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. 2025 Sep 22;10(38):43698–43705. doi: 10.1021/acsomega.5c03858

Non-IPR Fullertube Series C10+10+6n : A Theoretical Prediction

Kexin Ma †, Kai Tan †,*, Anan Wu †, Xin Lu ‡,*
PMCID: PMC12489693  PMID: 41048815

Abstract

While a few fullertubes satisfying the isolated pentagon rule have been experimentally synthesized, non-IPR isomers may become accessible through endohedral or exohedral functionalization. Density functional theory has been used to predict a novel class of non-IPR [3,3] fullertube chlorides, attributed to the release of strains from a triplet of directly fused pentagons (TDFP) in the fullertube end-caps. Additionally, we proposed that the growth of fullertubes proceeds via the continuous insertion of C2 fragments, involving nonclassical fullerene intermediates containing heptagonal rings. These findings have significant implications for the synthesis of novel fullertube structures and, more broadly, carbon nanotubes.

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1. Introduction

Fullertubes, also known as tubular fullerenes, are defined by two-half fullerene end-caps combining with a single layer of rolled graphene hexagons and regarded as a highly promising nanocarbon material for single-molecule electronic devices due to their properties such as a high aspect ratio and reproducible preparation processes. , Analogous to carbon nanotubes, fullertubes can be classified based on fullerene end-caps and belts, including armchair, zigzag, and spiral loop type. To date, several fullertubes with various forms of pristine, endohedral, and exohedral derivatization have been successfully synthesized and isolated. − The first pristine fullertube series C30+30+10n (n = number of added carbon belts), consisting of two pentagon symmetry half-C60 end-caps and a [5,5] armchair belt, has been experimentally reported, including [5,5] D 5h -C90(1) (2010), [5,5] D 5d -C100(1) (2020), [5,5] D 5d -C120(1) (2022), and [5,5] D 5h -C130(1) (2023). Moreover, D 3d -C96(3) belonging to other fullertube series C30+30+18n (n = number of added carbon belts) has been proven to be a structure of two hexagon-based symmetry axis half-C60 end-caps and a [9,0] zigzag CNT belt. Notably, these fullertubes that had been isolated are satisfying to the isolated pentagon rule (IPR). Fullertubes that violate this rule have been deemed too reactive to be synthesized. At present, the main synthetic strategies can be classified into methods such as halogenation, alkylation, and fluorination, which effectively stabilize target fullerenes. Among them, chlorination demonstrates remarkable utility in the preparation of non-IPR fullerenes due to its simple process (low synthetic difficulty and good functional group compatibility). If non-IPR fullertubes could be efficiently stabilized by exohedral and endohedral functionalization, the family member of fullertubes for practical applications will be much enriched.

As early as 2000, the smallest fullerene C20 have been made using a gas-phase reaction method. Simultaneously, Iijima et al. proposed that the smallest 4 Å nanotubes grow out of half of a C20 dodecahedron. They declaimed that this [3,3] nanotube is rather unstable and may not survive alone without the protection of an outer nanotube. These clues hint that non-IPR [3,3] fullertube could be produced by the unusual experimental condition. Many questions arise as follows: Is non-IPR [3,3] fullertube stable or unstable? Can non-IPR [3,3] fullertube be stabilized by chlorination? How do we understand the formation mechanism of non-IPR [3,3] fullertube?

Clarifying the formation mechanism of fullertubes is of particular interest, as it opens up a wide range of potential applications for these nanomaterials. In previous theoretical and experimental studies, fullerenes can form through different pathways, generally classified into three growth models: bottom-up, top-down, and size-up/size-down. − These growth processes are often linked to the Stone–Wales transformation (SWT) and C2 extrusion or insertion. Additionally, the process is accompanied by the generation of classical or nonclassical fullerene intermediates, i.e., C76(NC2a)­Cl24 and C88Cl22/24, which have been experimentally confirmed. − However, the transformation process of fullertubes and the underlying pathway remain unclear.

Herein, we construct non-IPR [3,3] fullertube series C10+10+6n , where n is the number of added carbon belts, and perform detailed density functional theory (DFT) computations to investigate the geometric and electronic structures of the pristine and chloride forms within these fullertube series. Furthermore, an optimal pathway for non-IPR fullertube growth has been identified, addressing the inheritance of stability in the C2 insertion reaction from both thermodynamic and kinetic perspectives for the first time. This discovery could significantly broaden the scope of the fullertube family and provide strong theoretical support for the preparation of undiscovered fullertubes.

