Chiral intertwined spirals and magnetic transitiondipole moments dictated by cylinder helicitySota Satoa,b,1, Asami Yoshiic, Satsuki Takahashia,b, Seiichi Furumid, Masayuki Takeuchie, and Hiroyuki Isobea,b,1

aDepartment of Chemistry, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; bJapan Science and Technology Agency, ExploratoryResearch for Advanced Technology (ERATO), Isobe Degenerate π-Integration Project, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; cDepartment of Chemistry,Tohoku University, Aoba-ku, Sendai 980-8578, Japan; dDepartment of Applied Chemistry, Tokyo University of Science, Kagurazaka, Shinjuku-ku, Tokyo162-8601, Japan; and eResearch Center for Functional Materials, National Institute for Materials Science, Sengen, Tsukuba 305-0047, Japan

Edited by Jerrold Meinwald, Cornell University, Ithaca, NY, and approved November 2, 2017 (received for review October 6, 2017)

The presence of anomalous chirality in a roll of graphitic carbonsheets has been recognized since the discovery of carbon nano-tubes, which are becoming available in higher quantities throughthe isolation of chiral single-wall congeners with high purity.Exploration of the properties arising from cylinder chirality isexpected to expand the scope of tubular entities in the future. Bystudying molecular fragments of helical carbon nanotubes, weherein reveal interesting properties that arise from this chirality.The chirality of nanoscale cylinders resulted in chirality of largerdimensions in the form of a double-helix assembly. Cylinderchirality in solution gave rise to a large dissymmetry factor ofmetal-free entities in circular polarized luminescence. Theoreticalinvestigations revealed the pivotal role of cylindrical shapes inenhancing magnetic dipole transition moments to yield extremerotatory strength. Unique effects of cylinder chirality in this studymay prompt the development of tubular entities, for instance, to-ward chiroptical applications.

chirality | carbon nanotubes | macrocycles | double helix |circularly polarized luminescence

Since the discovery of carbon nanotubes in 1991, the anoma-lous chirality of cylindrical entities has attracted much in-

terest (1). This chirality originates from unique helical arrange-ments of sp2-hybridized carbon atoms, i.e., helicity (2, 3), andfundamental properties of enantiomers of single-wall carbonnanotubes (SWNTs) are currently being revealed through theisolation of enantiomers (4–6). For instance, chiroptical prop-erties including circular dichroism (CD) have been reported, andan improved purity of the specimens recently allowed for theproposal of an analytic correlation of the CD spectra with cylinderhelicity through corrected electric transition dipole moments(ETDMs) (7). Although the nondiscrete nature of SWNTs in-trinsically precludes definite conclusions on the structural originsof chirality-related properties, relevant information derived fromdiscrete, segmental molecular models of SWNTs can deepensuch a structural understanding. We have previously reported thesynthesis of segmental molecules of helical SWNTs with stereo-chemical rigidity and revealed a few important features of thesecylindrical molecules possessing chiral isomeric structures (8, 9)(Fig. 1). In this study, we investigated properties associated withthe helicity of the nanoscale cylinders and found unique rolesin their assembly and optical properties. The helicity dictatedthe chiral packings of the cylinders and resulted in the as-sembly of double-helical, spiral-stair packings in the crystal. Insolution, the cylinder helicity played a determinant role togenerate large magnetic transition dipole moments (MTDMs),which led to observations of anomalous dissymmetry factorswith CD and circular polarized luminescence (CPL) spectros-copy (10). Notably, the nanoscale cylinders afforded an anoma-lously large luminescence dissymmetry factor (glum) for metal-free, organic molecules. The recorded glum value reached 10−1,which is one order of magnitude greater than those of previouslyreported molecules (11).

