DSpace at VNU: First principles study of the physisorption of hydrogen molecule on graphene and carbon nanotube surfaces add by Pt atom

Computational Materials Science 49 (2010) S15–S20

Contents lists available at ScienceDirect

Computational Materials Science
journal homepage: www.elsevier.com/locate/commatsci

First principles study of the physisorption of hydrogen molecule on graphene
and carbon nanotube surfaces adhered by Pt atom
Pham Tien Lam a, Phan Viet Dung a, Ayumu Sugiyama a, Nguyen Dinh Duc b, Tatsuya Shimoda a,c,
Akihiko Fujiwara a, Dam Hieu Chi a,b,c,*
a
b
c

Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan
Vietnam National University, 144 Xuan Thuy, Cau Giay, Hanoi, Vietnam
ERATO Shimoda Nano-Liquid Process Project, Japan Science and Technology Agency, 2-5-3-Asahidai, Nomi, Ishikawa 923-1211, Japan

a r t i c l e

i n f o

Article history:
Received 8 August 2009
Received in revised form 12 February 2010
Accepted 12 February 2010
Available online 27 April 2010
Keywords:
DFT
Fuel cell

Carbon nanotube
Catalysts

a b s t r a c t
Adsorptions of hydrogen, oxygen and carbon monoxide molecules on surfaces of single wall carbon nanotubes (SWNTs) and graphene adhered by a Pt atom have been investigated by density functional theory
calculation (DFT). Our calculations show that the Pt adatom significantly promotes the physisorption of
hydrogen in a region around it with radius of about 5 Å. The physisorption configuration in which oxygen
molecule aligned parallelly to the surfaces of SWNTs and graphene are most preferred. In contrast, both of
the physisorption configurations in which CO molecule aligned parallelly and perpendicularly with the
carbon end towards the graphene and SWNTs surfaces were preferred. The obtained results suggested
that the modification of the electronic structure by adhesion of Pt atom on surfaces of the support materials can modify their physisorption properties of gas molecules.
Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction
Poly electrolyte membrane fuel cells (PEMFCs) have been considered to be the most promising, among different types of fuel
cell, because they operate at low temperature and give high specific power and power density [7,2,1]. In PEMFCs platinum catalysts, as an active component, is the most important component
for electro-catalysts [7]. This brings up a major barrier to commercial application of fuel cells that suffer from high cost and low
stability.
Carbon materials are considered as the best support materials
for electro-catalysts in fuel cells because of its conductivity, surface
area, corrosion resistance and low cost [2,1]. Among various types
of carbon materials, carbon nanotubes with high surface area, good
electronic conductivity, and high chemical stability, have been
found to be an ideal support material for Pt clusters [4]. Highly dispersed and size-controlled small Pt clusters (less than 1 nm) made
from dispersed single Pt atoms were achieved by using carbon
nanotube supports [16]. The motion of Pt clusters on CNT was also

* Corresponding author at: Japan Advanced Institute of Science and Technology,
1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan. Tel.: +81 76 151 1584; fax: +81 76
151 1535.

E-mail address: (D.H. Chi).
0927-0256/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.commatsci.2010.02.041

observed experimentally by high-resolution transmission electron
microscopy. Further, the superior electro-catalytic activity and the
high tolerance to carbon monoxide poisoning of nanoparticle supported on carbon nanotube have been confirmed by several studies
[20,22,12]. In addition, our previous theoretical studies reveal several novel properties of Pt clusters on SWNTs, including the substrate mediated interaction and the structural fluxionality [8,9].
Fundamental information regarding properties of Pt nano clusters
on SWNTs under gas environment is strongly required for designing catalyst for fuel cell.
In this paper, we report our first principle study on the absorptions of gas molecules on surfaces of SWNTs and graphene adhered
by a Pt atom. Physisorptions of hydrogen, oxygen and carbon monoxide molecules on the systems have been investigated by density
functional theory calculation (DFT). Our calculations show that the
Pt adatom significantly promotes the adsorption of hydrogen in a
region around it with radius of about 5 Å. The adsorption configuration in which the oxygen molecule is aligned parallelly to the
surfaces of SWNTs and graphene are significantly more stable than
the others. In contrast, both of the adsorption configurations in
which the CO molecule was aligned parallelly and perpendicularly
with the carbon end towards the graphene and SWNTs surfaces
were preferred. The obtained results suggested that the modification of the electronic structure by adhesion of Pt nano clusters
on surfaces of SWNTs and graphene can modify their physisorption
properties of gas molecules.


