Stereoisomerism, crystal structures, and dynamics ofbelt-shaped cyclonaphthylenesZhe Suna,b, Takuya Suenagab, Parantap Sarkarb, Sota Satoa,b, Motoko Kotanib,c, and Hiroyuki Isobea,b,d,1

aIsobe Degenerate π-Integration Project, Exploratory Research for Advanced Technology (ERATO), Japan Science and Technology Agency, Aoba-ku, Sendai980-8577, Japan; bAdvanced Institute for Materials Research, Tohoku University, Aoba-ku, Sendai 980-8577, Japan; cMathematical Institute, TohokuUniversity, Aoba-ku, Sendai 980-8578, Japan; and dDepartment of Chemistry, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

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

The chemistry of a belt-shaped cyclic array of aromatic panels, a so-called “nanohoop,” has increasingly attracted much interest, partlybecause it serves as a segmental model of single-wall carbon nano-tubes with curved sp2-carbon networks. Although the unique molec-ular structure of nanohoops is expected to deepen our understandingin curved π-systems, its structural chemistry is still in its infancy de-spite structural variants rapidly accumulated over the past severalyears. For instance, structural characteristics that endow the beltshapes with rigidity, an important structural feature relevant to car-bon nanotubes, have not been clarified to date. We herein report thesynthesis and structures of a series of belt-shaped cyclonaphthylenes.Random synthesis methods using three precursor units with differentnumbers of naphthylene panels allowed us to prepare 6 congenersconsisting of 6 to 11 naphthylene panels, and relationships betweenthe rigidity and the panel numbers, i.e., molecular structures, wereinvestigated. Fundamental yet complicated stereoisomerism in thebelt-shaped structures was disclosed by mathematical methods, anddynamics in the panel rotation was revealed by dynamic NMR studieswith the aid of theoretical calculations.

stereoisomerism | macrocycles | carbon nanotubes | crystal structures |dynamic structures

The chemistry of hoop-shaped cycloarylenes (nanohoops) isbeing enriched by increasing variations in the molecular

structures (1–4). The structural diversity in the constitutionalarylene panels has gradually increased by starting from cyclo-para-phenylenes (CPP; Fig. 1) with the most primordial panelbeing benzene (5–7), and the nanohoop chemistry is deepeningour understanding of π-conjugated structures with belt-shaped,curved sp2-carbon networks that mimic single-wall carbon nano-tubes (SWNTs) (8).Composed of arylene panels connected via multiple single-

bond linkages, the belt-shaped nanohoop structures pose afundamental and important question related to the isomerismand persistency of the curved sp2-carbon networks (8). Previously,we synthesized the first, to our knowledge, belt-persistent nano-hoops to demonstrate that large arylene panels, such as chryseneand anthanthrene, endowed the nanohoop molecules with beltpersistency. The belt-shaped atropisomers of [4]cyclochrysenylenes([4]CC) (9, 10) and [4]cycloanthanthrenylenes ([4]CA) (11) wereseparated and identified as discrete molecular entities (Fig. 1), andthe atropisomerism uniquely originated from restricted sp2–sp2

rotations due to macrocyclic ring strain (12). However, the ex-perimental relationship between the structure and dynamics ofthe arylene rotations in the nanohoops remains unclear (13–16)and will add novel insight to biaryl atropisomerism with struc-tural and historical importance (17–20). We herein report ourfirst attempt to reveal the structure–dynamics relationship inbelt-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 instructural chemistry including stereoisomerism, belt-shapedcrystal structures, and dynamics of naphthylene rotations. In ourprevious paper reporting, to our knowledge, the first belt-shapedcyclonaphthylenes (21), we disclosed the dynamic, fluctuating

structure of one congener ([8]CaNAP) and demonstrated thatthe belt-shaped structures could be rigidified by bridging half ofthe biaryl linkages with methylene moieties. In this paper on a seriesof congeners, we determined that the arylene rotation depended onthe hoop size and was spectroscopically restricted in the smallestcongener ([6]CaNAP) at ambient temperature in solution.

