Unravelling the formation pathway and energetic landscape of lanthanide cages based on bis-β-diketonato ligands

Abstract

This study focuses on the self-assembly mechanisms of triple- and quadruple-stranded lanthanide cages and their solution behaviour, particularly concerning equilibrium and cage interconversion. A systematic investigation was conducted to unravel the formation process of lanthanide cages based on bis-β-diketonato ligands. By employing diamagnetic La³⁺ ions, NMR spectroscopy coupled with ESI-MS analyses revealed the consecutive and competitive formation of four different species: [La₂L]⁴⁺, [La₂L₂]²⁺, [La₂L₃], and [La₂L₄]²⁻. Moreover, stepwise and overall stability constants were derived. Further studies on the energetics of the equilibrium between the two most stable species, the triple-stranded [La₂L₃] and quadruple-stranded [La₂L₄]²⁻ cages, were conducted through variable temperature analyses, indicating that the interconversion is exergonic, endothermic and mainly entropy driven. DFT thermochemical calculations involving an explicitly coordinated solvent allowed for a better evaluation of the role of enthalpic and entropic factors in step-by-step ligand association.

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Introduction

Supramolecular self-assembly entails the spontaneous arrangement of molecular constituents into higher-order structures. Understanding the precise mechanisms driving this assembly process is essential for effectively controlling and maximizing system functionalities. Metallo-supramolecular coordination assemblies, particularly those leading to cage architectures, have emerged as significant systems for both foundational research and practical applications.¹ Despite extensive exploration of coordination-driven supramolecular cages over the past two decades, in-depth molecular-level comprehension of the self-assembly process of these cages is still scarce and has primarily focused on systems involving Pd(II)/Pt(II) ions and multi-topic pyridine ligands. This understanding has been facilitated by a combination of computational approaches^2–4 and experimental techniques, including the QASAP method (quantitative analysis of self-assembly process) proposed by Hiraoka.⁵ However, the complexity in understanding this process is further increased by the fact that coordination-driven systems are dynamic owing to the nature of metal–ligand bonds. Arguably, the first and most commonly reported example involves the self-assembly of linear ligands and 90° metal corners with Pd(II) and Pt(II) ions to form triangular and square molecular polygons.^6–9 Even supramolecular cages constructed from other metal ions can undergo interconversion, which may be controlled by external stimuli, including physical^10–13 and chemical^14–18 triggers. However, if we consider ions different from Pd(II)/Pt(II), the study of the interconversion mechanism^19–21 is very rare. Lanthanide-based assemblies have recently gained attention owing to their unique electronic and coordination properties, which offer new opportunities to construct intricate supramolecular architectures.^22,23 These features make lanthanide systems suitable for applications in areas such as sensing, imaging, and information storage. However, lanthanide architectures are challenging considering the variable coordination numbers and coordination geometries of these ions. In the context of Ln-based cages, we have recently reported on [Ln₂L₄]²⁻ systems based on bis-β-diketonate ligands, which exhibit intriguing supramolecular characteristics. Oligo-β-diketone ligands allow access to a wide range of metallo-supramolecular systems. In view of the seminal work of Saalfrank²⁴ and the extensive study by Lindoy,²⁵ these ligands can be used to prepare metallocycles, cages, MOFs,^15,26–29 and even interlocked structures.^30–33 Although less common, oligo-β-diketones allow access to Ln based architectures. For instance, we demonstrated that [Ln₂L₄]²⁻ quadruple-stranded helicates and their host–guest properties allow dynamic and adaptive helicity reorganization due to guest-to-host chirality transfer.³⁴ Helicate-mesocate isomerism in [Ln₂L₄]²⁻ cages is strongly affected by the guest size and ligand flexibility.³⁵ Moreover, these cages show Ln³⁺ ion exchange,³⁶ leading to the formation of heterometallic systems. These systems can also serve as luminophore with high brightness to realize transparent luminescent solar concentrators.³⁷ The reaction between a Ln³⁺ ion and a bis-β-diketonate can easily lead to [Ln₂L₃] triple- or [Ln₂L₄]²⁻ quadruple-stranded helicates.^34,38–46 [Ln₂L₃] and [Ln₂L₄]²⁻ architectures feature different behaviours in terms of host–guest, luminescence and magnetic properties. Hence it is paramount to fully understand the formation pathway and energetic landscapes governing the self-assembly and the possible interconversion of these two systems. In the case of Ln cages, previous studies^47–51 have taken advantage of Eu and Tb systems through spectrophotometric titrations usually coupled with factor analyses to rationalize spectroscopic data in terms of possible species and infer their formation constants. Mass spectrometry can also provide valuable insights into the formation of lanthanide-based systems, as demonstrated in studies investigating the self-assembly of high-nuclearity Ln clusters.^52–56

