第一原理量子状態計算コード”Naniwa”の開発と研究事例
Quantum adsorbed states of hydrogen isotope
atoms on graphene
H. Nakanishi, H. Kasai
Division of Precision Science & Technology and Applied Physics,
Graduate School of Engineering, Osaka University, JAPANA02-7：プロトン・ミューオンで探る新物性と量子ダイナミクス
ビルデ マーカス＠東京大学生産技術研究所
パラジウム(110)表面における水素吸収の機構
Hydrogen absorption mechanism at the palladium (110) surface
後藤英和＠大阪大学工学研究科
多体系量子状態計算手法の開発

下司雅章＠大阪大学ナノサイエンスデザイン教育センター
AlH3の圧力誘起金属－半導体転移及び希土類水化物の高圧下での構造安定性

第一原理量子状態計算コード”Naniwa”の開発と研究事例
Quantum adsorbed states of hydrogen isotope
atoms on graphene
H. Nakanishi, H. Kasai
Division of Precision Science & Technology and Applied Physics,
Graduate School of Engineering, Osaka University, JAPAN山梨大学

鳥養 映子
Amba Datt Pant.

Hydrogen storage technology
It is required for the green hydrogen economy
・Compressed hydrogen・Liquid hydrogen
・Metal Hydride・・・・・・
http://www.hydrogen.energy.gov

More efficient, safety, economy, moderate condition, environmentally friendly
technology are strongly pursued.
Graphite or graphene based hydrogen storage
C:H = 1:1,

Hydrogen storage weight ratio is 7.69 w%

Desired target values:
DOE (United States Department of Energy) :IEA (International Energy Agency) :Over 6 w% @ under 100℃
5.0 w％@ 80℃

“Identifying Hydrogen Atoms on Graphite”
T. ROMAN, W. A. DINO, H. NAKANISHI, H. KASAI, K. NOBUHARA, T. SUGIMOTO, and K. TANGE

Journal of the Physical Society of Japan
Vol. 76, No. 11, November, 2007, 114703

High-uptake graphene hydrogenation: a computational perspective
T Roman, W A Dino, H Nakanishi and H Kasai

J. Phys.: Condens. Matter 21 (2009) 474219

Realizing a Carbon-Based Hydrogen Storage Material

T. Roman, et al., JJAP. 45,(2006) 1765.

We want to treat the quantum behavior of the hydrogen in thematerial. Hydrogen is one of the key element for the futuretechnology.
“energy technology”, “biotechnology”

M Proton  melectrolytehydrogen bondaqueous solution

Photosynthesis

biochemistry

Enzyme catalysis

Conventional ab initio simulations can treat electrons by quantum
mechanics. We have been developing the quantum simulation code7
for both the nuclei and electrons, Naniawa: 浪速.

What is Naniwa ?
• NANIWA is a computational code for performing firstprinciples quantum mechanical calculations.
• Two kinds of Naniwa codes in Kasai lab.
Naniwa for quantum reaction: It is a quantum mechanicalversion of the first principles molecular dynamics (MD)calculations, for reactions.
“we can solve the scattering problems, and obtain the probability of some events,adsorption, desorption, reflection, excitation, etc.”

Naniwa for quantum state: It is a nucleus version of the firstprinciples quantum state calculations.
“We can solve the eigenvalue problem, and obtain the eigenstates and their eigenenergies
for atom (nuclear) motion”

8Our quantum simulation scheme: NaniwaInteractions between nucleus is calculated
by DFT based first principle calculations

Potential energy
for nucleus motions: U n (R)Solve the Schrödinger
equation for nucleus
motionWave function for
nucleus motion

Derive thevarious
physicalquantities-Parameters are only
atomic number of elements-No fitting and no artificial procedure
9Comparison between our simulation Naniwa-Staticand experimental results

Calculate the Eigen states
for the atomic motions

Surface-normal vibrationenergy of Hydrogen atomadsorbed on Cu(111) surface
Our simulation
result *135 meVExperimental
data **

129 meV

5% error*K. Nobuhara et al., J. Appl. Phys. 96 (2004) 5020.

for Excited stateElectron energy loss spectroscopy (EELS)**G. Lee, et al., Surf. Sci. 498 (2002) 229.

