Introduction

Graphitic networks of sp2-carbon atoms continuously attract much attention in materials science. Modulability of electronic characters of graphitic network, for instance, by periodicity controls and/or heteroatom doping is one of the most intriguing features of the graphitic networks. Incommensurate pairs of two-dimensional atomic layers have attracted considerable attention in particular1,2 because bilayers with twisted orientations give rise to unique periodicity that can alter the electronic characteristics of layered materials. The incommensurate bilayer systems can be also found in a pair of helical carbon nanotubes as incommensurate double-wall carbon nanotubes (i-DWNTs), which further highlights the uniqueness of periodicity as well as stereoisomerism of the incommensurate pairs3,4. Thus, for a helical nanotube specified with a unique (n,m) chiral index (n ≠ m)5, there exist (P)- and (M)-enantiomers6, and in i-DWNT combining small-bore and large-bore (n,m)-nanotubes, four stereoisomers of two diastereomers with two enantiomer pairs emerge (Fig. 1). Although the i-DWNT systems can dramatically diversify the periodicity and stereoisomerism of nanotubes, structural information with atomic precision cannot be defined with infinite carbon nanotubes due to the highly heterogeneous structures of nanotube mixtures. Recently, we introduced a molecular version of i-DWNTs by adopting (9,6)-[3]cyclo-3,11-dibenzochrysenylene ([3]CdbC)7 as an inner tube and (20,4)-[4]cyclo-3,11-fulminenylene ([4]CF) as an outer tube (Fig. 1)8. Stereoisomeric pairs of (P)- and (M)-isomers for inner and outer tubes were examined for the first time as a molecular version of i-DWNT complexes, which revealed that heterohelical combinations of (P):(M)-pairs [(P)⊃(M) and (M)⊃(P)] were preferred over homohelical combinations of (P):(P)- and (M):(M)-pairs [(P)⊃(P) and (M)⊃(M)]. Although the spontaneous assembly of i-DWNT complexes proceeded in a stereoselective manner to suppress structural diversity in this first instance, further structural investigations of nanotube structures are necessary to deepen our understanding of the structural chemistry of i-DWNTs. In addition, as elaborated below, the i-DWNT complex of this first instance relied on a fortuitous finding of matched DWNT pairs, which, in turn, showed the presence of synthetic challenges of rational, chemical design of i-DWNT complexes. In this study, we designed a large-bore nanotube molecule for the outer tube of the i-DWNT complex by exploring a target-oriented strategy. The i-DWNT assembly of helical nanotube molecules was successfully obtained, which showed that the handedness of nanotubes was not a sole factor that determined the stereoselectivity of bilayer formation.

Fig. 1: Incommensurate pairs of nanotube molecules.
figure 1

a Mixing a racemic mixture of small-bore (P)/(M)-nanotubes with a racemic mixture of large-bore (P)/(M)-nanotubes affords four diastereomeric i-DWNT complexes. b Finite nanotube molecules that afforded i-DWNT complexes in the previous study8. Heterohelical combinations of (P)⊃(M) and (M)⊃(P) were selectively obtained.

Full size image

Results and discussion

Molecular design

In our previous study on molecular i-DWNT complexes, we obtained the incommensurate pair of (P)-[4]CF⊃(M)-[3]CdbC and (M)-[4]CF⊃(P)-[3]CdbC by focusing on [n]phenacenes as a parent arylene panel for belt-persistent cycloarylenes (Fig. 1)8,9. It was merely fortuitous that we found [4]CF as a large-bore outer tube to encapsulate a small-bore tube of [3]CdbC, and the design was neither strategic nor rational. For this study, we first scrutinized cycloarylene structures to enumerate synthetically accessible helical nanotube molecules in full, which will be also instructive for further target-oriented syntheses of nanotube molecules in the future10,11,12,13,14.