Herein, a systematic study was conducted through NMR, ESI-MS and DFT calculations to unravel the self-assembly of [La₂L₃] and [La₂L₄]²⁻ systems considering three different bis-β-diketonate ligands in terms of the central scaffold. Four different species were found to be involved in the self-assembly between La³⁺ ions and bis-β-diketonate ligands, namely, [La₂L]⁴⁺, [La₂L₂]²⁺, [La₂L₃], and [La₂L₄]²⁻. The stepwise and overall formation constants were determined, and particular attention was devoted to the equilibrium between the triple-stranded [La₂L₃] and quadruple-stranded [La₂L₄]²⁻ cages and its energetics.

Results and discussion

Formation studies

We previously reported that pure [Ln₂L₄]²⁻ cages, based on three different bis-β-diketonate ligands (L^A, L^B, and L^M: Fig. 1), are straightforwardly prepared by employing stoichiometric ligand excess (Ln : L ratio of 1 : 2.5).^34,36,37 Using a Ln : L ratio of 2 : 3, [Ln₂L₃] triple-stranded helicate is formed. The possibility to control the formation of the two different systems [Ln₂L₃] and [Ln₂L₄]²⁻ by simply tuning the Ln : L ratio prompted us to undertake a systematic study of cage formation, with the aim of investigating, not only qualitatively but also quantitatively, the different species and steps leading to their self-assembly.

Fig. 1 (a–g) ¹H-NMR spectra (25 °C, 300 MHz, DMF-d₇) in the α-proton region of [La₂L^A_y]ⁿ, [La₂L^B_y]ⁿ and [La₂L^M_y]ⁿ (where y = 1, 2, 3, and 4 and n = 4+, 2+, 0, and 2−, respectively) following ligand addition. The different species are marked as follow: [La₂L]⁴⁺ = magenta, [La₂L₂]²⁺ = purple, [La₂L₃] = blue, and [La₂L₄]²⁻ = orange. (h) and (i) ESI-MS isotopic patterns for [La₂L^A₂]²⁺ and [La₂L^A₄]²⁻ species.

The formation of [Ln₂L₃] and [Ln₂L₄]²⁻ can be readily monitored through ¹H-NMR using La³⁺ ions^34,36,37 since the β-diketonate α proton is very diagnostic and easily allows to differentiate the species present in solution. For instance, in the case of L^A, the α proton is at 7.12 ppm for the free ligand, 6.00 ppm for the deprotonated ligand, 6.38 ppm for [La₂L^A₃] and 6.22 ppm for [La₂L^A₄]²⁻.

