Chapter 2 Epoch-Making Simulation

Large Scale Simulations for Carbon Nanotubes
Project Representative

Satoshi Nakamura

Research Organization for Information Science & TechnologyAuthors
1112

Satoshi Nakamura* , Takumi Araki* , Syogo Tejima* , Yoshiyuki Miyamoto* and1Hisashi Nakamura**1 Research Organization for Information Science &Technology (RIST)*2 National Institute of Advanced Industrial Science and Technology (AIST)
Nanosystem Research Institute (NRI)
CARBON NANOTUBE RESEARCH GROUP

Morinobu Endo, Eiji Osawa, Atushi Oshiyama, Yasumasa Kanada, Susumu Saito,Riichiro Saito, Hisanori Shinohara, David Tomanek, Tsuneo Hirano, Shigeo Maruyama,Kazuyuki Watanabe, Takahisa Ohno, Yutaka Maniwa, Yoshikazu Fujisawa,
Yoshiyuki Miyamoto, Hisashi Nakamura
Our study consists of two parts: development of a model and application of different models that had been optimized by ourgroup for the Earth Simulator. The first one is developing a new ab-initio method for treating finite-temperature systems. For thesecond one, we present the simulation results of the following three studies: (1) ability of CNT adsorbing Cesium in the environment,(2) CNT dynamics under pulse laser, and (3) simulation of Helium Ion Microscope of grapheme.
Keywords: Large scale simulation, ab-initio theory, Time-dependent DFT, Carbon Nanotube, Fullerenes, Graphene,
photoelectric material

2. Development of a model

1. INTRODUCTION
Nano-carbon materials such as nanotube, fullerene andThe linear combination of atomic orbitals (LCAO) method

graphene have potential for applications to the advanced

is one of the most powerful theoretical methods for computing

industries. For nano-carbon materials, it has been recognized

the electronic structure of materials. The conventional LCAO

that large-scale simulation is a powerful and efficient tool to findmethod, however, is formulated for ground-state systems withand create novel functional nano-carbon materials.

a fixed number of electrons. This makes it difficult to extract

Our aim is to investigate fundamental properties of nano-finite-temperature properties from those calculations. In thescale phenomena and to design nanostructure materials, using

preceding year, we have extended the LCAO method to finite

Earth Simulator. To this end, so far we have developed differenttemperature with the Mermin functional and developed codelarge-scale simulation models, including tight-binding molecular

to implement our method. The aim of the present study is todynamics model, ab-initio density functional theory (DFT)

optimize the simulation code corresponding to two-electron

model, and time-dependent DFT model.

repulsion integral which accounts for more than 90 percent of

Our subjects in the current year are classified into two

the total computation time. The procedure of the optimization

categories: development of a model and application of different

is as follows: (i) The six-fold integral in two electron repulsion

models that had been optimized by our group for the Earthintegral is transformed into five-fold summation and one-fold

Simulator. The first one is developing a new ab-initio method

integral as shown in eq. (1). (ii) Dividing five-fold summation

for treating finite-temperature systems. The second one contains

into two groups consisting of two-fold, and three-fold

the following three physical studies: (1) ability of adsorption

summation, we can perform effective calculation using vectorof radioactive cesium on carbon-nanotube (CNT), (2) CNT

processors. As a result, the computation time is reduced bydynamics under pulse laser, and (3) simulation of helium ion

about a third.

microscope of graphene.

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Annual Report of the Earth Simulator Center April 2012 - March 2013

Fig. 1 Bond dissociation potential for F2 molecule at T=300 K.

molecules rather than five ones. If Cs is Cs+ in the mixture ofAM+’s as Na+ and K+, the effect of Na+ or K+ on CNT adsorbing
Cs+ is small. In Fig. 3, the Cs+ cluster breaks a bond of with(1)one of three water molecules and then CNT adsorbs the Cs+cluster. But the K+ cluster stays in the initial position and isAs further development of the above method, we propose a new

not adsorbed on CNT. The Cs reacting with water vapor in air

type of self-consistent scheme beyond the GW approximation,

becomes to the compound of CsOH. CNT cannot adsorb CsOH.

which we call modified GW approximation. As an example,

It should be noted that CsOH is easily dissolved and ionized inFig. 1 shows the bond dissociation potential for the F 2water. Through adsorbing Cs+ or the ionized state, CNTs suchmolecule. According to the Hartree-Fock approximation, theas SWCNT and DWCNT can be basically applicable for theF2 molecule does not exist at all, whereas the fact is that it

environmental remediation of the radioactive products as inexists and is known. On the other hand, when the modified GW

river, lakes, marshes and coasts.

approximation is used, its bond dissociation potential has anenergy minimum and provides a reasonable description of theF2 molecule. This result indicates that our scheme includes theeffects of electron correlation in an appropriate way.

