quantum effect &temperature dependence on hydrogen ...and suggestion for the most suitable carbon...

Nuclear quantum effect &Temperature dependence on hydrogen adsorption site of Hydrogen store material

1Nanosystem Research institute, National Institute of Advanced Industrial Science and Technology (AIST)2Quantum Chemistry Division, Graduated School of Science, Yokohama‐city University3Institute of Multidisciplinary Research for Advanced Materials, Tohoku University

K. Suzuki1, M. Kayanuma1, M. Tachikawa2, H. Ogawa1, H. Nishihara3, T. Kyotani3, and U. Nagashima1

Hydrogen storage materials

ZTC materials have attracted attention as candidate for hydrogen storage.

Properties required for hydrogen storage materials are•High hydrogen storage capacity•Light weight•Reversible adsorption‐elimination of hydrogen under the moderate condition

AlloysTi compound, Mg compound

Inorganic materialsNaAlH4, LiBH4, NaBH4, etc.

Organic materialsAromatic hydrocarbon

Large surface materialsCarbon materials, Zeolite‐Templated Carbon(ZTC), etc.

Carbon materials

Zeolite‐Templated Carbon (ZTC) developmed by Kyotani group[1‐3]

[1]T. Kyotani, et al., Carbon, 41, 1451(2003). [2] Z. Ma, et al., Chem. Mater., 13, 4413 (2001). [3] H. Nishihara, et al., Carbon, 47, 1220 (2009).

CNT & Fullerene

Graphite

Amorphous

C‐H2 distance1.5~3.0Å

Many strange simulations

7 CNT tubes & many H2molecules with L‐J potential

Graphene & H2 molecules

Basis set dependency of H2-bond distance in Å

Basis set dependency of H2-total energy in a.u.

H2 molecule should be treated as 2H atoms in the electron rich region.

Zeolite‐Templated Carbon

[1]T. Kyotani, et al., Carbon, 41, 1451(2003). [2] Z. Ma, et al., Chem. Mater., 13, 4413 (2001). [3] H. Nishihara, et al., Carbon, 47, 1220 (2009)

Figure 1. High resolution TEM image of ZTC [2].

Zeolite‐Templated Carbon (ZTC) Development by Kyotani group[1‐3]

Large surface areaUniform microporeBuckybowl‐like curved graphene sheet

•Structural properties

•Hydrogen storage capacity2.2 wt% at 34 MPa at 303 K

Understanding of the hydrogen diffusion process, its adsorption siteand suggestion for the most suitable carbon framework are indispensableto improve the hydrogen storage capacity.


[1] H. Nishihara, et al., Carbon, 47, 1220 (2009)

Figure 1. Molecular model is constructed with buckybowl units following the regularity of the zeolite Y templates[1].

Zeolite‐Templated Carbon (ZTC) has been developed by Nishihara et al[1].

Large surface areaUniform micropore

•Structural properties

•Hydrogen storage capacity

2.2%wt 34 at MPa at 300 K

To improve the hydrogen storage capacity, it is an indispensable to 1) understand the hydrogen diffusion process and its adsorption site on carbon,2) determine the most suitable carbon framework.

PurposeTo evaluate the hydrogen adsorption site on Zeolite‐Templated Carbon (ZTC), path integral simulation is performed at 300 K.

I. Building of ZTC model.

II. Based on the result of I, we evaluate hydrogen adsorption site.

•To build efficient model structure, the orbital characters of ZTC are confirmed.

•To accurately evaluate the hydrogen behavior on carbon, some simulations including thermal and nuclear quantum effects are done using a pass integral tequnique.•For comparison, conventional MD simulations also are done.

Zeolite‐Templated Carbon (ZTC) Models

[1] H. Nishihara, et al., Carbon, 47, 1220 (2009)

Figure 3. Hydrocarbon cluster model of C150H36.Figure 2. An idealized molecular model constructed with six buckybowl unit of C36H9[1].

Molecular orbitals for ZTC

Molecular orbital is localized at each buckybowl (C36 unit).

We use C36 unit with hydrogen‐terminated models in this study to analyze the hydrogen adsorption site.

LUMO+1 LUMO HOMO

HOMO‐1 HOMO‐2 HOMO‐3

Level of theory: HF/STO‐3G

Results: Structures of C36H12 and C36H13

Figure 4. Optimized structures of ZTC models with a) C36H12 , adsorbed hydrogen atom on ZTC at b) α‐carbon, c) β1‐carbon, d)β2‐carbon, e) γ‐carbon, and f)δ‐carbon.

a) b) c)

d) e) f)

Nuclear Quantum effecton hydrogen adsorption site

Purpose

Information of the stable/unstable hydrogen adsorption site on ZTC material

Namely path integral simulation at 300 K for quantum mechanical treatment of both electrons and nuclei

Inclusion of thermal and nuclear quantum effects

Method

[4] R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw‐Hill, New York, 1965).