To an La³⁺ solution of known concentration, prepared by dissolving La(NO₃)₃·6H₂O in DMF-d₇, different aliquots of a deprotonated ligand solution of known concentration were added stepwise. ¹H-NMR spectra were recorded immediately after each ligand addition and again after three days to ensure equilibration, revealing no significant differences. It is important to note that all NMR investigations were conducted in DMF-d₇ to have a good coordinating solvent capable of effectively competing with the strong chelating ligands. In this way, La³⁺-ligand association constants are reduced to fall within an appropriate NMR range (i.e., K up to or slightly above 10⁶). Formation studies were carried out on the three ligands L^A, L^B and L^M. The obtained full ¹H-NMR spectra are reported in Fig. S8–S10,† while Fig. 1 shows the region relative to the diagnostic α-proton. After the addition of 0.25 ligand equivalents (La : L = 2 : 0.5), two singlets (6.43–6.48 ppm and 6.36–6.42 ppm, given as a magenta and purple circle, respectively, in Fig. 1a) are visible at lower fields as compared to the signals relative to [La₂L₃] and [La₂L₄]²⁻ cages. By further adding 0.25 equivalents (La : L = 2 : 1), the relative intensity of the two singlets changes toward the peak at a lower ppm value (Fig. 1b). Considering 1.00 ligand equivalent (La : L = 2 : 2), there are still two singlets, but the one at 6.43–6.48 ppm disappears, while the [La₂L₃] cage signal (6.30–6.38 ppm, blue circle in Fig. 1c) appears. [La₂L₃] species is the only one present at a 2 : 3 La : L ratio (Fig. 1d). Next, with 1.75 equivalents of ligand (La : L = 2 : 3.5), the signal at 6.15–6.24 ppm relative to [La₂L₄]²⁻ species (orange circle in Fig. 1e), appears, confirming the presence of an equilibrium between the 2 : 3 and 2 : 4 cages. Both cages were still present after the addition of 2.0 equivalents of the ligand (Fig. 1f). Finally, the [La₂L₄]²⁻ cage is the sole species present when an excess of ligand was added (2.50 equivalents, Fig. 1g). These experiments highlighted two new species at La : L ratios lower than 2 : 2. These species are systems with a lower number of coordinated ligands. In particular, the predominant species, as shown in Fig. 1c (purple), when the La : L ratio is 2 : 2, may be the [La₂L₂]²⁺ system, whereas the secondary species (magenta) observed in the first two spectra (Fig. 1a and b) appears only at an La : L ratio below 2 : 1, i.e. when the La³⁺ ion is in strong excess compared to the ligand, suggesting that this species may be the [La₂L]⁴⁺ complex. This [La₂L]⁴⁺ species, because of its higher positive charge, appears at lower fields. As the positive charge decreases, the α proton shifts to higher fields. DOSY-NMR spectra of the solutions with La : L^A ratios of 2 : 0.5, 2 : 2, 2 : 3 and 2 : 4 are reported in Fig. 2. The observed diffusion coefficients are all very similar (ca. 2.5 × 10⁻¹⁰ m² s⁻¹, Table S1†), i.e., the [La₂L^A]⁴⁺, [La₂L^A₂]²⁺, [La₂L^A₃] and [La₂L^A₄]²⁻ species possess similar hydrodynamic radii. This similarity can be explained by the fact that the Ln⋯Ln distance is mainly governed by the size of the ligand.

Fig. 2 DOSY-NMR spectra (25 °C, 400 MHz, DMF-d₇) at an La : L^A ratio of (a) 2 : 0.5, (b) 2 : 2, (c) 2 : 3 and (d) 2 : 4. DCHA is the dicyclohexylammonium cation.

In a similar manner, we conducted analyses using electrospray mass spectrometry (ESI-MS) in both positive and negative modes after adding 0.25, 0.5, 1.0, 1.5, 2.0, and 2.5 equivalents of the ligand L^A, (Fig. S11†). Across all scenarios, a single prominent peak at 828 m/z was observed in positive mode. In negative mode, a peak at 1226 m/z was discernible only when 1.5, 2.0 and 2.5 equivalents were added. The agreement between experimental and simulated isotopic patterns confirms that the 828 m/z peak corresponds to the solvated species [La₂L^A₂]²⁺ (Fig. 1h), whereas the negative mode peak is attributed to the quadruple-stranded cage [La₂L^A₄]²⁻ (Fig. 1i). Under conditions induced by the electrospray process, only these two species were detected, indicating that the other species identified through NMR likely undergo conversion into these two assemblies during the ionization process.

