Chapter 3 Epoch Making Simulation

Large Scale Simulations for Carbon Nanotubes
Project Representative

Kazuo Minami

Research Organization for Information Science & Technology

Authors

Syogo Tejima 1, Kazuo Minami 1, Satoshi Nakamura 1, Kohji Makino 1,
Yoshiyuki Miyamoto 2, Yoshikazu Fujisawa 3 and Hisashi Nakamura 1
1 Research Organization for Information Science &Technology (RIST)
2 Fundamental and Environmental Research Laboratories, NEC Corporation
3 Honda R&D Co., Ltd
CARBON NANOTUBE RESARCH GROUPE

Morinobu Endo, Eiji Osawa, Atushi Oshiyama, Yasumasa Kanada, Susumu Saito,
Riichiro Saito, Hisanori Shinohara, David Tomanek, Tsuneo Hirano, Shigeo Maruyama,
Kazuyuki Watanabe, Takahisa Ohno, Yoshikazu Fujisawa, Yoshiyuki Miyamoto,Hisashi Nakamura

Nano carbon materials as nanotubes (CNTs) and fullerenes in nanotechnology have a lot of potential for industrial applications. On the efforts of developing applications, it has been recognized that computational simulations are powerful and efficient tools to find and create new materials from nano scale. Aiming at realistic simulations for nonmaterial, we have developed a large-scale computation technique utilizing tight binding molecular dynamic method, ab initio density functional theory (DFT), Generalized Stone-Wales (GSW) rearrangement and time-dependent DFT method. We have studied various physical properties of nano-carbon and applications e.g., (1) Electron-ion dynamics under time-varying external field, (2)Generation of Mackay structure by using GSW rearrangements, (3) Hydrogen adsorption to Transition-metal -decorated CNT,
(4) Growth Mechanism of CNT, (5) Hole-doped diamond superconductor.
In addition to nano carbon as nanotube, diamond and graphite of traditional carbon material were also highlighted. Alongthese works, we have realized that the Earth Simulator is a very powerful tool for large-scale material simulations.
Keywords: Large scale simulation, TB theory, ab initio theory, DFT, Carbon Nanotube, Fullerenes, GSW, CNT growth,
Hydrogen storage, Hole-doped Diamond superconductor

1. INTRODUCTION

equation linearized with respect to the anomalous Green's
function applied to the prediction of high Tc superconductivity for a hole-doped diamond. The Generalized StoneWales rearrangement is used to find new novel nano carbon
structures.
We have carried out some subjects in this work, which aredescribed in the next section. There are three primary objectives with this work: (1) design of innovative nonmaterial
with certain desired properties; (2) obtaining fundamental
properties in nano-scale matter, and (3) nano-applications.
Our purpose is to give the clear explanation of properties
and phenomena of nano-scale events and deduce guiding
principle to design new materials for applications fromnanostructures using super-computers.

Carbon materials have been expected to make a breakthrough in material science and nanotechnology. A lot of
potential applications of nanotubes and fullerenes e.g.,
electronic field emitter and electronic devices have attracted
scientific community. In the investigation and utilizing
their material properties, numerical simulation using supercomputer has turned to be a very efficient tool. A recent
development in nanotechnology has required a more efficient supercomputing being capable of a large-scale simulation of up to 104 atoms. Aiming large-scale simulations
utilizing Earth Simulator, we have developed computational
package based on ab initio DFT theory and parameterizedtight-binding method. The TB code we have developed isshown to be suitable for the very large systems even though
the lack of symmetrical arrangement. The Eliashberg
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2. PHYSICAL STUDIES ON NANOMATERIALS
2.1 Electron-ion dynamics under time-varying external field
By means of the TDDFT, we have developed a computercode for electron-ion dynamics (electron dynamics coupledwith molecular dynamics) in materials under time-varying
external electric field. The code originates from currently
used TDDFT code, which was used for exploring excited state
dynamics in carbon nanotube with use of the Earth Simulator.
The new code can include time-varying external field beyond
perturbation theory which can be applied for a situation ofirradiation with strong and short pulse of laser beam.
Although there already been couples of trials simulating
electron-ion dynamics under time-varying external field, thenumerical accuracy in simulation has not been checked
clearly. In this work, we have found criteria which can guarantee numerical accuracy and stability throughout the simulation by the energy conservation rule. In the molecular
dynamics (MD) simulation, the summation of potential andkinetic energies of all ions (called as U later) must be conserved. This is also the case in electron-ion dynamics. Whena time-varying external field is applied to the system, thequantity U should increase due to the work done by theexternal field. The amount of the increase must be dependent
on the time-dependence and the strength of the external field
as well as intrinsic energy spectrum of the material.
We have found that the amount of increase U can simply
be expressed by following equation within a framework of
TDDFT, where the external field is expressed by the Hartree
potential generated by fictitiously introduced charge density→
ρext (r ) mimicking the external field.

