Helix-mediated over 1 nm-range chirality recognition by ligand-to-ligand interactions of dinuclear helicates

Abstract

Long-range chirality recognition between the two chiral guest ligands can be tuned based on the helix distances (d_Ln–Ln = 11.5 and 14.0 Å) of bis-diketonate bridged dinuclear lanthanide complexes (2Th and 3Th, respectively) used as mediators. Both 2Th and 3Th form one-dimensional (1D) helical structures upon terminal binding of two chiral guest co-ligands (L^R or L^S). Long-range chiral self-recognition is achieved in self-assembly of 2Th with L^R and L^S to preferentially form homochiral assemblies, 2Th-L^R·L^R and 2Th-L^S·L^S, whereas there is no direct molecular interaction between the two guest ligands at the terminal edges. X-ray crystal structure analysis and density functional theory studies reveal that long-range chiral recognition is achieved by terminal ligand-to-ligand interactions between the bis-diketonate ligands and chiral guest co-ligands. Conversely, in self-assembly of 3Th with a longer helix length, statistical binding of L^R and L^S occurs, forming heterochiral (3Th-L^R·L^S) and homochiral (3Th-L^R·L^R and 3Th-L^S·L^S) assemblies in an almost 1 : 1 ratio. When phenyl side arms of the chiral guest co-ligands are replaced by isopropyl groups (L′^R and L′^S), chiral self-recognition is also achieved in the self-assembly process of 3Th with the longer helix length to generate homochiral (3Th-L′^R·L′^R and 3Th-L′^S·L′^S) assemblies as the favored products. Thus, subtle modification of the chiral guests is capable of achieving over 1.4 nm-range chirality recognition.

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Introduction

Molecular recognition has an important role in chemistry. High-fidelity molecular recognition is typically achieved by short-range direct intermolecular contact that enables recognition of one molecule from another through noncovalent interactions.¹ Conversely, long-range molecular recognition is inherently important for understanding how molecular information is recognized and transferred across long distances in supramolecular systems, even without direct intermolecular interactions.² In this context, long-range molecular recognition is particularly challenging for enantiomers that have the same size and shape, with their only distinguishing feature being the spatial orientations of certain groups.^3–9 Such interactions have a pivotal role in various chemical and biological phenomena.

Herein, we report helix-length dependent over 1 nm-range chiral recognition by terminal binding of two chiral guest ligands across a one-dimensional (1D) helix. A helix is intrinsically chiral with either P- or M-helicity, where the preferred helicity is induced by local chirality at the terminal edges. Hence, a helix is a prototypical motif that can mediate terminal chiral information across long distances.¹⁰ In particular, a dinuclear helicate is a smart platform for investigating long-range chiral recognition because the helix distance can be tuned by adjusting the number of spacer units immobilized in bridging ligands.^11–17 However, most transition metal-based dinuclear helicates (such as M₂L₃) are coordinatively saturated, therefore guest ligands are not expected to have any access. Conversely, lanthanide-based dinuclear helicates (such as Ln₂L₃) are often coordinatively unsaturated because of the wide range of coordination numbers (n ≥ 8) of lanthanide(III) ions,^12,13 which enable sequential interactions with chiral co-ligands. In this context, we have extensively developed ternary lanthanide self-assembly systems comprising β-diketonate ligands and chiral co-ligands, which revealed that the attractive ligand-to-ligand interactions between β-diketonate ligands and chiral co-ligands give rise to overall chirality in the final self-assembled molecule.¹⁸ Such ligand-to-ligand interactions would be suitable for transfer of molecular chirality information across long distances. Scheme 1 illustrates helix-mediated long-range chirality recognition using the ligand-to-ligand interaction approach, where there is no direct molecular interaction between two chiral ligands at the terminal edges. Herein, an initial chiral ligand binding induces P- or M-helicity of a helicate (mediator) through ligand-to-ligand interactions at the terminal edge. When the resulting initial helicate interacts preferably with the second ligand of the same chirality (2K_RR = 2K_SS > K_(hetero)), chiral self-recognition takes place, forming homochiral assemblies. Here, K_(hetero) = K_RS + K_SR = 2K_RS = 2K_SR (since K_RS = K_SR). Conversely, chiral self-discrimination occurs when the second ligand binding prefers the opposite chirality (2K_RR = 2K_SS < K_(hetero)) to form heterochiral assemblies. Alternatively, when the initial helicates have no sufficient energy bias to distinguish the same and opposite chirality in the second binding event (2K_RR = 2K_SS = K_(hetero)), statistical binding of both enantiomers takes place. In this study, we show that chirality recognition of two chiral guest co-ligands (L^{(R or S)}) is highly sensitive to the helix length of the mediator, where a shorter helix (d_Ln–Ln = 11.5 Å, 2Th) causes chiral self-recognition and a longer helix (d_Ln–Ln = 14.0 Å, 3Th) results in statistical binding. Conversely, subtle modification of the chiral guest ligands (L^{(R or S)} → L′^{(R or S)}) enables even the longer helix (d_Ln–Ln = 14.0 Å, 3Th) to demonstrate chiral self-recognition. Thus, the present findings provide valuable insights for unravelling the principles of molecular recognition and transfer across long distances in supramolecular systems.