First, as the inner tube, we decided to adopt an identical molecule, [3]CdbC, with a chiral index of (9,6) due to its small diameter (dt) of 1.04 nm (Fig. 2)7. Considering the van der Waals radius of carbon atoms, we should then set the diameters of the outer target in the range of 1.72–1.80 nm8. In this range, as shown in the map in Fig. 2, 19 chiral indices were found to be chiral vectors of appropriate nanotube molecules with ideal diameters. In this study, an atlas of synthetically accessible nanotubes via tetrameric macrocyclization of arylenes was completed by expanding a previous list of D4-symmetric molecules15, which allowed us to find suitable synthetic targets. Thus, with the 19 chiral indices of candidates in hand, we inspected the atlas shown in Supplementary Figs. 2–4 and found two chiral indices, i.e., (20,4) and (18,6), in the maps of accessible cycloarylenes with D4 and C2 symmetry. Examining the structural details of these cycloarylenes, we found [4]cyclo-2,9-pentacenylene (“AAAA” with panel ID = 17, Supplementary Fig. 2) to be a feasible target with a minimum number of hexagons on the panel. Furthermore, we decided to avoid intact [4]cyclo-2,9-pentacenylene as the target because such large acenes are prone to oxidative degradation, particularly in the presence of structural constraints of curved structures15. Consequently, we decided to adopt preoxidized pentacene skeletons as an alternative panel and were delighted to find quinacridone as a doped congener of pentacene (Fig. 2). The quinacridone panel possessed two types of heteroatoms, i.e., N and O, installed in the pentacene skeleton, which should be stabilized against possible oxidation. More importantly, quinacridone is abundantly available as a pigment known as Pigment Violet 19 and can be readily converted to a 2,9-dibrominated congener16. Thus, a cyclic tetramer of quinacridone, i.e., [4]cyclo-2,9-quinacridonylene ([4]CQ), has become as a synthetic target as a large-bore nanotube molecule in this study.

Fig. 2: Design of large-bore nanotube molecules to encapsulate [3]CdbC with a chiral index of (9,6).
figure 2

In a range of 1.72-1.80 nm, there were 19 candidates, and by enumerating arylene panels for the synthesis (Supplementary Figs. 1–4), two chiral indices, i.e., (20,4) and (18,6), remained synthetically accessible candidates. By examining the chemical structures of these chiral indices, we found [4]CQ to be an ideal target for large-bore nanotubes.

Full size image

Synthesis of [4]CQ

We devised a robust synthetic route to [4]CQ from quinacridone (1; Pigment Violet 19) and synthesized belt-persistent cylindrical cycloarylenes with a chiral index of (20,4). Thus, boryl linkers at the 2,9-positions in quinacridone were introduced by multistep transformations via N-alkylation, 2,9-selective bromination and Miyaura borylation (Fig. 3). The final cyclization was performed by adopting Yamago’s method with our boryl-linker modification for the Pt-mediated tetrameric macrocyclization. Owing to panel orientations in the cycloarylene structures, four diastereomers were possible for this macrocyclization9,10,17, and we were delighted to obtain desired (20,4)-isomers (hereafter denoted as [4]CQ) in a selective manner as a single diastereomer with AAAA/BBBB panel orientations. The (20,4)-structure of [4]CQ was fully established by single-crystal X-ray diffraction analyses. Thus, the homogeneous panel orientations of AAAA/BBBB suggested by spectroscopic analyses were confirmed by the crystal structure. As suggested by the intrinsic D4-symmetry of [4]CQ, a pair of enantiomers was present with [4]CQ in the racemic crystal, and a representative (P)-isomer is shown in Fig. 3b. The molecular structure was deformed in an oval shape with major and minor diameters of 1.9 and 1.7 nm, respectively. Heteroatoms of nitrogen and oxygen were periodically located on the cylindrical structure of the (20,4)-nanotube, and their atomically precise positions on the graphitic sheet were also specified using vectorial nomenclature, as shown in Fig. 3b18, (https://physorg.chem.s.u-tokyo.ac.jp/applet/defect/).

Fig. 3: N,O-Doped cylindrical cycloarylene, [4]CQ.
figure 3

a Synthesis. b Crystal structure. Among two similar yet independent structures, a representative structure is shown. Solvent molecules and hydrogen atoms were omitted for clarity. See Supplementary Fig. 5 for details.