No fitting parameters
10 !

Comparison between our simulation Naniwa and experimental results
Surface-normal vibration excitation energy of hydrogen atom adsorbed on metal surface

NaniwaExperiment

Error

H on Cu(111)

135 meV

129 meV*

4.7%

D on Cu(111)104 meV

96 meV

8.3%

isotope effect

1.29*K. Nobuhara
1.34et al., J. Appl. Phys. 96 (2004)
3.4% 5020.

Ratio in harmonic potential is2 = 1.414*G. Lee, et al., Surf. Sci. 498 (2002) 229.

NaniwaH on Pd(111)

Experiment

124 meV**

114 meV

Error

8.1%

** H. Conrad, et al, J. Vac. Sci. Technol. A5, 452 (1987).

Less than 10% error
Ground state

Vivrational excited state

No fitting parameters !

Electron energy loss spectroscopy (EELS)*Comparison between our simulation Naniwa and experimental results
Momentum distribution of adsorbed hydrogen atom is observable in its ground state.

NRA : Nuclear Reaction Analysis

NaniwaK. Fukutani et al., PRL 48(2002)116101.

(Positive) muon μ＋Positive muon catches an electron, and forms
the hydrogen like atom.

Particle statistics

Fermionic

Mass:

105.658369(9) MeV/c2

mμElectric charge:

eSpin:

1⁄
2

Mean lifetime : τ2.19703(4)×10−6 sec

μ+＋e−
Muonium
Its reduced mass and magnetic
moment is different from ahydrogen atom.
Isotope of hydrogenmμ ～(1/9) mp～ 207 me

μ＋ Antimuon -------> positron ＋ Antimuon neutrino ＋ electron neutrinoLife time: τ～2.2μsec

Muon spin spectroscopy：μSR

Spin:1⁄2

positron emission------->The primary decay mode of a pion is a purely
leptonic decay into a muon and a muon neutrino.
And the muon is 100% spin polarized

Gyromagnetic ratio ：135.53 MHz/T

precession movement in
the magnetic moment
sensitive magnetic measurement13μSR time spectrum.
e+ detector

e+B
Fouriertransformation

precession movement

In the material
Muon plays as the small-mass proton with acommunication function.
We can detect the quantum behaviors ofHydrogen-like particles in material.

K. Shimomura et al., Phys. Rev. Lett. 89 (2002) 255051.

14

μSR time spectrum.
e+ detector

e+B
Fouriertransformation

precession movement

In the material
Muon plays as the small-mass proton with acommunication function.
We can detect the quantum behaviors ofHydrogen-like particles in material.

K. Shimomura et al., Phys. Rev. Lett. 89 (2002) 255051.

15

For electron
Hydrogen coverage: 1/18= 5.6%
Supercell: Slab model, 3x3 graphene units
with dipole correction parallel to c-axis
Spin: Polarized calculationk-sampling points: 5x5x1
GGA: Perdew-Burke-Ernzerhof (PBE)
Vdw: DFT-D2 method of Grimme
Basis set: plane wave
Cut off energy: 400eV
Code Package: VASP 5.2.12

For nucleus
Supercell: Slab model, 1x1 graphene unit
Potential grid: 20 x 20 x 20
Basis set: 20 x 20 x 20 Gaussians
Symmetry Correction in graphene plane
Code Package: Naniwa (Ver. Syk20130524)

Classical hydrogen adsorbed structure on graphene

Adsorbed site: Top site
Adsorbed type: chemisorption
Adsorbed energy: -0.816 eVHydrogen induces the corrugation ingraphene structure. And the sp3-likecovalent bond is formed betweenhydrogen and carbon atoms.