Scheme 1 Helix-mediated long-range chirality recognition: chiral self-recognition is favored when 2K_RR = 2K_SS > K_(hetero). Conversely, chiral self-discrimination will be predominant when 2K_RR = 2K_SS < K_(hetero). Alternatively, statistical binding will occur when 2K_RR = 2K_SS = K_(hetero). Here, K_(hetero) = K_RS + K_SR = 2K_RS = 2K_SR.

Results and discussion

X-ray structure of dinuclear helicates

For the chirality mediator, we used selected dinuclear lanthanide complexes (2Th and 3Th) having two and three thiophene spacer units, respectively, which were synthesized by reacting the corresponding bis-diketone ligands (L₂ and L₃, respectively) and europium acetate in a 3 : 2 stoichiometry (Fig. S1–S3†).^13b In this context, Yan et al. successfully revealed the helix structure of dinuclear lanthanide complexes with the bis-diketone ligands.^13b Both 2Th and 3Th formed 1D helical assemblies upon terminal binding of two chiral guest co-ligands [L^{(R or S)} or L′^{(R or S)}] (vide infra).^19,20 Among the series of helicate assemblies, we successfully grew crystals suitable for X-ray analysis by slow evaporation of an acetone solution containing 2Th with the presence of 2 equiv. of a racemic mixture of the chiral guest co-ligands (L^R and L^S) having phenyl side arms. The X-ray structure analysis (Fig. 1) revealed that the both terminal Eu^III ions of 2Th were occupied by chiral guest co-ligands of the same chirality to afford homochiral assemblies, 2Th-L^R·L^R and 2Th-L^S·L^S, which arranged alternatively in the crystal packing diagram (Fig. 1c). These results indicate that 2Th with chiral guest co-ligands favored ligand chiral self-recognition over chiral self-discrimination and statistical binding. Helical structures were found in the thiophene spacer units, i.e., P-helicity for 2Th-L^R·L^R and M-helicity for 2Th-L^S·L^S (Fig. 1c), whose helicity was induced by ligand-to-ligand interactions between the chiral guest co-ligands and the diketonate ligand units.¹⁸ While no direct interaction between the two chiral ligands at the terminal edges was detected, intra-complex π–π stacking (d_π–π = 3.567 Å) was indicated between the phenyl rings of L^S and the β-diketonate plane (Fig. 1b). Notably, the optimized structure of 2Th-L^S·L^S calculated by density functional theory (DFT) [DFT/CAM-B3LYP/def2SVP (C H N O S F)/def2TZVPP (La)] reproduced the crystal structure well (Fig. 1d and Table S1†).²¹ Therefore, rational structural modelling of the other helicates, such as 3Th with a flexible longer thiophene chain length that is not suitable for crystal growth, would be also possible with appropriate use of DFT calculations (vide infra).