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T.L. Pham et al. / Computational Materials Science 49 (2010) S15–S20

tionals, were very good agreement with the result of second order
Møller–Plesset perturbation (MP2) calculation [19].

Calculations of the interaction between hydrogen molecule and
a small graphene plate (C24H12) using Hatree–Fock method and
DFT method with several functionals were carried out in comparison with that using MP2/6-311++GÃÃ method for choosing the
most appropriate functional (Fig. 1a). All DFT [15,17] calculations
were carried out with triple numerical plus polarization basis set
(TNP) by Dmol3 package [11,10], and molecular orbital methods
were carried out by Gaussian 03 package [3].
Our calculations show that HF method almost predicts a repulsive interaction between hydrogen and garphene, while MP2
method predicts attraction interaction (Fig. 1b). This result indicates correlation energy correction plays an important role in simulating Van der Waals force, since MP2 method takes into account
the correlation energy correction as the perturbation. On the other
hand, results obtained from calculations using DFT methods
strongly depend on employed functionals (Fig. 1c). While LDA
functionals are good agreement with MP2 result, GGA functionals

2. Methodology
2.1. Evaluation of Van der Waals interaction
DFT methods are known as low computational cost methods,
and they are the most popular methods for calculating electronic
structure of many-atom systems. The interaction between these
gas molecules and SWNT, graphene surfaces is mainly driven by
Van der Waals force. Unfortunately, conventional DFT methods
do not describe well Van der Waals interaction, dispersion interaction [14,19]. It has been confirmed that local density approximation (LDA) functionals seem to well describe the physisorption of
H2 on graphene and carbon nanotube surfaces, compared to experimental data [19,6]. Okamoto and Miyamoto [19] have confirmed
that local density approximation (LDA) functionals predict physisorption of the hydrogen molecule on graphene plate, while some
generalized gradient approximation (GGA) and hybrid-DFT
functionals lead to repulsion interaction. Further more they also
indicated that the potential energy surfaces, given by LDA func-

(a)
Molecular orbital method / 6-311++G**

Density functional theory
100

HF
MP2

50

Potential energy / meV

Potential energy / meV

100

0

-50

-100

LDA-VWN
GGA-PW91
GGA-BLYP

50

0

-50

-100

-150

-150
2

2.5

3

3.5

4

4.5

5

2

2.5

3

3.5

4

4.5

5

Separation / Angstrom

Separation / Angstrom

(b)

(c)

(A)
(A)

(B)
(C)

(B)

(D)

(C)
(D)

(d)
Fig. 1. (a) Interaction model between graphene and hydrogen molecule. (b) Potential energy surface derived by molecular orbital methods (HF and MP2/6-311++GÃÃ). (c)
Potential energy surface derived by DFT methods: potential energy surfaces were estimated by taking potential energy at distance of 10 Å as zero. (d) Adsorption sites of H2 on
graphene and (10, 0)SWNT surfaces adhered by a Pt atom.

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T.L. Pham et al. / Computational Materials Science 49 (2010) S15–S20
Table 1
Interaction energy (Ead) and equilibrium distance (De) between H2 and graphene surface.
Functionals

MP2

De (Å)
Ead (meV)

2.89
93.1

LDA

GGA

VWN

PWC

PW92

PBE

RPE

HCTC

BOP

2.66
86.9

2.65
87.0

3.40
26.3

3.42
14.2

3.80
12.0

3.52
38.0

Repulsion

tend to underestimate interaction energy, and some GGA functionals even predict repulsion between hydrogen molecule and graphene (Table 1). Therefore, in this research we mainly used LDA
functionals to evaluate the interaction between gas molecules
and graphene and SWNT surfaces.
2.2. Calculation models
In this study, we used a periodic supper cell to simulate the
graphene sheet. The super cell included 128 carbon atoms with