Results and DiscussionSynthesis. We synthesized six congeners of [n]CaNAP where n =6–11 from two sets of macrocyclization reactions. A similarrandom synthesis route has been investigated by Yamago and co-workers to synthesize six [n]CPP congeners where n = 8–13 via acombination of double-panel biphenyl and triple-panel terphenylprecursors (22). In this study, we prepared three different pre-cursors including naphthalene 1, binaphthyl 2, and ternaphthyl 3and examined two different combinations in the Pt-mediatedmacrocyclization of diborylated precursors (9). A combination ofsingle- and double-panel precursors (1 and 2) afforded three[n]CaNAP congeners where n = 6–8 via Pt-mediated macro-cyclization followed by reductive elimination reactions (Scheme1A). The structural variation was increased in another combina-tion of double- and triple-panel precursors (2 and 3) to affordfour [n]CaNAP congeners where n = 8–11 (Scheme 1B). Thecongeners were chromatographically isolated by using gel per-meation chromatography with a polystyrene stationary phase(JAI GEL 1H-40, 2H-40, and 2.5H-40) and high-performanceliquid chromatography with a naphthalene-capped silica gelstationary phase (Cosmosil πNAP) (SI Appendix). Three possible

Significance

Stereoisomerism of molecules shapes an indispensable conceptin molecular science. Stereoisomerism becomes complicated incyclic structures such as saccharides but has now been estab-lished to form a fundamental knowledge in chemistry. Whendynamic conformations are involved in the stereoisomerism ofcyclic structures, there emerges a unique type of isomerism. Suchperplexing dynamic stereoisomerism is involved in belt-shapedcyclic arrays of aromatic molecules, known recently as carbonnanohoops, but has scarcely been clarified to date. In this paper,a series of nanohoops with multiple panels of naphthalene hasbeen synthesized. Their stereoisomerism, static structures, anddynamic behaviors have been investigated by using mathe-matical, crystallographic, and spectroscopic methods to revealthe unique structural chemistry present in segmental sp2-carbonnetworks of carbon nanotubes.

Author contributions: H.I. designed research, Z.S., T.S., P.S., S.S., and M.K. performedresearch; 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 beendeposited in the Cambridge Structural Database, Cambridge Crystallographic Data Cen-tre, www.ccdc.cam.ac.uk (CSD reference no. 1471735).1To whom correspondence should be addressed. Email: isobe@m.tohoku.ac.jp.

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

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congeners with n = 4, 5, and 12 were not obtained, most likelybecause of severe macrocyclic strain for the smaller congenersand low solubility for the larger one. During the synthesis oflarge congeners, we indeed observed formation of precipitates.

Stereoisomerism: Structural Mathematics. The number of possiblestereoisomers of the [n]CaNAP congeners requires mathematicalconsideration. Due to the C2h point symmetry of amphi-linkednaphthylene (21), two facial orientations of the arylene panelexist in the belt-shaped nanohoops (“a face” or “b face” in Fig.2). Owing to the D2h point symmetry of para-linked phenylenepanel, this stereoisomerism is absent in CPP congeners, which, inturn, makes it difficult to spectroscopically study their dynamics.The facial orientations in nanohoops with n panels generallyresult in 2n adoptable structures, and the number of stereoiso-mers (diastereomers and enantiomer pairs) must be extractedfrom these adoptable structures. This problem is common inany nanohoop with isomerism and complicated by increasingnumbers of arylene panels. Originally for [8]CaNAP, we manu-ally examined and counted the possible isomeric structures in the28 adoptable structures but made one mistake in the count

(21). Therefore, a versatile, mathematical solution has beendeveloped for nanohoop isomerism, which illustrates the potentialdifficulty in the synthesis, separation, and identification of corre-sponding 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 mathemat-ics (23). In short, this mathematical solution addresses thenumber of distinct necklaces with n beads with two differentcolors (red or blue), which corresponds to the number ofnanohoop stereoisomers with n arylene panels with two facialorientations (a or b) (Fig. 2). Therefore, the number of stereo-isomers [S(n)] is given by two equations including one equationfor n = odd number (Eq. 1) and another equation for n = evennumber (Eq. 2),

SðnÞ= 12n

Xnk=1

2ðn, kÞ + n× 2ðn+1Þ=2!, [1]

