Nano-Saturn: Energetics of the Inclusion Process of C60 into

Article pubs.acs.org/JPCC

Nano-Saturn: Energetics of the Inclusion Process of C60 into Cyclohexabiphenylene Shota Kigure,† Haruka Omachi,‡ Hisanori Shinohara,‡ and Susumu Okada*,† †

Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8577, Japan Department of Chemistry, Graduate School of Science, Nagoya University, Furo, Chikusa, Nagoya 464-8602, Japan

‡

ABSTRACT: We theoretically investigated the possibility of a carbon nanomaterial with Saturn shape (nano-Saturn) as a novel inclusion compound consisting of C60 and cyclohexabiphenylene based on total energy calculations using density functional theory. We found that nanoSaturn is energetically stable with similar or lower total energy to that of the other C60 inclusion compounds experimentally synthesized to date. Furthermore, the formation reaction of nano-Saturn is exothermic with an energy gain of about 0.7 eV per molecule.

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INTRODUCTION In the last few decades, carbon nanomaterials, such as fullerenes,1 carbon nanotubes (CNTs),2 and polycyclic aromatic hydrocarbon (PAH) molecules,3−5 have attracted much attention because of their unique physical and chemical properties that arise from their geometric structures and boundary conditions imposed on their atomic networks. For example, the electronic structure of fullerene molecules is strongly dependent on the arrangement of the 12 pentagons in their hollow-cage sp2 networks,6 whereas CNTs are either metallic or semiconducting depending on the atomic arrangement along their circumference.7−9 Besides the intrinsic variation of their electronic properties, further structural modification of these materials leads to unique electronic structures; CNTs with finite length with zigzag ends10 and chemically decorated C6011−14 are expected to exhibit various spin orderings because of the nonbonding π electrons at the Fermi level. The diversity of their physical and chemical properties caused by network topology makes these materials appealing as functional units for various advanced devices by assembling in an appropriate manner. Another important issue of carbon nanomaterials is their structural hierarchy. These materials are known to form condensed phases in which the materials act as a constituent unit, resembling atoms in usual solids. Fullerenes usually form the closed-pack or nearly closed-pack forms in condensed phases, which has been ascribed to their spherical cage structure.15,16 In contrast, planar hydrocarbon molecules possess herringbone structures consisting of columnar units formed by molecules stacking with each other.17,18 In addition to the zero-dimensional materials, CNTs also form a bundle structure caused by their tubular structure.19 Furthermore, these carbon nanomaterials can also form heterogeneous hybrid © 2015 American Chemical Society

structures that possess interesting structural morphologies and electronic properties. For example, CNTs can encapsulate fullerenes and coronenes inside of their internal space with nanometer diameter, leading to nanocarbon complexes with mixed dimensionality.20−24 These complexes possess unusual electronic and optical properties that are not the simple sum of those of each constituent because of the substantial interaction between constituent units.25−27 Recently, oligoarene molecules with a nanohoop structure have been synthesized as an example of the shortest CNTs.28−31 Novel inclusion compounds can be designed by inserting fullerene molecules into the internal spaces of these hoop-shaped oligoarene molecules.32−35 The hybrid networks of hoop and hollow-cage molecules are expected to have peculiar mechanical and electronic properties that may be suitable for the constituent units of future molecular devices. Thus, in the present work, we aim to theoretically design a nanoscale model of Saturn by assembling C60 and cyclohexabiphenylene (CBP), which possesses a ring structure of six hexagonally connected biphenyl groups, based on energetics using density functional theory. Because of its geometrical analogy between Saturn and the present complex consisting of C60 and CBP, we term the inclusion compound nano-Saturn. Our calculations showed that the nano-Saturn is energetically stable compared with the other known inclusion compounds consisting of C60 and cycloparaphenylene (CPP). Furthermore, the inclusion reaction of C60 is exothermic without any energy barriers during the reaction, indicating that C60 will be spontaneously included inside of CBP if CBP is successfully Received: January 15, 2015 Revised: March 31, 2015 Published: March 31, 2015 8931

DOI: 10.1021/acs.jpcc.5b00449 J. Phys. Chem. C 2015, 119, 8931−8936

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The Journal of Physical Chemistry C synthesized. In addition to the nano-Saturn, CBP is found to be more stable than [12]CPP; therefore, CBP may be able to be synthesized using appropriate synthesis procedures.