Results and DiscussionChiral Intertwined Spirals of Helical Cylinders. The cylindrical, seg-mental SWNT molecule used in this study was [4]cyclo-2,8-chrysenylene ([4]CC) (8, 12) (Fig. 1), and the effects of cylinderhelicity on the crystal packings were investigated with (12,8)isomers. A single crystal was grown with an enantiomericallypure isomer, (P)-(12,8)-[4]CC, and was subjected to crystallo-graphic analysis. As was the case with a racemate of (P)/(M)isomers (13), a thread-in-bead entanglement between alkyl chainsand cylinders was observed as a basic motif in the crystal pack-ings of the (P)-(12,8)-[4]CC molecules (SI Appendix, Fig. S1).The thread-in-bead entanglement of the (P)/(M) racemateresulted in a 2D, brick-wall-like network of molecules in an achiralCcca space group (13), but the same thread-in-bead entanglementof the (P) isomer resulted in a twisted orientation of adjacentstacks to form a chiral 3D network of molecules. The space groupof this (P)-(12,8)-[4]CC crystal was hexagonal P65, which revealedthe presence of helical chirality in the crystal packings. Unex-pectedly, the nanoscale cylinders formed two spiral-staircase stacksin the crystal, creating an intertwined double helix of the helicalcylinders (Fig. 2). A single turn of the double helix was composedof six cylinders, which formed a left-handed, M-type helix with apitch of 4 nm. The van der Waals diameter of the double helixmeasured 4 nm. A single crystal of the enantiomer, (M)-(12,8)-[4]CC,

Significance

Defining unique properties of anomalous molecular entities isone of the most important roles of chemistry. Revealed bydiscovery of carbon nanotubes, rolled sheets of graphitic car-bons are among such molecular structures possessing uniquechirality. Although the chirality in nanotubes is attractingrenewed interest in physical science, our understanding as wellas exploration of its utilities is still in its infancy due to scarcityof chiral congeners with discrete structures. In this paper,chirality-originated properties of tubular molecules have beendisclosed. The chirality in the cylindrical molecular structureresults in chiral double helices in crystals and in extremely largedissymmetry factors associated with circularly polarized light.Cylinder chirality would be characteristic features to be ex-plored in materials science of tubular structures.

Author contributions: S.S. and H.I. designed research; S.S., A.Y., and S.T. performed re-search; A.Y., S.F., and M.T. contributed new reagents/analytic tools; S.S., A.Y., S.F., M.T.,and H.I. analyzed data; and S.S. and H.I. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Published under the PNAS license.

Data deposition: The atomic coordinates have been deposited in the Cambridge Struc-tural Database, Cambridge Crystallographic Data Centre, www.ccdc.cam.ac.uk (accessioncodes CCDC 1570803 and 1570804).1To whom correspondence may be addressed. Email: satosota@chem.s.u-tokyo.ac.jp orisobe@chem.s.u-tokyo.ac.jp.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1717524114/-/DCSupplemental.

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was also obtained as an enantiomorphic crystal with a P61 spacegroup. Although structural differences such as molecular orienta-tions, chain conformations, and solvent structures were present, theoverall packing of the (M) isomer mirrored that of the (P) isomer,resulting in a right-handed, P-type double helix. This result showedthat the helicity of the double-helix assembly in the crystals wasdictated by the helicity of the nanoscale cylinders. A helical assemblyof molecules is often observed with proteins, such as actin filaments,that are assembled by sophisticated hydrogen-bonding networks(14), and it is interesting to find that pure, nondirectional van derWaals interactions between hydrogen and carbon atoms can inducesuch chiral double-helical assemblies (15). The transmission of mo-lecular chirality to nanoscale crystalline chirality has been demon-strated, which may be important for the development of nanocarbonmaterials in future (16).

