Research on the ability to generate electric current of the

H/Pd(100) system in a fuel cell

Pham Cong Thai1,2 , Tran Thi Thu Hanh1,2,∗

1
Ho Chi Minh City University of Technology (HCMUT), Ho Chi Minh City, 268 Ly
Thuong Kiet Street, District 10, Ho Chi Minh City, Vietnam.
2
Vietnam National University Ho Chi Minh City, Linh Trung Ward, Thu Duc District,
Ho Chi Minh City, Vietnam.
∗
E-mail: thuhanhsp@hcmut.edu.vn

Abstract. Hydrogen fuel cells are being explored as a sustainable energy source. To
study the electric current produced in the fuel cell, we used density functional theory
(DFT) to simulate the adsorption of hydrogen on the Pd(100) surface in a vacuum
environment. Our research focuses on the convergence of the initial k-point selection for
the palladium (Pd) system with and without hydrogen atoms. We specifically examined
the stability of chemical bonds in the model through the hydrogen adsorption sites. Our
simulation results demonstrate that the endothermic reaction of hydrogen atoms on the
top site of the Pd surface is the primary reason why it is considered the least favorable
site compared to the hollow site and bridge site.

1 INTRODUCTION

The implementation of direct methanol fuel cells (DMFCs) as alternative energy sources in electronic
devices is quickly relevant due to the evident increase in energy prices over recent years [1–4]. Many
research articles have been conducted on this topic with the objective of promoting their entrance into
the market. However, the high price of DMFCs is a significant barrier to their commercialization. The
high cost can be attributed to the utilisation of platinum and platinum based alloys, which are essential for
facilitating the electrochemical reaction in fuel cells. These expensive metals are rare and require complex
processing [5–7]. A number of potential alternatives with reduced platinum content have been investigated
in the context of the cathode such as transition metal macrocycles [8, 9], ruthenium chalcogenides [10,
11] and palladium alloys [12].
Within this context, we study the hydrogen (H) absorption on the Pd(100) in detail by using the DFT
method. It is well known that the Pd metal can absorb large amounts of hydrogen, forming a palladium
hydride. The face-centered cubic (fcc) structure of palladium allows hydrogen atoms to occupy octahedral
sites, facilitating their diffusion throughout the metal [13, 14]. The absorption process of hydrogen with
palladium is not limited to a pure physical phenomenon, as such it has implications for the material’s
structural integrity [15]. Furthermore, the addition of other elements, such as gold or copper, can alter
the hydrogen absorption characteristics of palladium. In some cases, this can enhance the process, while
in others it can inhibit it, depending on the alloy composition [16, 17]. Based on Pd unit cell data
obtained by crystallography database in Ref. [18], we construct the superlattice consisting of Pd ions
and conduct a series of structural optimization calculations to determine a relaxed Pd(100) slab. The
k-points convergence of the model and H-absorption energy with the H atom on the top site have been
calculated in the study.
2 CALCULATION
2.1 Spanish Initiative for Electronic Simulations with Thousands of Atoms Simulation
The DFT method, implemented in the SIESTA (Spanish Initiative for Electronic Simulations with Thou-
sands of Atoms) package, was used to calculate the ground-state energies and optimised structures of
all simulation models. This method combines a self-consistent field loop, a norm-conserving pseudopo-
tential, and a plane-wave basis set [19–21]. The Pd slab model and its comprehensive DFT calculation
used for the simulation are shown in Figure 1. In depth, we used the generalized gradient approximation
(GGA) to the exchange correlation functional [22], energy cutoff of 200 Ry and employed the double-zeta
polarized basis sets for all calculations. The Pd slab was periodically repeated in x-axis and y-axis to
perform structural relaxations with a vacuum gap of 28.94 Å in the z-axis to disregard the majority of
interactions between the periodic lateral layers. The geometry constraints was set to fixed the bottom
of the model and the optimisation loop is terminated when the maximum stress component is found to
be less than 0.02 eV Å−1 . In order to ensure the most accurate results, the surface irreducible Brillouin
zone was sampled using the k-point mesh originated from the Monkhorst–Pack (MP) scheme [23]. After
relaxing at 300 K, The solid Pd model exhibits a relaxed structure, with bond lengths between Pd atoms
of approximately 2.77 Å within the same layer and 2.91 Å between layers. The result is very close to
other studies of 2.55 Å - 3.05 Å [24–26]. Furthermore, we check the converged data in regard of increasing
k-point grid from (3 × 3 × 1) to (15 × 15 × 1) MP scheme.

Figure 1: The Pd(100) model used for the DFT calculations. In the SIESTA simulation, we constructed
the Pd(100) slabs using a (3 × 3) lateral unit cell and adsorbed H atoms on the top site such that the
coverage ranges from zero to one. We then calculated the total energy after relaxing all Pd atoms, with
the exception of the bottom layer.