SðnÞ= 12n

Xnk=1

2ðn, kÞ + 3n× 2ðn−2Þ=2!, [2]

where (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 mathe-matical treatment that considers the symmetry types of the periodicsequences (24, 25). The equations proposed by mathematicianswere simplified to be applied to static stereoisomerism of polyols(26). After minor corrections, equations for the numbers of dia-stereomers [D(n)] are shown in Eqs. 3 and 4 for n = odd numberand even number, respectively,

DðnÞ= 14n

Xnk=1

2ðn,kÞ + 2ðn−3Þ=2, [3]

DðnÞ= 14n

Xnk=1

2ðn,kÞ+14n

Xnl=1

2jn=ðn, lÞ

2ðn,lÞ + 2ðn=2Þ−1, [4]

where the summation of the second term of the right-hand sideof Eq. 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 6for n = odd number and even number, respectively,

R

R

R

R4

4

R

R4

[4]CC2,8 [4]CC3,9

[4]CA2,8

n

[n]CaNAP

n

[n]CPP

Fig. 1. Representative examples of nanohoop molecules.

BpinpinB

+

BpinpinB

2

1. PtCl2(cod), CsFTHF70 C, 24 h

2. PPh3, o-DCB,180 C, 24 h

n = 6: 2.4%n = 7: 2.8%n = 8: 3.6%

BpinpinB

+

BpinpinB

3

2

n = 8: 1.1%n = 9: 1.6%n = 10: 1.8%n = 11: 0.7%n = 12: 0%

1. PtCl2(cod), CsFTHF70 C, 24 h

2. PPh3, o-DCB,180 C, 24 h

1

2

2

3

[n]CaNAP

[n]CaNAP

A

B

Scheme 1. Two methods of random synthesis. (A) Synthesis of [n]CaNAP ofn = 6–8. (B) Synthesis of [n]CaNAP of n = 8–11.

n

or

or

mathematics

nanohoop chemistry

"a" face "b" face

"red" "blue"

Fig. 2. Structures of nanohoops and the binary necklace problem inmathematics.

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EðnÞ= 14n

Xnk=1

2ðn,kÞ + 2ðn−3Þ=2, [5]

EðnÞ= 14n

Xnk=1

2ðn,kÞ−14n

Xnl=1

2jn=ðn, lÞ

2ðn,lÞ + 2ðn=2Þ−2, [6]

where the summation of the second term of the right-hand sideof Eq. 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 dia-

stereomers [D(n)] and the number of enantiomer pairs [E(n)].We may also use

SðnÞ=DðnÞ+EðnÞ, [7]

to elucidate the numbers by using two sets of complicated equations.With these equations, the numbers of stereoisomers of synthe-

sized [n]CaNAP congeners with n = 6–11 can be determined (Table1), which indicates the complicated stereoisomerism of nanohoopstructures. The breakdown of calculations for each n value is alsoshown in SI Appendix, and typical numbers for an expanded range ofn 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 firstinvestigated by using theoretical calculations. Conformational searchcalculations with a large-scale low-mode method using the Merckmolecular force field (MMFF) located a conformer with an identicalfacial orientation of naphthylene panels (hereafter denoted thean conformer) as the most stable isomers commonly observed for[n]CaNAP with n = 6–11 (29, 30) The helical arrangement ofnaphthylene panels in the an conformers may be reasonable forthe relaxation of the C2h symmetric panels in the belt-shapedstructures. More precise energetics were obtained by geometryoptimizations using density functional theory (DFT) calculationsat the B3LYP/6–31G(d,p) level of theory for [n]CaNAP with n =6–8. All of the diastereomeric geometries from molecular me-chanic calculations were used as the initial geometries, and theirstructures and energetics are summarized in Fig. 3. The structuresin Fig. 3 are designated with developed names for the a(n–m)bm

conformers, which is essential for conveying the sequence. Aswas the case with the force-field calculations, the DFT calculationsidentified the an conformers as the most stable structure. As an-other common feature of [n]CaNAP with n = 6–8, a conformerpossessing one flipped panel (i.e., a(n–1)b1 conformer) was located asthe second most stable structure. A comparison of the theoreticalenergetics with crystal structures shows that the stable conformersare not necessarily found in crystal structures (vide infra; ref. 21).For instance, two of the most stable structures of [8]CaNAP wereabsent in the crystal, and the existing a6b2 conformer wastheoretically located approximately +2 kcal/mol above the

Table 1. Numbers of nanohoop stereoisomers with n arylenepanels

n 6 7 8 9 10 11

S(n)* 13 18 30 46 78 126D(n)† 8 9 18 23 44 63E(n)‡ 5 9 12 23 34 63

*Number of stereoisomers.†Number of diastereomers.‡Number of enantiomer pairs. See SI Appendix for the breakdown.