CD. Interesting effects arising from cylinder helicity were observedin the solution-phase chiroptical measurements. Considering re-cent advances in the study of chiral SWNT congeners (6, 7), wecarefully investigated the CD spectra of our system. Kataura andcoworkers (6) recently succeeded in obtaining high-purity chiralSWNT specimens and investigating CD spectra in depth. Withthese spectra, an analytic and numerical procedure to predict CDspectra from a given enantiomeric cylinder was also proposed (7).In short, the analytic method used the corrected ETDM to predictthe CD signals. Independently, in our previous studies with segmental[4]CC cylinders, we adopted time-dependent density-functionaltheory (TDDFT) to correlate CD spectra with enantiomeric struc-tures (8), which was later confirmed to be valid by experimentallydetermined crystal structures of enantiomers (13). In this study, wefurther investigated the origin of the representative CD signals usingtheoretical analyses and observed several unique chiroptical featuresin nanoscale cylinders. Experimentally, CD spectra of (P)- and(M)-(12,8)-[4]CC in toluene showed exceptionally large absorp-tion dissymmetry factors (10), gabs = −0.167 and +0.166, at 443 nm,

respectively (Fig. 3A). The CD spectra of another set of enantio-mers, (P)- and (M)-(11,9)-[4]CC, also showed large gabs values of−0.111 and +0.110 at 446 nm (Fig. 3B). These jgabsj values areextraordinarily large, as jgabsj values of 10−3 are regarded as largefor molecular entities (17).

Large Magnetic Dipole Transition Moments in Cylinders. To deducethe origin of these anomalously large jgabsj values, we performedTDDFT analyses with methyl-substituted [4]CC. We observedno concentration dependency of the CD/CPL spectra (SI Ap-pendix, Fig. S9), which showed that the spectra were ascribed tomonomeric, molecularly dispersed species in solution (18). Theabsence of assembly in solution was also indicated in previousstudies of the nanoscale cylinders with NMR spectroscopy (15,19, 20). The largest jgabsj of (P)-(12,8)-[4]CC corresponded to thefirst S1 transition, which was predominantly ascribed to a single-electron excitation from the highest occupied molecular orbital tothe lowest unoccupied molecular orbital with a coefficient of 0.69

Fig. 1. Chiral cylindrical molecules.

Fig. 2. Crystal structures of (P)- and (M)-(12,8)-[4]CC. The two intertwinedspirals are shown in different colors. Disordered structures of one sub-stituent with a minor population and solvent molecules were omitted forclarity.

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(SI Appendix, Fig. S3 and Table S1). Details of the S1 transitionwere further analyzed using the transition density and transitiondipole moments (21, 22). The transition density of the S1 excita-tion is shown in Fig. 3C. The red isosurface shows the “hole”distributions where the single electron leaves upon excitation, andthe green isosurface shows the “electron” distributions where theexcited electron goes after the excitation. Because this electronictransition occurs over the cylinder, the total ETDM (μ) was parallelto the cylinder axis (z axis, SI Appendix, Fig. S5). The cancellation ofthe ETDM in the other directions, i.e., the X- and Y components(μX and μY), can be visually understood by the breakdown analysisof the ETDM density shown in SI Appendix, Fig. S5. Thus, the μXand μY moments were distributed similarly on opposite sides of thecylinder’s wall but faced opposite directions (23) (blue vs. greenin SI Appendix, Fig. S5). The cylindrical π-systems exhibited evenmore important features in the analysis. As shown in Fig. 3C, alarge MTDM (m) was parallel to the cylinder axis. In principle, theMTDM is generated by the angular momentum operator due tosingle-electron movement during excitation (24) and therefore is avector product of the distance vector r and the ETDM μ: m ∝ r × μ(25–27). The large, Z-oriented m of the present nanoscale cylinderwas therefore generated by the local μ-vectors, distributed over thewhole cylinder, together with the r vectors, which radiated toward