Full size image

Chiral resolution

The large-bore [4]CQ molecules were segments of (20,4)-helical nanotubes and possessed chirality originating from the helicity of atomic networks in the cylindrical conjugated systems. We were delighted to find that a method developed for chiral resolution of hydrocarbon cylindrical molecules was applicable to chiral resolution of this N,O-doped cylindrical molecules. Thus, when a racemate of [4]CQ was injected on columns of cholesterol-loaded silica gels (COSMOSIL Cholester) under high-performance liquid chromatography (HPLC) conditions with 50%-methanol/dichloromethane eluent, two enantiomers were separated: one isomer, (+)275-[4]CQ, appeared at a retention time of 4.1 min, and its enantiomer, (–)275-[4]CQ, appeared at 5.6 min (Fig. 4a). With the separated enantiomers in hand, we recorded CD spectra of these isomers to find mirror-image spectra, as shown in Fig. 4b. We then performed time-dependent (TD) DFT calculations for the spectral simulation using (P)-[4]CQ with methyl substituents as a model6. The CD spectrum of the (P)-isomer matched (+)275-[4]CQ, showing that (+)275-[4]CQ should be assigned as (P) for the helicity of atomic arrangements in cylindrical conjugated systems.

Fig. 4: Chiral resolution of [4]CQ.
figure 4

a HPLC chromatograms before and after being resolved. HPLC conditions: eluent = 50% CH3OH/CH2Cl2, temperature = 40 °C, flow rate = 1 mL/min. b CD spectra of (+)275-[4]CQ (CH2Cl2, 298 K, 3.02 × 10–6 M) and (–)275-[4]CQ (CH2Cl2, 298 K, 3.97 × 10–6 M). The theoretical CD spectrum was obtained by TD DFT calculations (B3LYP/6-31 G(d,p)) for the (P)-isomer of methyl-substituted [4]CQ as the model.

Full size image

Assembly of i-DWNT

The formation of the i-DWNT complexes between [4]CQ and [3]CdbC was then confirmed by 1H NMR spectra. An unexpected spectrum was first obtained, when we analysed a mixture of rac-[4]CQ and rac-[3]CdbC. In a previous study, when [4]CF with 6 aromatic 1H resonances was mixed with [3]CdbC with 6 aromatic 1H resonances, we observed 12 aromatic 1H resonances (i.e., 12 = 6 + 6), which resulted from the selective formation of a single diastereomer of [4]CF⊃[3]CdbC complexes from (P):(M)- and (M):(P)-heterohelical combinations8. In this study, however, using [4]CQ with 4 aromatic 1H resonances, 20 aromatic 1H resonances appeared upon mixing with [3]CdbC (i.e., 20 > 6 + 4) (Fig. 5a). When the ratio of inner and outer nanotubes deviated from an equimolar amount, we separately observed complexed and uncomplexed species as two independent species (Supplementary Figs. 7 and 8). The observation showed that the 20-resonance spectrum corresponded to the i-DWNT complexes due to the slow in-and-out exchange equilibrium8. Among a few possible scenarios to explain the observation of increased aromatic resonances, nonstereoselective formation of i-DWNT complexes was most plausible: by mixing rac-[4]CQ and rac-[3]CdbC, the i-DWNT formation proceeded in a nonselective manner to afford four diastereomers from heterohelical [(P)⊃(M) and (M)⊃(P)] and homohelical [(P)⊃(P) and (M)⊃(M)]combinations (see also Fig. 1).

Fig. 5: 1H NMR spectra of i-DWNT complexes between [4]CQ and [3]CdbC.
figure 5

Spectra were recorded in CD2Cl2 (1.0 mM, 600 MHz, 298 K). a 1H NMR spectrum of rac-[4]CQ + rac-[3]CdbC. b Heterohelical combination of (P):(M)-nanotubes. c Homohelical combination of (M):(M)-nanotubes.

Full size image

The formation of i-DWNT from the nonstereoselective complexation was confirmed by the preparation of two diastereomeric complexes in separate experiments. Thus, when we recorded the 1H NMR spectrum by mixing the heterohelical combination of (P)-[4]CQ and (M)-[3]CdbC, a spectrum with 10 aromatic resonances was obtained, as shown in Fig. 5b. Likewise, a homohelical mixture of (M)-[4]CQ and (M)-[3]CdbC gave another spectrum with 10 aromatic resonances (Fig. 5c). By comparing these 1H NMR spectra shown in Fig. 5, the spectrum obtained from the racemate mixture should be best interpreted as a sum of the spectra of (P)-[4]CQ⊃(M)-[3]CdbC and (M)-[4]CQ⊃(M)-[3]CdbC. The obtained result confirmed the nonstereoselective formation of i-DWNT complexes of [4]CQ⊃[3]CdbC from the racemates.