Fig. 1 (a) Chemical structure, (b) X-ray crystal structure (ORTEP view, 50% probability) of 2Th-L^S·L^S (CCDC 2036830†). (c) Crystal packing diagrams of the crystal structures of 2Th-L^R·L^R (red) and 2Th-L^S·L^S (blue). (d) Overlapping image of X-ray crystal structure (yellow) of 2Th-L^S·L^S and optimized structure [DFT/CAM-B3LYP/def2SVP (C H N O S F)/def2TZVPP (La)] of 2Th-L^S·L^S, where the Eu atoms were replaced by La atoms. Hydrogen atoms are omitted for clarity. One of the disordered structures was shown for clarity (Fig. S5†).

Allosteric effects on formation of dinuclear helicates

Next, we used circular dichroism (CD) spectroscopy to investigate the helicate formation of 2Th and 3Th through the terminal binding of chiral guest co-ligands [L^{(R or S)} and L′^{(R or S)}] in solution.^22–24 Upon addition of the chiral guest co-ligand, 2Th and 3Th began to show biphasic (splitting) CD spectra with intense CD signals, whereas neither 2Th nor 3Th themselves exhibited CD (Fig. 2a and S5–S8†). Conversely, no notable UV-vis absorption spectral changes were observed because of the lack of absorption by the chiral guest co-ligand (L^R) in this region (Fig. 2b and ESI Fig. S5–S8†). A titration plot was obtained by plotting Δε at 389 nm against the molar ratio of 2Th and the chiral guest co-ligand ([L^R]/[2Th]₀), which exhibited saturation at approximately [L^R]/[2Th]₀ = 2.0 (Fig. 2a inset). Subtle difference between the experimental titration curve and the theoretical one around [L^R]/[2Th]₀ = 2.0 (as well as less defined saturation point) should be ascribed to a minor contribution of the mono-coordinated species (2Th-L^R). This result indicates a 1 : 2 binding mode between 2Th and L^R (Scheme 2a and Fig. S5–S8†) as confirmed by the X-ray structure (vide supra, Fig. 1b). The 2Th-L^R·L^R assembly was also analyzed by ESI mass spectrometry of 2Th with L^R in acetone solution (Fig. 2b inset).²⁵

Fig. 2 (a) CD and (b) UV-vis absorption spectra of 2Th (6.9 × 10⁻⁶ M) in the presence of L^R [0 (green line) – 7.2 × 10⁻⁵ M (red line)] in acetone at 298 K. (Insets) (a) Plot of Δε at 389 nm versus [L^R]/[2Th]₀. Simulated curves were obtained based on the consecutive binding model (K_RR ≫ K_R): [L^R] = (α/(K_R·K_RR(1 − α)))^0.5 + 2α[2Th]₀, using K_R·K_RR = 10⁷–10¹⁴ M⁻². Here, [2Th]₀ denotes the initial concentration of 2Th, and α = [2Th-L^R·L^R]/[2Th]₀. (b) Negative ESI mass spectrum of 2Th in the presence of L^R in acetone with the calculated isotopic distributions for {(Eu)₂(L₂-2H)₃(L^R)₂ + CH₃COCH₃ + 2H₂O}. For ESI mass spectrum in the whole region (Fig. S9†).

Scheme 2 Self-assembly formation of (a) 2Th and (b) 2Th′ with L^R (left) and that with L^S (right). Here, K_R denotes the binding constant between 2Th and L^R to form 2Th-L^R, and K_RR means the binding constant between 2Th-L^R and L^R to generate the final assembly 2Th-L^R·L^R. Conversely, K′_R denotes the binding constant between 2Th′ and L^R to form 2Th′-L^R.