E(k

cal/m

ol)

aaaaaa

aaaaab

aaaabb

aabaab

aaabab

aabbab aaabbb

ababab

0

+1.92

+3.25+3.60

+3.39

+4.63 +4.76

+5.53

P/M

E(k

cal/m

ol)

aaaaaaa

aaaaabbaaabaab

aaabbab

aababab

aaaabbb

aabbaab

0

+0.90

+1.58+1.92+1.81

+2.36

+4.11

+4.96

+3.05

aaaaaab

P/M

P/M P/MP/M

P/M

P/M

P/MP/M P/M

P/M

P/M

P/M

P/M

A B

aaaabab

E(k

cal/m

ol)

0

+1.92 +1.94

+3.24

+2.45

+2.84

+0.96

+3.47+3.71

+4.45

+3.25

+3.69 +3.70

+4.15

+0.48

aabbaabb

aaaaabbb

+4.77

P/M

P/M

P/M P/M

P/M

P/M

P/M

P/M P/M

P/M

(+)/(–)

aaaabbab

aaaaaabb

aaabbaab

aaaaabab

P/M

+3.43abaababb

aabaabbb

aabababbaaaabbbb

aaababab+4.24

aaababbb

abababab

aaabaaab

aaaaaaab

aaaaaaaa

C

aaaabaab

aabaabab

Fig. 3. Diastereomeric structures and energetics of [n]CaNAP from DFTcalculations [B3LYP/6–31G(d,p)]. Chiral isomers with segmental structures ofhelical SWNTs are labeled with P/M, a chiral isomer with segmental struc-tures of armchair SWNTs is labeled with (+)/(–), and structures found in singlecrystals are indicated by the labels in red. (A) n = 6. (B) n =7. (C) n = 8.

E‡

(kca

l/mol

)

1.26(n = 6)

1.47(n = 7)

1.68(n = 8)

1.89(n = 9)

2.10(n = 10)

2.31(n = 11)

20

30

40

50

n = 11

n = 10

n = 9

n = 8

n = 7

n = 6

1.05(n = 5)

0.84(n = 4)

0

10

diameter of [n]CaNAP (nm)

38.5

21.515.4

12.4 10.5 9.2 8.0 5.8

Fig. 4. TS structures and rotational barriers from DFT calculations [B3LYP/6–31G(d,p)]. Each TS structures possessed one imaginary frequency. The di-ameters were obtained as geometrical diameters (11).

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most stable conformer. This observation indicates that crystallinenanohoop structures are affected by packing, and care must betaken during structural discussions based on the crystal structures.Next, the theoretical rotational barriers (ΔE‡) were estimated for a

single-panel rotation from the an conformer to the a(n–1)b1 conformerof [n]CaNAP. Based on the nonlinear increase in ΔE‡ values uponreduction in the hoop size, we extended the calculations to includeelusive structures with n = 4 and 5. Transition state (TS) structureswere 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 = 4–11are summarized in Fig. 4. The rotational barriers depended on thehoop size with an nonlinear decay toward the larger nanohoops. Atheoretical rotational barrier for the rotation of 2,2’-binaphthyl wasseparately estimated to be +2.74 kcal/mol, and the deviations fromthis reference value indicated the contributions from macrocyclicring strain to the rotational barriers of each congener (12).