Association constants of i-DWNT assembly

By determining the association constants for the formation of heterohelical and homohelical i-DWNT complexes, we revealed the fundamental parameters of the association thermodynamics. As shown in Fig. 6, upon addition of small-bore [3]CdbC, we observed redshifts with absorption of [4]CQ, and using characteristic absorbance of [4]CQ at 539 nm, we determined the association constants (see “Methods” for details)19. Thus, the association constant (Ka) of the heterohelical (P)-[4]CQ⊃(M)-[3]CdbC complex was determined to be (6.6 ± 0.5) × 107 M–1, whereas that of the homohelical (M)-[4]CQ⊃(M)-[3]CdbC complex was elucidated to be (6.3 ± 1.0) × 107 M–1. The Gibbs free energy gains (ΔG) for the association were thus determined as –10.7 ± 0.0 kcal mol–1 for (P)-[4]CQ⊃(M)-[3]CdbC and –10.6 ± 0.1 kcal mol–1 for (M)-[4]CQ⊃(M)-[3]CdbC (298 K). The Ka values for both complexes were comparable and were as high as ~107 M–1, which clarified the origin of the observations of both forms from a mixture of racemates (cf. Fig. 5a). Interestingly, the association constants with this large-bore [4]CQ nanotubes were much higher than those of previous large-bore [4]CF nanotubes with an identical chiral index of (20,4) to record two to three orders of magnitude larger Ka values8.

Fig. 6: Titration experiments to determine the association constants of i-DWNT complexes.
figure 6

Experiments were performed in triplicate, and representative data are shown. a UV–vis data. b Fitting curves of the absorbance changes (ΔAbs) at 539 nm for Ka determination. See “Methods” and Supplementary Data 4 for details.

Full size image

Crystal structures of i-DWNT

Detailed structural comparisons of i-DWNT complexes with [4]CQ and [4]CF became feasible because we obtained a single crystal of the heterohelical (P)-[4]CQ⊃(M)-[3]CdbC complex. Thus, as shown in Fig. 7a, the molecular structure of the (P)-[4]CQ⊃(M)-[3]CdbC complex possessed an ideal i-DWNT structure with coaxial alignment, which was similar to that of the previous (P)-[4]CF⊃(M)-[3]CdbC complex (Fig. 7b). The small-bore nanotube at the inner site was identical [i.e., (M)-[3]CdbC] and served as a probe for detailed structural comparisons. As highlighted in Fig. 7, one of the arylene panels of the outer tube covered one dibenzochrysenylene panel of the inner tube for both structures, which provided an ideal segment for the structural comparisons. The Hirshfeld surfaces of [3]CdbC were then mapped with intermolecular contacts for structural analyses20. The de mapping shows distances from the surface to the external atoms of the outer tubes. Although the chiral index and the geometric diameter (dt) were identical for [4]CQ and [4]CF, the skeletal network of the arylene panels was different and resulted in different mapping of contact areas. The shape index that revealed the convex and concave areas of the surface also differed between the two i-DWNT complexes. However, the surface areas for π-contacts between inner and outer tubes were similar in these two i-DWNT complexes. Thus, when we measured the surface areas of [3]CdbC for π-contacts in (P)-[4]CQ⊃(M)-[3]CdbC, a value of 17.9% was obtained. When we measured the π-contact areas of [3]CdbC in (P)-[4]CF⊃(M)-[3]CdbC, a value of 16.7% was obtained. The obtained results showed that the overlapping areas were similar in the two complexes despite different arrangements of the atomic networks.

Fig. 7: Crystal structures of i-DWNT complexes.
figure 7

The Hirshfeld surfaces were determined for atoms involved in the π-conjugate systems and were divided into arylenes to clarify the locations of the panels. See Supplementary Fig. 10 for details of panel-panel overlaps. Solvent molecules were omitted for clarity. a (P)-[4]CQ⊃(M)-[3]CdbC. b (P)-[4]CF⊃(M)-[3]CdbC. The CIF data were taken from the previous work (CCDC 2034189)8.