Next, by using ¹⁹F NMR spectroscopy, we investigated whether the two chiral guest co-ligands (L^R) associate with 2Th sequentially or continuously in terms of allosteric effects.^26,27 If the second binding constant is larger than the initial binding constant (K_RR ≥ K_R), continuous association of the two guest co-ligands (L^R) to 2Th will occur to yield the final assembly of 2Th-L^R·L^R in a formally single step. Conversely when the second binding constant is comparable with the initial binding constant (K_RR ≤ K_R), association of L^R to 2Th will occur sequentially through the mono-coordinated species (2Th-L^R). Upon addition of 2 equiv. of L^R to 2Th, a single ¹⁹F NMR signal at −83.7 ppm assigned to 2Th (itself) split into three signals at −78.3, −85.2, and −85.4 ppm (Fig. 3c to a). Since the original 2Th has a threefold axis, the terminal CF₃ groups are in the same chemical environment (Fig. 3c left).^18a However, the terminal binding of the chiral guest co-ligands removes this threefold axis and places the three CF₃ groups in different chemical environments (Fig. 3a left). Thus, the observed ¹⁹F NMR signal split, clearly suggested the formation of a helical structure of 2Th-L^R·L^R based on terminal binding of the two guest co-ligands (L^R) to 2Th (Fig. S5–S8†). Conversely when addition of 1 eq. of L^R into 2Th in acetone-d₆, ¹⁹F NMR signals corresponding to 2Th (green circle) and 2Th-L^R·L^R (red triangles) were observed, while that corresponding to the mono-coordinated species (2Th-L^R) was not detected (Fig. 3b). Further addition of L^R (2 eq.) resulted in development of ¹⁹F NMR signals due to 2Th-L^R·L^R (red triangles), where the signals corresponding to 2Th (green circle) were completely disappeared (vide supra, Fig. 3a). Such observation suggested the continuous binding model.

Fig. 3 ¹⁹F NMR spectra of 2Th (c) in the absence and presence of (b) 1 eq. and (a) 2 eq. of L^R in acetone-d₆ at 298 K. Left figures show the optimized structures of 2Th-L^R·L^R and 2Th [DFT/CAM-B3LYP/def2SVP (C H N O S F)/def2TZVPP (La)].

With these results in hand, we rationalized the above CD titration plot (Fig. 2a inset) based on the theoretical titration curve based on the continuous binding model. Since binding between 2Th and L^R is almost stoichiometric judging from the titration curve (Fig. 2a inset), the binding constant (K_R·K_RR) could not be determined accurately. Conversely, the theoretical titration curve suggested that the observed stoichiometric binding agreed with the binding constant at least larger than 10¹² M⁻² (K_R·K_RR > 10¹² M⁻², red line in Fig. 2a inset). For further verification on the allosteric effects, we prepared a mononuclear complex 2Th′ and a 1 : 1 binding constant (K′_R) with L^R was determined to be (7.2 ± 0.7) × 10⁵ M⁻¹ from a CD titration experiment of 2Th′ with L^R (Scheme 2b and Fig. S8†). Since the twice value of the resulting 1 : 1 binding constant (K′_R) between 2Th′ and L^R is probably nearly equal to the initial binding constant (K_R) between 2Th and L^R (2K′_R ≈ K_R), the second binding constant (K_RR) should be larger than 6.9 × 10⁵ M⁻¹ (K_RR > 6.9 × 10⁵ M⁻¹). Although it could not be concluded whether binding between 2Th and L^R follows the continuous binding model based on the estimated binding constants, the determined 4K_RR/K_R value (4K_RR/K_R > 1.9) suggested the allosteric effect in the present system. The observed allosteric effect could result from the initial binding event, which causes a conformational change of the helicate suitable for the second binding of the chiral co-ligand with the same chirality. The initial and the second binding energy (E⁽¹⁾_R and E⁽²⁾_RR, respectively) were estimated from the optimized structures of L^R, 2Th, 2Th-L^R, and 2Th-L^R·L^R [DFT/CAM-B3LYP/def2SVP (C H N O S F)/def2TZVPP (La)], where the second binding energy (E⁽²⁾_RR) is 7.66 kcal mol⁻¹ larger than that of the initial binding energy (E⁽¹⁾_R) (Table 1), which agreed with the experimentally observed allosteric effect.

Table 1 Initial and second binding constants (K_R and K_RR), binding energy (E⁽¹⁾_R and E⁽²⁾_RR) in self-assembly formation of 2Th with L^R

	K R (M^−1)	K RR (M^−1)	E ^(1) R (kcal mol^−1)	E ^(2) RR (kcal mol^−1)
a Determined from the titration experiments of 2Th′ with chiral guest co-ligands. b Determined from the titration experiments of 2Th′ and 2Th with the chiral guest co-ligands. c Determined from the optimized structures of L^R, 2Th, 2Th-L^R, and 2Th-L^R·L^R [DFT/CAM-B3LYP/def2SVP (C H N O S F)/def2TZVPP (La)].
	1.4 × 10^6	>6.9 × 10^5	36.54	44.20