Table 1. Relative Total Energies of Nano-Saturn with Staggered and Flat Conformations and the Total Energies of C60 Included in CPP (CPP ⊃ C60) with Staggered and Flat Conformations Calculated Using GGA and vdW-DF2 Exchange−Correlation Functionalsa

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CALCULATION METHODS All calculations were performed within the framework of density functional theory36,37 using the Simulation Tool of Atom TEchnology (STATE).38 For the calculation of the exchange−correlation energy among interacting electrons, we used the generalized gradient approximation (GGA) including the spin degree of freedom with functional forms of Perdew− Burke−Ernzerhof (PBE).39 To describe the weak dispersive interaction between C60 and CBP, we considered the van der Waals (vdW) interaction by treating vdW-DF2 with the C09 exchange−correlation functional.40−42 Vanderbilt ultrasoft pseudopotentials were used to describe electron−ion interactions. The valence wave functions and charge density were expanded using plane wave basis sets with cutoff energies of 25 and 225 Ry, respectively. Structural optimization was performed until the remaining forces on each atom were less than 5 mRy/Å, which allows us to discuss the total energy of the complexes within the numerical accuracy of 10 meV.43 To simulate an isolated nano-Saturn complex, we considered a supercell with a rectangular parallelepiped whose cell size are 32.8, 32.8, and 15.9 Å. With the choice of the unit cell, the nano-Saturn is separated by 12 and 7 Å of vacuum spacing, with its adjacent periodic images along lateral and normal to the ring, respectively. Integration in the first Brillouin zone was carried out using Γ point sampling.

saturn (staggered) saturn (flat) CPP ⊃ C60 (staggered) CPP ⊃ C60 (flat)

GGA (eV)

vdW-DF2 (eV)

0 0.65 1.31 1.79

0 1.02 1.71 2.41

a

Energies are measured from that of the nano-Saturn with the staggered conformation.

Table 2. Inclusion Energies of the Nano-Saturn with Staggered and Flat Conformations and the Total Energies of CPP ⊃ C60 with Staggered and Flat Conformations Calculated Using GGA and vdW-DF2 Exchange− Correlation Functionals saturn (staggered) saturn (flat) CPP ⊃ C60 (staggered) CPP ⊃ C60 (flat)

GGA (eV)

vdW-DF2 (eV)

0.37 0.22 −0.10 −0.16

−0.61 −0.55 −0.64 −0.57

ascribed to the fact that the inner space of the ring is too small to readily accommodate C60. Furthermore, because of the small space in the ring with a flat conformation, the ring is slightly dislodged from the equator of C60 in the metastable structure. Note that the staggered structure retains its conformation and is not destabilized under the ambient condition because the energy difference between the ground and metastable states is too large to induce the structural reconstruction from the staggered to flat conformations at room temperature. By comparison with the other C 60 inclusion compounds synthesized to date, we found that the total energy of the nano-Saturn is lower than that of C60 included, for example, in [12]CPP ([12]CPP ⊃ C60) by about 1−2 eV. Thus, nanoSaturn is an energetically favorable structure for a complex consisting of C60 and CBP and is expected to be stable under appropriate conditions by analogy with the [12]CPP ⊃ C60. It is important to investigate the energetics of the formation process of the nano-Saturn. The inclusion energy ΔE of the following inclusion reaction is evaluated in Table 2.

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RESULTS AND DISCUSSION Figure 1a and b shows the optimized structure of nano-Saturn in the ground and metastable states, respectively. As listed in

CBP + C60 → nano‐Saturn − ΔE

We found that this inclusion reaction is exothermic with energy gains of 0.61 eV for the vdW-DF2 calculation for the staggered conformation. For the flat conformation, the reaction is still exothermic and has energy gains of 0.55 eV for the vdW-DF2 exchange−correlation functional. Note that the GGA could not reproduce the vdW interaction between sp2 carbon materials. Interestingly, although the contact area between C60 and CBP is ultimately small (atom thickness), the formation energy is comparable to that of the [12]CPP ⊃ C60 compound. Furthermore, the formation energy is about one-third that of conventional C60 peapods (ΔE ≈ 1.90 eV26). This large inclusion energy for CBP is ascribed to the cooperation between the vdW and CH/π interactions between C60 and CBP. To further discuss the energetics of the synthesis of the nanoSaturn, we calculated the energy potential surfaces for the

Figure 1. Top and side views of optimized structures of C60 included within CBP with (a) staggered and (b) flat conformations. Gray and white circles denote H and C atoms, respectively.