Full size image

Thermodynamics of i-DWNT assembly

Finally, isothermal titration calorimetry (ITC) allowed us to reveal the in-depth thermodynamics of i-DWNT formation21. Because the associations of this i-DWNT complex were extremely exothermic processes with Ka values of >107 M–1, the ITC curve were inappropriate for fitting analyses to derive Ka determinations (see Supplementary Data 4)22,23. Nonetheless, the titration allowed us to determine enthalpy gains (ΔH) for the association via measurement of the exchanging heat. Using the ΔG values from UV-vis titration experiments, we can complete the thermodynamic parameters including the entropy changes (ΔS) for the associations. Thus, the thermodynamic parameters for the association of the heterohelical (P)-[4]CQ⊃(M)-[3]CdbC complex were ΔH = –5.9 ± 0.1 kcal mol–1 and –TΔS = –4.8 ± 0.1 kcal mol–1, and those for the homohelical (M)-[4]CQ⊃(M)-[3]CdbC complex were ΔH = –7.7 ± 0.3 kcal mol–1 and –TΔS = –2.9 ± 0.3 kcal mol–1 (Fig. 8). Although the Ka values for the heterohelical complexes with [4]CQ and [4]CF differed considerably (see above), the difference in the ΔH values for these complexes was small (ΔΔH ~ 0.1 kcal mol–1). The obtained result is qualitatively consistent with the similar surface area of π-contacts determined by the Hirshfeld analyses for these complexes (17.9% and 16.7%; see above). The DFT calculations of i-DWNT complexes reproduced the preference of stereoisomeric combinations (homohelical > heterohelical for [4]CQ; heterohelical > homohelical for [4]CF) (Supplementary Data 5). Although the calculated energies for association matched finely with ΔH values24,25, differences between [4]CQ systems and [4]CF systems were so subtle (~1 kcal mol–1) that should be difficult to be reproduced by theoretical calculations. The present system should also be interesting subjects to be investigated by state-of-the-art theoretical and physical investigations, because of the presence of rapid dynamic rotational motions (Supplementary Fig. 9) on top of due considerations of appropriate theoretical models26,27. The ΔG difference between these complexes was largely ascribed to the entropy (–TΔS). Similarly, favourable entropy contributions for the association (–TΔS < 0) were observed with complexes with large curved π-systems in preceding studies of nanocarbon molecules22,28,29,30,31, which was most likely due to desolvation of solvent molecules from the curved surface. Therefore, we believe that the large favourable entropy gain with [4]CQ (–TΔS ~ 4 kcal mol–1) should be best explained by changes in the solvation in the presence of N,O-heteroatoms. In contrast, although the Ka values were similar between diastereomeric complexes of (P)-[4]CQ⊃(M)-[3]CdbC and (M)-[4]CQ⊃(M)-[3]CdbC (~107 M–1), the contributing factors showed subtle differences of ΔΔH ~ 1.8 kcal mol–1 and ΔΔS ~ 6 cal mol–1 K–1. Presently, we do not understand the origins of these differences that show enthalpy-entropy compensation trends32,33,34,35. Compensation can involve dynamic behaviours including the solvation and rolling dynamics of i-DWNT36, which should be further investigated in the future.

Fig. 8: Thermodynamics of i-DWNT assembly.
figure 8

Data with (P)-[4]CF were taken from the previous work8.

Full size image

Conclusion

Target-oriented design of cylindrical cycloarylenes as segmental models of helical carbon nanotubes was devised, and a large-bore cylindrical molecule ([4]CQ) was synthesized from an abundantly available pigment. The large-bore molecule was obtained in a stereoselective manner as a racemate, and owing to the heteroatoms embedded in the arylene panels, the molecule should serve as a segmental model of N,O-doped helical carbon nanotubes with a chiral index of (20,4). The large-bore cylinder encapsulated a small-bore cylindrical molecule ([3]CdbC) to afford a molecular version of i-DWNTs. When compared with a preceding hydrocarbon outer tube ([4]CF), the outer tube in this study increased the affinity to the small-bore molecule to result in a larger association constant of 107 M–1. The assembly of i-DWNT complexes proceeded in a nonstereoselective manner, which was also in contrast to the previous case with [4]CF that had unfavourable i-DWNT complexes. These observations show that further studies of other structural variants are necessary to clarify the mechanism and origins of the stereoselectivity of i-DWNT assembly. Crystallographic analyses and thermodynamic studies revealed favourable enthalpy contributions via π-contacts for the i-DWNT assembly and important roles of subtle changes in the favourable entropy contributions that tweaked the affinity between inner and outer tubes. We hope that this study will stimulate further studies on i-DWNT complexes as well as heteroatom-doped nanotube molecules in the future37,38,39,40.