2. Computational Details

The calculations in this study were performed by using DFT as implemented in the Gaussian 16 software package. The predicted isomers of the fullertubes were fully optimized employing the dispersion-corrected hybrid generalized gradient approximation functional, B3LYP-GD3BJ. The split-valence d-polarized 6-311G­(d) basis set was used. The computations incorporated zero-point energy and thermal free-energy corrections to ensure accurate energetic predictions. The simulations of NMR spectra using the gauge-independent atomic orbital method (GIAO) are performed at the xOPBE/6-311 + G­(2d,p), , in which the chemical shifts were first evaluated relative to C60 and then were referenced to tetramethylsilane (TMS) (d (C60) 143.15 ppm vs TMS). The binding energy (BE) of C2 addition reaction is defined as the difference between the total energy of a C n+2 and the sum of the total energies of the separated ground-state C n and C2 fragment (i.e., BE = [E tot(C n ) + E tot(C2)] – E tot(C n+2)). BEC–Cl is defined as the C–Cl BE per chlorine atom. In this study, Symm­(y)-C x denotes IPR and non-IPR classical fullertube, which were identified by their symmetry and by the number assigned according to the spiral algorithm, where x is the number of carbon atoms and y is the spiral code for the fullertube cage. Hept-Symm­(y)-C x denotes heptagon-containing nonclassical fullertube, where y represents the series number generated by CaGe software.

3. Results and Discussion

3.1. The [3,3] Fullertube Series C10+10+6n (n = 1–9)

As depicted in Figure , the [3,3] fullertube C10+10+6n series is constructed with repeated additions of a 6-belts to C20 dodecahedron. These calculated fullertube structures show an alternating D 3h or D 3d symmetry and consist of D 3h (1)-C26, D 3d (3)-C32, D 3h (2)-C38, D 3d (3)-C44, D 3h (3)-C50, D 3d (3)-C56, D 3h (2)-C62, D 3d (3)-C68, D 3h (2)-C74, and so forth. Our calculations revealed that the short axis of the structures in this series ranges from 4.16 Å to 4.44 Å, which is close to the experimental result of 4 Å. Additionally, with each increment of six carbon atoms, corresponding to one additional ring in the structure, the length of the long axis experiences an increase of 1.04 to 1.39 Å. The detailed structural information is meticulously documented in Table S1.

1.

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Molecular structures of fullertube series C10+10+6n (n = 1–9). Yellow and blue sticks denote half of C20 end-caps.

The binding energies and HOMO–LUMO gaps of [3,3] fullertube C10+10+6n at the B3LYP/6-311G* level are listed in Table . The BE values are all positive, indicating that the C2 addition reactions are exothermic. The BE of D 3d (3)-C32 is 198.91 kcal/mol, which is the highest in the series. Moreover, D 3d (3)-C32 shows the lowest VEA and AEA values, approximately 2.96 and 3.00 eV, respectively, suggesting its relatively high stability. The corresponding electrostatic potential diagrams are presented in Figure S1. However, the [3,3] fullertubes C10+10+6n have moderately small HOMO–LUMO gaps, and the calculated HOMO–LUMO gaps of D 3h (2)-C38, D 3d (3)-C44, D 3h (3)-C50, and D 3d (3)-C56 are 1.25, 1.17, 1.23, and 1.11 eV, respectively. Due to small HOMO–LUMO gaps lowering the [3,3] fullertube C10+10+6n stability, it was suggested to difficultly separate the pristine non-IPR fullertube from arc-generated soot extract. ,

1. Calculated HOMO–LUMO Gap Energies (in eV), Binding Energies (BE, in eV) of C2 Addition, the Vertical Electron Affinity (VEA, in eV) and Adiabatic Electron Affinity (AEA, in eV) for the Pristine Fullertube Series C10+10+6n (n = 1–9), and Binding Energies (BECl, in eV) of C–Cl for Chlorination Fullertube Series C10+10+6n Cl8 (n = 1–9).

  HOMO–LUMO gap
        
isomer pristine chlorination BE BECl VEA AEA
D 3h (1)-C26 1.64 2.01 8.23 3.04 3.19 3.30
D 3d (3)-C32 1.55 2.95 8.63 2.97 2.96 3.00
D 3h (2)-C38 1.25 2.96 7.83 3.13 3.44 3.49
D 3d (3)-C44 1.17 1.61 7.94 3.05 3.55 3.59
D 3h (3)-C50 1.23 2.08 8.03 3.19 3.47 3.51
D 3d (3)-C56 1.11 2.52 8.04 3.23 3.74 3.78
D 3h (2)-C62 0.96 1.80 8.10 3.13 3.81 3.85
D 3d (3)-C68 1.30 1.50 8.10 3.09 3.55 3.59
D 3h (2)-C74 1.19 1.93 8.05 3.15 3.65 3.69
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3.2. Chlorination of [3,3] Fullertube C10+10+6n

It is well-established that non-IPR fullerenes can be stabilized as exohedral derivatives. Similar to the triple directly fused pentagons (TDFP) chlorination pattern of C 3v (1911)-C64Cl4, we conducted computational analyses of geometric and electronic structures for fullertube chlorides C10+10+6n Cl8. The optimized structures of chlorinated fullertube D 3d (3)-C32 and C32Cl8 are represented in Figure a,b. Chlorination results in a relaxation in the end-caps of the fullertube, leading to a noticeable increase in the C–C bond lengths. For instance, the calculated C–C bond lengths of TDFP for C32Cl8 are found to be 1.588 Å, 1.588 Å, and 1.588 Å, as compared to the corresponding values of 1.441 Å, 1.442 Å, and 1.445 Å for the bare C32 fullertube. Within the TDFP unit, C–Cl bond lengths are 1.762, 1.801, 1.800, and 1.802 Å, respectively.