Table 1, the CBP possesses a staggered arrangement in the ground state, while the flat conformation of CBP has a higher total energy than the staggered conformation by 0.64 and 1.02 eV determined using GGA and vdW-DF2 exchange− correlation functionals, respectively. The higher total energy of the metastable structure than that of the ground state is 8932


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The Journal of Physical Chemistry C

Figure 2. Total energies of the nano-Saturn with (a) staggered and (b) flat conformations as a function of the C60 position along the z axis corresponding to the molecular axis of CBP molecules using the local density approximation. The energies are measured from the sum of those of C60 and CBP.

with a flat conformation, the center of the CBP is energetically unfavorable because of the steric hindrance of phenyl groups (Figure 2b). To realize the nano-Saturn, it is necessary to investigate the possibility of CBP from an energetic viewpoint. Table 3 shows the total energy of CBP and [12]CPP. CBP with a staggered conformation is more stable than CBP with a flat conformation. Furthermore, CBP with the staggered conformation also has lower total energy than that of [12]CPP with staggered and flat conformations by 1.6 and 1.8 eV, respectively. Therefore, CBP possesses the same or higher stability than CPP; therefore, it should be possible to synthesize CBP under appropriate conditions. Because of its structural analogy to CPP, it is likely to synthesize CBP using a similar procedure to that for CPP.44 A previous experiment shows that cyclic oligophenylene molecules with alkyl groups were synthesized using a crosscoupling technique.45,46 Note that the cyclic oligophenylene molecules with chemical functional groups are not suitable for the use of the nano-Saturn’s ring because of the steric hindrance of the functional groups. Finally, we investigated the electronic structure of the nanoSaturn. Figure 3 shows the energy levels of the nano-Saturn

Table 3. Relative Total Energies of CBP with Staggered and Flat Conformations and the Total Energies of [12]CPP with Staggered and Flat Conformations Calculated Using the GGA Exchange−Correlation Functionala GGA (eV) CBP CBP CPP CPP

(staggered) (flat) (staggered) (flat)

0 0.79 1.78 2.31

a

Energies are measured from the energy of CBP with a staggered conformation.

inclusion reaction of C60 into CBP. As shown in Figure 2a, the energy monotonically decreases without any energy barriers as C60 approaches the optimum position at the center of CBP. Thus, C60 is spontaneously incorporated inside of the inner space of CBP to form a compound with a structure resembling Saturn. Because the inclusion energy for nano-Saturn is almost the same as that for CPP ⊃ C60, a similar synthetic procedure to that used to synthesize CPP ⊃ C60 should be suitable to synthesize the nano-Saturn.44 In the case of the nano-Saturn

Figure 3. Electronic energy levels of (a) nano-Saturn with a staggered conformation, (b) nano-Saturn with a flat conformation, (c) CBP with a staggered conformation, (d) CBP with a flat conformation, and (e) the C60 molecule. The energy is measured from the vacuum level. HO and LU denote the highest occupied and the lowest unoccupied states, respectively. 8933


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(Figure 3b) conformations, respectively, which are narrower than those of staggered CBP (Figure 3c), flat CBP (Figure 3d), and C60 (Figure 3e). Therefore, the electronic states near the gap of nano-Saturn possess the character of both constituent units. To determine the character of each state, we analyzed the squared wave functions of the HO and LU states of nanoSaturn with staggered and flat conformations. Figure 4a−d shows the HO and LU states of nano-Saturn with the staggered conformation and those with the flat conformation, respectively. We find that HO and LU states are distributed on the CBP and C60, respectively, for both conformations. Further investigation of the squared wave function for each electron state revealed substantial hybridization between the electron states of CBP and those of C60 (Figures 5 and 6) in the case of the nano-Saturn with the staggered conformation. Therefore, nano-Saturn with a staggered conformation may exhibit different optical properties from those observed for each constituent unit. In contrast, because of the smaller contact area in the flat conformation, the hybridized nature is absent and the state retains its isolated nature. Thus, in the case, the spectra may be the simple sum of those of C60 and CBP.

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SUMMARY We theoretically designed the nanocarbon Saturn as a possible inclusion compound by combining C60 and CBP based on total energy calculations using density functional theory. Our calculations corroborated that nano-Saturn is energetically stable compared with the other inclusion compound consisting of C60 and CPP. More importantly, the formation reaction of nano-Saturn is exothermic without any energy barrier during the inclusion process. Thus, C60 and CBP could easily form the Saturn structure, which should be stable under appropriate environmental conditions. In addition to nano-Saturn, we also investigated the possibility of CBP, which is an important unit of nano-Saturn, by evaluating its total energy and found that

Figure 4. Isosurfaces of squared wave functions of the (a) HO and (b) LU states of nano-Saturn with a staggered conformation. Isosurfaces of squared wave functions of the (c) HO and (d) LU states of nanoSaturn with a flat conformation.