Methods

Physical techniques

Flash silica gel column chromatography was performed on silica gel 60 N (spherical and neutral gel, 40–50 μm, Kanto). Gel permeation chromatography (GPC) was performed on an LC-5060 with JAIGEL 2HR-40 and 2.5 HR-40 polystyrene column (Japan Analytical Industry) with chloroform as the eluent. The purity of the target molecule was confirmed by high-performance liquid chromatography (HPLC) with two different columns (COSMOSIL πNAP, 4.6ϕ × 250 mm and COSMOSIL BuckyPrep, 4.6ϕ ×  250 mm, Nacalai Tesque). Chromatographic chiral resolution was performed with chiral columns (COSMOSIL Cholester, Nacalai Tesque) using a 4.6ϕ × 250 mm column for analytical scales and a 20ϕ × 250 mm column for preparative scales. The analytical HPLC was performed at 40 °C in a column oven (CO2060PLUS, JASCO) under detection of UV–vis absorption (MD2018PLUS, JASCO) and CD (CD2095PLUS, JASCO) with a flow rate of 1.0 mL/min. The preparative HPLC was performed at ambient temperature under UV-vis detection (UV2075PLUS, JASCO) with a flow rate of 18 mL/min. ITC analyses were performed on a microcalorimeter (MicroCal iTC200, Malvern). High resolution mass spectra (HRMS) were recorded on an autoflex speed device (Bruker Daltonics) using the matrix-assisted laser desorption ionization (MALDI) method with pyrene or dithranol as a matrix under reflector positive mode. UV–vis and CD spectra were recorded on a V-670 and J-1500 instruments (JASCO) with a temperature controller to adjust the temperature to 25 °C. Nuclear magnetic resonance (NMR) spectra were recorded on RESONANCE JNM-ECA 600 II equipped with the UltraCOOL UC5AT probe (JEOL). Chemical shift values were given with respect to internal CHCl3 (7.26) and CHDCl2 (5.32) for 1H NMR spectra and CDCl3 (77.16) and for 13C NMR spectra. Methyl (CH3), methylene (CH2) and methine (CH) signals in 13C NMR spectra were assigned by DEPT spectra.

Materials

Anhydrous THF (stabilizer-free) was purified by a solvent purification system (GlassContour) equipped with columns of activated alumina and supported copper catalyst (Q-5)41, and oDCB was dried with 4 A molecular sieves before use. Small-bore tubes, (P)- and (M)-[3]CdbC, were prepared and purified by methods reported in the literature7. For the experiments with [3]CdbC, the quantity of the compound was determined using the molar absorption coefficients (ε412 = 1.42 × 105 M–1 cm–1) derived from specimens with combustion elemental analysis data. PtCl2(cod) was prepared according to the reported procedure42. All other chemicals were of reagent grade and used without any further purification. The reactions were performed under N2 atmosphere, unless otherwise noted.

Atlas of synthetically accessible chiral indices

An atlas of synthetically accessible chiral indices was made in this study. For arylene panels with ≤7 hexagon arrays, cylindrical cycloarylenes accessible via tetrameric macrocyclization were enumerated and listed in maps. See Supplementary Methods and Supplementary Figs. 1–4 for details.