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[3,3] fullertube chlorides (a) D 3d (3)-C32 and (b) C32Cl8 isomers optimized at the B3LYP level of theory. C and Cl atoms are gray and green, respectively. Calculated frontier molecular orbital diagrams of (c) D 3h (2)-C38 and (d) C38Cl8.

As listed in Table , these values of BECl in fullertube chlorides were found to be similar to those in other non-IPR fullerenes detected so far. Compared to the C 3v (1911)-C64Cl4 (reported to be 2.52 eV), the BECl of C56Cl8 and C62Cl8 are 3.23 and 3.13 eV, respectively. Moreover, we observe that the HOMO–LUMO gaps increase significantly from C10+10+6n to C10+10+6n Cl8. For example, the gap of D 3h (2)-C38 is 1.25 eV, whereas that of C38Cl8 is 2.96 eV. As shown in Figure c,d, the HOMO and LUMO of D 3h (2)-C38 are mainly located at end-caps with minor contribution from the tube body, whereas the HOMO and LUMO of C38Cl8 are mainly located at the tube body. This change can be understood considering fullertube relaxation. The inherent strain of fullertube end-caps can be quantitatively described using π-orbital axis vector (POAV) analysis in Table S2. POAV analysis showed that chlorination leads to a change in hybridization from sp2 to sp3 for the carbon atom (TDFP), and accordingly, θp increases, thus relieving local strain. The remarkable relieving strain implies that the chemical deriving could indeed enhance the stability of non-IPR fullertubes.

3.3. Spectroscopic Properties of [3,3] Fullertube C10+10+6n

To provide a verifying basis for the experimental identification of [3,3] fullertube C10+10+6n , we have predicted the IR, Raman spectra, and NMR spectra. As shown in Figure a, there are some particular features of fullertube pristine structures, including cage breathing vibrational modes (mainly from 200 cm–1 to 800 cm–1) and C–C stretching vibrational modes (mainly from 1000 cm–1 to 1500 cm–1). Compared to the fullertube chlorinated structures, the great change of peaks in the IR spectra corresponds to the C–Cl stretching modes (mainly from 800 cm–1 to 1100 cm–1).

3.

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(a) IR and (b) NMR spectra of pristine structures (black) and chlorinated structures (green) for [3,3] fullertube series C10+10+6n (n = 1–9). Among them, the red oval identifies the chemical shifts of the atoms in the TDFP part.

The Raman spectra of the pristine and chlorinated forms in [3,3] fullertube C10+10+6n are slightly different, detailed in Figure S2. In addition, the UV–vis spectra of [3,3] fullertube C10+10+6n are also plotted in Figure S3. Compared to the fullertube chlorinated structures, the Raman spectra of fullertube pristine structures lack a clear region of C–Cl stretching modes. Moreover, we have computed the 13C NMR chemical shifts of the non-IPR [3,3] fullertube C10+10+6n . Ideally, the D 3h or D 3d symmetric fullertube pristine cage has four unique C atoms, i.e., pentagon–pentagon–pentagon (5/5/5), pentagon–pentagon–hexagon (5/5/6), hexagon–hexagon–hexagon (6/6/6), and hexagon–pentagon–hexagon (6/5/6) fusion apex. After chlorination, these eight atoms (5/5/5) change from sp2 to sp3, and therefore, the chemical shifts also change. For example, the two center atoms of TDFP at D 3h (1)-C26 shifted from 132.539 to 88.990 ppm. The carbon atoms labeled in TDFP exhibit a chemical shift change from 80 to 120 ppm, as shown in Figure b.

3.4. The Formation Mechanism of Non-IPR [3,3] Fullertube C10+10+6n

Since the growth of the [3,3] fullertube involves periodic tube-body addition, we study the growth of fullertubes from C38 to C44 as typical examples. We have investigated global pathways from D 3h (2)-C38 to D 3d (3)-C44 based on this strategy for step-by-step cage formations of isomers through C2 insertions and bond rearrangements. Despite the complexity of the processes involved, it is extraordinary that several relatively simple pathways exist, as shown in Figure a. Initiating from D 3h (2)-C38 structure progression, we find reaction paths to D 3d (3)-C44 that involve two nonclassical fullertube intermediates, Hept-C1(70)-C40 and Hept-C1(145)-C42 in the final reaction sequence.