→
Here, ρ (r ) means electron charge and ZI means charge of→→ion I, while r and R I (t) mean coordinates of electrons andions, respectively. By integrating the above equation
with respect to time-axis, the work given by external field iscomputed and the subtraction of the work from U must be
constant.
Next, we demonstrate the numerical stability of our computer code by simulating energy accumulation in graphite
layers by pulse laser. Here the maximum strength of theelectric field is hundred times bigger than typical values ofthe scanning microscope spectroscopy such as 10 eV/Å.
Figure 1(a) shows contour lines of external potential varying
along with a direction normal to the graphite layers. Figure1(b) shows time-dependence of the external-field shown in
Fig. 1(a), which is a combination of Gaussian and sin curves.
With this applied external field, the energy increase ofgraphite is observed up to the simulation time of 6 fs. The
computed size contains 80 carbon atoms with the slab geometry including vacuum region of 10 Å. Figure 2 shows thatthe energy conservation rule still works even with thisunusually strong external field showing robustness of thenumerical accuracy in our computer code. With use of currently developed code, we will investigate response of nanocarbons against irradiation with the Femtosecond laser

Fig. 1 (a) Contour lines of applied potential which gives electric field in normal direction to the graphite layers.
(b)Time-dependence of the applied field shown in (a). The Gaussian envelope is also shown.

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Chapter 3 Epoch Making Simulation

Fig. 2 Time evolution of internal energy of graphite shown in Fig. 1 (a)(blue line), and the same value extracted by integral of dU/dt,
which is shown in an equation in the main text and corresponds
to zero.

beam, and monitor induction of coherent phonon and structural deformation as well as electronic excitations. Thesephenomena will be useful for simulating non-thermal nanofabrication process.

Fig. 3 Snapshot of path (192 atoms times 8 primitive cells).

Energy (calculated by CRTMD)

2.2 Generation of Mackay structure by using GSW
rearrangements
The aim of the research is to investigate whether a certain
nano carbon structure (including fullerenes and carbon nanotubes) is transformed to an objective structure by using
only some sequential GSW rearrangements. Especially, thisresearch can be applied to the process generating a "Mackay
structure". It is expected that the Mackay structure is very
stable and rigid, because it has three-dimensional high-symmetric property. For this reason, many researchers have beeninterested in the structure, and have analyzed its characteristics by the computer simulation. However, the process togenerate the Mackay structure has not been clear yet.
It is known that a Mackay structure can consist of various
numbers of the atoms. We have already found out thesequential process (it is named `path') for two Mackay structure consisting of 48 and 144 atoms. The larger the numberof atoms, the more difficult we find the path. In this report,
the path of a Mackay structure consisting of 192 atoms isfound out newly. Figure 3 illustrates snapshots of the structure (192 atom times 8 primitive cells). The isomerization isrealized by 232 GSW steps. The initial structure is 4-connected CNT shown in Fig. 3 (upper figure). The 4- connected CNT is also used as initial structure of other small
Mackay structures, but the connecting position is different.
We guess that the initial structure of larger size Mackay

Fig. 4 Energy of each structure.