Synthesis of [4]CQ

In a 100-mL three-necked round bottom flask, CsF (3.03 g, 19.9 mmol), 3 (487 mg, 0.665 mmol) PtCl2(cod) (249 mg, 0.665 mmol) and oDCB (33 mL) were mixed. The mixture was stirred at 100 °C in the dark for 4 h. After the mixture was cooled to ambient temperature, PPh3 (1.75 g, 6.68 mmol) was added. The mixture was stirred in the dark for 30 min at ambient temperature and for 24 h at 100 °C. Methanol (250 mL) was added to the mixture, and the precipitate was collected by filtration. The precipitate was dissolved in CHCl3 (180 mL), and the insoluble materials were removed by filtration. The crude material was passed through a pad of alumina (eluent: CHCl3) and purified by GPC (columns: JAIGEL 2HR-40 and 2.5 HR-40, eluent: CHCl3) to afford [4]CQ as a racemic mixture of (20,4)-isomers of “AAAA” panel orientations in 21% yield (68.2 mg, 35.6 µmol). The purity was confirmed by analytical HPLC performed with two different columns (Supplementary Data 1). The stereochemistry and chiral index of [4]CQ were determined by a method adopted in a previous study9. Thus, NMR spectra assigned the symmetry of either D4 or D2d, and the presence of enantiomers (see below) finalized the assignment as D4-(20,4)-isomers. The assignment was further confirmed by crystallographic analysis (see below). The molar absorption coefficient (ε357) of rac-[4]CQ was determined to be 2.02 × 105 M–1 cm–1 as follows. A specimen was determined to have a chemical composition of (C128H136N8O8)•(CHCl3)0.17•(H2O)1.74 using data from combustion elemental analysis of C: 78.42%, H: 7.04%, N: 5.56% and Cl: 0.96%. Using this specimen to prepare three solutions with different concentrations in dichloromethane (0.1032 mg in 50.0 mL = 1.05 × 10–6 M, 0.1092 mg in 25.0 mL = 2.22 × 10–6 M, 0.1834 mg in 20.0 mL = 4.67 × 10–6 M), the UV–vis spectra were recorded to determine the ε357 value. 1H NMR (600 MHz, CDCl3): δ 8.53 (s, 8H), 8.36 (dd, J = 9.4, 2.3 Hz, 8H), 8.32 (d, J = 2.3 Hz, 8H), 7.51 (d, J = 9.4 Hz, 8H), 4.44 (m, 16H), 2.00-1.80 (m, 16H), 1.56 (m, 16H), 1.44-1.33 (m, 32H), 0.92 (t, J = 7.2 Hz, 24H); 13C NMR (151 MHz, CDCl3): δ 179.2, 141.4, 137.4, 131.8, 131.2 (CH), 126.6, 126.4 (CH), 121.2, 115.8 (CH), 113.5 (CH), 47.2 (CH2), 31.6 (CH2), 26.8 (CH2), 26.8 (CH2), 22.8 (CH2), 14.1 (CH3); HRMS (MALDI-TOF) (m/z): [M + H]+ calcd. for C128H137N8O8 1915.0587, found 1915.0570. See Supplementary Data 2 for NMR spectra. UV–vis and CD spectra were recorded in dichloromethane (Supplementary Data 3). See Supplementary Methods for the synthesis of other compounds.

Crystal structure of rac-[4]CQ

See Supplementary Methods, Supplementary Table 1 and Supplementary Data 6.

Chiral resolution of [4]CQ

See Supplementary Methods and Supplementary Fig. 6.

Theoretical calculations

See Supplementary Methods and Supplementary Data 5.

NMR spectra of the i-DWNT assembly

Specimens for i-DWNT spectra were weighed on aluminium pans (6 × 2.5 mm, Lüdi Swiss) using ultramicrobalance (SE2, Sartorius). Each specimen was dissolved in CD2Cl2 by adding the solvent to the specimen on the pan. The quantities of the specimens and CD2Cl2 are as follows. Racemate i-DWNT complexes (rac-[4]CQ⊃rac-[3]CdbC, Fig. 5a): CD2Cl2 (0.70 mL) was added to a mixture of rac-[4]CQ (0.6685 mg, 0.3492 µmol), (P)-[3]CdbC (0.2586 mg, 0.1742 µmol) and (M)-[3]CdbC (0.2591 mg, 0.1745 µmol) were added, and the mixture was subjected to NMR analyses (Fig. 5a). Heterohelical i-DWNT complexes [(P)-[4]CQ⊃(M)-[3]CdbC, Fig. 5b]: A specimen of (P)-[4]CQ (2.4052 mg, 1.2563 µmol) was dissolved in CD2Cl2 (1.26 mL), and a specimen of (M)-[3]CdbC (1.8989 mg, 1.2794 µmol) was dissolved in CD2Cl2 (1.28 mL). Aliquots of 0.30 mL from each solution were mixed, and the mixture was subjected to NMR analyses (Fig. 5b). Homohelical i-DWNT complexes [(M)-[4]CQ⊃(M)-[3]CdbC, Fig. 5c]: A specimen of (M)-[4]CQ (1.3602 mg, 0.7105 µmol) was dissolved in CD2Cl2 (0.71 mL), and a specimen of (M)-[3]CdbC (0.7624 mg, 0.5137 µmol) was dissolved in CD2Cl2 (0.51 mL). Aliquots of 0.30 mL from each solution were mixed, and the mixture was subjected to NMR analyses (Fig. 5c). See Supplementary Methods and Supplementary Figs. 7–9 for spectral analyses of in-and-exchange processes.

