# Stereoisomerism, crystal structures, and dynamics of belt-shaped cyclonaphthylenes

^{a}Isobe Degenerate π-Integration Project, Exploratory Research for Advanced Technology (ERATO), Japan Science and Technology Agency, Aoba-ku, Sendai 980-8577, Japan;^{b}Advanced Institute for Materials Research, Tohoku University, Aoba-ku, Sendai 980-8577, Japan;^{c}Mathematical Institute, Tohoku University, Aoba-ku, Sendai 980-8578, Japan;^{d}Department of Chemistry, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

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Edited by Jerrold Meinwald, Cornell University, Ithaca, NY, and approved May 26, 2016 (received for review April 25, 2016)

## Significance

Stereoisomerism of molecules shapes an indispensable concept in molecular science. Stereoisomerism becomes complicated in cyclic structures such as saccharides but has now been established to form a fundamental knowledge in chemistry. When dynamic conformations are involved in the stereoisomerism of cyclic structures, there emerges a unique type of isomerism. Such perplexing dynamic stereoisomerism is involved in belt-shaped cyclic arrays of aromatic molecules, known recently as carbon nanohoops, but has scarcely been clarified to date. In this paper, a series of nanohoops with multiple panels of naphthalene has been synthesized. Their stereoisomerism, static structures, and dynamic behaviors have been investigated by using mathematical, crystallographic, and spectroscopic methods to reveal the unique structural chemistry present in segmental sp^{2}-carbon networks of carbon nanotubes.

## Abstract

The chemistry of a belt-shaped cyclic array of aromatic panels, a so-called “nanohoop,” has increasingly attracted much interest, partly because it serves as a segmental model of single-wall carbon nanotubes with curved sp^{2}-carbon networks. Although the unique molecular structure of nanohoops is expected to deepen our understanding in curved π-systems, its structural chemistry is still in its infancy despite structural variants rapidly accumulated over the past several years. For instance, structural characteristics that endow the belt shapes with rigidity, an important structural feature relevant to carbon nanotubes, have not been clarified to date. We herein report the synthesis and structures of a series of belt-shaped cyclonaphthylenes. Random synthesis methods using three precursor units with different numbers of naphthylene panels allowed us to prepare 6 congeners consisting of 6 to 11 naphthylene panels, and relationships between the rigidity and the panel numbers, i.e., molecular structures, were investigated. Fundamental yet complicated stereoisomerism in the belt-shaped structures was disclosed by mathematical methods, and dynamics in the panel rotation was revealed by dynamic NMR studies with the aid of theoretical calculations.

The chemistry of hoop-shaped cycloarylenes (nanohoops) is being enriched by increasing variations in the molecular structures (1⇓⇓–4). The structural diversity in the constitutional arylene panels has gradually increased by starting from cyclo-*para*-phenylenes (CPP; Fig. 1) with the most primordial panel being benzene (5⇓–7), and the nanohoop chemistry is deepening our understanding of π-conjugated structures with belt-shaped, curved sp^{2}-carbon networks that mimic single-wall carbon nanotubes (SWNTs) (8).

Composed of arylene panels connected via multiple single-bond linkages, the belt-shaped nanohoop structures pose a fundamental and important question related to the isomerism and persistency of the curved sp^{2}-carbon networks (8). Previously, we synthesized the first, to our knowledge, belt-persistent nanohoops to demonstrate that large arylene panels, such as chrysene and anthanthrene, endowed the nanohoop molecules with belt persistency. The belt-shaped atropisomers of [4]cyclochrysenylenes ([4]CC) (9, 10) and [4]cycloanthanthrenylenes ([4]CA) (11) were separated and identified as discrete molecular entities (Fig. 1), and the atropisomerism uniquely originated from restricted sp^{2}–sp^{2} rotations due to macrocyclic ring strain (12). However, the experimental relationship between the structure and dynamics of the arylene rotations in the nanohoops remains unclear (13⇓⇓–16) and will add novel insight to biaryl atropisomerism with structural and historical importance (17⇓⇓–20). We herein report our first attempt to reveal the structure–dynamics relationship in belt-shaped nanohoop molecules via the synthesis of a series of [*n*]cyclo-*amphi*-naphthylenes ([*n*]CaNAP, *n* = 6–11; Fig. 1) (21). Albeit simple at first glance, the molecular structures were rich in structural chemistry including stereoisomerism, belt-shaped crystal structures, and dynamics of naphthylene rotations. In our previous paper reporting, to our knowledge, the first belt-shaped cyclonaphthylenes (21), we disclosed the dynamic, fluctuating structure of one congener ([8]CaNAP) and demonstrated that the belt-shaped structures could be rigidified by bridging half of the biaryl linkages with methylene moieties. In this paper on a series of congeners, we determined that the arylene rotation depended on the hoop size and was spectroscopically restricted in the smallest congener ([6]CaNAP) at ambient temperature in solution.

