Quantification of Stereochemical Communication in Metal–Organic Assemblies

Abstract The derivation and application of a statistical mechanical model to quantify stereochemical communication in metal–organic assemblies is reported. The factors affecting the stereochemical communication within and between the metal stereocenters of the assemblies were experimentally studied by optical spectroscopy and analyzed in terms of a free energy penalty per “incorrect” amine enantiomer incorporated, and a free energy of coupling between stereocenters. These intra‐ and inter‐vertex coupling constants are used to track the degree of stereochemical communication across a range of metal–organic assemblies (employing different ligands, peripheral amines, and metals); temperature‐dependent equilibria between diastereomeric cages are also quantified. The model thus provides a unified understanding of the factors that shape the chirotopic void spaces enclosed by metal–organic container molecules.

To emulate the enantioselectivity displayed by enzymes, insights into the conditions under which chiral ligands induce the formation of an enantiopure metal-organic self-assembled capsule are required. Such rules can guide the design of new container molecules offering enantioselective guest binding or catalysis,a nd may have implications for the understanding of the origin of biological homochirality. [10] A quantitative analysis based on statistical mechanics has proven useful in the description of chiral amplification in covalent and supramolecular polymers. [11] Thep resent work provides aq uantitative description of the degree of stereochemical information transfer within discrete metal-organic cages.B uilding upon the pioneering work of Piguet on quantifying subtle thermodynamic effects in the self-assembly of polynuclear complexes, [12] we develop as imple statistical mechanical model that quantifies the effects of various factors,s uch as the choice of metal, chiral residue,l igand length, and temperature.W es tart with the phenomenon of amplification of stereochemical information as previously observed in aF e II 4 L 6 cage with as trong preference to have all metal centers with the same all-D configuration. [13] We then examine this phenomenon in related tetrahedral cages with different metals,ligand lengths, or geometries ( Figure 1). We also apply the model to the temperature-dependent diastereomer distributions in tetrahedral cages with weaker stereochemical coupling between metal centers.
Sergeant-and-soldiers experiments ( Figure 1, top), involving the substitution of residues of achiral amine a within aracemic Fe II 4 L 6 cage (2a;F igure 1, bottom) with increasing amounts of am ore nucleophilic enantiopure amine (S)-b, resulted in the quantitative induction of asingle stereochemical configuration at all Fe II centers before 100 %( 12 equiv) of the chiral amine was added, as monitored by the chiroptical response. [13] This effect was shown to be enhanced in the cage with respect to ar elated mononuclear complex (1a)a s ar esult of stereochemical coupling between metal centers in the cage.
To devise as tatistical model to quantify this effect, we separate the two ways in which stereochemical information can be amplified in multinuclear structures.F irst, at each metal center, intra-vertex amplification can manifest itself when fewer than three chiral amine residues suffice to quantitatively induce as ingle D or L stereoconfiguration. Second, inter-vertex communication:the mechanical connection between metal centers by rigid ligands allows stereochemical information to be relayed between vertices in the framework. [14] As ar esult, the configuration at one metal center can influence or even dictate the configuration of its neighbors.T he resulting model is af inite Ising system with quenched field disorder controlled by the distribution of chiral amines.R elated models [15] have been used to describe the binding of ions to polyelectrolytes [15a, b] and cooperativity in supramolecular chemistry. [15c] We consider first the case of amononuclear ML 3 complex which we treat as at wo-state system with D and L states, where D is the preferred configuration for all (S)-chiral amines in this work. [13] Taking the D state as reference,an(S)amine attached to a L center incurs af ree energy penalty, denoted f 1 ,inunits of the thermal energy k B T (where k B is the Boltzmann constant). The f 1 value quantifies the strength of coupling between carbon and metal stereocenters.W et reat each amine in ag iven metal coordination sphere as acting independently,and we take the probability of substitution as equal for all amines in the system. Fort etrahedral cages,w et reat each of the four metal centers as at wo-state system, as in the mononuclear case. Now,h owever, there is also inter-vertex communication, as ar esult of the preference of al igand to have the same stereoconfiguration at its two ends in agiven structure.T aking the DD and LL states of aligand as the reference,wequantify the inter-vertex stereochemical coupling through the parameter f 2 ,d efined as the free energy of the DL and LD states, divided by k B T.The total dimensionless free energy of agiven tetrahedral complex is am ultiple of f 1 plus am ultiple of f 2 depending on the number and location of chiral amines,a nd the stereoconfiguration at each of its metal centers.