edge length of a and b of 17.07 and 19.71 Å, respectively, correspond to the C–C bond length of 1.42 Å. These lattice parameters
were considered to be large enough to neglect the interaction of
Pt, gas molecules with their periodic image. The c lattice was of
30 Å, that was large enough to neglect the interaction between
graphene sheets.
We also applied a periodic super cells to simulate SWNTs. The c
lattices (which were aligned along the axes of the SWNTs) of these
super cells are of 17.04 Å and 19.68 Å for (10, 0)SWNT and
(5, 5)SWNT, respectively. These values were chosen to correspond
to the C–C bond length of 1.42 Å and to match the periodic condition. The edge lengths of both a and b lattices of these super cells
were of 25 Å which were large enough to ensure that there are
no interactions Pt, gas molecules and their periodic images. The
super cells consisted of 160 carbon atom for both (10, 0)SWNT
and (5, 5)SWNT.
We used local density approximation Vosoko–Wilk–Nusair
(VWN) [21] functional to treat exchange–correlation energy. Double numerical plus polarization function (DNP) basis set was used
for all calculation. Brillouin-zone integrations were performed by
using (1 Â 1 Â 4) k-point mesh, and (4 Â 4 Â 1) k-point for SWNTs
and graphene respectively with Monkhorsh-Pack scheme [18]. All
calculations were performed by DFT using Dmol3 package.
3. Results and discussion
3.1. Physisorption of hydrogen
Our calculations as well as several previous publications
[14,6,5] indicated that H2 prefers to be physisorbed at the center
of hexagon and aligned parallelly to the surface of graphene and
(10, 0)SWNT. In this research, we used parallel adsorption configuration of H2 on the surface at the center of hexagon. The adsorption
energies of H2 on graphene and (10, 0)SWNT surfaces were calculated by formula:

Ead ¼ EH2 þ EGraphene

or SWNT

À EH2 =Graphene

or SWNT

VWN-PB

BP

BLYP

optimization calculation confirmed that no stable physisorption
configuration of hydrogen was found in a region with radius of
about 5 Å around Pt adatom. When H2 move into this region, it is
pulled toward the Pt adatom. We also considered several adsorption sites of hydrogen around this area (Fig. 1d). Our calculations
clearly show that at these adsorption sites, H2 prefers to be adsorbed parallel to the surfaces at the center of hexagon. Adsorption
energies and equilibrium distance from center of mass of H2 to
graphene and SWNT surfaces are summarized in Table 2. It means
that outside of this region the effect of the Pt adatom is not clear.
3.2. Physisorption of oxygen
Oxygen reduction plays an essential role in the performance of
fuel cells, as oxygen reduction reaction is four-electrons-transfer
reaction in which the first step is the adsorption of oxygen molecule on catalysts. In this section we mainly focus on the adsorption
of oxygen on carbon support materials, including graphene,
(10, 0)SWNT, and (5, 5)SWNT, as well as the effect of the Pt adatom
on it.
We considered several adsorption configurations of oxygen on
graphene, (10, 0)SWNT and (5, 5)SWNT surfaces, including top,
center, and parallel (Fig. 2a). The interaction energies between O2

and the surfaces were estimated by the depth of the potential wells
on potential energy surfaces. The potential energy surfaces were
calculated by changing the distance between O2 and the surface
and calculating total energy at each point. The depth of potential
wells was estimated by taking the potential energy as zero when
O2 was placed at the center of super cells. Fig. 2b shows potential
energy surfaces of the singlet and triplet states of O2 molecule
when it approaches to graphene surface. It is apparent that in a
physisorption on a graphene surface, the distance between O2
and the surface is in a range from 2.5 to 3.0 Å, the triplet sate is
more stable than the singlet state. Similar results were obtained
for the physisorptions of O2 on (10, 0) and (5, 5)SWNT surfaces.
Therefore, in this research we used triplet potential energy surfaces
to evaluate interaction between O2 and the surfaces.
Typical triplet potential energy surfaces of O2 on the surfaces
are showed in Fig. 2c. It is apparent that the adsorption energies
of O2 on the surfaces strongly depend on adsorption configurations,
and the configuration in which oxygen molecule aligned parallelly
to the surfaces of SWNTs and graphene are most preferred (Table 3). This result can be explained by the interaction between p
electrons of O2 and p electrons of the surfaces. The distance from
O2 molecule to the surface seems not to depend significantly on