¹H-NMR experiments allowed for the addition of one ligand at a time to the forming cage, starting from [La₂L]⁴⁺ species and concluding with the [La₂L₄]²⁻ cage. Fig. 3 summarizes the species present in solution at different La : L^A ratios and their relative percentages. Fig. S12† reports the same quantities for L^B and L^M. A La : L ratio of 2 : 3 leads to the pure triple-stranded [La₂L₃], while a La : L ratio of 2 : 4 gives a mixture of [La₂L₃] and [La₂L₄]²⁻. The pure quadruple-stranded cage can be obtained only in the presence of ligand excess. The stepwise formation constant (K) and overall stability constant (β) of each [La₂L^X_y]ⁿ species were hence derived. In the presence of a slow equilibrium⁵⁷ between the species, as in this case, formation constants can be obtained from ¹H-NMR spectra via integration of peaks relative to the single species. Once the relative concentration of the species was obtained, these values were converted into concentrations by exploiting an internal standard (4-(4-formylphenoxy) benzaldehyde) according to eqn (1) and (2). The dialdehyde was chosen as internal standard in order to have a stable compound that does not react with the investigated systems and whose NMR signals do not overlap with those of the cages. This assures the presence of easily integrable signals, which reduce possible errors in area integration and, hence, in the formation constants determination. Concentrations at the equilibrium of the free ligand ([L²⁻]_eq) and La³⁺ ions ([La³⁺]_eq) were derived by considering the mass balance described in eqn (3) and (4), respectively:

where n_La2Ly is the number of moles of [La₂L_y]ⁿ species; n_st is the number of moles of the standard; area_La2Ly is the area of the α-proton peak for the [La₂L_y]ⁿ system; area_st is the area of the dialdehyde singlet due to proton H1 (Fig. S7†); y is the number of coordinated ligands and the values in square brackets are initial (°), added (ad) and equilibrium (eq) concentrations. Cage formation can be described stepwise, i.e. considering the addition of a ligand at a time according to eqn (5)–(8), as described in Fig. 4.

Fig. 3 Relative percentage of [La₂L^A_y]ⁿ species (where y = 1, 2, 3, and 4 and n = 4+, 2+, 0, and 2−, respectively) as derived from ¹H-NMR analyses following L^A ligand additions.

Fig. 4 Schematic of the stepwise formation process.

The stepwise (K_2y) and overall (β_2y) formation constants are reported in Table 1. The order of magnitude of the constants for the three different systems [La₂L^A_y]ⁿ, [La₂L^B_y]ⁿ and [La₂L^M_y]ⁿ is nearly the same. Nevertheless, both constants are generally higher for [La₂L^A_y]ⁿ. As is usually observed,^58,59 K_2y decreases from the first to the final step. Indeed, the coordination of the first ligand to the metal ion is strongly favoured, while the coordination of successive ligands becomes more difficult with every step because of steric hindrance and charge effect considerations. Nevertheless, the overall formation constants β₂₃ and β₂₄ for the [La₂L₃] and [La₂L₄]²⁻ cages are relatively high (log β₂₃ = 15.0–16.7 and log β₂₄ = 17.8–19.8). For example, for mononuclear complexes such as Ln³⁺ tetrakis- and tris-(acetylacetonate), general overall values (in water) are log β_LnL3 ≈ 13 and log β_LnL4 ≈ 15.^60–63 Moreover, it has to be noted that the constants have been obtained in DMF, a highly coordinating solvent that can compete with the ligand in coordinating the La³⁺ ion.

Table 1 Stepwise (K_2y) and overall (β_2y) formation constants for [La₂L_y]ⁿ cages with ligands L^A, L^B and L^M (where y = 1, 2, 3, and 4 and n = 4+, 2+, 0, and 2−, respectively)