AB oltzmann-weighted average over all stereoconfigurations yields the overall fraction x D of D centers in an equilibrium solution of the cages (see Section S3.1 in the Supporting Information). Thev alue of x D depends on the parameters f 1 and f 2 ,providing aphysical interpretation of the populations of D and L centers observed in experiments.F or given values of f 1 and f 2 ,t he model predicts how the excess chirality (i.e.t he relative excess of D over L metal centers) increases with the fraction (s)o fs ubstituted amine.P lots of chiral excess as afunction of s approach alimiting form as the f 1 and f 2 values become large,t hat is,t he shape of the curve eventually becomes insensitive to the precise values of f 1 and f 2 (see Section S3.2).
We first apply the model to analyze sergeant-and-soldiers experiments, [13] which started either with ar acemic Fe II L 3 complex (1a), or with the racemic cage Fe II 4 L 6 (2a), and to which different amounts of (S)-amine were added (see Section S2 in the Supporting Information). We examined three chiral amines,( S)-b, [13] (S)-c,a nd (S)-d [16] (Figure 1, bottom), to differentiate between the abilities of the amines to induce as ingle-metal stereochemical configuration, as expressed by the f 1 value.F igure 2A shows how the excess chirality,a sp robed by circular dichroism, varied with the amount of added amine.Inthese plots,both the experimental

Angewandte Chemie
Communications and fitted curves have been renormalized to 1a tachiral amine concentration of 100 %(see Section S3.3). Va lues of f 1 were obtained by least-squares fitting to data from experiments with the Fe II L 3 complexes ( Figure S1). These values were then fixed and used in as econd fit to the experimental data obtained for the related Fe II 4 L 6 cages ( Figure S4), to obtain an f 2 value for each cage ( Figure 2E).
Themodel accounts well for the shape of the experimental curves (Figure 2A). The f 1 values of 38, 0.90, and 1.4 obtained for amines (S)-b,( S)-c,a nd (S)-d,r espectively,h ighlight the much stronger ability of amine (S)-b than amine (S)-c in controlling the configuration at the metal center.T he free energy penalty of 38k B T for (S)-b lies in the limiting regime of al arge f 1 value,w here the sergeant-and-soldiers effect is overwhelming and the chiroptical response is insensitive to the exact value ( Figure S8). Between (S)-c and (S)-d,( S)-d exhibited astronger ability to control the configuration at the metal center, which we attribute to the greater bulk of the side group (cyclohexyl versus isopropyl). [16a, 17] We infer that both sterics and p-stacking effects between phenyl and pyridyl rings are responsible for the strong influence of amine (S)-b upon the metal-centered configuration. [16a] Using the f 1 values from the Fe II L 3 complexes,e xperimental data could be fitted for the Fe II 4 L 6 cages 2b and 2c; precipitation during the substitution of cage 2a with (S)-d precluded sergeant-and-soldiers studies with this amine.I n these cages the Fe II vertices are held together by the same ligand so similar f 2 values are expected as f 2 measures the ligands ability to mediate stereochemical communication between the individual metal centers (as explained above). Gratifyingly,t he values of f 2 for cages 2b and 2c of 0.40 and 0.51, respectively,a re similar. We attribute the small difference between the two values to uncertainty in fitting experimental data and to small differences in cage geometry as ar esult of the different amines.
Next, the effect of metal choice on the degree of amplification was studied by performing substitution experiments with (S)-b on the Co II and Zn II -containing analogues of the Fe II L 3 complex 1a (namely 3a and 4a)a nd the Co IItemplated analogue of the Fe II 4 L 6 cage 2a (namely 5a;f or each metal the chiroptical data were normalized at adifferent wavelength;F igure S3). Our model correctly predicts the sharp decrease in f 1 value from 38 for Fe II ,to1.3 for Co II (3b), to approximately 0f or Zn II (4b). Remarkably,n oa mplification was observed for Zn II :t he excess chirality of the Zn II L 3 complex 4b increased linearly as af unction of added (S)-b. These observations can be understood in terms of the increased metal-ligand distance when going from Fe II through Co II to Zn II , [16a] with aconcomitant reduction in bond strength (see Section S5 in the Supporting Information), which in turn decreases the steric gearing of the chiral amine residues required for effective stereochemical control around the metal center.
Despite similar f 2 values,b ecause of the smaller f 1 value for Co II ,the enhancement in nonlinear effects in aM 4 L 6 cage with respect to aML 3 complex is more pronounced in the case of the Co II -containing structures, 3b and 5b,t han for their Fe II -templated analogues 1band 2b( Figure 2B). Because the Zn II -analogue of 2a could not be prepared without an anionic template (see Section S1), its amplification behavior was not studied.
