Solution‐State Cooperative Luminescence Upconversion in Molecular Ytterbium Dimers

Two homometallic ytterbium dimers are prepared and their solution‐state photoluminescence and upconversion properties are investigated. Both complexes exhibit two‐photon cooperative luminescence upconversion in the visible region (λem ≈ 510 nm) upon excitation into the near‐infrared Yb 2F5/2 ← 2F7/2 absorption band at 980 nm. This miniaturization of the cooperative luminescence phenomenon down to just two Yb ions unequivocally proves the mechanistic origins of this process. Time‐resolved measurements and excited‐state modeling indicate the presence of a slow recombination of two singly excited ions Yb*Yb* into a virtual excited state, which ultimately gives rise to the observed emission at ≈510 nm.


Introduction
Upconversion (UC), converse to conventional photoluminescence, is an anti-Stokes process whereby emission is generated via the piling up of multiple photons. [1] As a result of the solid-state or nanoparticular UC but is uniquely possible using a discrete molecular approach. As such we envisaged a miniaturization of the solution-state CL phenomenon down to its mechanistically simplest components using homo-dinuclear Yb 2 complexes, based upon both cryptate and tetra-imine bridging ligands.
Single crystals of [Yb 2 L 1 (NO 3 ) 2 ](NO 3 ) and [L 2 (Yb(ttfa) 3 ) 2 ] suitable for single-crystal X-ray diffraction (SCXRD) analysis were obtained from slow evaporation of EtOH and CH 3 CN solutions respectively. The coordination geometry of Yb III for both complexes was initially investigated using the SHAPE 2.1 software using continuous shape measurement (CShM) ( Table 1). [38] This software gives an indication of the metal center geometry where 0.000 corresponds to perfect polyhedron, i.e., a number closer to zero indicates a best fit for a given polyhedron. For the [Yb 2 L 1 (NO 3 ) 2 ](NO 3 ) complex the geometry is best described as an octacoordinated triangular dodecahedron (TDD; Yb1 = 1.718, Yb2 = 1.964) but also resembles an octacoordinate biaugmented trigonal prism (BTPR; Yb1 = 2.311, Yb2 = 1.702). The two Yb III centers are crystallographically nonequivalent and thus have different geometries in the solid state; however, this is likely due to crystallographic packing effects. Corresponding ChSM analysis of the DFT optimized structure of [Yb 2 L 1 (DMSO) 2 ] 3+ (vide infra DFT results), show much more symmetric Yb ions that indicates a TDD structure in solution (Yb1 = 1.599, Yb2 = 1.580). For the [L 2 (Yb(ttfa) 3 ) 2 ] complex the geometry is clearly that of an eight-coordinate square antiprism (SAP) environment (Yb1 = 0.424), exhibiting minimal distortion, the hetero leptic coordination environment notwithstanding. This is again reflected in the DFT results (vide infra) for L 2 (Yb(ttfa) 3 ) 2 ] which confirms the SAP geometry (Yb1 = 0.415).
Analyzing the structure of [Yb 2 L 1 (NO 3 ) 2 ](NO 3 ), the complex crystallizes in the P4 1 2 1 2 space group with solvent molecules in the unit cell, perpetuated by an H-bonding network with cocrystallized disordered H 2 O which primarily interacts with the free and bound nitrate counterions (Figure 2; Table S1 and Figures S8 and S9, Supporting Information). Bond lengths and angles are summarized in Figure S10 and Tables S2 and S3 (Supporting Information). Both of the crystallographically distinct Yb ions are encapsulated in the trianionic cryptate cavity, although both display similar geometries at the Yb centers. They are each octacoordinated, bound to the bridgehead tertiary nitrogen and three flanking imine groups of the tren moiety.