ð1Þ

The adsorption energy of hydrogen on graphene, 112.29 meV, is
close to the value found by Arelano et al., 86 meV with planar periodic graphene layer [5] and by Henwood et al., 93.10 meV with the
hexagonal plate consisting of 96 carbon atoms [6]. The adsorption
energy of H2 on (10, 0)SWNT, 107.36 meV, is close to the value
found by Henwood and David Carey [14], 89.98 meV, and larger
than the result found by Han and Lee [13], 34 meV, by GGAPW91 functional.

For the physisorption of hydrogen on SWNTs and graphene adhered by a Pt atom, our careful examination by full geometry

Table 2
Adsorption energy (Ead) of hydrogen on graphene and distance between hydrogen and
graphene surface (De).
Adsorption sites

Pristine
A
B
C
D

Ead (meV)

De (Å)

Graphene

(10, 0)SWNT

Graphene

(10, 0)SWNT

112.29
112.54
113.31
112.74
112.69

107.36
108.36
112.16
114.38
106.19

2.66
2.66
2.67
2.67
2.67

2.55
2.55
2.54
2.57
2.56


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T.L. Pham et al. / Computational Materials Science 49 (2010) S15–S20

Total energy + 4987 / Ha

0.005

Top

Center

Parallel

Parallel Singlet
Parallel Triplet

0
-0.005
-0.01
-0.015
-0.02
-0.025
-0.03
2.2

2.4

2.6

2.8

3

3.2

3.4

Distance / Angstrom

Potential energy surface / meV

(a)

(b)

0

Parallel
Center
-50

-100

-150

-200
2.2

2.4

2.6

2.8

3

3.2

3.4

Distance / Angstrom

(c)

(d)

Fig. 2. (a) Adsorption configuration of O2 on graphene, (10, 0)SWNT surface, and (5, 5)SWNT surfaces. (b) Singlet and triplet potential energy surface. (c) Triplet potential
energy surface with different adsorption configurations of O2 on graphene surface. (d) Adsorption site of O2 and CO on graphene surface.

Table 3
Adsorption energy (Ead) of O2 on graphene and SWNT surfaces and distance between the center of mass of O2 and the surfaces (De).
Adsorption configuration

Center
Top
Parallel

Ead (meV)

De (Å)

Graphene

(10, 0)SWNT

(5, 5)SWNT

Graphene

(10, 0)SWNT

(5, 5)SWNT

132.55
114.14
177.93

125.69
87.82
158.26

124.18
90.11
155.81

3.35
3.48
2.88

3.24
3.51
2.80

3.29
3.47
2.90

adsorption configurations and curvature of the surfaces. Our obtained result also indicates that the adsorption energies of oxygen
on SWNTs are slightly lower than that on graphene.

To investigate the effect of the Pt adatom, we calculated the
adsorption energies of O2 on the surfaces adhered by a Pt atom.
Our calculations showed that on the surfaces adhered by a Pt atom,
triplet still is the most stable state. The physisorption energies of
O2 at triplet state on the surfaces of graphene and SWNTs adhered
by a Pt atom with parallel configuration are summarized in Table 4.
It is apparent that adhesion of Pt promotes the interaction between
oxygen and the surfaces.
3.3. Physisorption of carbon monoxide
In direct methanol fuel cell, CO is one of the most important
intermediate substance, therefore information about the adsorption of CO on catalysts is important for understanding properties
of catalysts. In this section, we focus on the absorptions of CO on
graphene, (10, 0)SWNT, and (5, 5)SWNT surfaces as well as the effect of the Pt atom on these adsorptions.