the outside of the large, nanoscale molecule. The breakdown of thetopological analysis of the MTDM is shown in SI Appendix, Fig. S6.Finally, these two transition dipole moments, μ and m, are oppo-sitely oriented (i.e., with an angle of 180°), resulting in a large ro-tatory strength (R), which is defined as R = jμj•jmj•cosθ. Thebreakdown analyses of the (P)-(11,9)-isomer also revealed a dom-inant contribution from m (Fig. 3D), which was again generated bythe cylindrical conjugated systems (SI Appendix, Figs. S7 and S8).The g value is then derived as a combination of jmj and jμj in arelationship of g ∝ (jmj/jμj)•cosθ (28). Thus, unlike conventionalorganic molecules with negligible MTDM contributions (22, 24, 29),π-conjugated systems on nanoscale cylinders achieve extraordinarilylarge jgabsj values due to unique MTDM along the cylinder axis. Webelieve that these chiroptical characteristics and dominant MTDMshould also be observed in other cylindrical entities, includingSWNT congeners (20), and that the recently reported numericalcorrelation method that solely adopts ETDM without considerationof MTDM should be interpreted with caution (6, 7).

CPL, Large jglumj Value. Finally, the helicity of the nanoscale cyl-inders resulted in a large luminescence dissymmetry factor glumwith organic molecules. The intense photoluminescence (PL)of (P)-(12,8)-[4]CC was quantified, yielding a significantly high

Fig. 3. Chiroptical properties of cylindrical molecules. (A) CD spectra of (P)- and (M)-(12,8)-[4]CC in toluene at 25 °C. (B) CD spectra of (P)- and (M)-(11,9)-[4]CC intoluene at 25 °C. (C) Transition density (Left) and transition dipole moments (Right) of methyl-substituted (P)-(12,8)-[4]CC. In the transition density isosurface, hole(green) and electron (red) distributions are shown at an isovalue of 0.0004. For the dipole moments, the ETDM vector is shown in red, and the MTDM vector isshown in blue. (D) Transition density (Left) and transition dipole moments (Right) of the methyl-substituted (P)-(11,9)-[4]CC. In the transition density isosurface,hole (green) and electron (red) distributions are shown at an isovalue of 0.0004. For the dipole moments, the ETDM vector is shown in red, and theMTDM vector isshown in blue.

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quantum yield of ϕPL = 0.80 in toluene, which prompted us tomeasure its CPL spectra (28). Achieving both a high ϕPL yieldand a large glum factor is ideal for practical photonics applicationssuch as CPL, and extensive efforts are currently being devoted todeveloping small molecules (11). However, achieving these tworequirements simultaneously has been proven difficult. To the bestof our knowledge, the highest jglumj value for organic molecules(0.035) was recorded with a chiral ketone derivative with a ϕPL =∼0.001 (30). A comparable jglumj value of 0.032 was reported for a[6]helicene derivative with a much-improved yet moderate ϕPLyield of 0.296 (31). A significantly high ϕPL of 0.88 was achievedwith a binaphthyl derivative, albeit with an inferior jglumj value of0.003 (32). In this study of cylindrical molecules, an extraordinarily largeglum value of −0.152 was recorded at 443 nm with (P)-(12,8)-[4]CC(Fig. 4) and, intriguingly, with a high ϕPL value, which suggests thatorganic molecules could rival lanthanide complexes in CPL perfor-mances (33). The other chiral isomers, (P)- and (M)-(11,9)-[4]CC,also achieved large glum values of −0.101 and +0.099, respectively,with a high ϕPL yield of 0.74.

ConclusionsChirality originating solely from the anomalous arrangement ofsp2-carbon networks gave rise to unique properties in nanoscalecylinders. Shape recognitions, driven only by van der Waals in-teractions, resulted in an intertwined, double-helix formationof the cylinders (15), and the helicity of the spiral stacks was

dictated by the helicity of the cylinders. The occurrence of anextremely large jglumj value for organic molecules reveals an inter-esting design principle for CPL emitters: The π-conjugated systemsdistributed over a nanoscale cylinder possess an ideal topology forelectric transitions that enhance MTDM and, consequently, dramati-cally increase the rotatory strength through R = jμj•jmj•cosθ.Achieving large jmj without risking jμj has been recognized as anideal design for CPL emitters but also has been regarded as aparadoxical requirement for organic molecules (11, 27). This studyunequivocally demonstrates that rigid nanoscale cylinders, includingSWNT congeners, are promising CPL emitters that can fulfill suchapparently paradoxical requirements. Taking advantage of otherfunctional macrocylic molecules (34–36), we are currently investi-gating device applications of these hydrocarbon cylinders (11).Combinations of cylinders with aggregate/assembly-induced CPLenhancements in the solid state may be of practical interest (37).