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(a) All possible growth pathways from C38 to C44; the C2 units in beeline and SWT in others. The numbers within the circles represent the structure serial numbers. For example, “2” represents D 3h (2)-C38 and “h70” represents Hept-C1(70)-C40. (b) [3,3] fullertube C10+10+6n representative Schlegel diagrams from D 3h (2)-C38 to D 3d (3)-C44.

Interestingly, Figure b shows a bottom-up sequence of three direct C2 insertions (the added C2 is denoted in red) without any SW rearrangement results. Based on the above-mentioned C2 insertion chemical reactions, the growth of [3,3] fullertube C10+10+6n from D 3h (2)-C38 to D 3d (3)-C44 will be studied step by step at the DFT level of theory. It should be noted that although each isomer surface includes several addition sites, only those active sites related to special growth processes have been taken into account in this work.

3.4.1. From D 3h (2)-C38 to Hept-C1(70)-C40: Generation of Heptagonal Rings

As illustrated in Figure , Hept-C1(70)-C40 is generated by embedding a C2 fragment into one of the 5/6/6 fragments of D 3h (2)-C38. Due to the difference of the [6,6] and [5,6] conjunction on fragment 5/6/6, two feasible pathways for the initial embedding of the C2 fragment are delineated as path-1 and path-2. Structurally, one atom of the C2 unit is attached to the D 3h (2)-C38 cage surface, and the other one is dangling to generate a stick-like intermediate (INT-1 and INT-2). Experimentally, this stick adduct was discovered using higher solution ion-mobility measurements. At this point, the adsorption energies are −3.93 eV and −3.91 eV, respectively.

5.

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Growth process from D 3h (2)-C38 to Hept-C1(70)-C40. Red represents C2 addition, and blue represents the heptagon.

As the structure stabilizes, the unsaturated carbon atom gradually moves toward the fullertube surface, approaching a carbon atom on the opposite side of the pentagon/hexagon. At distances of 2.11 Å and 2.16 Å, the structure exhibits pendulum-like motion, characterizing it as a transition state structure (TS-1 and TS-2), which plays a crucial role in the fullertube growth process. From an energetic standpoint, [6,6] of D 3h (2)-C38 exhibits a stronger adsorption capacity for the C2 cluster compared to [5,6], approximately 0.02 eV as shown in Table . However, the energy barriers that path-1 and path-2 need to overcome are 2.04 and 1.85 eV, respectively. Clearly, path-2 has a lower energy barrier than path-1. Furthermore, the reaction rates for both pathways are examined to be 6.58 × 109 s–1 and 1.09 × 1010 s–1 based on the Eyring equation, respectively, at 2000 K. Eventually, due to the embedding of the C2 fragment, the central hexagon is split into two adjacent pentagons, forming Hept-C1(70)-C40 with a heptagon and shared-edge fused pentagons.

2. Adsorption Energies (E ad, in eV), Energy Barriers (E b, in eV), Reaction Energies (E r, in eV), and Reaction Rates at 2000 K (in s–1)­ for the C2 Addition Reactions from D 3h (2)-C38 to D 3d (3)-C44 .
reaction path E ad E b E r reaction rate
D 3h (2)-C38 → Hept-C1(70)-C40 1 –3.93 2.04 –7.58 6.58 × 109
  2 –3.91 1.85 –7.58 1.09 × 1010
Hept-C1(70)-C40 → Hept-C1(145)-C42 1 –4.09 3.10 –6.67 4.33 × 107
  2 –4.03 4.58 –6.67 3.63 × 104
Hept-C1(145)-C42 → D 3d (3)-C44 1 –4.77 2.39 –9.57 2.84 × 109
  2 –4.59 2.21 –9.57 5.59 × 109
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a

E ad = E(INT) – E(C n ) – E(C2).

b

E b = E(TS) – E(INT).

c

E r = E(C n+2) – E(C n ) – E(C2).

d

The calculation of reaction rate is based on the Eyring equation.

3.4.2. From Hept-C1(70)-C40 to Hept-C1(145)-C42: Continuation of Heptagonal Rings

Hept-C1(70)-C40 serves as the precursor for the growth of Hept-C1(145)-C42, with C2 addition occurring at sites involving heptagonal rings at the [6,7] and [5,7] conjunctions on the 5/7/6 fragment. Accordingly, path-1 and path-2 are defined and analyzed. As shown in Figure , a stick-like intermediate is formed in both path-1 and path-2 during the transition from Hept-C1(70)-C40 to Hept-C1(145)-C42. The intermediate formed in the first step of path-1 is energetically 0.06 eV lower than that of path-2 (−4.09 eV for path-1 and −4.03 eV for path-2). After overcoming an asynchronous transition state, Hept-C1(70)-C40 transforms into Hept-C1(145)-C42 with a new TDFP, and the reaction energy of this process is −6.67 eV. Eventually, the original heptagon is cleaved by the C2 fragment into a pentagon and hexagon, while simultaneously generating a metastable hollow cage structure Hept-C1(145)-C42 containing a new heptagon. Energy analysis reveals not only that path-1 exhibits a more stable intermediate structure than path-2 but also a lower energy barrier about 3.10 eV. Furthermore, the reaction rates of path-1 and path-2 are 4.33 × 107 s–1 and 3.63 × 104 s–1, respectively, suggesting that the transition from Hept-C1(70)-C40 to Hept-C1(145)-C42 is more likely to occur via path-1.