Constant^a	Equilibrium	L^A	L^B	L^M
a Values determined in DMF-d7 at 25 °C.
K21	2La^3+ + L^2− ⇌ La2L^4+	2.99 × 10^7	1.55 × 10^6	8.97 × 10^6
K22	La2L^4+ + L^2− ⇌ La2L2^2+	3.62 × 10^5	6.36 × 10^4	1.35 × 10^5
K23	La2L2^2+ + L^2− ⇌ La2L3	4.60 × 10^3	1.33 × 10^4	9.26 × 10^2
K24	La2L3 + L^2− ⇌ La2L4^2−	1.33 × 10^3	1.29 × 10^3	5.73 × 10^2
β21	2La^3+ + L^2− ⇌ La2L^4+	2.99 × 10^7	1.55 × 10^6	8.97 × 10^6
β22	2La^3+ + 2L^2− ⇌ La2L2^2+	1.08 × 10^13	9.86 × 10^10	1.21 × 10^12
β23	2La^3+ + 3L^2− ⇌ La2L3	4.97 × 10^16	1.31 × 10^15	1.12 × 10^15
β24	2La^3+ + 4L^2− ⇌ La2L4^2−	6.58 × 10^19	1.27 × 10^18	6.40 × 10^17

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Thermochemical analyses of the triple- versus quadruple-stranded cage equilibrium

Since the triple- and quadruple-stranded cages [La₂L^A₃] and [La₂L^A₄]²⁻ are the species that have potential applications and the two systems that can be easily isolated by tuning the La : L ratio, we focused on the thermochemical analysis of the equilibrium between these two cages. Using variable temperature ¹H-NMR studies (VT-NMR), we determined the Gibbs free energy (ΔG), enthalpy (ΔH) and entropy (ΔS) differences of the equilibrium between [La₂L₃] and [La₂L₄]²⁻ (eqn (8)) for the three ligands L^A, L^B and L^M. A series of ¹H-NMR spectra were recorded between 313 and 233 K (Fig. S14–S16†) with a La : L ratio of 2 : 4. The equilibrium constant K₂₄ at different temperatures was determined using eqn (1)–(4). K₂₄ values were plotted as a function of the inverse of temperature (1/T) (Fig. 5a) and fitted with an expanded van't Hoff model⁶⁴ (see ESI† for more details) to derive ΔH and ΔS. The ΔG, ΔH and TΔS of the reaction are reported in Fig. 5b. In all the three cases (L^A, L^B, and L^M), over the range of studied temperatures, the addition of a fourth ligand to [La₂L₃] affording [La₂L₄]²⁻ is endothermic, entropy driven and exergonic. Hence, the formation of a quadruple-stranded helicate from a triple-stranded one is a spontaneous process stabilized by the favourable entropy factor, which predominates over the unfavourable enthalpy effect. Indeed, in this case, the high entropy value could be mainly associated with the displacement of solvent molecules.

Fig. 5 (a) van't Hoff plot of K₂₄ (eqn (8)) for the three cages fitted with the expanded van't Hoff model. (b) ΔG, ΔH and TΔS.

First, the coordination of the chelating bis-β-diketonate ligand releases two solvent molecules for each ligand, increasing the entropy of the system (chelate effect). Secondly, it has been reported that solvent molecules bound to the metal ion experience reduced conformational, rotational, and translational degrees of freedom, resulting in lower entropy.^65,66 Thus any process which releases solvent molecules from this type of strain results in an entropy increase. On the contrary, enthalpic contribution is positive within the investigated temperature range. These results are in line with the idea of the displacement of tightly bound solvent molecules around Ln ions. Indeed, DMF is a well-known coordinating solvent that requires energy input for displacement from the coordination sphere of the metal ion by a ligand. Hence, although the reaction requires an input of energy in the form of heat (positive ΔH), the increase in disorder (positive ΔS) makes the overall process energetically favourable.

