Luminescent Ln3+-based silsesquioxanes with a β-diketonate antenna ligand: toward the design of efficient temperature sensors

We report the synthesis and single-crystal X-ray diffraction, magnetic, and luminescence measurements of a novel family of luminescent cage-like tetranuclear silsesquioxanes (PhSiO1.5)8(LnO1.5)4(O)(C5H8O2)6(EtOH)2(CH3CN)2⋅2CH3CN (where Ln = Tb, 1; Tb/Eu, 2; and Gd, 3), featuring seven-coordinated lanthanide ions arranged in a one-capped trigonal prism geometry. Compounds 1 and 2 exhibit characteristic Tb3+ and Tb3+/Eu3+-related emissions, respectively, sensitized by the chelating antenna acetylacetonate (acac) ligands upon excitation in the UV and visible spectral regions. Compound 3 is used to assess the energies of the triplet states of the acac ligand. For compound 1, theoretical calculations on the intramolecular energy transfer and multiphonon rates indicate a thermal balance between the 5D4 Stark components, while the mixed Tb3+/Eu3+ analog 2, with a Tb:Eu ratio of 3:1, showcases intra-cluster Tb3+-to-Eu3+ energy transfer, calculated theoretically as a function of temperature. By utilizing the intensity ratio between the 5D4→7F5 (Tb3+) and 5D0→7F2 (Eu3+) transitions in the range 11–373 K, we demonstrate the realization of a ratiometric luminescent thermometer with compound 2, operating in the range 11–373 K with a maximum relative sensitivity of 2.0% K−1 at 373 K. These findings highlight the potential of cage-like silsesquioxanes as versatile materials for optical sensing-enabled applications.

In Eq.S7,   is the spin operator in the ligand and   is the dipole operator (its -component), the value of the element matrix of these coupled operators is ~10 −36 () 2 •  2 15,22 .The ⟨ ′  ′ ‖‖⟩ is the reduced matrix elements of the spin operator, which were calculated using free-ion wavefunctions in the intermediate coupling scheme 23,24 .The  term in Eqs.S5-S7 is the spectral overlap factor that considers the energy mismatch condition between donor and acceptor states 11,15 .
For the case of ligand-to-metal energy transfer,  can be estimated by: where Δ is the band maximum energy difference between the donor state and lanthanide ion acceptor state, Δ =   −   .  is the bandwidth at half-height for the donor state, assumed here a typical value of   = 4000 cm -1 for both S1 and T1 states.(Δ, ) = (∆    ⁄ ) if ∆ is negative and (Δ, ) = 1 if ∆ ≥ 0, where   is the Boltzmann constant and  is the temperature.
Then, the energy transfer rates () are calculated by the sum over Eqs.S5-S7 in the same pathway: Having justified that the dominant process for energy transfer to sensitize Tb 3+ is through S1, which feeds 5 D4 only indirectly via successive multiphonon decays (vide manuscript), it is important to note that these multiphonon decays are orders of magnitude lower than the direct T1→ 5 D4 sensitization.Therefore, Table S3 provides a summary of the rates for compound 1.

Tb-to-Eu energy transfer rates
In this section, a theoretical procedure is presented to estimate the Tb-to-Eu energy transfer rates based on crystallographic structure and the theory of nonradiative energy transfer between lanthanide ions. 14,25Utilizing crystallographic data allows for the determination of the arrangement of host sites that can be occupied by Eu 3+ (acceptor) or Tb 3+ (donor) ions.
The pairwise energy transfer rates between lanthanide ions were calculated, considering the dipoledipole ( − ), dipole-quadrupole ( − ), quadrupole-quadrupole ( − ), exchange (  ), and magnetic dipole-magnetic dipole ( − ) mechanisms, 26,27 according to Eqs.S10-S14, respectively: where the intensity parameters   are those obtained using the FED contribution, likewise in the Ligand-Ln 3+ energy transfer procedure.The sets of   (FED) values obtained, in units of 10 In Eq.S13,  − represents the overlap integral between 4f subshells of the donor and acceptor lanthanide ions.The values of  − as a function of the Tb-Eu distance (  ) were obtained using the parametric function  − () = ( +  +  2 ), with a=-0.032,b=-0.261, and c=-0.34. 21The  − decreases rapidly to zero with the increase of the donor-acceptor distance , as demonstrated in Reference 26 for the case of Tb-Eu.This is why the   term can often be neglected in the Ln-Ln energy transfer processes, where the donor-acceptor distances are typically higher than 4 Å, 14 in contrast to the case of intramolecular energy transfer processes in lanthanide chelates. 14,15n all equations related to Ln-Ln energy transfer mechanisms, the spectral overlap factor (F) is involved.This quantity is associated with the energy mismatch conditions between the donor and acceptor states, and the following expression for F has been utilized: 14 ] where ℏ  and ℏ  correspond to the bandwidths at half-height of the Tb 3+ (donor) and Eu 3+ (acceptor) transitions, respectively.ΔE is the energy difference between donor and acceptor transitions ( =   −   ).In the present work, ℏ  = ℏ  =250 cm −1 is considered, a value deemed acceptable concerning the nature of 4f transitions.
For each pathway, the energy transfer rates were calculated by the sum over Eqs.S10-S14 ( =  − +  − +  − +   +  − ) and all results are shown in Table S4.Figures          3 Tables Table S1.Crystal data and structure refinement for 1-3.Table S3.A) Direct intramolecular energy transfer rates from the T1 to the 5 D4 from the rising of the population in 7 F5 and 7 F6 levels: Δ is the donor-acceptor energy difference;  − ,  − , and   are the dipole-dipole, dipole-multipole, and exchange mechanisms (Eqs.S5 -S7) while  is the sum of these mechanisms in the same pathway (Eq.S9);  is the sum of these pathways, which is mainly constituted by the exchange mechanism of the T1→[ 7 F5→ 5 D4] pathway.B) Multiphonon decay rates from 5 D3 to 5 D4 considering N-phonons involved in the process (N from 2 to 5): Δ is the 5 D3-5 D4 energy difference 19 ; ℏ ̅ is the mean phonon energy; the  factor was estimated from Miyakawa-Dexter approach 5 (Eq.S2);   is the multiphonon rate between 5 D3-

