**3. Results**

To probe the cage-based catalysis of this reaction, we first examined the pH profile of the uncatalysed 'background' reaction, looking for conditions where this was as slow as possible to allow the e ffects of any catalysis to be most apparent. Monitoring the formation of bindone by UV/Vis spectroscopy (it has a strong absorption maximum at 510 nm in water) [44] at a range of di fferent pH values showed that the reaction proceeds quickest in the pH range 6–7 where, based on the pKa of the starting material, there will be substantial amounts of both nucleophilic enolate anions and electrophilic neutral **ID** present; the reaction becomes slower at greater extremes of high or low pH. To facilitate the analysis of the reaction by UV/Vis spectroscopy, we therefore performed our subsequent experiments in the range of pH 3–4, reasoning that—as with the Kemp elimination reactions we examined earlier [29,30]—the high positive charge of the cage should stabilise the anionic enolate form of **ID**, even under relatively acidic conditions. Furthermore, at this pH, the intense yellow colour of the enolate anion, which would make the observation of the emerging colour of bindone more challenging, was not present.

We measured the binding constant of **ID** in the cage cavity with a 1H NMR titration, adding several equivalents of **ID** in small aliquots to a D2O solution of **H w** at pD 3.8 (when the uncatalysed aldol reaction is extremely slow). The evolution of the 1H NMR spectra is shown in Figure 2. It is clear that **ID** binds in the cage cavity in slow exchange with free gues<sup>t</sup> in solution, as separate signals for free cage **H w,** and the complex **H <sup>w</sup>**•**ID** could be observed with the former progressively reducing in intensity and the latter increasing during the titration. The occurrence of a single signal for each host proton in the complex **H <sup>w</sup>**•**ID** implies rapid motion of the **ID** gues<sup>t</sup> in the cavity, such that the symmetry of the cage is preserved on the NMR timescale when the gues<sup>t</sup> binds [49].

**Figure 2.** Evolution of paramagnetic 1H NMR spectra during additions of**ID** (0–5 equivalents, indicated for each spectrum on the right) to a solution of **H w** in D2O (298 K). Signals associated with empty **H w** (bottom spectrum) are replaced by new signals for the **H <sup>w</sup>**•**ID** complex as the titration proceeds. Regions where this is particularly clear, and separate signals for the free and bound cage can be deconvoluted and integrated, are shown by the black diamonds.

Estimates of the binding constant *K* could be obtained by deconvoluting and integrating the separate (but closely spaced) **H w** and **H <sup>w</sup>**•**ID** signals at several di fferent points across the 1H NMR spectrum for known concentrations of cage and added guest. In this case, the close overlap of signals for the free and bound cage, coupled with uncertainties associated with deconvoluting and integrating broad signals from a paramagnetic compound, resulted in a high uncertainty: the average value of *K* obtained from several such measurements was 2.4(±1.2) × 10<sup>3</sup> <sup>M</sup>−1, where the e.s.d. quoted is double the standard deviation obtained from averaging multiple measurements. We note that our algorithm for estimating binding constants using molecular docking software with a customised scoring function suggested a binding constant of 1200 M−<sup>1</sup> [38,39], which is in good agreemen<sup>t</sup> with our estimate, and many structurally similar guests have binding constants in the 103–104 M−<sup>1</sup> range [31,38].

A crystal structure of the cage/gues<sup>t</sup> **H**/**ID** complex could be obtained using the crystalline sponge method that we have used in previous work by preparing crystals of the free host cage **H** by a solvothermal synthesis, followed by slow cooling [28], and immersing them in a concentrated solution of **ID** in MeOH for several hours, which resulted in gues<sup>t</sup> uptake without loss of crystallinity [48]. Details of the structure are shown in Figures 3–5.

**Figure 3.** Two views of the crystal structure of the complex of host **H** with **ID**, showing the presence of a stacked pair of **ID** guests (which are shown in space-filling mode) in the cavity (host cage shown in wireframe) lying astride an inversion centre (N atoms, blue; O atoms, red; Co atoms, orange; C atoms, grey).