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Growth process from Hept-C1(70)-C40 to Hept-C1(145)-C42. Red represents C2 addition, and blue represents the heptagon.

3.4.3. From Hept-C1(145)-C42 to D 3d (3)-C44: Disappearance of Heptagonal Rings

The growth process from Hept-C1(145)-C42 to D 3d (3)-C44 marks the final stage from D 3h (2)-C38 to D 3d (3)-C44. Due to the perfect closure of a loop of the carbon belt, the embedding of the last C2 cluster takes place on fragment 5/7/5. As depicted in Figure , similarly, the adsorption of the C2 cluster at [5,7] is simulated at the B3LYP-GD3BJ/6-311G­(d) level. Geometrically, Hept-C1(145)-C42 serves as the last intermediate structure containing a new TDFP and a heptagon. With the addition of a C2 cluster, the rod-shaped intermediate structures, INT-1 and INT-2, are formed in path-1 and path-2. Now, the INT-1 is energetically 0.18 eV lower than that of INT-2. Subsequently, before another carbon atom is embedded for the second time, the transition state structures (TS-1 and TS-2) exist, and the energies of the transition state structures for the two paths are almost the same.

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Growth process of from Hept-C1(145)-C42 to D 3d (3)-C44. Red represents C2 addition, and blue represents the heptagon.

As the chemical reaction progresses, the heptagon ultimately disappears, restoring the structure to the non-IPR fullertube structure, D 3d (3)-C44. Additionally, the computational results indicate that path-2 needs to overcome a lower energy barrier than path-1 (2.39 eV for path-1, and 2.21 eV for path-2), with reaction rates at 2000 K being 5.59 × 109 s–1. Clearly, path-2 serves as a more kinetically advantageous reaction route, and this process is most likely to occur via path-2 in Table . Also, the activation energy for this reaction is −9.57 eV, which is significantly lower than for other processes, showing that the resulting structure D 3d (3)-C44 is the most stable.

Above all, the transformation from D 3h (2)-C38 to D 3d (3)-C44 represents a repeatable growth stage of the [3,3] fullertube. Energetically, as shown in Table , all addition reactions are highly exothermic with activation barriers lower than 3.10 eV. Additionally, all C2 insertions demonstrate a consistent trend in both thermodynamic and kinetic controls. Furthermore, the growth path from D 3h (1)-C26 to D 3h (2)-C74 embedded merely by C2 is plotted in Figure S4. This mechanism is of profound value for the directional synthesis of fullertube and their derivatives.

4. Conclusion

A new non-IPR [3,3] fullertube series C10+10+6n has been predicted here using the results obtained from density functional calculations. The results showed that non-IPR [3,3] fullertube can be stabilized in the exohedral derivate as C10+10+6n Cl8. Structural, electronic, and spectroscopic properties for the pristine and chloride form of non-IPR [3,3] fullertube C10+10+6n have been provided. Besides, structure topological analysis demonstrates that the growth of this fullertube series can be achieved entirely in a bottom-up growth mechanism merely by means of the insertion of C2 units. A thermodynamically and kinetically favorable pathway from D 3h (2)-C38 to D 3d (3)-C44 was proposed based on a reaction PES survey. The discovery of this series of fullertubes is of great significance for predicting new materials in the fullertube family.

Supplementary Material

ao5c03858_si_001.pdf (663.4KB, pdf)

Acknowledgments

The author thanks the financial support from the National Natural Science Foundation of China (No. 21931009, No. 92161117).

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.5c03858.

  • Full details of DFT calculation: geometry optimization, electrostatic potential map, Raman spectra, the growth pathway from D 3h (1)-C26 to D 3h (2)-C74 via merely C2 insertion, computational details, the coordinates for optimized structures and reference (PDF)

The authors declare no competing financial interest.