structure is also (8,8) 4-connecting CNT, but that the connecting position is different.
Next, we focus on the energy of the structure. The energyof each structure was calculated by using Huckel method.
However, this method is not sufficient for calculating theenergy of the system. Thus, we adopted the CRTMD insteadof Huckel mehod. This report deals with the structure consisting of 48 atoms, because it is difficult to calculate thestructure consisting of the large number of atoms. The energy of each structure is shown in Fig. 4. Although there isenergy barrier in the path, the barrier is not so high.
Furthermore, the energy of the Mackay structure is lower
than that of initial structure. These results confirm that there
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Annual Report of the Earth Simulator Center April 2007 - March 2008is the possibility of the realization of the Mackay structure.
The energy of paths of other Mackay structures (144and 192 atoms) will be calculated by using CRTMD. We
will investigate the possibility of realization of the Mackay
structure.

duced on the surface of a CNT, Ti atoms tends to form a Ti
cluster by strong bonding force. As for Hydrogen adsorption, some hydrogen molecules are dissociated into individual hydrogen due to a strong chemical adsorption effectinside the Ti cluster shown in Fig. 5. Such an interaction
between Ti atoms changes the properties of Hydrogen
adsorption. The segregation of Ti atoms reduces the weightpercent of storing hydrogen molecule. Finding more advantaged transition metal for hydrogen adsorption, we also
investigated the properties of another transition metals interms of the binding energy between transition metals andthe state of hydrogen adsorption. It is concluded that hydrogen storage materials be able to be synthesized from the firstprinciple molecular dynamics.

2.3 Hydrogen adsorption on Transition-metal -decorated
Carbon Nanotube
Global warming and abnormal weather caused byexhausted gas by fossil fuel are serious environmental problems in the world. Efforts to reduce carbon dioxide gas are
required for environmental protections. In this context theclean energy system such as hydrogen fuel is at a human's
desire. But it would highly cost us enormously under thenecessity of sustaining high pressure or low temperature to
hold it in a tank because of strong quantum effect of hydrogen atom. From safety points it is still under the way to use
such type of fuel for practical application.
The success of hydrogen storage technologies criticallydepends upon discoveries of novel materials that could store
and extract large amounts of hydrogen under economical
and ambient conditions. Finding new materials of storinglarge amount of hydrogen at ambient temperature and relatively low pressures with small volume is crucial for hydrogen fuel storage.
We approached to the hydrogen storage by means of CNT
through the first principle molecular dynamics. The hydrogen adsorption ability on a single Ti covering the surface of
CNT has been reported in papers. However the researchers
are based on an assumption that Ti atoms have never been
segregated on the surface of CNT. The interaction between
Ti atoms is not taken into account in the discussion about theHydrogen storage.
We have carried out a large-scale simulation for hydrogen
and Ti atoms dynamics considering the direct interaction
between Ti atoms on CNT. Our simulation revealed that if
many Ti atoms taken account of Ti-Ti interaction are intro-

2.4 Growth Mechanism of CNT
Controlling growth process of CNT on metallic catalysts
is an essential requirement to provide pure crystalline CNT
for electrical applications as device and wire. There has been
large progress in the experimental production of CWNTs.
Nevertheless, the growth mechanism of pure CNT is still
poorly understood.
As for theoretical calculation, classical molecular dynamics simulations based on empirical potential were mainly
used to study the behavior of metallic Fe nano-particle catalyst and growth of CNT in chemical vapor deposition(CVD). The calculated CNT structures are not complete withlarge number of defects. The results gave rough explanation
for the growth mechanism of CNT and the empirical potential using simulation is under development.
We have carried out the investigation on growth of CNT

Fig. 5 Hydrogen adsorption for CNT. Hydrogen atoms and molecules are
chemically and physically adsorbed on Ti cluster, respectively.

Fig. 6 Structure of interface between Fe cluster and CNT.

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Chapter 3 Epoch Making Simulationfrom first principle MD method. Firstly the conformity of
CNT structure with Fe catalyst cluster was calculated. Iron
catalyst cluster of 55 atoms with γ -phase (FCC) contacting
the up-growth CNT was choose for the initial structure to
start MD. In the simulation, we revealed that nano interface
between Fe cluster and CNT is energetically stable as shownin Fig. 6. The results suggest that if the provided carbon
atoms are flying to Fe surface, the provided carbon atoms
are able to jump into CNT for the growth by advantage ofthe interface. As the next stage we will consider behavior of
the provided carbon through simulation.

porate hydrogen atoms. Under such circumstances, further theoretical and experimental studies will resolve the discrepancy.
As seen from Fig. 7, the value of Tc's are rather sensitive
to the used approximation; therefore in order to improve oursimulation, it is necessary to incorporate the other neglected
effects listed below:(1) Charge fluctuation by the non-linear response to the lattice vibration,(2) Off diagonal elements with respect to orbital of effective
interaction between electrons,(3) Use of the renormalized Green's function in the self-energy.
Henceforth we will take into account these effects.
Our simulation method has marked an important first step
toward estimating Tc's of various superconductors with highaccuracy far beyond the limitation of the previous methods.