**Figure 4.** Partial view of the structure of the **H**/**ID** complex showing how each **ID** gues<sup>t</sup> molecule forms a network of CH···O contacts (shown by green dotted lines) with a convergen<sup>t</sup> set of CH groups associated with the cage interior surface around the two *fac* tris-chelate metal complex vertices of **H**.

Rather than the expected one molecule of guest, which we have often observed in previous work, we found a pair of guests stacked across an inversion centre in the cage cavity (Figure 3). This is not a 50:50 disorder as each gues<sup>t</sup> molecule (the two are crystallographically equivalent) refines with unit site occupancy, and the distance between them is typical of π-stacking (3.48 Å). The combined volume of two **ID** guests (74%) significantly exceeded the value of 55 ± 9% of the host cavity volume (409 Å3), which Rebek showed a while ago afforded optimal gues<sup>t</sup> binding in solution [50,51]. However, a crystalline sponge experiment was performed under highly forcing and non-equilibrium conditions using a large excess of the guest; we [48] and others [52–54] have observed packing coefficients for guests inside supramolecular host cavities of >80% when favourable interactions such as π-stacking between multiple guests and favourable interactions between guests and the cage interior surface result in a particularly compact gues<sup>t</sup> array. In dilute solution—the conditions under which gues<sup>t</sup> binding is normally evaluated—we can imagine that for this reason, the second binding constant *K*2 would be substantially smaller than the first binding constant *K*1, in which case, the single-guest binding would dominate the solution speciation behaviour [48].

**Figure 5.** A view of the crystal structure of the complex of host **H** with **ID**, emphasising how the host cage brings together molecules at binding sites inside the cage cavity (*cf.* Figure 3) and around the exterior cage surface. It is not possible to tell whether the external guests are neutral **ID** or are the enolate anions stabilised by the high positive charge of the cage surface.

The (crystallographically equivalent) guests interact with the cage interior surface through multiple CH···O hydrogen bonds between the ketone O atoms, which are weak hydrogen-bond acceptors, and inwardly-directed C–H bonds from the ligand set, whose ability to act as weak H-bond donors is improved by the high positive charge of the assembly (Figure 4) [49,55]. One of the O atoms [O(14G)] lies in an H-bond donor pocket close to a *fac* tris-chelate metal ion, which contains several convergen<sup>t</sup> CH groups (from methylene CH2 and naphthyl CH protons) whose combined H-bond donor effect is comparable to a phenol group in terms of its overall hydrogen-bond donor strength [49,55]. The penetration of one of the C=O groups of the **ID** gues<sup>t</sup> into this pocket results in non-bonded H···O distances associated with these CH···O interactions in the range of 2.5–3 Å. The other carbonyl O atom [O(15G)] likewise forms CH···O interactions with inwardly-directed naphthyl and pyrazolyl CH protons from the cage surface, with O···H distances of 2.8–2.9 Å.

There is an additional molecule of **ID** in each asymmetric unit (which contains half of a complete cage unit). This was refined with a site occupancy of 0.42; it lies in the space between cage molecules, and interacts with the cage exterior surface (Figure 5) through a similar set of CH···O hydrogen-bonds, as we saw for the interior guests, with O···H distances in the range 2.5–2.7 Å [thus the overall formulation, ignoring solvent molecules, is **H**•**(ID)2.84**]. We have assumed, for the purposes of the crystallographic refinement, that this is a neutral **ID** molecule incorporating a CH2 fragment between the two ketones. However, the possibility exists that this could be the enolate anion of **ID**, stabilised by the highly cationic cage surface. For a structure of this type (a large supramolecular assembly with weak scattering due to solvent/anion disorder), there is no way to ascertain this crystallographically. Marginal differences in the C–C and C–O distances between the neutral and enolate forms of **ID** are not meaningful, given the extensive use of geometric restraints in the refinement (see CIF for details, Supplementary Materials), and charge balance considerations are not helpful either due to the solvent/anion disorder that required the use of SQUEEZE [56] to eliminate diffuse electron density from the refinement. We note, however, that the CH···O H-bonding interactions between the carbonyl oxygen atoms of the external **ID** molecule and the CH groups of the cage surface are shorter, on average, than those of the cavity-bound guest, consistent with the 'external' gues<sup>t</sup> being in its anionic form. Whether the 'external' **ID** molecules in the crystal structure are in the neutral form or are actually the enolate anions, this structure provides a nice illustration of how the cage host can simultaneously co-locate a hydrophobic gues<sup>t</sup> (in the cavity) and additional reaction partners around the exterior surface [30].