## Results and Discussion

### Synthesis.

We synthesized six congeners of [*n*]CaNAP where *n* = 6–11 from two sets of macrocyclization reactions. A similar random synthesis route has been investigated by Yamago and co-workers to synthesize six [*n*]CPP congeners where *n* = 8–13 via a combination of double-panel biphenyl and triple-panel terphenyl precursors (22). In this study, we prepared three different precursors including naphthalene **1**, binaphthyl **2**, and ternaphthyl **3** and examined two different combinations in the Pt-mediated macrocyclization of diborylated precursors (9). A combination of single- and double-panel precursors (**1** and **2**) afforded three [*n*]CaNAP congeners where *n* = 6–8 via Pt-mediated macrocyclization followed by reductive elimination reactions (Scheme 1*A*). The structural variation was increased in another combination of double- and triple-panel precursors (**2** and **3**) to afford four [*n*]CaNAP congeners where *n* = 8–11 (Scheme 1*B*). The congeners were chromatographically isolated by using gel permeation chromatography with a polystyrene stationary phase (JAI GEL 1H-40, 2H-40, and 2.5H-40) and high-performance liquid chromatography with a naphthalene-capped silica gel stationary phase (Cosmosil πNAP) (*SI Appendix*). Three possible congeners with *n* = 4, 5, and 12 were not obtained, most likely because of severe macrocyclic strain for the smaller congeners and low solubility for the larger one. During the synthesis of large congeners, we indeed observed formation of precipitates.

### Stereoisomerism: Structural Mathematics.

The number of possible stereoisomers of the [*n*]CaNAP congeners requires mathematical consideration. Due to the *C*_{2h} point symmetry of *amphi*-linked naphthylene (21), two facial orientations of the arylene panel exist in the belt-shaped nanohoops (“a face” or “b face” in Fig. 2). Owing to the *D*_{2h} point symmetry of *para*-linked phenylene panel, this stereoisomerism is absent in CPP congeners, which, in turn, makes it difficult to spectroscopically study their dynamics. The facial orientations in nanohoops with *n* panels generally result in 2^{n} adoptable structures, and the number of stereoisomers (diastereomers and enantiomer pairs) must be extracted from these adoptable structures. This problem is common in any nanohoop with isomerism and complicated by increasing numbers of arylene panels. Originally for [8]CaNAP, we manually examined and counted the possible isomeric structures in the 2^{8} adoptable structures but made one mistake in the count (21). Therefore, a versatile, mathematical solution has been developed for nanohoop isomerism, which illustrates the potential difficulty in the synthesis, separation, and identification of corresponding nanohoops that are prepared in the future.

The solution for the numbers of nanohoop isomers was found from the binary necklace problem in the field of mathematics (23). In short, this mathematical solution addresses the number of distinct necklaces with *n* beads with two different colors (red or blue), which corresponds to the number of nanohoop stereoisomers with *n* arylene panels with two facial orientations (a or b) (Fig. 2). Therefore, the number of stereoisomers [*S*(*n*)] is given by two equations including one equation for *n* = odd number (Eq. **1**) and another equation for *n* = even number (Eq. **2**),*n*,*k*) is the greatest common divisor of *n* and *k*.

The diastereomers must account for structural equivalence that emerges due to mirror symmetry and requires another mathematical treatment that considers the symmetry types of the periodic sequences (24, 25). The equations proposed by mathematicians were simplified to be applied to static stereoisomerism of polyols (26). After minor corrections, equations for the numbers of diastereomers [*D*(*n*)] are shown in Eqs. **3** and **4** for *n* = odd number and even number, respectively,**4** is taken over all *l* so that *n*/(*n*,*l*) is even.

The solution for the number of enantiomer pairs [*E*(*n*)] was found from the self-dual two-colored necklaces problem (27). The equations for the numbers of *E*(*n*) are shown in Eqs. **5** and **6** for *n* = odd number and even number, respectively,**6** is taken over all *l* so that *n*/(*n*,*l*) is even.

The *S*(*n*) number is defined as a sum of the number of diastereomers [*D*(*n*)] and the number of enantiomer pairs [*E*(*n*)]. We may also use

With these equations, the numbers of stereoisomers of synthesized [*n*]CaNAP congeners with *n* = 6–11 can be determined (Table 1), which indicates the complicated stereoisomerism of nanohoop structures. The breakdown of calculations for each *n* value is also shown in *SI Appendix*, and typical numbers for an expanded range of *n* values can be found in Sloane's *On-Line Encyclopedia of Integer Sequences* (28) with ID numbers of A000029 for stereoisomers, A000011 for diastereomers, and A007147 for enantiomer pairs.