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The bridgehead nitrogen displays relatively elongated distance (d(Yb-N amine (mean)) = 2.64 Å) compared to the imine donors (d(Yb-N imine (mean)) = 2.40 Å), arising from the geometric constraints of the ligand. The two metal centers display an internuclear distance of 3.4450(3) Å and are linked via three µ 2 -phenolate groups (d(Yb-O phenolate (mean)) = 2.32 Å). The metal ions sit at the apical and basal vertices of a highly symmetrical trigonal bipyramid, the equatorial sites comprising the three oxygen donors, with a high degree of linearity compared to the phenolate centroid (∡Yb1-Cnt phenolate -Yb2 = 176.67 (14)°; d(Yb1-Cnt phenolate ) = 1.721(2)Å, d(Yb2-Cnt phenolate ) = 1.726(2)Å) . The final eighth coordination site is occupied by an oxygen atom of a nitrate counterion (d(Yb-O nitrate (mean)) = 2.35 Å). A second oxygen atom provides a weak interaction with Yb1 (Yb1-O8 = 2.993(5) Å). The compound is enantiopure in the solid state; the ligand overall exhibits chirality imparted to helical twisting of the phenolate moieties to satisfy the metal coordination, while each half displays a syn-rotatory helicity at the metal center [35,36] (i.e., Δ,Δ arrangements with Flack parameter = 0.016 (12)). SCXRD analysis of [L 2 (Yb(ttfa) 3 ) 2 ] (Figure 3; Table S4 and Figures S11 and S12, Supporting Information) reveals that the complex crystallizes in the orthorhombic P2 1 /n space group, displaying a plane of symmetry through the central 2,2′-bipyrimidine ligand with one ytterbium ion in the asymmetric unit. The internuclear lanthanide Yb1-Yb1 distance was found to be 6.639 Å, with only a slight deviation from the mean plane defined by the 2,2′-bipyrimidine (Yb1-Pln bpm = 0.220 Å; Figure S13, Supporting Information). The Yb ions are eight-coordinated ( Figure S14 and Table S5, Supporting Information), satisfied by three anionic ttfa ligands corresponding to six oxygen donors (Mean distance Yb-O ttfa = 2.26 Å), with the coordination sphere completed by two nitrogen donors from the bridging 2,2′-bipyridimine ligand (Mean distance Yb-N bpm = 2.52 Å). Aside from the heteroleptic donor environment around the Yb ion, the geometry is consistent with a slightly distorted square antiprism (SAP-D 4d ) with average skew angles (ϕ) of 45.03° between the upper and lower square faces, which are separated by 2.532(2) Å. Other metrics which can be analyzed are the structure geometry versus an ideal square anti-prism. Figure 3c,d shows the sides formed by the upper and lower square faces of the SAP polyhedron (d in ) as well as the distance between the two mean square faces (d pp (Pln-Pln)). d pp is only slightly perturbed from parallel (∡Pln-Pln = 1.54(9)°). Other salient observations are the d pp (Pln-Pln) distance (2.53 Å), which is shorter than the average internuclear distance (d in ) between the atoms lying on the vertices of the square faces (Mean value of d in = 2.75 Å), while d pp = d in in a perfect SAP geometry. Likewise, the average calculated value of α of 57.06° is more open compared to the perfect SAP (α ideal = 54.73°). [39,40] Both these observations indicate that the geometry at Yb exhibits a splaying and compression versus the ideal geometry.