DFT thermochemical analyses of step-by-step ligand association

In coordination-driven self-assembly, the formation of metallo-supramolecular ensembles is typically explained by the enthalpic stabilization resulting from the formation of metal–ligand bonds.¹ However, in the [La₂L₃] to [La₂L₄]²⁻ equilibrium (eqn (8)), the enthalpic factor is unfavourable, making the reaction primarily entropy-driven. As a matter of fact, gas-phase studies on Pd(II) coupled with pyridine-based ligands have shown that enthalpic stabilization decreases as the number of ligands coordinated to the metal increases, favouring the formation of unsaturated structures.⁶⁷ To better evaluate the roles of the enthalpic and entropic factors in step-by-step ligand coordination, we performed DFT thermochemical calculations involving the explicitly coordinated DMF solvent. Fig. 6 reports the DFT optimized structures of four DMF solvated [La₂L^A_y(DMF)_16−4y]ⁿ species (where y = 1, 2, 3, and 4 and n = 4+, 2+, 0, and 2−, respectively), see ESI† for computational details. The DFT optimized structures of [La₂L^B_y(DMF)_16−4y]ⁿ and [La₂L^M_y(DMF)_16−4y]ⁿ are reported in Fig. S18.† We considered only 8-coordinated species. This is supported by the fact that in Ln³⁺ DMF solutions, the dominant species is the Ln(DMF)₈³⁺ complex, although it must be outlined that for lighter Ln³⁺ ions, a solvation equilibrium involving Ln(DMF)₉³⁺ takes place.⁶⁸ In fact, we previously isolated and characterized single crystal XRD [Eu₂L₄]²⁻ cages with different coordination environments: a first structure with both Eu ions 8-coordinated by four ligands,³⁴ a second structure with both Eu ions 9-coordinated by four ligands and one solvent molecule,³⁶ and a third structure with one Eu ion 8-coordinated by four ligands while the other 9-coordinated by four ligands and one solvent molecule.³⁷ Moreover, previous DFT calculations³⁶ showed that this extra solvent molecule has a binding energy close to 8 kcal mol⁻¹, suggesting that it can be easily lost in solution. Fig. 6b illustrates that for the solvated [La₂L₂(DMF)₈]²⁺ species, two different isomers are possible: cis-[La₂L₂(DMF)₈]²⁺ with a saddle shape and trans-[La₂L₂(DMF)₈]²⁺ with the two ligands almost lying on the same plane. Calculations showed that for the L^A ligand, cis-[La₂L₂(DMF)₈]²⁺ is more stable (4.5 kcal mol⁻¹), while for the L^M and L^B ligands, the stabilization of the cis isomer is below 2 kcal mol⁻¹. Consequently, it can be inferred that both isomers coexist in solution at least for the systems based on L^M and L^B. Unfortunately, [La₂L_y(DMF)_16−4y]ⁿ structures contain too many atoms to perform DFT thermochemical analyses in terms of Hessian computational cost. Therefore, we used a smaller model system of a mononuclear complex with acetylacetonate (acac). [La(acac)_y(DMF)_8−2y]ⁿ complexes were optimized using PBE functional with the inclusion of implicit solvent effects (COSMO model) and dispersion corrections (Grimme model). Thermodynamic parameters (H, S and G) were calculated for each optimized species involved in eqn (9)–(12). ΔH, ΔS and ΔG associated with a specific reaction were obtained in accordance with Hess's law. Additional computational details are reported in the ESI.†

La(DMF)₈³⁺ + acac⁻ ⇌ La(acac)(DMF)₆²⁺ + 2DMF (9)

La(acac)₃(DMF)₂ + acac⁻ ⇌ La(acac)₄⁻ + 2DMF (12)

Fig. 6 DFT optimized structures for DMF solvated [La₂L^A_y(DMF)_16−4y]ⁿ species (where y = 1, 2, 3, and 4 and n = 4+, 2+, 0, and 2−, respectively). (a) [La₂L^A(DMF)₁₂]⁴⁺, (b) cis-[La₂L^A₂(DMF)₈]²⁺ and trans-[La₂L^A₂(DMF)₈]²⁺, (c) [La₂L^A₃(DMF)₄], (d) [La₂L₄]²⁻. Red, blue, grey and green sticks represent O, N, C, and F atoms, respectively. The yellow spheres are La atoms. H atoms are omitted for clarity.