Relaxed graphene
Potential energy
Adiabatic potential energy for hydrogen on
relaxed graphene

Naniwa results

Eigen energies of positive muon,
proton and deuteron on relaxed
graphene
Quantum adsorbed energy of Muon: -0.22 eV
Quantum adsorbed energy of proton: -0.58eV

Wave function of proton in its ground states

Adsorbed energy: -0.58 eV<2 degenerate energy states > in unit cell

TDS experimental data : -0.59 eV or -0.65eV
X. Zhao, et al., J.Chem.Phys. 124(2006)194704

Wave function of proton in its 1st excited states
Vibrational excited parallel to the graphene plane<4 degenerate energy states > in unit cell

Wave function of muon in its ground stateand 1st excited state
Adsorbed energy: --0.22eV
Split energy: δ = 0.03eV

Wave function of muon in its ground stateand 1st excited state
Adsorbed energy: --0.22eV
Split energy: δ = 0.03eV

Relaxed graphene
Naniwa results
Eigen energies of positive muon, proton and deuteron on relaxed grapheneFlat graphene
Potential energy

Naniwa results

Adiabatic potential energy calculation forhydrogen on fixed flat graphene

Eigen energies of positive muon,
proton and deuteron on fixed flatgrapheneFlat graphene
Potential energy

Wave function for proton
in its ground statewith adsorbed energy: -0.019eV

Naniwa results

Eigen energies of positive muon,
proton and deuteron on freezed
grapheneHow about the charged states of particles
𝑛𝑎 ↑ +𝑛𝑎 ↓ =0,1,H+H0

Muon: μ+Muonium: μ+ + e-2
H-Negative ion : μ+ + 2e-Charged states of target particle on Pd（００１）
By use of Bader analysis<100>

H+ positive<001>

H-0.2negative

1st layer atom
2nd layer atom
3rd layer atommuonium

H0 neutral

Vacuum area27

Electron charge of the proton and anti-muonon Pd (001) surfaces
Ground state+∞

Ψ0 𝑅 for proton

𝑑𝑟 𝜑𝑎↑ (𝑟; 𝑅)

Ψ0 𝑅 for anti-muon

2+ 𝜑𝑎↓ (𝑟; 𝑅)−∞

Expectation value of electron number on the particle’+∞𝑛𝑎↑ + 𝑛𝑎↓ 𝑛 =+∞𝑑𝑅−∞𝑑 𝑟 𝜑𝑎↑ (𝑟; 𝑅)−∞2+ 𝜑𝑎↓ (𝑟; 𝑅)2∙ Ψ𝑛 (𝑅)22

Electron charge of target particle on Pd（００１）Ground stateCore

Number of electron(Anti)Muon

1.05

Proton1.09

1.2↑ negative ion←neutral atom

Numebr of electron

1.0↓positive ion

0.8
0.6

Anti-Muon

Proton

0.4

0.2
0.0
024

68

1012quantum number

14161820

超微細相互作用

potential energy (eV)for μSR experimentSummary
We have developing the parameter-free quantum simulation code “Naniwa: 浪速”We investigate the quantum adsorbed states of positive muon (Mu +) and hydrogen
atom nuclei (H+, D+) on graphene by our quantum simulation codes, Naniwa .
For hydrogen atom nuclei (H+, D+)
The ground state wave function of hydrogen nucleus adsorbed on graphene isstrongly localized at top site.
The adsorption energy is reduced from that expected by conventional DFTsimulation. “It is more convenient for hydrogen storage usage.”
Vibrational excited states exist around this top site.

For positive muon (Mu+)
There are only two adsorbed states, which are in their ground states.
No vibrational excited state.
Only the ground states can be measured by MuSR experiment.
*We can estimate the hyperfine interactions, which is useful
to know the state of hydrogen isotope on graphene.