Table 4
Adsorption energy (Ead) of O2 on graphene and SWNT surfaces.
Adsorption
configuration

Center
Top
Parallel

Graphene

(10, 0)SWNT

(5, 5)SWNT

Without

Pt

With
Pt

Without
Pt

With
Pt

Without
Pt

With
Pt

132.55
114.14
177.93

132.71
117.56
179.26

125.69
87.82
158.26

129.89

89.18
159.06

124.18
90.11
155.81

121.81
91.90
160.63

We considered several adsorption configurations of CO on
graphene, (10, 0)SWNT, and (5, 5)SWNT surfaces (Fig. 3a). We also
evaluated the interaction between CO and the surfaces by the
depth of potential wells on potential energy surfaces. The potential
energy surfaces were calculated by changing the distance between
CO and the surfaces, and calculating energy at each point (Fig. 3b).
These potential energy surfaces indicate that the adsorptions of CO
molecules on graphene and SWNT surfaces strongly depend on the
adsorption configurations. We found that CO molecules prefer to


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T.L. Pham et al. / Computational Materials Science 49 (2010) S15–S20

Parallel

(a)
Potential energy / meV

0

Carbon center
Oxy center
Parallel

-25
-50
-75
-100
-125
-150
2.4

2.6

2.8

3

3.2

3.4

Distance /Angstrom

(b)
Fig. 3. (a) Adsorption configurations of CO on graphene and SWNTs. (b) Potential energy surface.

Table 5
Adsorption energy (Ead) of CO on graphene and SWNT surfaces and distance between the center of mass of CO and the surfaces (De).
Adsorption configuration

Ead (meV)

Carbon top
Carbon center
Oxygen top
Oxygen center
Parallel

De (Å)

Graphene

(10, 0)SWNT

(5, 5)SWNT

Graphene

(10, 0)SWNT

(5, 5)SWNT

106.84
143.49
87.60
108.19

148.52

89.91
137.92
68.49
101.04
131.18

80.88
136.12
68.16
98.70
127.92

3.76
3.52
3.57
3.42
2.96

3.82
3.41
3.60
3.32
2.97

3.79
3.48
3.58
3.39

3.02

adsorb parallelly, or perpendicularly to the surfaces with the carbon end toward the surfaces (Table 5).
The difference in adsorption energy between configurations can
be attributed to the polarization of CO molecule. For configuration,
in which oxygen atom orients toward the surfaces, the negative
charge of oxygen atom weakens the interaction between CO and
graphene or SWNT surfaces, while the positive charge of carbon
atom promotes the interaction between CO and the surfaces. For
graphene surface, the adsorption energies of two most preferring
adsorption configurations, carbon center and parallel, are almost
the same. For (10, 0)SWNT and (5, 5)SWNT surfaces carbon center
configuration seems to be more stable than parallel configuration.

Table 6
Adsorption energy (Ead) of CO on graphene and SWNT surfaces.
Adsorption
configuration

Carbon center
Oxygen center
Parallel

Graphene

(10, 0)SWNT

(5, 5)SWNT

Without

Pt

With
Pt

Without
Pt

With
Pt

Without
Pt

With
Pt

143.49
108.19
148.52

142.92
108.27
145.78

137.92
101.04
131.18

137.47

100.82
129.58

136.12
98.70
127.92

130.41
96.14
125.30

The distance between CO molecule and the surfaces does not seem
to significantly depend on the adsorption configuration.
To investigate the effect of the Pt adatom, we also evaluated the
adsorption of CO on graphene and SWNT surface adhered by a Pt
atom with carbon center, oxygen center, and parallel configuration
at the adsorption site as in Fig. 2d. The adsorption energies are
summarized in Table 6. In contrast with the case of O2, adhesion
of Pt atom does not show a clear influence to the interaction between CO and the surfaces.

4. Conclusions
Our calculations indicated that the adsorption of the Pt atom on
graphene and (10, 0)SWNTs leads to the formation of an active region with radius of about 5 Å for the adsorption of hydrogen atom.
In this region the Pt adatom significantly promotes the adsorption
of hydrogen by creating a deep and wide potential well on the potential energy surface for hydrogen molecules. For the adsorption
of oxygen, we found that oxygen molecule do not change it its spin
state, the most stable state is triplet state. Oxygen molecules prefer
to be adsorbed parallel at the center of hexagons on graphene and
SWNT surfaces. For the adsorption of CO, we found that CO molecules prefer to be aligned parallelly to the graphene and SWNT

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T.L. Pham et al. / Computational Materials Science 49 (2010) S15–S20

surfaces, or perpendicularly to the surfaces with the carbon end
towards the surfaces.
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