First, we applied the model to the equilibrium between the tris- and the tetrakis-chelate (eqn (12)), the analogue of eqn (8) that describes the equilibrium between the triple- and quadruple-stranded cages. Fig. 7a shows the calculated values of TΔS, ΔH and ΔG of the reaction in eqn (12) within the analysed temperature range. The reaction is energetically favoured. As the studied model is different from the experimental one, the numerical values differ, but the trend of the three quantities (Fig. 7a) follow the experimental models, as shown in Fig. 5: by increasing the temperature, their values smoothly decrease. Moreover, as experimentally found, the main driving force for negative ΔG is the entropic factor. These findings confirm that the smaller model system satisfactorily reproduces the experimental trends. Hence, the same calculations have been extended to other equilibria (eqn (9)–(11)). Fig. 7b–d depict the values of TΔS, ΔH and ΔG for the four reactions (eqn (9)–(12)), detailing the step-by-step association of the acac ligand with solvated La(DMF)₈³⁺. The trends observed in ΔG indicate a decrease in stepwise formation constants from the first to the final ligand association, as experimentally observed (Table 1). Additionally, as previously discussed, enthalpic gain decreases as the number of ligands coordinated to the metal increases. The trends in ΔH and TΔS further illustrate that for the first ligand association, enthalpic stabilization plays a more significant role than the entropic factor. However, starting from the second ligand association, entropic contribution becomes comparable to ΔH, and finally, it becomes the dominant stabilizing factor for both the third and fourth ligand associations.

Fig. 7 Thermochemical parameters derived from the DFT calculations. (a) TΔS, ΔH and ΔG for the equilibrium of eqn (12). (b) ΔG for the four equilibria of eqn (9)–(12). (c) ΔH for the four equilibria of eqn (9)–(12). (d) TΔS for the four equilibria of eqn (9)–(12).

Experimental

See ESI.†

Conclusions

The systematic study of three different triple- and quadruple-stranded cages with the general formula [La₂L₃] and [La₂L₄]²⁻ provided valuable insights into the formation process of these metallo-supramolecular systems and interconversion between the triple- and quadruple-stranded cages. The study involved tracking the different species formed during the self-assembly pathway through ¹H-NMR analyses, which led to the identification of four species: [La₂L]⁴⁺, [La₂L₂]²⁺, [La₂L₃], and [La₂L₄]²⁻. The subsequent determination of association constants for each chemical system revealed that [La₂L₃] and [La₂L₄]²⁻ are the most stable. Variable temperature ¹H-NMR studies provided valuable thermodynamic data, showing that the transition from the triple-stranded to the quadruple-stranded cage is endothermic, entropy-driven, and energetically favourable. The obtained high entropy values were attributed to the displacement of solvent molecules, emphasizing the importance of the coordination environment. To delve deeper into this aspect, DFT thermochemical calculations were performed on smaller model systems, which successfully reproduced experimental trends and provided insights into the contributions of enthalpic and entropic stabilization in stepwise ligand association.

Author contributions

Maria Rando: investigation, formal analysis, original draft, writing – review and editing. Alice Carlotto: investigation, formal analysis, writing – review and editing. Silvia Carlotto: investigation, formal analysis, writing – review and editing. Roberta Seraglia: investigation, formal analysis, writing – review and editing. Marzio Rancan: conceptualization, investigation, formal analysis, funding acquisition, writing – original draft, review and editing. Lidia Armelao: conceptualization, funding acquisition, supervision, writing – review and editing.

Data availability

The data supporting this article have been included as part of the ESI.†

Conflicts of interest

The authors declare no conflict of interest.

Acknowledgements

M. R. thanks the National Research Council for “PROGETTI@CNR P@CNR_01_TerMoSmart”, “FOE2020 Capitale naturale e risorse per il futuro dell'Italia”, “FOE2022 FuturRaw” and the research project “nuovi Concetti, mAteriali e tecnologie per l'iNtegrazione del fotoVoltAico negli edifici in uno scenario di generazione diffuSa” (CANVAS), funded by the Italian Ministry of Environment and Energy Security, through the research fund for the Italian Electrical System (type-A call, published in G. U. R. I. no. 192 on 18-08-2022). L. A. thanks the University of Padova P-DiSC#01-BIRD2021 for financial support. M. Rando thanks the Department of Chemical Sciences and Materials Technologies of the National Research Council for providing financial support through a Ph.D. scholarship.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4qi02530j

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