References

  1. Stevenson S., Dorn H. C.. Fullertubes: A 30-Year Story of Prediction, Experimental Validation, and Applications for a Long-Missing Family of Soluble Carbon Molecules. Acc. Chem. Res. 2024;57:2154–2165. doi: 10.1021/acs.accounts.4c00302. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Li W., Wang C., Wang T.. Metallofullertube: From Tubular Endohedral Structures to Properties. ChemPhysChem. 2022;23:e202200507. doi: 10.1002/cphc.202200507. [DOI] [PubMed] [Google Scholar]
  3. Iijima S.. Helical microtubules of graphitic carbon. Nature. 1991;354:56–58. doi: 10.1038/354056a0. [DOI] [Google Scholar]
  4. Yang H., Beavers C. M., Wang Z., Jiang A., Liu Z., Jin H., Mercado B. Q., Olmstead M. M., Balch A. L.. Isolation of a small carbon nanotube: The surprising appearance of D5h (1)-C90 . Angew. Chem., Int. Ed. 2010;49:886–890. doi: 10.1002/anie.200906023. [DOI] [PubMed] [Google Scholar]
  5. Chilingarov N. S., Troyanov S. I.. Unstable isomer of C90 fullerene isolated as chloro derivatives, C90 (1) Cl10/12 . Chem.Eur. J. 2016;11:1896–1899. doi: 10.1002/asia.201600713. [DOI] [PubMed] [Google Scholar]
  6. Cai W., Bao L., Zhao S., Xie Y., Akasaka T., Lu X.. Anomalous Compression of D5 (450)-C100 by Encapsulating La2C2 Cluster instead of La2 . J. Am. Chem. Soc. 2015;137:10292–10296. doi: 10.1021/jacs.5b05668. [DOI] [PubMed] [Google Scholar]
  7. Koenig R. M., Tian H.-R., Seeler T. L., Tepper K. R., Franklin H. M., Chen Z.-C., Xie S.-Y., Stevenson S.. Fullertubes: cylindrical carbon with half-fullerene end-caps and tubular graphene belts, their chemical enrichment, crystallography of pristine C90-D5h (1) and C100-D5d (1) fullertubes, and isolation of C108, C120, C132, and C156 cages of unknown structures. J. Am. Chem. Soc. 2020;142:15614–15623. doi: 10.1021/jacs.0c08529. [DOI] [PubMed] [Google Scholar]
  8. Stevenson S., Liu X., Sublett Jr D. M., Koenig R. M., Seeler T. L., Tepper K. R., Franklin H. M., Wang X., Huang R., Feng X., Cover K., Troya D., Shanaiah N., Bodnar R. J., Dorn H. C.. Semiconducting and metallic [5, 5] Fullertube nanowires: characterization of pristine D5h (1)-C90 and D5d (1)-C100 . J. Am. Chem. Soc. 2021;143:4593–4599. doi: 10.1021/jacs.0c11357. [DOI] [PubMed] [Google Scholar]
  9. Liu X., Bourret E., Noble C. A., Cover K., Koenig R. M., Huang R., Franklin H. M., Feng X., Bodnar R. J., Zhang F., Tao C., Sublett Jr D. M., Dorn H. C., Stevenson S.. Gigantic C120 fullertubes: Prediction and experimental evidence for isomerically purified metallic [5,5] C120-D5d (1) and nonmetallic [10,0] C120-D5h (10766) J. Am. Chem. Soc. 2022;144:16287–16291. doi: 10.1021/jacs.2c06951. [DOI] [PubMed] [Google Scholar]
  10. Bourret E., Liu X., Noble C. A., Cover K., Davidson T. P., Huang R., Koenig R. M., Reeves K. S., Vlassiouk I. V., Côté M., Baxter J. S., Lupini A. R., Geohegan D. B., Dorn H. C., Stevenson S.. Colossal C130 Fullertubes: Soluble [5,5] C130-D5h (1) Pristine Molecules with 70 Nanotube Carbons and Two 30-Atom Hemifullerene End-caps. J. Am. Chem. Soc. 2023;145:25942–25947. doi: 10.1021/jacs.3c09082. [DOI] [PubMed] [Google Scholar]
  11. Yang H., Jin H., Che Y., Hong B., Liu Z., Gharamaleki J. A., Olmstead M. M., Balch A. L.. Isolation of Four Isomers of C96 and Crystallographic Characterization of Nanotubular D3d (3)-C96 and the Somewhat Flat-Sided Sphere C2 (181)-C96 . Chem.Eur. J. 2012;18:2792–2796. doi: 10.1002/chem.201103852. [DOI] [PubMed] [Google Scholar]
  12. Kroto H.. The stability of the fullerenes Cn, with n= 24, 28, 32, 36, 50, 60 and 70. Nature. 1987;329:529–531. doi: 10.1038/329529a0. [DOI] [Google Scholar]
  13. Jarrold M. F.. The smallest fullerene. Nature. 2000;407:26–27. doi: 10.1038/35024178. [DOI] [PubMed] [Google Scholar]