Titration experiments (UV–vis) for K a and ΔG

Association constants for i-DWNT [4]CQ⊃[3]CdbC assembly were determined by titration experiments with UV-vis spectra. The concentrations of [4]CQ and [3]CdbC for the titration were determined using the molar absorption coefficients of each compound ([4]CQ: ε357 = 2.02 × 105 M–1 cm–1, [3]CdbC: ε412 = 1.42 × 105 M–1 cm–1). The concentrations of the samples used for the titration were as follows. For the heterohelical (P)-[4]CQ⊃(M)-[3]CdbC complex: [(P)-[4]CQ] = 1.49 × 10–6 M and [(M)-[3]CdbC]  = 7.87 × 10–6 M. For the homohelical (M)-[4]CQ⊃(M)-[3]CdbC complex: [(M)-[4]CQ] = 1.64 × 10–6 M and [(M)-[3]CdbC] = 8.04 × 10–6 M. A typical titration procedure is described for the heterohelical (P)-[4]CQ⊃(M)-[3]CdbC complex. An aliquot of (M)-[3]CdbC solution in dichloromethane (50 µL) was added to a solution of (P)-[4]CQ (dichloromethane, 2.50 mL) in a cuvette at the temperature of the spectrometer of 25 °C. After stirring for 1 min, the UV–vis spectrum was recorded. The addition of (M)-[3]CdbC solution was repeated 15 times, and the change in absorbance was recorded (Fig. 6a and Supplementary Data 4). The changes of absorbance at 539 nm (ΔAbs) were subjected to fitting analyses to derive the association constant (Ka)19. At this wavelength, the molar absorption coefficient of (M)-[3]CdbC was negligible (ε539 ~ 0 M–1 cm–1) in contrast to a large value of (P)-[4]CQ (ε539 ~ 104 M–1 cm–1), which was a precondition for the fitting equation. The titration experiments were performed in triplicate to obtain the mean value with the error in standard deviation. The Ka values were converted to the Gibbs free energy changes (ΔG) by ΔG = –RT ln Ka. The titration experiments for the homohelical (M)-[4]CQ⊃(M)-[3]CdbC complex were likewise performed (Fig. 6b and Supplementary Data 4).

Titration experiments (ITC) for ΔH

The enthalpy gains (ΔH) for i-DWNT [4]CQ⊃[3]CdbC assembly were determined by isothermal titration calorimetry (ITC) experiments. The concentrations of [4]CQ and [3]CdbC for the titration were determined using the molar absorption coefficients of each compound ([4]CQ: ε357 = 2.02 ×  105 M–1 cm–1, [3]CdbC: ε412 = 1.42 × 105 M–1 cm–1). The concentrations of the samples used for the titration were as follows. For the heterohelical (P)-[4]CQ⊃(M)-[3]CdbC complex: [(P)-[4]CQ] = 1.85 × 10–4 M and [(M)-[3]CdbC] = 2.50 × 10–3 M. For the homohelical (M)-[4]CQ⊃(M)-[3]CdbC complex: [(M)-[4]CQ] = 2.16 × 10–4 M and [(M)-[3]CdbC] = 2.12 × 10–3 M. A typical titration procedure is as follows. A solution of [3]CdbC was added to a solution of [4]CQ in a microcalorimeter cell using the automated titration mode via a syringe. Using the ORIGIN program provided with the instrument, the ΔH value was derived. The titration experiments were performed in triplicate to obtain the mean value with the error in standard deviation. By combining the ΔH value from ITC and the ΔG value from UV–vis, the –ΔS value was determined. Based on the principle of the propagation of errors43, the error with ΔS was calculated by (error ΔH 2 + error ΔG2)1/2. The titration data are provided in Fig. 8 and Supplementary Data 4).

Crystal structure of (P)-[4]CQ⊃(M)-[3]CdbC

See Supplementary Methods, Supplementary Table 2 and Supplementary Data 7.

Hirshfeld surface analyses

See Supplementary Methods, Fig. 7 and Supplementary Fig. 10.