Thee ffect of ligand structure on the degree of stereochemical communication within tetrahedral cages was studied by examining the substitution with the same amine ((S)-b)of two other Fe II cages:c age 6a, [18] built from al onger ditopic ligand (compared to 2a), and cage 7a,b ased upon at ritopic ligand. [16b] Forc age 6b,t he f 2 value of 0.45 is only slightly higher than the value of 0.40 for 2b,v erifying quantitatively the previous observation that linker length does not strongly affect the degree of stereochemical communication in these cages. [17a] In stark contrast with the behavior of the ML 3 complexes and M 4 L 6 cages studied, the substitution of the Fe II 4 L 4 cage 7a with (S)-b was observed to occur through acooperative imine exchange process (see Section S4), confirming the previously reported kinetic stability of this Fe II 4 L 4 framework. [16b] Not being able to use cage 7a to investigate the degree of stereochemical coupling between metal centers in M 4 L 4 structures,w et urned to its Co II -containing congener (8a), which was not observed to undergo cooperative amine exchange ( Figure S7, Figures S36-S37). ForC o II 4 L 4 cage 8b, stronger inter-vertex communication was observed, as expressed by an f 2 parameter of 1.5, which is significantly higher than the value of 0.55 for the corresponding Co II 4 L 6 cage 5b ( Figure 2E). We infer that the tritopic ligands have astrong "gearing" effect within the rigid structure,forcing the four metal centers in the cage to adopt ah omochirally pure D state.T his strong inter-vertex stereochemical coupling has been shown to enable stereochemical memory in aF e II 4 L 4 cage. [16b] In addition to analyzing the transmission of stereochemical information in all-D or all-L cages,w ehave also applied our model to as et of racemic Fe II 4 L 6 cages (9-12;F igure 1) that have been previously observed to form heterochiral species.
Themodel can be employed to make adirect prediction of universal curves for the equilibrium distribution of the three diastereomers as af unction of f 2 value ( Figure 3). We have placed the temperature-dependent distribution of diastereomers for cages 9-12 on these curves by finding the point on the f 2 axis where each set of three yields fits best. There is no guarantee that an arbitrary set of three diastereomer fractions could be consistently placed on the curves.H ence,t he observation that all data sets,a part from those for cage 9, can be superimposed on the plot provides strong support for the underlying model. Thebehavior of the four cages is very different. Cage 11 has strongly negative values for f 2 (< À2), indicating that the ligand prefers to connect two metal centers of opposite handedness,t hus favoring the S 4 diastereomer (wherein four of the six ligands link metal centers of opposite configuration). Cage 10 shows the opposite behavior:t he homochiral T diastereomer is favored by the positive f 2 value (about 0.9 at room temperature). However,r aising the temperature decreases the f 2 value,t hereby increasing the proportions of the S 4 and C 3 diastereomers at the expense of the T diastereomer.F or cage 12 the f 2 value was found to be close to 0( independent of the temperature), resulting in an early unbiased statistical distribution (which would be 1:4:3f or T:C 3 :S 4 ). Forcage 9 some discrepancies between the data and the model were observed for the S 4 and C 3 diastereomers.H owever,i ts behavior can still be characterized by the moderately positive f 2 value of 0.35 that slightly favors the T diastereomer.
Thedirection and sensitivity of the change in f 2 value with respect to temperature are determined by the sign and magnitude of the enthalpic contribution to the free energy. Theenthalpic and entropic components of f 2 can be extracted by aV ant Hoff type analysis and can be shown by our model to relate to all three of the pairwise equilibria [6b] between the T, S 4 ,a nd C 3 states (see Section S6 in the Supporting Information). Theg enerally good agreement between the separately determined entropies and enthalpies and those derived from our model further validates the applicability of the model, providing au nifying understanding of the equilibria. Apart from the case of cage 9,w ef ound that it is entropically favorable to have opposite stereoconfiguration at the two ends of each ligand, even when that combination is enthalpically unfavorable. Our statistical mechanical model thus accounts for the specific nonlinear response of excess chirality in metalorganic tetrahedra due to stereochemical communication within the structures.F or the first time for metal-organic cages,t he effect of structural features on the degree of stereochemical communication has been quantified in terms of two energy parameters with clearly defined physical meanings,a nd an overarching description of the temperature-dependent equilibrium between diastereomeric cages has been provided. Thegeneral nature of the model allows for its extension to new cage geometries [19] and related structures, such as metal-organic frameworks. [20] We anticipate that the physical insight our model provides into the nuanced stereochemistry of the chirotopic cavities of these structures will translate into control over stereoselective guest binding and catalysis. [8b, 9b]