### Structures and Energetics Obtained from Theoretical Calculations.

The molecular structures and energetics of [*n*]CaNAP were first investigated by using theoretical calculations. Conformational search calculations with a large-scale low-mode method using the Merck molecular force field (MMFF) located a conformer with an identical facial orientation of naphthylene panels (hereafter denoted the a^{n} conformer) as the most stable isomers commonly observed for [*n*]CaNAP with *n* = 6–11 (29, 30) The helical arrangement of naphthylene panels in the a^{n} conformers may be reasonable for the relaxation of the *C*_{2h} symmetric panels in the belt-shaped structures. More precise energetics were obtained by geometry optimizations using density functional theory (DFT) calculations at the B3LYP/6–31G(d,p) level of theory for [*n*]CaNAP with *n* = 6–8. All of the diastereomeric geometries from molecular mechanic calculations were used as the initial geometries, and their structures and energetics are summarized in Fig. 3. The structures in Fig. 3 are designated with developed names for the a^{(n–m)}b^{m} conformers, which is essential for conveying the sequence. As was the case with the force-field calculations, the DFT calculations identified the a^{n} conformers as the most stable structure. As another common feature of [*n*]CaNAP with *n* = 6–8, a conformer possessing one flipped panel (i.e., a^{(n–1)}b^{1} conformer) was located as the second most stable structure. A comparison of the theoretical energetics with crystal structures shows that the stable conformers are not necessarily found in crystal structures (*vide infra*; ref. 21). For instance, two of the most stable structures of [8]CaNAP were absent in the crystal, and the existing a^{6}b^{2} conformer was theoretically located approximately +2 kcal/mol above the most stable conformer. This observation indicates that crystalline nanohoop structures are affected by packing, and care must be taken during structural discussions based on the crystal structures.

Next, the theoretical rotational barriers (*ΔE*^{‡}) were estimated for a single-panel rotation from the a^{n} conformer to the a^{(n–1)}b^{1} conformer of [*n*]CaNAP. Based on the nonlinear increase in *ΔE*^{‡} values upon reduction in the hoop size, we extended the calculations to include elusive structures with *n* = 4 and 5. Transition state (TS) structures were obtained using the quadratic synchronous transit (QST3) method (31) by adopting saddle-point structures from scan analyses (12). The TS structures of *n* = 6–11 and the *ΔE*^{‡} values of *n* = 4–11 are summarized in Fig. 4. The rotational barriers depended on the hoop size with an nonlinear decay toward the larger nanohoops. A theoretical rotational barrier for the rotation of 2,2'-binaphthyl was separately estimated to be +2.74 kcal/mol, and the deviations from this reference value indicated the contributions from macrocyclic ring strain to the rotational barriers of each congener (12).

### Crystal Structures of [*n*]CaNAP with *n* = 7.

We obtained a single crystal of [7]CaNAP to reveal the belt-shaped structure in the crystalline solid state, which supplemented our observations of belt-shaped crystal structures of [8]CaNAP (21). Six distinct structures of [7]CaNAP were obtained from two sets of disordered structures in the unit cell of the single crystal grown in a mixture of isopropanol and CH_{2}Cl_{2} (Fig. 5 and *SI Appendix*). In the first disordered set, the major structure with 52% occupancy was an a^{6}b^{1} conformer and the minor structure with 48% occupancy was an a^{7} conformer. In the second disordered set, four structures consisting of the a^{6}b^{1}, b^{7}, a^{7}, and a^{1}b^{6} conformers were identified with occupancies of 33%, 25%, 21%, and 21%, respectively. Possessing belt shapes with sp^{2}-carbon networks, the structures can also be designated with SWNT chiral indices (8) as follows: a^{6}b^{1}/a^{1}b^{6} conformers are (13,8), and a^{7}/b^{7} conformers are (14,7). The bond-filling and atom-filling indices of the a^{7}/b^{7} conformers were 100% (8), which indicates that the structure serves as the shortest segmental model of the helical (14,7)-SWNT. Interestingly, the total occupancies of the *P* and *M* enantiomers were not identical, and the crystal was in the chiral *P*2_{1} space group. This observation indicated that optical resolution may have existed in the present crystal even though the data quality precluded a reliable conclusion.