MethodsSynthesis of [4]CC. Compounds were synthesized, isolated, and characterizedby a method reported in the literature (8).

Crystallographic Analysis. Single crystals of (P)- and (M)-(12,8)-[4]CC weregrown at 3 °C from a solution in CH2Cl2:methanol (1:1; 0.5 mg/mL) afterfiltration through a membrane filter (0.45-μm pore). A microseeding methodeffectively improved the reproducibility and crystal quality. X-ray diffractionanalysis of single crystals was conducted on a Rigaku XtaLAB P200 diffractometerwith multilayer mirror monochromated CuΚα radiation (λ = 1.54187) at −180 °C.A single crystal was mounted on a thin polymer tip with a cryoprotectant oil andfrozen at −180 °C via flash-cooling. The collected diffraction data were pro-cessed with the CrysAlisPro software program (38). The structures were solvedusing a direct method in the SHELXD software program (39) and refined usinga full-matrix least-squares method on F2 in the SHELX program suite (36)running on the Yadokari-XG 2009 software program (40) and CrystalStructure(41). In the refinements, disordered alkyl groups and solvent molecules wererestrained by SIMU and DFIX. The nonhydrogen atoms were analyzed aniso-tropically, and hydrogen atoms were input at calculated positions and refinedwith a riding model. Merohedral twinning was refined by TWIN. CambridgeCrystallographic Data Centre (CCDC) accession codes 1570803 and 1570804contain the supplementary crystallographic data for this paper (SI Appendix,Fig. S2). These data can be obtained free of charge from the CCDC.

CD Spectroscopy. CD spectroscopy was performed on JASCO J-1500 at 25 °Cwith a toluene solution. The error range of the CD measurement is ±5% (42),and the jgabsj values of enantiomers can be considered identical within theerror range. Measurements were performed with (P)-(12,8)-, (M)-(12,8)-,(P)-(11,9)-, and (M )-(11,9) isomers at the concentrations of 6.91 × 10−6,6.13 × 10−6, 5.27 × 10−6 and 5.05 × 10−6 M, respectively.

Density-Functional Theory Calculations. Theoretical calculations were per-formed at the density-functional theory (DFT) level with the B3LYP functional,the gradient correction of the exchange functional by Becke (43, 44) and thecorrelation functional by Lee et al. (45) on Gaussian 09 (46). The 6–31G(d,p) split valence plus polarization basis set was used (47–51). TDDFT cal-culations were performed for the first 30 singlet–singlet transitions with anadditional keyword of IOP(9/40 = 2). Spectral analysis with the B3LYP func-tional agreed well with the ordering of the states in the experimental resultsbut underestimated the excitation energy, affording slightly redshiftedtheoretical spectra (8, 52) (SI Appendix, Figs. S3 and S4 and Tables S1 and S2).TDDFT calculations at solvated states with polarizable continuum modelswere also performed, but we did not observe dramatic improvements particularlyin the S1 transition of current interest (SI Appendix, Fig. S10 and Tables S3 and S4).Other sophisticated solvation models might improve minor discrepancies, whichmay provide interesting subjects for state-of-the-art theoretical studies (53, 54).DFT data were visualized and analyzed with the GaussView program.

Analyses of Transitions. Transition density and transition dipole momentswere generated through analyses of the DFT data with Multiwfn (19). Thetransition density was visualized with GaussView (Fig. 3), and the break-down data of transition dipole moments were visualized with Multiwfn (SIAppendix, Figs. S5–S8).

CPL Spectroscopy. CPL spectroscopy was performed on JASCO CPL-300. Theerror range, ±5%, is similar to that of the CD spectra. A solution of each

Fig. 4. CPL spectra in toluene. (A) (P)- and (M)-(12,8)-[4]CC. (B) (P)- and(M)-(11,9)-[4]CC.