The absorption, excitation and luminescence spectra of [Yb 2 L 1 (NO 3 ) 2 ](NO 3 ) in DMSO are presented in Figure 4, with the main spectroscopic data gathered in Table 2. The UV-vis absorption spectrum displays a strong absorption band (maximum at λ = 370 nm, ε = 20200 m −1 cm −1 ) attributed to the π* ← π transitions of the coordinated bis-iminophenolate moieties. In the NIR domain, weak Stark-split Yb III 2 F 5/2 ← 2 F 7/2 absorption bands are observed between 900 and 1050 nm (maximum at λ = 977 nm, ε = 13.3 m −1 cm −1 ). The downshifted emission spectra of the complex upon ligand excitation induces Yb III -centered 2 F 5/2 → 2 F 7/2 emission bands with maxima at 977 nm, with weaker lower energy bands at 1006 and 1030 nm. Time resolved studies measured on the main emission band of [Yb 2 L 1 (NO 3 ) 2 ](NO 3 ) revealed a biexponential decay with lifetimes of 8.3 µs (83%) and 18.7 µs (17%), likely a result of a combination of DMSO and NO 3 − ligands competing for the 8th coordination site not satisfied by ligand L 1 .
From the NIR absorption spectra, the methodology of Werts and co-workers [41] was applied to determine the radiative lifetime of Yb in the complex using Equation (1) and (2) Adv. Optical Mater. 2023, 11, 2202307

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In which N A is Avogadro's number, υ is the barycenter of the transition (cm −1 ), c is the speed of light in vacuum (cm s −1 ), n is the refractive index of the solvent, ε( υ) is the absorption spectrum of the transition (m −1 cm −1 ).
Weighted by the number of Yb centers (divided by 2 in comparison to the values reported in Table 2), g l and g u are related to the degeneracies of the ground and excited states, respectively, and are equal to 2J + 1 where J = 7/2 for g l and J = 5/2 for g u .
A radiative lifetime of 587 µs was determined for Yb in the [Yb 2 L 1 (NO 3 ) 2 ](NO 3 ) complex. The Yb centered luminescence quantum yield, Yb Yb Φ , could then be calculated using Equation (3) Yb Yb obs Considering that the [Yb 2 L 1 (NO 3 ) 2 ](NO 3 ) complex displayed a biexponential behavior, the intensity averaged luminescence decay lifetime [42] of 10.1 µs was used for the calculations. The Yb centered quantum yield was then calculated to be 0.017.
The fine structure of the absorption and downshifted photoluminescence ( Figure 4a) indicates Stark-split sublevels of the 2 F 7/2 and 2 F 5/2 ground and excited states (Figure 4b), which was further investigated using CASSCF/NEVPT2/QDPT calculations. For the complex of L 1 , calculations were performed on the [Yb 2 L 1 (DMSO) 2 ] system, as the NO 3 − anions coordinated in the solid state are very likely replaced by DMSO ligands, as a result of their similar donor character and the large excess of DMSO present in solution. [43] Results of the theoretical calculations are presented in Table 3. The three main emission bands as well as the shoulder at 1050 nm observed in the emission spectrum correspond to transitions between the lowest Stark level of the 2 F 5/2 excited state to the Stark levels of the ground 2 F 7/2 state. Thus, the main emission band at 977 nm matches with the calculated (4 → 0) transition, denoted A. This is borne out for the other emission bands at 1002 nm (4 → 1, transition B), 1024 nm (4 → 2, transition C), and 1050 nm (4 → 3, transition D). We note that the emission components at 1002 and 1024 nm match very well the weak (hot) absorptions observed on the low energy side of the absorption spectrum. The theoretical CASSCF/NEVPT2/ QDPT calculations provide reasonably good agreement with the experimental data, which supports our assignment. Furthermore, calculations provided the highest oscillator strength for the (4 ← 0) transition calculated at ≈987 nm, which also contains further intensity contribution from the hot (5 ← 1) transition, in agreement with the experimental spectra.
The speciation of [Ln(ttfa) 3 ) 2 ] complexes has been widely reported in the literature [46][47][48][49][50][51] and it is known that at very low concentrations complex mixtures can occur through dissociation of one or more of the ligands. Our study within reports these results with care and does not discount the possibility of some dissociation. However, the UC spectra reported are on relatively concentrated samples which minimize the potential for dissociation and we can conclude that the dimetallic species are the main species at these concentrations.