Identification code
Figure S1.a) Perspective view of the crystal packing for 2 along the crystallographic axis b.Hydrogen atoms and solvate acetonitrile molecules have been omitted for clarity; b) Molecular structure of 2 showing the prism-like polyhedron in the form of a New Year paper lantern; c) Molecular structure of 2 showing the square arrangement of the Tb/Eu atoms in the [(Tb/EuO2)4]-core.Colour code: green Tb/Eu; yellow Si; red O; blue N; grey C.

Figure S2 .
Figure S2.a) Perspective view of the crystal packing for 3 along the crystallographic axis b.Hydrogen atoms and solvate acetonitrile molecules have been omitted for clarity; b) Molecular structure of 3 showing the square arrangement of the Gd atoms in the [(GdO2)4]-core; c) Molecular structure of 3 showing the prism-like polyhedron in the form of a new year paper lantern.Colour code: orange Gd; yellow Si; red O; blue N; grey C.

Figure S3 .
Figure S3.Excitation spectrum (black curve) monitored at 393 nm and emission spectrum (red curve) performed under excitation at 246 nm in solid state at 77 K for 3.

Figure S4 .
Figure S4.a) Emission spectrum of 1 upon 485.6 nm excitation performed in the 11 -297 K temperature range; b) Emission spectrum of 1 upon 485.6 nm excitation at 11 K.The shadowed regions represent the integration ranges for each transition; c) Normalized integrated intensity area of bands indicated as 2, 3 and 4 as a function of temperature.

Figure S5 .
Figure S5.Temperature dependence of the I1/I2 ratio (the I1 and I2 correspond to the Starks components indicated in Figure4) performed for the ⁵D4→⁷F5 transition emission band for 1 upon the excitation at 330 nm in the: 11 -297 K (c) and 298 -378 K (d) intervals.The red curves represent a single exponential function as the best fit to the experimental data (r 2 > 0.99).

Figure S6 .Figure
Figure S6.Temporal decay trace of 1 monitoring at 543 nm upon 330 nm excitation recorded at room temperature.The red solid curve represents a single-exponential function as the best fit to the experimental data (r>0.99).

Figure S8 .
Figure S8.a) Emission spectra performed with the excitation at 464 nm in solid state in the temperature range 11 -300 K for 2. b) Normalized integrated intensity area of transition 5 D0→ 7 F2 within the temperature range from 11 K to 300 K.

Figure S9 .
Figure S9.Energy transfer rates in the {Ln4} cluster as a function of temperature.(a) shows the first two shortest distances, while (b) shows the longest two distances.The average energy transfer is shown in (A).

Figure S10 .
Figure S10.a) Temperature dependence of the normalized 5 D4→ 7 F5/ 5 D0→ 7 F2 ratio performed for the emission spectra under the excitation at 484 nm in the temperature range 11 -300 K for 2 with 3 experimental cycles (circles) and the associated fit (red curve) with a single exponential function (full line) (r>0.99);b) Temperature dependence of the corresponding thermal sensitivity (Sr).

Table S4 .
Pairwise Tb-to-Eu energy transfer rates for the shortest Tb-Eu distance (3.728 Å) at 300 K.