Path integral method [4]

Path integral scheme express N body quantum problem as N×P classical problem.N=2 N(=2) × P(=8)

Nuclear quantum fluctuation is expressed by bead‐expansion.Internuclear interaction is evaluated by the same suffices of beads.

Computational details on simulation

Temperature: 100 K, 300 K, 900 K Time step: 0.1 (fs)Potenatil: PM3Target system: C36H13

Total stepsNumber of beads

[5] M. Shiga, et al., J. Chem. Phys., 115, 9149 (2001). [6] M. E. Tuckerman, et al., J. Chem. Phys., 99, 2796 (1993).

Conventional MD

300 0001

(Classical nuclei)Path integral MD[5,6]

50 00024

(Quantum nuclei)

*There are five different kinds of carbons (α, β1, β2, γ, and δ) inside of buckybowl from outer to inner carbon for additional hydrogen adsorption sites.

Fig. 2. Buckybowl structure (C36H12).

αβ1

β2γδ

αβ1 β2

δγ

b)

αβ1

β2γδ

αβ1 β2

δγ

αβ1

β2γδ

αβ1 β2

δγ

b)

δ

αβ1 β2

γ

Results of conventional MO (Without thermal and nuclear quantum effects)

Binding energy decrease from outer to inner carbon.

Table 1. Binding energies* of C36H12(kcal/mol)α β2 γ δβ1

60.4 32.2 18.3 16.9 4.1

*

Outer carbon Inner carbon

αβ1

β2γδ

αβ1 β2

δγ

b)

αβ1

β2γδ

αβ1 β2

δγ

αβ1

β2γδ

αβ1 β2

δγ

b)

δ

αβ1

β2γ

α‐carbon β2‐carbon

γ‐carbon δ‐carbon

Results of conventional MO (Without thermal and nuclear quantum effects)

sp3‐like structural changes arise around hydrogen adsorption site.

αβ1

β2γδ

αβ1 β2

δγ

b)

αβ1

β2γδ

αβ1 β2

δγ

αβ1

β2γδ

αβ1 β2

δγ

b)

δ

αβ1

β2γ

Results of Conventional MD (Inclusion of thermal effect)

R is distance from the centroid of buckybowl.

α‐carbon

β1‐carbon

β2‐carbon

γ‐carbon

δ‐carbon

R (Å)21 3 4 5 6

Additional hydrogen atom is fluctuating at around the each carbon by thermal effect.Adsorption sites of additional hydrogen are on every carbon .

R

Thermal effect

R (Å)21 3 4 5 6

Results of PIMD (Comparison between conventional and path integral MD)

Fluctuations of path integral MD are larger than that of Conventional MD.Adsorption site of additional hydrogen is not appeared on δ‐carbon.

α‐carbon

β1‐carbon

β2‐carbon

γ‐carbon

δ‐carbon

R (Å)21 3 4 5 6

Thermal and nuclear quantum effects

Trajectory of conventional MD on δ‐carbon

Additional hydrogen atom is fluctuating at around the δ‐carbon by thermal effect, but it does not move to other site.

δ

Hydrogen transfers from δ‐ to β1‐carbon.

δβ1

β2

γ

Trajectory of path integral MD on δ‐carbon

Energy diagram of moving additional hydrogen atom from one to the other carbon

αβ1

β2γδ

b)

αβ1

β2γδ

αβ1

β2γδ

b)

α‐carbon β1‐carbon γ‐carbon δ‐carbonβ2‐carbon

Relativ

e energy (k

cal/m

ol)

0

29.2

42.1 43.5

56.4

48.650.954.1

51.854.1

51.8

61.0 61.4 61.6

Additional hydrogen atom goes over the barrier from δ‐ to β1‐carbon at 300 K.

Conclusion for nuclear quantum effect part

1. Hydrogen atom fluctuates at around the each carbon at 300 K.2. Hydrogen atom adsorbs on α‐, β1‐, β2‐, γ‐, and δ‐carbon.

Thermal effect but quantum effect (300 K, conventional MD)

1. Fluctuations are larger than that of conventional MD.2. Hydrogen atom adsorbs on α‐, β1‐, β2‐, and γ‐carbon at 300 K. (not on δ‐carbon)

Thermal and nuclear quantum effects (300 K, path integral MD)

No thermal and quantum effects (0 K, conventional MO)1. Binding energy decrease from outer to inner carbon.2. Hydrogen atom adsorbs on α‐, β1‐, β2‐, γ‐, and δ‐carbon at 0 K.