with staggered and flat conformations together with those of isolated C60 and CBP. The energy gaps between the highest occupied (HO) and lowest unoccupied (LU) states of nanoSaturn are 1.2 and 0.9 eV for the staggered (Figure 3a) and flat

Figure 5. Isosurfaces of squared wave functions of the valence bands near the highest occupied states of nano-Saturn with the staggered conformation. HO and HO−n denote the highest and the (n − 1)-th highest occupied states of the nano-Saturn with the staggered conformation. 8934


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Figure 6. Isosurfaces of squared wave functions of the valence bands near the highest occupied states of nano-Saturn with the staggered conformation. LU and LU+n denote the lowest and the (n + 1)-th lowest unoccupied states of the nano-Saturn with the staggered conformation. (7) Hamada, N.; Sawada, S.; Oshiyama, A. New One-Dimensional Conductors: Graphitic Microtubules. Phys. Rev. Lett. 1992, 68, 1579− 1581. (8) Saito, R.; Fujita, M.; Dresselhaus, M.; Dresselhaus, G. Electronic Structure of Chiral Graphene Tubules. Appl. Phys. Lett. 1992, 60, 2204−2206. (9) Tanaka, K.; Okahara, K.; Okada, M.; Yamabe, T. Electronic Properties of Bucky-tube Model. Chem. Phys. Lett. 1992, 191, 469− 472. (10) Okada, S.; Oshiyama, A. Nanometer-Scale Ferromagnet: Carbon Nanotubes with Finite Length. J. Phys. Soc. Jpn. 2003, 72, 1510−1515. (11) Sawamura, M.; Kawai, K.; Matsuo, Y.; Kanie, K.; Kato, T.; Nakamura, E. Stacking of Conical Molecules with a Fullerene Apex into Polar Columns in Crystals and Liquid Crystals. Nature 2002, 419, 702−705. (12) Matsuo, Y.; Nakamura, E. Syntheses, Structure, and Derivatization of Potassium Complexes of Penta(organo)[60]fullerene-Monoanion, -Dianion, and -Trianion into Hepta- and Octa(organo)fullerenes. J. Am. Chem. Soc. 2005, 127, 8457−8466. (13) Matsuo, Y.; Nakamura, E. Selective Multi-addition of Organocopper Reagents to Fullerenes. Chem. Rev. 2008, 108, 3016−3028. (14) Nitta, H.; Matsuo, Y.; Nakamura, E.; Okada, S. Magnetic Properties of Deca-Methyl Fullerenes: Radical Spin Interaction on Chemically Functionalized Fullerenes. Appl. Phys. Express 2013, 6, 045102. (15) Kratchmer, W.; Lamb, L. D.; Fostiropoulis, K.; Huffman, D. R. Solid C60: A New Form of Carbon. Nature 1990, 347, 354−358. (16) Saito, S.; Oshiyama, A. Cohesive Mechanism and Energy Bands of Solid C60. Phys. Rev. Lett. 1991, 66, 2637. (17) Fawcett, J. K.; Trotter, J. The Crystal and Molecular Structure of Coronene. Proc. R. Soc. London, Ser. A 1966, 289, 366−376. (18) Scott, L. T.; Hashemi, M. M.; Meyer, D. T.; Warren, H. B. Corannulene. A Convenient New Synthesis. J. Am. Chem. Soc. 1991, 113, 7082−7084. (19) Thess, A.; Lee, R.; Nikolaev, P.; Dai, H.; Petit, P.; Robert, J.; Xu, C.; Lee, Y.; Kim, S.; Rinzler, A.; Colbert, D.; Scuseria, G.; Tománek, D.; Fischer, J.; Smalley, R. Crystalline Ropes of Metallic Carbon Nanotubes. Science 1996, 273, 483.

CBP is more stable than [12]CPP by about 1 eV per molecule. Thus, it is plausible that CBP could be synthesized using a similar experimental technique to that employed to prepare CPP.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81(0) 298535921. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We would like to thank Dr. Cuong for fruitful discussions. This work was supported in part by CREST, the Japan Science and Technology Agency, and a Grant-in-Aid for scientific research from the Ministry of Education, Culture, Sports, Science and Technology of Japan. Computations were performed on an NEC SX-8/4B at the University of Tsukuba, NEC SX-9 at the Institute for Solid State Physics, The University of Tokyo, and NEC SX-Ace at the Cybermedia Center, Osaka University.

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Nano-Saturn: Energetics of the Inclusion Process of C60 into

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