The two-photon behavior of the UC emission was confirmed using Log/Log plots (Figure 6b,e), showing a quadratic dependence of the incident laser intensity. The calculated slopes of the Log/Log plots, 1.93 and 1.66, respectively, for [Yb 2 L 1 (NO 3 ) 2 ] (NO 3 ) and [L 2 (Yb(ttfa) 3 ) 2 ], were indeed close to the theoretical value of two, indicating that it operates through a two-photon process consistent with the phenomenon of CL. One notable observation is the respective maxima of the UC emission.
[L 2 (Yb(ttfa) 3 ) 2 ] (λ UC = 512 nm) displays a 10 nm bathochromic shift with respect to [Yb 2 L 1 (NO 3 ) 2 ](NO 3 ) (λ UC = 502 nm), which can be understood by the increased prevalence of the low energy emission bands (B and C; Figures 4b and 5b) and thus a bigger contribution from the two-photon lower-energy transitions. [55] Considering that CL arises from the relaxation of two transitions on two distinct Yb excited ions, the intensity F(λ) of the CL at wavelength λ is the result of all possible combinations between these levels and can be calculated by a convolution of the NIR emission spectrum f(ʋl) (Equation (4); Section S5.1 and Figures S16 and S17, Supporting Information) [29,56,57] The convoluted spectra can be found in Figure 6a,d, respectively, for [Yb 2 L 1 (NO 3 ) 2 ](NO 3 ) and [L 2 (Yb(ttfa) 3 ) 2 ]. The maxima of the calculated CL emissions are found at 513.0 and 516.5 nm, respectively, in rather good agreement with the observed maxima in the measured spectra (resp. 502 and 512). As anticipated, the maximum for [L 2 (Yb(ttfa) 3 ) 2 ] is bathochromically shifted, as a result of the larger contributions from the more intense band at low energy observed in the emission spectrum of [L 2 (Yb(ttfa) 3 ) 2 ] ( Figure 5) compared to that of [Yb 2 L 1 (NO 3 ) 2 ] (NO 3 ) (Figure 4).
Finally, we investigated the evolution of the UC signal using time-resolved measurements in which the sample is excited during 100 µs irradiation with a repetition rate of 50 kHz (Figure 7c,f). During the excitation period, the UC signal develops to reach a quasi-steady state within ≈30 µs. When the excitation is switch off, the UC CL decays rapidly after the pulse. The energy-level diagram in Figure 7 shows the excitedstate process occurring to engender upconverted CL, inspired by the mechanism proposed by Güdel et al. for weakly coupled dimers generating CS. [58] Firstly a single Yb III ion is excited (k exc ) to form Yb*Yb, which subsequently absorbs another photon to form a Yb*Yb* doubly excited state. This is proceeded by a slow recombination step (k UC ) to form a doubly excited (YbYb)** ion pair which then emits in the visible region with a corresponding lifetime τ Yb** .
Considering the rise and decay of the luminescence intensity of the (YbYb)** CL of the Yb dimers, the populations of the  www.advopticalmat.de different states, denoted as |0〉 to |3〉 (Figure 7) can be modeled with the following matrix where k exc , the pumping rate constant can be defined as exc p Yb where λ p is the excitation wavelength (980 nm), h is Planck's constant, c is the vacuum speed of light, P is the incident pump intensity and Yb 0 1 σ → is the absorption cross section (in cm 2 per molecule) of the Yb 2 F 7/2 → 2 F 5/2 transition obtained from the electronic absorption spectrum. In the case of [Yb 2 L 1 (NO 3 ) 2 ] (NO 3 ), the decay rate of Yb, k Yb* is fixed at 0.099 × 10 6 s −1 (averaged lifetime of 10.1 µs). k Yb** is the decay rate of the CL from (YbYb)** and k UC is the energy transfer from Yb*Yb* to (YbYb)**. The temporal evolution of the (YbYb)** was fitted according to the proposed model in two steps, first fitting the rise of the signal (k exc ≠ 0), then fitting the decay (k exc = 0) keeping other parameters as constants to the rise in the fitting. The luminescence intensity is assumed to be proportional to the population of state |3〉. Full experimental details about the fitting procedure are given in the Supporting Information (Section S5.2, Supporting Information).