Crystal Structures of [n]CaNAP with n = 7. We obtained a singlecrystal of [7]CaNAP to reveal the belt-shaped structure in the

crystalline solid state, which supplemented our observations ofbelt-shaped crystal structures of [8]CaNAP (21). Six distinctstructures of [7]CaNAP were obtained from two sets of disor-dered structures in the unit cell of the single crystal grown in amixture of isopropanol and CH2Cl2 (Fig. 5 and SI Appendix). Inthe first disordered set, the major structure with 52% occupancywas an a6b1 conformer and the minor structure with 48% occu-pancy was an a7 conformer. In the second disordered set, fourstructures consisting of the a6b1, b7, a7, and a1b6 conformers wereidentified with occupancies of 33%, 25%, 21%, and 21%, re-spectively. Possessing belt shapes with sp2-carbon networks, thestructures can also be designated with SWNT chiral indices (8) asfollows: a6b1/a1b6 conformers are (13,8), and a7/b7 conformersare (14,7). The bond-filling and atom-filling indices of the a7/b7

conformers were 100% (8), which indicates that the structureserves as the shortest segmental model of the helical (14,7)-SWNT. Interestingly, the total occupancies of the P and M en-antiomers were not identical, and the crystal was in the chiral P21space group. This observation indicated that optical resolutionmay have existed in the present crystal even though the dataquality 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 experimentaldynamics of the nanohoops (32, 33). Note that the presentamphi-linked naphthylene panel provided an ideal, simpleststructure to realize stereoisomerism required for the dynamicNMR study. The aromatic regions of the 1H NMR spectra of allof the congeners of [n]CaNAP (n = 6–11) in a temperature rangeof 80 °C to –90 °C are shown in Fig. 6. A singlet resonance wasassigned to the protons at the 1-position of the naphthylenepanel, and two doublet resonances were assigned to the pro-tons at the 3- and 4-positions. Although the splitting patterns ofthe resonances did not change upon VT analyses, a careful exam-ination revealed the presence of two transitions that are most typ-ically observed for [7]CaNAP. The resonances of the sharp peaksat a high temperature (80 °C) were broadened upon cooling toapproximately –20 °C and sharpened again upon further cool-ing to approximately –60 °C. This broadening–resharpening be-havior is a typical characteristic of the exchange of a dominantspecies with hidden, unobservable partners of minor populations(34, 35). At a high temperature, the peaks are sharp and origi-nate from one time-averaged structure via rapid exchange, and atlow temperature, they are sharp again and originate from one

aaaaaab aaaaaaachiral index = (13,8)tf = 2.15

Fb = 72%Fa = 76%

chiral index = (14,7)tf = 1.42

Fb = 100%Fa = 100%

52% occupancy 48% occupancy

chiral index = (13,8)tf = 2.15

Fb = 72%Fa = 76%

chiral index = (13,8)tf = 2.15

Fb = 72%Fa = 76%

chiral index = (14,7)tf = 1.42

Fb = 100%Fa = 100%

chiral index = (14,7)tf = 1.42

Fb = 100%Fa = 100%

aaaaaab

bbbbbba

aaaaaaa

bbbbbbb

33% occupancy 21% occupancy

21% occupancy 25% occupancy

A

B

Fig. 5. Crystal structure of [7]CaNAP. (A) Two structures located in one setof disordered structures. (B) Four structures located in another set of disor-dered structures.

Fig. 6. VT NMR spectra of [n]CaNAP in toluene-d8 (aromatic regions).

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dominant, rigidified species without exchanging with minor spe-cies. Therefore, for the nanohoop structures, the sharp peaks atthe high temperature indicate the presence of flexible, rapidlyfluctuating structures, and the sharp peaks at the low temperatureindicate the presence of belt-persistent structures. At an inter-mediate temperature, the peaks are broad due to slow exchangethat 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 peakbroadening by measuring the full width at half maximum of theLorentzian line of one singlet from the 1-position protons (Δ1/2-1;Fig. 7A). One doublet from the 3-position protons was also decon-voluted with the two Lorentzian lines to afford another set of fullwidth at half maximum values (Δ1/2-2; Fig. 7B). Two distinct struc-tures (i.e., the fluctuating structure and the belt-persistent structure)were observed for [n]CaNAP with n = 6, 7, and 8 in the currenttemperature range, showing two transition in the Δ1/2-values. Thesimple spectra of the single rigid species at the low temperature alsoindicated that the observed molecule possessed a high symmetry.This result along with the theoretical results (Fig. 3) suggested thepresence of an isomers as the dominant, observable species. For thelarger [n]CaNAP congeners with n ≥ 9, fluctuating structures were