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A DFT prediction on long-range chirality recognition

The biphasic CD spectra of 2Th-L^R·L^R and 2Th-L^S·L^S (Fig. 4a, red and blue lines, respectively) were successfully reproduced in calculated CD spectra obtained with the use of time-dependent (TD) DFT (Fig. 4b, red and blue lines, respectively), from the structures of 2Th-L^R·L^R optimized with P-helicity and 2Th-L^S·L^S optimized with M-helicity (Fig. 4b, inset). The TD DFT calculation suggested that electronic transition corresponding to the first cotton band (excited state 1) arises from molecular orbitals along with the three bridged bis-diketone ligands (Fig. 4c), indicating that the origin of the biphasic CD spectra is excitonic splitting inside the helicates.¹⁸ The helix sense of the other helicates was determined in the same manner (Fig. S10–S12†), to reveal that both 2Th and 3Th favor P-helicity with R guest co-ligands (L^R and L′^R), and M-helicity with S guest co-ligands (L^S and L′^S). The DFT calculations also indicated that M-2Th-L^S·L^S and P-2Th-L^R·L^R are 12.33 kcal mol⁻¹ lower in energy than that of P-2Th-L^S·L^S and M-2Th-L^R·L^R (diastereomers), respectively (Fig. 5a). The M-2Th-L^S·L^S and P-2Th-L^R·L^R have two ligand-to-ligand interactions (π–π interactions) with the guest co-ligands, while P-2Th-L^S·L^S and M-2Th-L^R·L^R (diastereomers) contain only one ligand-to-ligand interaction inside the assembly (Fig. 5a). In the same manner, the optimized structures of M-2Th-L′^S·L′^S and P-2Th-L′^R·L′^R are 7.44 kcal mol⁻¹ lower in energy than that of P-2Th-L′^S·L′^S and M-2Th-L′^R·L′^R (diastereomers), respectively (Fig. 5b). These DFT results can explain the fact that 2Th favored P-helicity with the R-guest co-ligands (L^R and L′^R), and M-helicity with the S-guest co-ligands (L^S and L′^S). More importantly, the DFT calculations predict that homochiral assemblies (2Th-L^R·L^R, 2Th-L^S·L^S, 2Th-L′^R·L′^R, and 2Th-L′^S·L′^S) are 5.99–7.00 kcal mol⁻¹ lower in energy than that of heterochiral assemblies (2Th-L^R·L^S and 2Th-L′^R·L′^S) [Fig. 5a and b].²⁸ Additionally, the DFT calculations provide an important prediction concerning on the performed complexes (1 : 1 complexes): even the initial terminal binding of the chiral guest co-ligands will induce the helical conformation of 2Th and 3Th, where the M-helix structures (1 : 1 complexes) with the S-guest co-ligands (L^S and L′^S) are 4.16–6.45 kcal mol⁻¹ lower in energy than that of the P-helix structures (Fig. 5c) as in the case of the final assemblies (1 : 2 complexes).

Fig. 4 (a) Experimentally obtained UV-vis and CD spectra of 2Th-L^R·L^R (red line) and 2Th-L^S·L^S (blue line) in acetone. (b) Theoretical CD spectrum [time dependent-DFT/CAM-B3LYP-6-31G(d) [C H N O S F]/LANL2DZ (Sc)] of the optimized structure [DFT/CAM-B3LYP-6-31G(d) [C H N O S F]/LANL2DZ (Sc)] of P-2Th-L^R·L^R and M-2Th-L^S·L^S, where Eu atoms are replaced by Sc atoms to reduce the calculation complexity (Fig. S10–S12†). (c) Summary of excited state 1.

Fig. 5 Relative energy difference between the optimized structures of (a) P-2Th-L^S·L^S, M-2Th-L^S·L^S, 2Th-L^R·L^S, P-2Th-L^R·L^R, and M-2Th-L^R·L^R, (b) P-2Th-L′^S·L′^S, M-2Th-L′^S·L′^S, 2Th-L′^R·L′^S, P-2Th-L′^R·L′^R, and M-2Th-L′^R·L′^R, (c) M-2Th-L^S and P-2Th-L^S, M-2Th-L′^S and P-2Th-L′^S, M-3Th-L^S and P-3Th-L^S, M-3Th-L′^S and P-3Th-L′^S [DFT/CAM-B3LYP/def2SVP (C H N O S F)/def2TZVPP (La)], where the Eu atoms were replaced by La atoms. (d) Chemical structures of L^R, L^S, L′^R, L′^S, 2Th, and 3Th.