  14. Qin L.-C., Zhao X., Hirahara K., Miyamoto Y., Ando Y., Iijima S.. The smallest carbon nanotube. Nature. 2000;408:50. doi: 10.1038/35040699. [DOI] [PubMed] [Google Scholar]
  15. Alekseyev N., Dyuzhev G.. Fullerene formation in an arc discharge. Carbon. 2003;41:1343–1348. doi: 10.1016/S0008-6223(03)00058-7. [DOI] [Google Scholar]
  16. Irle S., Zheng G., Wang Z., Morokuma K.. The C60 formation puzzle solved: QM/MD simulations reveal the shrinking hot giant road of the dynamic fullerene self-assembly mechanism. J. Phys. Chem. B. 2006;110:14531–14545. doi: 10.1021/jp061173z. [DOI] [PubMed] [Google Scholar]
  17. Cai W., Li F.-F., Bao L., Xie Y., Lu X.. Isolation and crystallographic characterization of La2C2@Cs (574)-C102 and La2C2@C2 (816)-C104: evidence for the top-down formation mechanism of fullerenes. J. Am. Chem. Soc. 2016;138:6670–6675. doi: 10.1021/jacs.6b03934. [DOI] [PubMed] [Google Scholar]
  18. Zhang J., Bowles F. L., Bearden D. W., Ray W. K., Fuhrer T., Ye Y., Dixon C., Harich K., Helm R. F., Olmstead M. M., Balch A. L., Dorn H. C.. A missing link in the transformation from asymmetric to symmetric metallofullerene cages implies a top-down fullerene formation mechanism. Nat. Chem. 2013;5:880–885. doi: 10.1038/nchem.1748. [DOI] [PubMed] [Google Scholar]
  19. Chuvilin A., Kaiser U., Bichoutskaia E., Besley N. A., Khlobystov A. N.. Direct transformation of graphene to fullerene. Nat. Chem. 2010;2:450–453. doi: 10.1038/nchem.644. [DOI] [PubMed] [Google Scholar]
  20. Dunk P. W., Mulet-Gas M., Nakanishi Y., Kaiser N. K., Rodríguez-Fortea A., Shinohara H., Poblet J. M., Marshall A. G., Kroto H. W.. Bottom-up formation of endohedral mono-metallofullerenes is directed by charge transfer. Nat. Commun. 2014;5:5844. doi: 10.1038/ncomms6844. [DOI] [PubMed] [Google Scholar]
  21. Dunk P. W., Kaiser N. K., Hendrickson C. L., Quinn J. P., Ewels C. P., Nakanishi Y., Sasaki Y., Shinohara H., Marshall A. G., Kroto H. W.. Closed network growth of fullerenes. Nat. Commun. 2012;3:855. doi: 10.1038/ncomms1853. [DOI] [PubMed] [Google Scholar]
  22. Endo M., Kroto H.. Formation of carbon nanofibers. J. Phys. Chem. 1992;96:6941–6944. doi: 10.1021/j100196a017. [DOI] [Google Scholar]
  23. Brotsman V. A., Troyanov S. I.. Non-classical (NC), heptagon-containing fullerenes obtained via chlorination-promoted cage transformations: C76 (NC2a) Cl24 and C76 (NC2b) Cl28 . Chem. Commun. 2024;60:893–896. doi: 10.1039/D3CC05336A. [DOI] [PubMed] [Google Scholar]
  24. Ioffe I. N., Mazaleva O. N., Sidorov L. N., Yang S., Wei T., Kemnitz E., Troyanov S. I.. Cage shrinkage of fullerene via a C2 loss: from IPR C90 (28) Cl24 to non-classical, heptagon-containing C88Cl22/24 . Inorg. Chem. 2013;52:13821–13823. doi: 10.1021/ic402556g. [DOI] [PubMed] [Google Scholar]
  25. Tan Y.-Z., Chen R.-T., Liao Z.-J., Li J., Zhu F., Lu X., Xie S.-Y., Li J., Huang R.-B., Zheng L.-S.. Carbon arc production of heptagon-containing fullerene [68] Nat. Commun. 2011;2:420. doi: 10.1038/ncomms1431. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. Frisch, M. J. ; Trucks, G. W. ; Schlegel, H. B. ; Scuseria, G. E. ; Robb, M. A. ; Cheeseman, J. R. ; Scalmani, G. ; Barone, V. ; Petersson, G. A. ; Nakatsuji, H. ; Li, X. ; Caricato, M. ; Marenich, A. V. ; Bloino, J. ; Janesko, B. G. ; Gomperts, R. ; Mennucci, B. ; Hratchian, H. P. ; Ortiz, J. V. ; Izmaylov, A. F. ; Sonnenberg, J. L. ; Williams-Young, D. ; Ding, F. ; Lipparini, F. ; Egidi, F. ; Goings, J. ; Peng, B. ; Petrone, A. ; Henderson, T. ; Ranasinghe, D. ; Zakrzewski, V. G. ; Gao, J. ; Rega, N. ; Zheng, G. ; Liang, W. ; Hada, M. ; Ehara, M. ; Toyota, K. ; Fukuda, R. ; Hasegawa, J. ; Ishida, M. ; Nakajima, T. ; Honda, Y. ; Kitao, O. ; Nakai, H. ; Vreven, T. ; Throssell, K. ; Montgomery, J. A., Jr. ; Peralta, J. E. ; Ogliaro, F. ; Bearpark, M. J. ; Heyd, J. J. ; Brothers, E. N. ; Kudin, K. N. ; Staroverov, V. N. ; Keith, T. A. ; Kobayashi, R. ; Normand, J. ; Raghavachari, K. ; Rendell, A. P. ; Burant, J. C. ; Iyengar, S. S. ; Tomasi, J. ; Cossi, M. ; Millam, J. M. ; Klene, M. ; Adamo, C. ; Cammi, R. ; Ochterski, J. W. ; Martin, R. L. ; Morokuma, K. ; Farkas, O. ; Foresman, J. B. ; Fox, D. J. . Gaussian 16, Revision C.01; Gaussian, Inc.: Wallingford CT, 2016. [Google Scholar]