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specimen was prepared in toluene and degassed by a freeze–pump–thawmethod before the measurements. The absolute quantum yield of thephosphorescence was separately measured in the same medium using aHamamatsu PL quantum yield spectrometer C9920-02G. Measurements wereperformed with (P)-(12,8)-, (M)-(12,8)-, (P)-(11,9)-, and (M)-(11,9) isomers atthe concentrations of 6.77 × 10−6, 4.90 × 10−6, 4.67 × 10−6, and 5.05 × 10−6 M,respectively.

ACKNOWLEDGMENTS. We thank T. Matsuno (University of Tokyo), R. Arita(RIKEN), and T. Izumi (ERATO) for discussion, M. Oinuma (ERATO) for thepreparation of [4]CC, and J. Xu (JASCO) for the use of CPL instruments. Thisstudy is partly supported by Japan Science and Technology Agency ERATO(JPMJER1301) and KAKENHI (17H01033, 16K04864, and 25102007). A.Y. thanksDivision for Interdisciplinary Advanced Research and Education (DIARE, TohokuUniversity) for a predoctoral fellowship.

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by g

uest

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27,

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0

Correction

CHEMISTRYCorrection for “Chiral intertwined spirals and magnetic transi-tion dipole moments dictated by cylinder helicity,” by Sota Sato,Asami Yoshii, Satsuki Takahashi, Seiichi Furumi, MasayukiTakeuchi, and Hiroyuki Isobe, which was first published No-vember 27, 2017; 10.1073/pnas.1717524114 (Proc Natl Acad SciUSA 114:13097–13101).The authors wish to note the following: “The values for jmj in

Fig. 3 are incorrect due to usage of an incorrect conver-sion factor. The correct unit conversion is 1 a.u. = 9.27400968 ×10−21 erg G–1.” The corrected Fig. 3 and its legend appear below.

5194–5195 | PNAS | March 12, 2019 | vol. 116 | no. 11 www.pnas.org

Published under the PNAS license.

Published online March 4, 2019.

www.pnas.org/cgi/doi/10.1073/pnas.1902266116

0.09

0

0.18g abs

0.09

0

0.18

g abs

480330 380 430 580Wavelength (nm)

280 530

(M)-(12,8)-[4]CC

(P)-(12,8)-[4]CC

(M)-(11,9)-[4]CC

(P)-(11,9)-[4]CC

480330 380 430 580Wavelength (nm)

280 530

(P)-(12,8)-[4]CC (P)-(11,9)-[4]CC

S1 transition density S1 transition dipole moments S1 transition density S1 transition dipole moments

| | = 1.25 10 esu cm|m| = 1.01 10 erg G

,m

red = holegreen = electron = 457 nm

| | = 0.687 10 esu cm|m| = 0.955 10 erg G

,m

red = holegreen = electron = 449 nm

A B

C D

Fig. 3. Chiroptical properties of cylindrical molecules. (A) CD spectra of (P)- and (M)-(12,8)-[4]CC in toluene at 25 °C. (B) CD spectra of (P)- and (M)-(11,9)-[4]CCin toluene at 25 °C. (C) Transition density (Left) and transition dipole moments (Right) of methyl-substituted (P)-(12,8)-[4]CC. In the transition density iso-surface, hole (green) and electron (red) distributions are shown at an isovalue of 0.0004. For the dipole moments, the ETDM vector is shown in red, and theMTDM vector is shown in blue. (D) Transition density (Left) and transition dipole moments (Right) of the methyl-substituted (P)-(11,9)-[4]CC. In the transitiondensity isosurface, hole (green) and electron (red) distributions are shown at an isovalue of 0.0004. For the dipole moments, the ETDM vector is shown in red,and the MTDM vector is shown in blue.

PNAS | March 12, 2019 | vol. 116 | no. 11 | 5195

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ECTION