### Solution-Phase Structures: Belt Persistency.

Finally, the solution-phase structures of [*n*]CaNAP were investigated by variable-temperature (VT) NMR analyses to reveal the experimental dynamics of the nanohoops (32, 33). Note that the present *amphi*-linked naphthylene panel provided an ideal, simplest structure to realize stereoisomerism required for the dynamic NMR study. The aromatic regions of the ^{1}H NMR spectra of all of the congeners of [*n*]CaNAP (*n* = 6–11) in a temperature range of 80 °C to –90 °C are shown in Fig. 6. A singlet resonance was assigned to the protons at the 1-position of the naphthylene panel, and two doublet resonances were assigned to the protons at the 3- and 4-positions. Although the splitting patterns of the resonances did not change upon VT analyses, a careful examination revealed the presence of two transitions that are most typically observed for [7]CaNAP. The resonances of the sharp peaks at a high temperature (80 °C) were broadened upon cooling to approximately –20 °C and sharpened again upon further cooling to approximately –60 °C. This broadening–resharpening behavior is a typical characteristic of the exchange of a dominant species with hidden, unobservable partners of minor populations (34, 35). At a high temperature, the peaks are sharp and originate from one time-averaged structure via rapid exchange, and at low temperature, they are sharp again and originate from one dominant, rigidified species without exchanging with minor species. Therefore, for the nanohoop structures, the sharp peaks at the high temperature indicate the presence of flexible, rapidly fluctuating structures, and the sharp peaks at the low temperature indicate the presence of belt-persistent structures. At an intermediate temperature, the peaks are broad due to slow exchange that proceeds at a rate similar to the NMR time scale.

Due to the importance of the broadening–resharpening behavior for elucidating the structural dynamics, we quantified the peak broadening by measuring the full width at half maximum of the Lorentzian line of one singlet from the 1-position protons (Δ_{1/2}-1; Fig. 7*A*). One doublet from the 3-position protons was also deconvoluted with the two Lorentzian lines to afford another set of full width at half maximum values (Δ_{1/2}-2; Fig. 7*B*). Two distinct structures (i.e., the fluctuating structure and the belt-persistent structure) were observed for [*n*]CaNAP with *n* = 6, 7, and 8 in the current temperature range, showing two transition in the Δ_{1/2}-values. The simple spectra of the single rigid species at the low temperature also indicated that the observed molecule possessed a high symmetry. This result along with the theoretical results (Fig. 3) suggested the presence of a^{n} isomers as the dominant, observable species. For the larger [*n*]CaNAP congeners with *n* ≥ 9, fluctuating structures were commonly observed throughout the studied temperature range. To clearly visualize this dynamic behavior, we drew a threshold line for the structural transition at the threefold increase in Δ_{1/2} from the narrowest peak, and after averaging the threshold temperatures from Δ_{1/2}-1 and Δ_{1/2}-2, we obtained the dynamics diagram shown in Fig. 7*C*. Most importantly, the belt shape of the smallest congener ([6]CaNAP) was persistent at 20 °C, and the a^{6} structure possessing a segment of (12,6)-SWNT with 100% bond-filling and atom-filling indices was observed in solution. Although it is important to note that the persistency is present in terms of spectroscopic observations (*vide infra*; refs. 32, 33), its effect over the characteristics relevant to SWNTs such as fullerene-peapod assembly may be of interest to be explored in the future (36, 37).

Then, we derived experimental kinetic parameters for the panel rotation by using two independent methods developed for the analysis of broadening–resharpening behaviors (34, 35). The two methods commonly use the Δ_{1/2} values of the widest singlet (*p*_{B}) as well as the dominant species (*p*_{A}) is also estimated by comparing the integrals of the widest peak at high temperature and the narrowest peak at the low temperature. In short, the method developed by Anet and Basus (34) simply uses the Δ_{1/2} values to derive the rate constant (*k*) as*k* via

The experimental data for [6]- and [7]CaNAP are summarized in Table 2. It is important to note that the small *p*_{B} value that is used in the Okazawa and Sorensen method also ensures the pA >> pB condition required for the Anet and Basus method. The rotational barriers from the two different methods (i.e., *ΔG*^{‡}_{Anet} and *ΔG*^{‡}_{Okazawa}) were consistent with each other, indicating the reliability of these energy values. A barrier of 16 kcal/mol for [6]CaNAP confirmed that the diastereomeric conformers should be observed as distinct entities by NMR spectroscopy at ambient temperature (32, 33). However, this value may also suggest that the isolation of these diastereomers at ambient temperature is not feasible (38). The rotational barrier of the larger congener of [7]CaNAP was decreased by 3 kcal/mol, confirming that the nanohoop structures became more flexible as the hoop size increased. A comparison of the experimental data shown in Table 2 and the theoretical data shown in Fig. 4 indicates that the theoretical DFT calculations afforded reasonable, albeit slightly lower, estimates of the rotational barriers.