Acknowledgements: This work has been supported by New Energy and Industrial Technology Development Organization (NEDO) under “Advanced Fundamental Research Project on Hydrogen Storage Materials”

Both nuclear quantum and thermal effects are indispensable to evaluate the hydrogen adsorption site on ZTC materials.

Information of the stable/unstable hydrogen adsorption site on ZTC material

Temperature dependence on hydrogen adsorption site

αβ1

β2γδ

αβ1 β2

δγ

b)

αβ1

β2γδ

αβ1 β2

δγ

αβ1

β2γδ

αβ1 β2

δγ

b)

δ

αβ1 β2

γ



[1] M. Kayanuma, et al., Chem. Phys. Lett., [2] K. Suzuki, et al., submitted to Comp. Theo. Chem.[3] K. Suzuki, et al., J. Alloys and compd., in press.

Understanding of the hydrogen diffusion process and its adsorption site are indispensableto improve the hydrogen storage capacity of ZTC.

We have already performed some simulations using a model fragment structure of ZTC [1‐3].

Previous works for path integral MD at 300 K

R is distance from the centroid of buckybowl.

α‐carbon

β1‐carbon

β2‐carbon

γ‐carbon

δ‐carbon

21 3 4 5 6R (Å)

Adsorption site is not appeared on δ‐carbon, since additional hydrogen atom goes over the barrier from δ‐ to β1‐carbon at 300 K [3].

However, it is unknown whether adsorption site of hydrogen atom on ZTC is affected by temperature or not.

[3] K. Suzuki, et al., J. Alloys and compd., in press.

R

Purpose

Information of temperature and isotope effects on the stable H/D adsorption site on ZTC material

Namely path integral simulation at various temperatures

Inclusion of thermal and nuclear quantum effects

αβ1

β2γδ

αβ1 β2

δγ

b)

αβ1

β2γδ

αβ1 β2

δγ

αβ1

β2γδ

αβ1 β2

δγ

b)

Computational details on simulation

Temperature: 100 K, 300 K, 900 K Time step: 0.1 (fs)Potenatil: PM3Target system: C36H13, C36D13

Total stepsNumber of beads

[4] M. Shiga, et al., J. Chem. Phys., 115, 9149 (2001). [5] M. E. Tuckerman, et al., J. Chem. Phys., 99, 2796 (1993).

Path integral MD[4,5]

50 00064, 24, 8

(Quantum nuclei)

Fig. 2. Buckybowl structure (C36H12).


Isotope effect at 100 K

α‐carbon

β1‐carbon

β2‐carbon

γ‐carbon

δ‐carbon

*Fluctuations of H species are larger than that of D species due to the difference of zero point energy.*Adsorption site of both H and D is observed at every carbon at 100 K.

C36H13 C36D13


α‐carbon

β1‐carbon

β2‐carbon

γ‐carbon

δ‐carbon

C36H13 C36D13

*Adsorption site at δ‐carbon are not appeared in H species but in D species.


α‐carbon

β1‐carbon

β2‐carbon

γ‐carbon

δ‐carbon

Stable adsorption site of H species is observed at two carbons, however that of D species is appeared at four carbons.

C36H13 C36D13

At 300 K α‐carbon

β1‐carbon

β2‐carbon

γ‐carbon

δ‐carbon

*Fluctuations at 900 K are larger than that at 300 K.*Additional hydrogen on γ‐carbon transfers to β1‐carbon.

At 900 K

R (Å)21 3 4 5 76

R (Å)21 3 4 5 76

These results strongly suggest that adsorption site is controlled by temperature.

Temperature dependence for H species (300 K and 900 K)

Temperature dependency of H2/D2adsorption*

temperature

Amou

nt of

adsorptio

n

D

H

80℃30℃ 110℃

*Nishihara et al, Carbon, in preparation

Conclusion for Temperature dependence part

Acknowledgements: This work has been supported by New Energy and Industrial Technology Development Organization (NEDO) under “Advanced Fundamental Research Project on Hydrogen Storage Materials”

Information of temperature and isotope effects on the stable H/D adsorption site on ZTC material

Temperature effectStable adsorption site of H and D species is decreasing at high temperature, since additional H and D atom go over the potential barrierfrom one to the other carbon as temperature becomes higher.

Isotope effectThe number of stable adsorption site of H species is fewer than that of D species due to the difference of zero point vibration energy.

D replacement is seems as temperature lowering. In low temperature region, amount of D adsorption is larger than H because of larger number of adsorption sites in a small local area.In high temperature region, amount of D adsorption is smaller than H because of diffusion difficulty .

This isotope effects is strongly supported by observations.

Basis set dependency of H2- bond distance in ÅBasis set dependency of H2- total energy in a.u.Temperature dependency of H2/D2�adsorption*

quantum effect &temperature dependence on hydrogen ...and suggestion for the most suitable carbon...

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