6600 spectrometer was used to measure emission quantum yields. Emission lifetimes were measured using the third harmonic (355 nm) of a Q-switched Nd:YAG laser. The temperature was controlled using an Oxford Instruments OptistatDN2 cryostat.
Crystallography. Colorless single crystals of Gd 9 cluster obtained from solutions in methanol were mounted on a glass fiber by using epoxy resin glue. All measurements were made using a Rigaku RAXIS RAPID imaging plate area detector with graphite-monochromated MoKα radiation. Corrections for decay and Lorentz-polarization effects were made using a spherical absorption correction, solved by direct methods, and expanded using Fourier techniques. Non-hydrogen atoms were refined anisotropically except for disordered atoms. Hydrogen atoms were refined using the riding model. The final cycle of full-matrix least-squares refinement was based on observed reflections and variable parameters. All calculations were performed using a CrystalStructure crystallographic software package. We confirmed the CIF data by using the checkCIF/PLATON service. CCDC-1479981 (Gd 9 cluster) contains the crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Center via www.ccdc.cam.ac.uk/data_request/cif.