3. Physical studies on nano carbon-based materials
3.1 The ability of CNT adsorbing Cesium in theenvironment
For investigating the applicability of nanocabons to theenvironmental remediation, CNT has been studied on theadsorption for Cesium (Cs) by the first principle calculation.
Our simulations give results that there are no clear differences
between a single or double walled CNT (SWCNT, DWCNT).
But the adsorption becomes strong as the CNT radius decreases,or curvature increases. Furthermore, applicability of CNT isinfluenced in the environment. A metal or atomic state of Cs
in vacuum space can be well adsorbed on CNT. A ionic stateof Cs+ as in water or seawater environments can be also welladsorbed on CNT. Figure 2 shows that Cs +’s with three or

Fig. 2 Two Cs+ adsorption with twenty water molecules. CNT adsorbs

four water molecules are well adsorbed on CNT. This implies

the Cs+ equilibrated with three or four water molecules rather
than five ones.

+that CNT adsorbs Cs equilibrated with three or four water138

Chapter 2 Epoch-Making Simulation

Fig. 3 In the Cs+ case in (a), the Cs+ cluster is leaving a water molecule and is adsorbed stably on CNT, taking with the rest of water molecules. On
the other hand, K+ in (b) shows that K+ bonds easily with water molecules and becomes more stable structure than that adsorbed on CNT.

3.2 CNT dynamics under pulse laser

emission and limit of resolution of HIM with a thin beam-size

Last year we investigated the possibility of applying CNTof He ion. (This work was published in PRL, Vol. 109, 265505

as testing-tube of photochemical reactions of molecules insidein 2012.) Figure 5 (a) shows intensity of secondary emitted

CNT (Publications in PNAS, Vol. 109, 8861 in 2012, and PRL,

electron as a function of He-impact point (white color means

Vol. 105, 248301 in 2011). This year, for practical purpose, wehighest intensity and dark green means lowest intensity). Figure

investigated the toughness of CNT against a strong pulse laser

5 (b) shows similarity of valence charge density of graphene topulse According to the first-principles simulation, very shortthe HIM image. The current result shows feasibility of taking

pulse can induce large radial deformation on semiconducting

lattice image of graphene by HIM with narrower beam-size andCNT, and interestingly, a larger diameter (14,0) CNT was foundrecognition of presence of defects.

to be weaker than smaller diameter (8,0) tube as denoted byFig. 4, which shows radial breathing motion of (8,0) and (14,0)
CNTs under a pulse laser shot.

3.3 S i m u l a t i o n o f H e l i u m I o n M i c r o s c o p e o fgrapheme[1]The Helium Ion Microscopy (HIM) is newly developed
experimental technique, which has recently applied for imaginggraphene devices. The imaging is made by counting secondary
emitted electron upon impact of fast He ion on the sample as
a function of impact position. We has performed electron-ion

Fig. 5 (a) Simulated HIM image and (b) valence charge density ofgraphene.

dynamics simulation to clarify the physical origin of electron

4. Summary
We have developed a new computational scheme based on
the preceding year’s study. We also have performed large-scale
simulations for nano materials by using large-scale simulation
models, including ab-initio DFT model and time-dependent
DFT model. Our achievements are summarized as follows:(a) We optimized our simulation code to calculate freeenergy of systems at finite-temperature systems based on
the LCAO method. Furthermore, we developed a new
type of electron correlation technique for a more accurate
calculation of the free energy.
(b) W e p e r f o r m e d t h e a b - i n i t i o s i m u l a t i o n f o r t h eapplicability of CNT to the environmental remediation.