Helix length-dependent over 1 nm-range chirality recognition

On the basis of these results, we investigated the effects of the helix length on the long-range chirality recognition by monitoring the induced CD signals of 2Th and 3Th (d_Ln–Ln = 11.5 and 14.0 Å, respectively) on changing the enantiomeric excess (ee) of the chiral guest co-ligands in the range from ee = ([R] − [S])/([R] + [S]) = 0 to +1 and to −1 (Fig. 6 left, red and blue lines, respectively). Here, the total concentration of chiral ligands ([R] + [S]) remained constant at each molar ratio, ca. a 90-fold excess against 2Th and 3Th. Such excess conditions are required for a clear distinguishment on whether the plot of Δε versus ee (Fig. 6 right) follows the positive nonlinear (sigmoidal) or linear relationship (vide infra). A positive nonlinear relationship was clearly observed for the combination of 2Th with L^R and L^S (Fig. 6a, right). The experimentally obtained nonlinear relationship is explained by eqn (1) derived from Scheme 3a (Appendix 1†):

Δε/Δε_∞ = 4ee(K_RR/K_(hetero))/(2(1 + ee²)(K_RR/K_(hetero)) + (1 − ee²)) (1)

where Δε_∞ denotes the Δε value of the homochiral assemblies at ee = +1. A positive nonlinear relationship is expected when the system follows chiral-self recognition because K_RR/K_(hetero) > 0.50, and the degree of sigmoidal character increases together with the K_RR/K_(hetero) value (here, K_(hetero) = K_RS + K_SR = 2K_RS = 2K_SR).^29,30 The observed positive nonlinear relationship (Fig. 6a, right) agreed well with the calculated curve with K_RR/K_(hetero) = 2.7, with the use of eqn (1). Therefore, chiral self-recognition occurred in the self-assembly process of 2Th with L^R and L^S (Scheme 3a). The larger K_RR value than that of K_RS suggested a higher thermodynamic stability of the homochiral 2Th-L^R·L^R over the heterochiral 2Th-L^R·L^S, which is consistent with the above energy estimation from their DFT-optimized structures (ΔE = 5.99 kcal mol⁻¹, Fig. 5a). Notably, the degree of chiral self-recognition is highly temperature dependent. Whereas a high K_RR/K_(hetero) value was obtained at lower temperature, K_RR/K_(hetero) = 2.4 at 323 K, 2.7 at 298 K, and 7.0 at 273 K (Table 2 and Fig. S15†). This trend implies a major role of the enthalpy term in the chiral-self-recognition nature, which likely arises from ligand-to-ligand interactions between 2Th and L^R or L^S (vide supra, Fig. 1b). Conversely, 3Th with a longer helix length (d_Ln–Ln = 14.0 Å) had an almost completely linear relationship between Δε and ee in their self-assembly process with L^R and L^S (Fig. 6b, right). The linear relationship between Δε and ee can be described by eqn (1) with K_RR/K_(hetero) = 0.46, suggesting statistical binding of L^R and L^S to 3Th (Scheme 3b). The value of K_RR/K_(hetero) = 0.46 indicates that homochiral (3Th-L^R·L^R and 3Th-L^S·L^S) and heterochiral assemblies (3Th-L^R·L^S) have almost the same thermodynamic stability, which is likely attributed to the longer thiophene spacer units of 3Th that create flexibility in the helix chain and prohibit effective chirality information transfer.²⁸ Hence, the value of K_RR/K_(hetero) in self-assembly of 3Th with L^R and L^S was almost temperature independent (Table 2 and Fig. S16†). Conversely, a complete linear relationship was success-fully obtained between Δε and ee during the self-assembly of mononuclear complex 2Th′ with L^R and L^S (Fig. 6c, right), where 2Th′ exhibited induced biphasic CD signals (Fig. 6c, left) similar to the case of the dinuclear helicates (2Th and 3Th). Therefore, the negative control experiments revealed that even the initial terminal binding of L^R or L^S to 2Th induced helicate structures prior to the final assembly (Scheme 3), which is also in good agreement with the DFT prediction (Fig. 5c, vide supra). Conversely, when the phenyl groups of L^R and L^S were replaced by isopropyl groups (L′^R and L′^S, respectively), a higher degree of chiral self-recognition was achieved by a combination of 2Th with L′^R and L′^S in terms of a higher value of K_RR/K_(hetero) (2.7 → 6.4, Fig. 6d and Table 1), where the chiral self-recognition feature was maximized at 273 K (K_RR/K_(hetero) > 10.0, Fig. S15† and Table 2). The above DFT calculations indicate that homochiral 2Th-L′^S·L′^S is 7.00 kcal mol⁻¹ lower in energy than that of heterochiral 2Th-L′^R·L′^S (Fig. 5b), which was larger than that between 2Th-L^S·L^S and 2Th-L^R·L^S (5.99 kcal mol⁻¹, Fig. 5a). Notably, a plot of Δε versus ee obtained in combination of 3Th with L′^R and L′^S suggested K_RR/K_(hetero) = 1.0 (Fig. 6e), indicating that chiral self-recognition can be achieved even for 3Th with longer helix lengths (Scheme 3e and Fig. S17–S19†).