## Conclusions

We have synthesized a series of belt-shaped, *amphi*-linked cyclonaphthylene congeners through a random synthesis method and isolated six hydrocarbon congeners as discrete molecular entities. The belt-shaped structure with *C*_{2h} panels gave rise to stereoisomerism originating from the facial orientations of the naphthylenes. The stereoisomerism was clarified with the aid of mathematics and revealed the complicated nature of the stereoisomerism of belt-shaped nanohoops. Structures of several stereoisomers with belt shapes were elucidated by crystallographic analyses, and comparison with theoretical energetics indicated that the crystal structure does not necessarily adopt the most stable conformation. The stereoisomerism further allowed us to reveal the presence of fluctuating and rigid structures in solution by VT NMR analyses, and the smallest congener with six naphthylene panels was observed as a rigid belt-shaped species at ambient temperature. Thus, for the present arylene panel of naphthylene, the diameter of 1.26 nm is the spectroscopic threshold that divides fluctuating nanohoops and rigid nanohoops. Another obvious structural factor that controls the structural rigidity is the size of the arylene panels: A chrysenylene nanohoop, (16,0)-[4]CC, with a nearly identical geometrical diameter of 1.27 nm, possessed an extreme rigidity and did not fluctuate for 2 months at 200 °C (10). Dynamics studies with nanohoops possessing various arylene panels are of fundamental interest to reveal the correlations between the hoop/panel size with the rigidity in the future. We hope that the present study may stimulate further studies to deepen our understanding of the unique structural chemistry of nanohoops.

## Materials and Methods

### Synthesis.

Diborylated precursors (**1**-**3**) were prepared by a method reported in the literature (21). Macrocylization with PtCl_{2}(cod) was performed by using an equimolar amount of two diborylated precursors, and subsequent reductive elimination was performed through ligand exchange with PPh_{3} (9). Structures of isolated compounds were identified by spectroscopic analyses, and the purities were confirmed by HPLC analyses using several stationary phases. Further details of procedures and results are described in *SI Appendix*.

### Crystallographic Analysis.

A single crystal (∼0.13 × 0.04 × 0.02 mm^{3}) suitable for X-ray analysis was obtained by evaporation of isopropanol and dichloromethane solution of [7]CaNAP. A single crystal was mounted on a thin polymer tip with cryoprotectant oil and frozen at –178 °C via flash-cooling. After a laboratory diffractometer failed to afford reliable diffraction data due to the severe disorders of solvent molecules, the diffraction analysis of a single crystal with a synchrotron X-ray source was conducted at –178 °C by using a beamline at the KEK Photon Factory (PF-AR NE3A) using a diffractometer equipped with an Dectris Pilatus 2M-F pixel array detector to afford the final data with a resolution of ∼0.86 Å. Note that this resolution assures the precision of C–C bonds in 0.0206 Å. Further details of data processing are described in *SI Appendix*.

### Theoretical Calculations.

Molecular mechanics calculations were performed by using MacroModel (39), and DFT calculations were performed by using Gaussian 09 (40). Further details of calculations are described in *SI Appendix*.

### NMR Analyses.

Specimens in toluene-*d*_{8} were sealed in glass sample tubes (ϕ 5 mm), and VT NMR spectra were recorded on a JEOL JNM-ECS 600II (^{1}H: 600 MHz; ^{13}C: 150 MHz) spectrometer equipped with a temperature controller. Full-range spectra as well as those of synthetic intermediates are included in *SI Appendix*.

## Change History

March 30, 2021: The article’s Acknowledgements have been updated.

## Acknowledgments

We thank KEK Photon Factory (2015G097) for the use of the X-ray diffraction instruments. This study was partly supported by Grant-in-Aid for Scientific Research, KAKENHI (24241036, 25102007) and ERATO (JPMJER1301).

## Footnotes

- ↵
^{1}To whom correspondence should be addressed. Email: isobe{at}m.tohoku.ac.jp.

Author contributions: H.I. designed research, Z.S., T.S., P.S., S.S., and M.K. performed research; Z.S. and S.S. analyzed data; and Z.S. and H.I. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Data deposition: The crystallography, atomic coordinates, and structure factors have been deposited in the Cambridge Structural Database, Cambridge Crystallographic Data Centre, www.ccdc.cam.ac.uk (CSD reference no. 1471735).

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1606530113/-/DCSupplemental.

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