Fig. 4 Expansion of diameter of (a) (8,0) CNT and (b) (14,0) CNT upon

CNT was studied on the mechanism of adsorption and its

applying ultra- short laser pulse with perpendicular polarization
to tube axis.

ability for Cesium in the environment. It turned out that139

Annual Report of the Earth Simulator Center April 2012 - March 2013

References

CNT has applicability to environmental remediation.
(c) W e a r e e x p l o r i n g t h e a p p l i c a t i o n o f C N T a s[1] H. Zhang, Y. Miyamoto and A. Rubio, “Ab initio simulation

photochemical test-tube. The simulation tool for electron-of helium-ion microscopy images: The case of suspended

ion dynamics were applied for testing stability of carbon

grapheme”, Phys. Rev. Lett. 109, 265505 (2012).

nanotube (CNT) against strong laser field.
(d) We examined feasibility of measuring graphene by
newly developed experimental technique (Helium IonMicroscopy), which will be powerful tool to characterizefabricated devices made of graphene.

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Chapter 2 Epoch-Making Simulation

カーボンナノチューブの特性に関する大規模シミュレーション
プロジェクト責任者

中村賢

高度情報科学技術研究機構

著者

中村賢 * ，荒木1

拓海 * ，手島1*1

高度情報科学技術研究機構*2

産業技術総合研究所

正吾 * ，宮本1

良之 * ，中村2

壽*1

ナノシステム研究部門

1. 研究目的
優れた物性が予想されたナノテクノロジーの基本材料であるナノ炭素類（カーボンナノチューブ（CNT）、フラーレン、グラフェン）を対象として、熱伝導、機械特性、新奇な物質であるマッカイ構造体の生成パス、次世代 CPU の CNT 配線における電磁作用の影響など、実験では得がたい物理現象、新物質創成法、新機能発現法を大規模な第一原理・強結合近似動力学シミュレーションによって明らかにし、その成果を学界、先端産業へ提供するとともに、地球シミュレー
タの性能を実証する。加えて、ナノ炭素類の新奇特性を人類的課題である温暖化対策としての環境技術・新エネルギー開発に役立てる大規模シミュレーション研究を実施する。
2. 成果
本研究により産業応用、学術応用、計算科学に係わる以下のような成果をあげることができた。
(1) 計算律速となる２電子積分計算のアルゴリズムを見直し、高精度化を図るとともに高速化を行った。原子数が多くなると、４つの分子軌道の組み合わせが増えるために、２電子積分の計算量は膨大となる。そこで２つの分子軌道から構成される項を事前に並列計算して配列に格納し、その配列を計算に用いることで、高速かつ効率良く２電子積分を計算することが可能になった。また強相関電子系の電子状態を適切に記述するために、電荷揺らぎに基づく電子相関を考慮したポスト - ハートリー - フォック法の開発を行った。
(2) ナノ炭素類の環境回復への利用の調査として、第一原理計算コードを用いて CNT のセシウム（Cs）吸着特性を調べた。
吸着における CNT 特性の効果は、単層 CNT（SWCNT）、二層 CNT（DWCNT）のような構造間での明確な違いはないが、CNT の半径の減少もしくは曲率の増大に伴い CNT の Cs 吸着能力が強くなることが分かった。環境の効果について
は、Cs の状態が CNT の吸着能力評価の判断要因になることが分かった。Cs が真空中で金属状態もしくは原子状態にある場合、CNT は Cs を非常に良く吸着する。また Cs の状態がイオン状態（Cs+）である水中もしくは海水中においても、CNT は Cs を吸着する。特に海水中では Cs+ が他のアルカリ金属イオン（Na+、K+）と混在している海水中では、Na+ と K+ は CNT の Cs 吸着を妨げる大きな要因とはならないことが分かった。また Cs が水酸化セシウム（CsOH）等の化合物を生成する大気中では、CsOH は CNT に吸着しない結果となった。
(3) 昨年度は、CNT をナノ試験管として内部にアセチレン分子ダイマーをいれてレーザーパルスを照射した場合と、直接照射した場合との反応を比較した。本年度は、応用の限界を見極めるために、レーザーによる試験管たる CNT へのダメージの直径依存性を調べ、直径の細いチューブの方が耐性は高いという結果を得た。
(4) ヘリウムイオン顕微鏡（HIM）像を予測する計算技術を開発し、グラフェンの格子像を観測するために必要な HIMの解像度を求めた。シミュレーションを応用した結果、ヘリウムイオンのビーム径を小さくすることで高解像度のグラフェン格子像が観察できる可能性があることが判明した。
キーワード : 第一原理手法 , 時間依存 DFT, カーボンナノチューブ , フラーレン , グラフェン , 光電材料

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