commonly observed throughout the studied temperature range. Toclearly visualize this dynamic behavior, we drew a threshold line forthe structural transition at the threefold increase in Δ1/2 from thenarrowest peak, and after averaging the threshold temperaturesfrom Δ1/2-1 and Δ1/2-2, we obtained the dynamics diagram shownin Fig. 7C. Most importantly, the belt shape of the smallest con-gener ([6]CaNAP) was persistent at 20 °C, and the a6 structurepossessing a segment of (12,6)-SWNT with 100% bond-filling andatom-filling indices was observed in solution. Although it is im-portant to note that the persistency is present in terms of spec-troscopic observations (vide infra; refs. 32, 33), its effect over thecharacteristics relevant to SWNTs such as fullerene-peapod as-sembly 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 forthe analysis of broadening–resharpening behaviors (34, 35). Thetwo methods commonly use the Δ1/2 values of the widest singlet(Δmax

1=2 ) and those of the narrowest singlet (Δmin1=2). The population

of the hidden partners (pB) as well as the dominant species (pA)is also estimated by comparing the integrals of the widest peak athigh temperature and the narrowest peak at the low tempera-ture. In short, the method developed by Anet and Basus (34)simply uses the Δ1/2 values to derive the rate constant (k) as

k= 2π�Δmax

1=2 −Δmin1=2

�. [8]

The method developed by Okazawa and Sorensen (35) affords k via

k= ð6.32− 3.90pBÞΔmax

1=2 −Δmin1=2

1+ pB�2ð1− pBÞ2

. [9]

Because these two methods require elucidation of the widestpeak, we can apply them to [6]CaNAP and [7]CaNAP, which exhibitedtwo transitions that clarify the locations of the widest peak.The experimental data for [6]- and [7]CaNAP are summarized in

Table 2. It is important to note that the small pB value that is usedin the Okazawa and Sorensen method also ensures the pA >> pBcondition required for the Anet and Basus method. The rotationalbarriers from the two different methods (i.e., ΔG‡

Anet andΔG‡

Okazawa) were consistent with each other, indicating the reliabilityof these energy values. A barrier of 16 kcal/mol for [6]CaNAP con-firmed that the diastereomeric conformers should be observed asdistinct entities by NMR spectroscopy at ambient temperature (32,33). However, this value may also suggest that the isolation of thesediastereomers at ambient temperature is not feasible (38). Therotational barrier of the larger congener of [7]CaNAP was decreasedby 3 kcal/mol, confirming that the nanohoop structures becamemore flexible as the hoop size increased. A comparison of the ex-perimental data shown in Table 2 and the theoretical data shown inFig. 4 indicates that the theoretical DFT calculations afforded rea-sonable, albeit slightly lower, estimates of the rotational barriers.

–100 –80 –60 –40 –20 0 20 40 60 80temperature (°C)

100

60

48

36

24

12

1/2-

2(H

z)

72

84

30

24

18

12

6

1/2-

1(H

z)

36

–100 –80 –60 –40 –20 0 20 40 60 80temperature (°C)

100

6 7 8 9 10number of naphthylene unit, n

–80

–60

–40

20

tem

pera

ture

(°C

)

–20

0

40

60

fluctuating structure

rigid structure

1/2 -1

slowexchange

nH1

H1

n

H3

H3

1/2 -2

n = 6n = 7n = 8n = 9n = 10n = 11

n = 6n = 7n = 8n = 9n = 10n = 11

A

B

C

Fig. 7. Broadening–resharpening behaviors of resonances in the VT NMRspectra of [n]CaNAP. Several Δ1/2 values were not obtained due to severeoverlaps and are not included. (A) Broadening–resharpening behaviors ob-served with singlet from the 1-position protons. (B) Broadening–resharp-ening behaviors observed with doublet from the 3-position protons.(C) Dynamics elucidated based on a threefold broadening threshold.