Fig. 6 Left: CD spectra of (a) and (d) 2Th (7.2 × 10⁻⁶ M), (b) and (e) 3Th (5.3 × 10⁻⁶ M), and (c) 2Th′ (9.4 × 10⁻⁶ M) in the presence of different enantiomeric excess (ee) of L^{(R or S)} [total concentrations: (a) 6.6 × 10⁻⁴ M, (b) 4.9 × 10⁻⁴ M, (c) 8.7 × 10⁻⁴ M], L′ ^{(R or S)} [total concentrations: (d) 7.5 × 10⁻⁴ M and (e) 5.1 × 10⁻⁴ M] in acetone at 298 K. Right: plots of Δε versus ee of (a)–(c) L^{(R or S)}, (d) and (e) L′ ^{(R or S)}.

Scheme 3 Summary of self-sorting for L^R and L^S with (a) 2Th, (b) 3Th, (c) 2Th′, and those for L′^R and L′^S with (d) 2Th and (e) 3Th, where K_(hetero) = K_RS + K_SR = 2K_RS = 2K_SR.

Table 2 Ratios of binding constants (K_RR/K_(hetero)) in self-assembly formation of 2Th and 3Th with chiral guest co-ligands, where K_(hetero) = K_RS + K_SR = 2K_RS = 2K_SR

	2Th K RR /K(hetero)			3Th K RR /K(hetero)
	323 K	298 K	273 K	323 K	298 K	273 K
R = Ph (L^R, L^S)	2.4	2.7	7.0	0.70	0.46	0.56
R = ^iPr (L′^R, L′^S)	4.6	6.4	>10.0	0.90	1.00	1.05

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Finally, conclusive evidence for the chiral self-recognition versus statistical binding mechanism was obtained by ¹⁹F NMR measured under enantiopure and racemic conditions of the chiral guest co-ligands (Fig. 7). Under the racemic conditions ([3Th] : [L^R] : [L^S] = 1 : 1 : 1), the ¹⁹F NMR spectrum of 3Th (Fig. 7b) had new signals (purple squares) other than those corresponding to the homochiral assemblies (3Th-L^R·L^R and 3Th-L^S·L^S, red and blue circles) observed under the enantiopure conditions ([3Th] : [L^R] : [L^S] = 1 : 2 : 0, Fig. 7c). Hence, the new signals (Fig. 7b, purple squares) are responsible for the heterochiral assembly(3Th-L^R·L^S) formed under the racemic conditions. The ratio between the homochiral and heterochiral assemblies was determined to be [3Th-L^R·L^R + 3Th-L^S·L^S] : [3Th-L^R·L^S] = 1.0 : 1.2 from the integrated ratio of the ¹⁹F NMR signals, which agreed well with the theoretical product ratio at ee = 0 calculated from K_RR/K_(hetero) = 0.46 (Fig. 7a). This assignment is consistent with the statistical binding mechanism for a self-assembly process of 3Th with L^R and L^S (Scheme 3b). Conversely, the ¹⁹F NMR spectrum of 2Th measured under racemic conditions ([2Th] : [L′^R] : [L′^S] = 1 : 1 : 1, Fig. 7e) was identical to that obtained under the enantiopure conditions ([2Th] : [L′^R] : [L′^S] = 1 : 2 : 0, Fig. 7f). The theoretical product ratio between homochiral and heterochiral assemblies is [2Th-L′^R·L′^R + 2Th-L′^S·L′^S] : [2Th-L′^R·L′^S] = 92.8 : 7.2 (at ee = 0) calculated from K_RR/K_(hetero) = 6.4 (Fig. 4d),³¹ which also underlines the strong chiral self-recognition behavior for self-assembly of 2Th with L′^R and L′^S (Scheme 3d).