Catalysis experiments were performed with an aqueous solution of **Hw** (0.09 mM) and up to 10 equivalents of **ID** at pH 3.4 (Figure 6). Under these conditions, in the absence of the cage, no measurable conversion of **ID** to bindone was seen over prolonged periods (days), presumably due to the absence of any significant amount of the enolate anion of **ID**. Metal fluoroborate salts on their own, likewise had no catalytic effect. However, in the presence of cage **Hw**, steady growth in the absorbance associated with bindone was seen. This has a maximum at 510 nm, but it was monitored at 550 nm to avoid any possible competition from absorbance associated with the enolate anions, which is significant at 510 nm. The virtually straight-line growth of bindone over this period of time means that the reaction progress cannot meaningfully be fitted to a specific kinetic model; leaving the reaction for longer to let more bindone form results in solutions becoming cloudy as the product has poor water solubility. We can say, however, that after 12 h, around 3% of the **ID** was converted to bindone, increasing to 10% after 36 h, corresponding to approximately one turnover per catalyst molecule over 36 h. Although the absolute rate of the formation of bindone catalysed by the cage is therefore extremely low, compared to the undetectable formation of bindone in the absence of catalyst at this pH, the catalysis of the reaction under these conditions is clear.

**Figure 6.** Cage-catalysed conversion of **ID** to bindone (0.9 mM **ID** at start; 298 K, pH 3.4), performed in a UV/Vis cuvette and monitored by measuring the increase in optical density at 550 nm arising from product formation. Green circles represent the background reaction (no significant reaction in the absence of cage **Hw**). Red circles represent the progress of the reaction in the presence of 0.09 mM **Hw** (i.e., the catalysed reaction). Blue circles represent catalysis under the same conditions as the red circles, but with 1.8 mM cycloundecanone added to block the cage cavity, showing that blocking the host cavity does not inhibit the catalysis, which must therefore occur at the external surface of the cage (see main text).

Control experiments suggested that the reaction does not actually occur inside the cage cavity, but at the external surface, which is a possibility that has very recently emerged from related studies on catalysis with this cage system [57]. In the confined space of the cavity, any successful reaction would require an ideal configuration of the cavity-bound and surface-bound reacting partners, and when this happens, it can lead to very large rate enhancements [10,29]. However, hydrophobic substrates that do not bind in the cavity, or that cannot react for geometric reasons whilst inside the cavity, can also interact with the cage exterior surface, which is just as hydrophobic as the interior surface and has a greater area: these substrates can thereby be brought into the region around the cationic surface where anions have accumulated because of ion-pairing e ffects [57]. The key control experiment here is to perform the reaction in the presence of an excess of cycloundecanone. This binds strongly in the cage cavity (>10<sup>6</sup> <sup>M</sup>−1) [32] and therefore prevents the substrate **ID** from binding, however, it has no e ffect on the rate at which bindone is formed. This clearly indicates that cavity-based binding of **ID** is not necessary for the catalysis to occur, therefore it follows that the catalysed reaction occurs at the external surface of the cage where enolate anions of **ID** accumulate [57].