Table 2. Experimental data for the kinetic analyses and resultantrotational barriers

Parameters [6]CaNAP [7]CaNAP

Tmax, °C* 50 −10Δmax

1=2 −Δmin1=2 , Hz 14.8 19.5

pB 0.10 0.07kAnet, s

–1 93.2 122.5kOkazawa, s

–1 82.9 113.3ΔG‡

Anet, kcal/mol† 16.1 12.8ΔG‡

Okazawa, kcal/mol† 16.1 12.9

*Temperature at the widest singlet.†The rate constant (k) was converted to ΔG‡ using the Eyring equation, ΔG‡ =–RT[ln(h/kB)+ln(k/T)], where R is the gas constant, h is the Planck constant, and kBis the Boltzmann constant.

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ConclusionsWe have synthesized a series of belt-shaped, amphi-linkedcyclonaphthylene congeners through a random synthesis methodand isolated six hydrocarbon congeners as discrete molecularentities. The belt-shaped structure with C2h panels gave rise tostereoisomerism originating from the facial orientations of thenaphthylenes. The stereoisomerism was clarified with the aid ofmathematics and revealed the complicated nature of the ste-reoisomerism of belt-shaped nanohoops. Structures of severalstereoisomers with belt shapes were elucidated by crystallo-graphic analyses, and comparison with theoretical energeticsindicated that the crystal structure does not necessarily adopt themost stable conformation. The stereoisomerism further allowedus to reveal the presence of fluctuating and rigid structures insolution by VT NMR analyses, and the smallest congener withsix naphthylene panels was observed as a rigid belt-shaped spe-cies at ambient temperature. Thus, for the present arylene panelof naphthylene, the diameter of 1.26 nm is the spectroscopicthreshold that divides fluctuating nanohoops and rigid nano-hoops. Another obvious structural factor that controls thestructural rigidity is the size of the arylene panels: A chrys-enylene nanohoop, (16,0)-[4]CC, with a nearly identical geo-metrical diameter of 1.27 nm, possessed an extreme rigidity anddid not fluctuate for 2 months at 200 °C (10). Dynamics studieswith nanohoops possessing various arylene panels are of funda-mental interest to reveal the correlations between the hoop/panel size with the rigidity in the future. We hope that the pre-sent study may stimulate further studies to deepen our un-derstanding of the unique structural chemistry of nanohoops.

Materials and MethodsSynthesis. Diborylated precursors (1-3) were prepared by a method reported inthe literature (21). Macrocylization with PtCl2(cod) was performed by using anequimolar amount of two diborylated precursors, and subsequent reductiveelimination was performed through ligand exchange with PPh3 (9). Structuresof isolated compounds were identified by spectroscopic analyses, and the pu-rities were confirmed by HPLC analyses using several stationary phases. Furtherdetails of procedures and results are described in SI Appendix.

Crystallographic Analysis. A single crystal (∼0.13 × 0.04 × 0.02 mm3) suitable forX-ray analysis was obtained by evaporation of isopropanol and dichloro-methane solution of [7]CaNAP. A single crystal was mounted on a thin polymertip with cryoprotectant oil and frozen at –178 °C via flash-cooling. After alaboratory diffractometer failed to afford reliable diffraction data due to thesevere disorders of solvent molecules, the diffraction analysis of a single crystalwith a synchrotron X-ray source was conducted at –178 °C by using a beamlineat the KEK Photon Factory (PF-AR NE3A) using a diffractometer equipped withan Dectris Pilatus 2M-F pixel array detector to afford the final data with a res-olution of ∼0.86 Å. Note that this resolution assures the precision of C–C bondsin 0.0206 Å. Further details of data processing are described in SI Appendix.

Theoretical Calculations.Molecular mechanics calculations were performed byusing MacroModel (39), and DFT calculations were performed by usingGaussian 09 (40). Further details of calculations are described in SI Appendix.

NMR Analyses. Specimens in toluene-d8were sealed in glass sample tubes (ϕ 5mm),and VT NMR spectra were recorded on a JEOL JNM-ECS 600II (1H: 600MHz; 13C:150 MHz) spectrometer equipped with a temperature controller. Full-rangespectra as well as those of synthetic intermediates are included in SI Appendix.

ACKNOWLEDGMENTS. We thank KEK Photon Factory (2015G097) for theuse of the X-ray diffraction instruments. This study was partly supportedby Grant-in-Aid for Scientific Research, KAKENHI (24241036, 25102007).

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