Fig. 7 Theoretical product ratio at ee = 0 between (a) 3Th-L^R·L^R (red) and 3Th-L^S·L^S (blue) and 3Th-L^R·L^S (purple) calculated based on eqn (1) with K_RR/K_(hetero) = 0.47, (d) 2Th-L′^R·L′^R (red) and 2Th-L′^S·L′^S (blue) and 2Th-L′^R·L′^S (purple) calculated based on eqn (1) with K_RR/K_(hetero) = 6.4, where K_(hetero) = K_RS + K_SR = 2K_RS = 2K_SR. ¹⁹F NMR spectra of 3Th under the (b) racemic conditions [3Th] : [L^R] : [L^S] = 1 : 1 : 1, (c) enantiopure conditions [3Th] : [L^R] : [L^S] = 1 : 2 : 0, those of 2Th under the (e) racemic conditions [2Th] : [L^R] : [L^S] = 1 : 1 : 1, (f) enantiopure conditions [2Th] : [L^R] : [L^S] = 1 : 2 : 0, in acetone-d₆ at 298 K. Symbols correspond to those for the structures of (a) and (d), red circles: 3Th-L^R·L^R, blue circles: 3Th-L^S·L^S, purple squares: 3Th-L^R·L^S, red triangles: 2Th-L′^R·L′^R, blue triangles: 2Th-L′^S·L′^S.

Conclusions

In conclusion, we successfully demonstrated that helix chain (mediator) length can control when long-range chiral recognition occurs through chiral self-recognition or in statistical manner. Self-assembly of the shorter helicate 2Th (d_Ln–Ln = 11.5 Å) with chiral guest co-ligands (L^R and L^S) resulted in chiral self-recognition (Scheme 3a), forming mainly homochiral assemblies (2Th-L^R·L^R and 2Th-L^S·L^S) rather than heterochiral assemblies (2Th-L^R·L^S). Conversely, self-assembly of the longer helicate 3Th (d_Ln–Ln = 14.0 Å) with L^R and L^S occurred in a statistical binding manner (Scheme 3b), resulting in formation of the heterochiral (3Th-L^R·L^S) and homochiral assemblies (3Th-L^R·L^R and 3Th-L^S·L^S) in an almost 1 : 1 ratio. Subtle modification on the side arms of the chiral guest co-ligands (L^{(R or S)} → L′^{(R or S)}) enables even the longer helicate 3Th to achieve over 1.4 nm-range chirality recognition (Scheme 3e). Thus, the present findings open up opportunities for rational planning of molecular communication through the use of chirality as simple chemical input across long distances.

Author contributions

N. S., H. I., and N. O. performed the synthesis and characterization of materials, and also contributed the titration experiments. Y. O. contributed the analysis of the X-ray crystal structure. J. Y. designed the study, analysed the experimental data and wrote the manuscript.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was partly supported by JSPS KAKENHI Grant Numbers JP19H02693, JP19K22207, and JP19H04596 in Scientific Research on Innovative Areas “Coordination Asymmetry”, Grant-in-Aid for the ASAHI Glass Foundation. We thank the Edanz Group (www.edanzediting.com/ac) for editing a draft of this manuscript.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available: Additional experimental details and additional data. CCDC 2036830. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/d1sc01611c

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