  27. Huang H., Zhang L., Gao X. J., Guo X., Cui R., Xu B., Dong J., Li Y., Gan L., Chang F., Gao X., Sun B.. Regioselective Polyamination of Gd@ C2v (9)-C82 and Non-High Performance Liquid Chromatography Rapid Separation of Gd@ C82 (morpholine)7 . Chem. Mater. 2018;30:64–68. doi: 10.1021/acs.chemmater.7b03787. [DOI] [Google Scholar]
  28. McLean A., Chandler G.. Contracted Gaussian basis sets for molecular calculations. I. Second row atoms, Z= 11–18. J. Chem. Phys. 1980;72:5639–5648. doi: 10.1063/1.438980. [DOI] [Google Scholar]
  29. Zhang J., Ye Q., Yin C., Wu A., Xu X.. xOPBE: a specialized functional for accurate prediction of 13C chemical shifts. J. Phys. Chem. A. 2020;124:5824–5831. doi: 10.1021/acs.jpca.0c02873. [DOI] [PubMed] [Google Scholar]
  30. Wolinski K., Hinton J. F., Pulay P.. Efficient implementation of the gauge-independent atomic orbital method for NMR chemical shift calculations. J. Am. Chem. Soc. 1990;112:8251–8260. doi: 10.1021/ja00179a005. [DOI] [Google Scholar]
  31. Zurek E., Pickard C. J., Walczak B., Autschbach J.. Density functional study of the 13C NMR chemical shifts in small-to-medium-diameter infinite single-walled carbon nanotubes. J. Phys. Chem. A. 2006;110:11995–12004. doi: 10.1021/jp064540f. [DOI] [PubMed] [Google Scholar]
  32. Brinkmann G., Dress A. W.. A constructive enumeration of fullerenes. J. Algorithm. 1997;23:345–358. doi: 10.1006/jagm.1996.0806. [DOI] [Google Scholar]
  33. Aihara J.-i.. Weighted HOMO-LUMO energy separation as an index of kinetic stability for fullerenes. Theor. Chem. Acc. 1999;102:134–138. doi: 10.1007/s002140050483. [DOI] [Google Scholar]
  34. Diener M. D., Alford J. M.. Isolation and properties of small-bandgap fullerenes. Nature. 1998;393:668–671. doi: 10.1038/31435. [DOI] [Google Scholar]
  35. Han X., Zhou S.-J., Tan Y.-Z., Wu X., Gao F., Liao Z.-J., Huang R.-B., Feng Y.-Q., Lu X., Xie S.-Y., Zheng L.-S.. Crystal structures of saturn-like C50Cl10 and pineapple shaped C64Cl4: geometric implications of double-and triple-pentagon-fused chloro-fullerenes. Angew. Chem., Int. Ed. 2008;47:5340–5343. doi: 10.1002/anie.200800338. [DOI] [PubMed] [Google Scholar]
  36. Dang J.-S., Wang W.-W., Zhao X., Nagase S.. Unconventional electronic structure and chlorination/dechlorination mechanisms of #1911C64 fullerene. Inorg. Chem. 2016;55:6827–6829. doi: 10.1021/acs.inorgchem.6b00642. [DOI] [PubMed] [Google Scholar]
  37. Haddon R. C.. π-Electrons in three dimensiona. Acc. Chem. Res. 1988;21:243–249. doi: 10.1021/ar00150a005. [DOI] [Google Scholar]
  38. Shvartsburg A. A., Hudgins R. R., Dugourd P., Gutierrez R., Frauenheim T., Jarrold M. F.. Observation of “stick” and “handle” intermediates along the fullerene road. Phys. Rev. Lett. 2000;84:2421. doi: 10.1103/PhysRevLett.84.2421. [DOI] [PubMed] [Google Scholar]
  39. Bettinger H. F., Yakobson B. I., Scuseria G. E.. Scratching the surface of buckminsterfullerene: the barriers for stone-wales transformation through symmetric and asymmetric transition states. J. Am. Chem. Soc. 2003;125:5572–5580. doi: 10.1021/ja0288744. [DOI] [PubMed] [Google Scholar]
  40. Rooney J. J.. Eyring transition-state theory and kinetics in catalysis. J. Mol. Catal. A: Chem. 1995;96:L1–L3. doi: 10.1016/1381-1169(94)00054-9. [DOI] [Google Scholar]

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