With this mathematical model, the best fitting curve yields the values of k UC and k Yb** as 18.03 ± 0.05 × 10 6 s −1 and 0.74 ± 0.03 × 10 6 s −1 , respectively. It is worth noting that the rate    3 and 336 for [L 2 (Yb(ttfa) 3 ) 2 ]; b) Using cardiogreen (IR125) in MeOH (Φ = 0.078; λ exc = 765 nm) as reference [44] ; c) Calculated using an intensity average lifetime; d) Excitation at 980 nm in DMSO-d 6 , CH 3 CN, or CD 3 CN (P = 6.9 W cm −2 ), using Rhodamine6G in water (Φ = 0.76; λ exc = 488 nm) as reference [45] for the UC quantum yield, and errors estimated at 15%; e) Value obtained in DMSO-d 6 ; f) Obtained in CD 3 CN. of k Yb** (corresponding to a lifetime τ Yb** = 1/k Yb** = 1.4 µs) is faster than expected according to previous reports assuming it to be twice the rate of de-excitation of Yb*, [55] but such a phenomenon has already been observed for solid state CL. [29] When fixing the value of k Yb** to 2k Yb* , the fitting process failed to adjust the experiment time-resolved luminescence spectra ( Figure S18, Supporting Information). On the other hand, changing the k UC changes the decay behaviour of the Yb** luminescence, implying the key role of k UC in the CL ( Figure S19, Supporting Information).

Conclusion
Two homo-dimetallic Yb complexes have been prepared, based upon a triphenolic cryptate and a bipyridine-bridged ttfa complex via operationally simple one-step protocols. Both complexes were crystallized and analysis by SCXRD displays intermetallic distances of 3.445 and 6.639 Å, respectively. The absorption and emission properties of the complexes were fully studied and photoluminescence experiments upon ligand excitation gave rise to Yb-centered emission in the NIR region (λ em = 976 nm), for which theoretical calculations elucidated the Starks splitting of the 2 F 5/2 and 2 F 7/2 energy levels. Upon direct Yb excitation (λ ex = 980 nm) CL could be observed in the visible region (λ em ≈ 510 nm). The slight bathochromic shift observed in the CL spectrum of [L 2 (Yb(ttfa) 3 ) 2 ] compared to [Yb 2 L 1 (NO 3 ) 2 ] (NO 3 ) could be rationalized by convolution of the emission arising from the Yb centered 2 F 5/2 ← 2 F 7/2 emission band. The observed CLQY were found to be still modest, but similar or better than nonanuclear complexes in solution. [32] The CL was also analyzed using time-resolved spectroscopy and modeling of the excited state kinetics, revealing a slow UC energy-transfer step from an intermediate Yb*Yb* state which converts to a doubly excited state (YbYb)**, which is ultimately responsible for the CL emission. Although slow, the energy transfer rate for UC appeared faster than the direct de-excitation of Yb*, allowing the UC to occur. Possible improvements of CL in Yb dimers may be found in the further development of very long lived Yb complexes. [59] This molecular approach using only two Yb ions allows us unique insight into probing this enigmatic CL process, fully confirming the purported mechanism. The factors affecting the CLQY appear to be complicated but clearly determinants for efficient UC performance are related to the intermetallic distance and the lifetime of the double excited state (Yb**). Future rational design for improving the QY would focus on reducing this intermetallic distance and reducing nonradiative quenching pathways. One significant contribution is the potential of Yb to Yb energy transfer deactivation which results-perhaps unexpectedly-in improved UCQY for molecular dimers versus Yb 9 clusters.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.