2.5 hole-doped diamond superconductor
We have been evaluating the superconductivity of novel
materials on the basis of a new superconducting mechanismthat the interaction between electrons changes from repulsive to attractive through the charge density fluctuationinduced by the lattice vibration.
In the current year, we have developed further this superconducting mechanism, taking into account the time dependence of the bare Coulomb interaction between electrons. Asan application, we investigated that at what temperature ideally hole-doped diamond becomes superconducting. For
quantitative analyses using our scheme, it is inevitable toperform large-scale tight-binding molecular dynamics simulation consisting of at least several thousand atoms; therefore
we executed our scheme on the Earth Simulator. Our code
has been highly tuned to perform calculation on the Earth
Simulator. The sustained performance of 4.82 Tera flops
was achieved for the simulation with 8192 carbon atoms byusing 256 nodes (2048 PEs) of the Earth Simulator. The
resulting computing efficiency is 60.2% of the peak performance. To estimate Tc for a given hole concentration, thesimulation took about 8 hours of computing time.
Our result shown in Fig. 7(b) indicates that pure diamondwith 0.03 holes per atom is possibly the superconductor with
75 K. On the other hand, the Tc's observed in experiments arelower than those estimated by simulation. Recent precise
measurements, however, show that synthesized samples incor-

3. SUMMARY
The large-scale simulations on nonmaterial have been carried out by ab initio density functional method and the parameterized tight-binding calculations. The optimized codes
showed that the computation on the Earth Simulator could
give an exceptional performance and enables us morechance for large-scale and realistic simulations. Our large
scale simulations can provide the nanotechnology industries
valuable information on novel nano material properties andon nano electrical designs for application.

References[1] Y. Miyamoto, Applied Physics Letters, "Ultrafast reconstruction of graphite by irradiating with highly chargedions", Vol.91, p113120 (2007).
[2] Y. Miyamoto, "Deformation of sp2 Graphitic Nanostructure
by Irradiation with Highly Charged Ion", APS March
Meeting (2007).
[3] S. Nakamura, "A New Method for Calculating theDielectric Response Function - Application to hole-doped
diamond superconductors -", International Symposium on
Frontiers in Computation Science of Nanoscale Transport(Poster Session), Tokyo University of Science, Tokyo,

Fig. 7 Tc versus hole concentration in case of (a) neglecting the time dependence of the bare Coulomb interaction,(b) incorporating the time dependence of the bare Coulomb interaction.

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June, 2007.
[4] S. Nakamura, S. Tejima, D. Tomanek, and H. Nakamura,"New Large Scale Simulation for Evaluating
Superconductivity", SC2007, HPCNano07 workshop,
Reno-Sparks Convention Center, Reno, NV, November,
2007.
[5] Y. Miyamoto, Electron-Ion Dynamics throughout
Collision of Highly-Charged Ar on Stacked Graphite andSubsequent Structural Change, Third Symposium on
Computational Challenges and Tools for Nanotubes(CCTN07), Rio de Janeiro, Brazil, June 22, 2007.
[6] S. Tejima, Large Scale Density functional simulation of
Hydrogen adsorption on Carbon, Third Symposium on
Computational Challenges and Tools for Nanotubes(CCTN07), Rio de Janeiro, Brazil, June 22, 2007.

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1

1

1

1

2

3

1

1
2 NEC

CNT

3

1.
CNT

2.
H14
H16 H17 H18

H15
1

TDDFT

2
8,8 CNT
Huckel
CRTMD
3
CNT

4
CNT

CNT
CVD

CNT

CNT
CNT

5

TC
TC
TC

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