2.2 Adsorption energy calculations

Palladium is well-known for its exceptional capacity to absorb hydrogen, forming palladium hydride,
which has a profound impact on its electronic and structural characteristics. This phenomenon is in-
strumental in applications involving hydrogen storage and catalysis, where the formation of palladium
hydride can optimize the material’s reactivity and efficiency [27–29].
In this study, it is crucial to accurately determine the bond lengths and energies of hydrogen molecules
in order to understand the long-range interactions of adsorbed hydrogen atoms. The extended simulation
profile was incorporated into the calculations of hydrogen binding energies. The energy shift of 60 meV
and the split norm of 0.53 were set for H atoms. We firstly set the single point calculation of hydrogen
molecule that its bond length varies from 0.05 Å to 5.0 Å and run the optimization to find the energy
of the strongest hydrogen bond. After that, we used the following equation [30, 31] to calculate the
hydrogen absorption energy:
nH
Eads = E(nH ) − E(0) − EH2 (1)
2
Where Eads is the hydrogen adsorption energy, E(nH ) is the total energy of the H/Pd(100) system with
nH hydrogen atoms, E(0) is the total energy of bare Pd slab, and EH2 is the total energy of the isolated
H2 molecule.

3 RESULTS AND DISCUSSIONS

3.1 K-points convergence test

The analysis of the convergence with respect to the density of k-point MP grids represents a fundamental
preliminary step in any plane-wave self-consistent field calculations. This is due to the fact that inadequate
convergence tests inevitably lead to the inaccurate estimation of the total energy. In Figure 2, the total
energy of Pd slab model is independent of the number of k-points at a given point, indicating that the
values are well converged. There is a considerable change in overall energy as the number of k-points
is varied, up to a certain point where it remains constant. For instance, it can be observed that as the
number of k-points increases from 3 × 3 × 1 to 11 × 11 × 1, the total energy of the system is dependent
on the number of k-points. However, increasing the number of k-points from 11 × 11 × 1 to 15 × 15 ×
1 does not lower the total energy, but produces comparable results as shown in Table 1.

Number of Runs K-point ET OT (eV)

1 3×3×1 -44360.428623
2 5×5×1 -44360.462694
3 7×7×1 -44360.415659
4 9×9×1 -44360.412404
5 11 × 11 × 1 -44360.404347
6 12 × 12 × 1 -44360.404073
7 13 × 13 × 1 -44360.403607
8 14 × 14 × 1 -44360.404088
9 15 × 15 × 1 -44360.404379

Figure 2: The DFT calculations of the total energy Table 1: The convergence test results of the ground-
in regard of increasing k-point grid from (3 × 3 × state energy with respect to k-point grid from (3 × 3
1) to (15 × 15 × 1) MP scheme. × 1) to (15 × 15 × 1) MP scheme.

3.2 Hydrogen adsorption site

The binding energy diagram of hydrogen diatomic in Figure 3, illustrates bond dynamic with with the
atoms oscillating around an equilibrium distance. Region between 3.5 Å and 5.0 Å depicts the atoms in a
state of complete separation. As the atoms approach one another, the atom begin to be attracted to the
nuclei of the other atom, as shown in region below 3.5 Å. This attraction lowers the energy of the system
and results in the formation of a bond. Region from 0.5 Å to 1.5 Å represents the equilibrium bond
length, which is the lowest point in the binding energy spectrum, 31.5 eV. The bond length obtained in
this study is 0.75 Å, which is in good agreement with the findings of the recent study [32].
Figure 3: The binding energies for isolated hydrogen molecule is plotted as a function of the inter-nuclear
distance (Å).

To test the possible adsorption site, the hydrogen atoms can be placed on the relaxed Pd surface on
the high symmetry possible adsorption sites such as Top (TP d ), Bridge and Hollow. The top site of the
Pd slab, constituted of 18 Pd atoms, represents the primary focus of our investigation, as it is easily
accessible in comparison with other sites, where interactions between hydrogen atoms and Pd surface are
more complex. The results of the k-points convergence test indicate that the total energy of the Pd slab
remains constant when the k-point grid is set to (11 × 11 × 1) or larger. For this reason, the hydrogen
atoms were positioned at a distance of 1.5 Å from the top site of the Pd surface using a (11 × 11 × 1) MP
scheme and surface coverage of 1/18 and 1. After the conjugate gradient steps between the self-consistent
field cycles, the H/Pd system will be relaxed to nearby stable positions as shown in Figure 4 and Figure
5. The adsorption energies of hydrogen on TP d site with optimized Pd-H bond lengths and constrained
Pd atoms are presented in Table 2.
Figure 4 illustrates the distortion observed in the vicinity of the adsorbent position. It can be seen that
there are minor displacements (≈ 0.012 Å and ≈ 0.027 Å) between Pd atoms on the surface, indicating
that the distortion is not visible from the top view. At the site of absorption, the hydrogen atoms are
repelled upwards along the vertical axis with approximately the same force (≈ 0.088 Å), resulting in
the formation of local deformations around the adsorbent palladium atom at the hydrogen adsorption
site (Figure 5). The Pd-H bond lengths of the relaxed system, dP d−H , shown in Table 2, are in good
agreement with the previous study calculated by Dong et al. (1.55 Å) [33] and Tománek (1.56 Å) [34]. The
values of the adsorption energy per atom, Eads , calculated using equation 1, represent an endothermic
reaction of hydrogen atoms onto the top site, which is in accordance with the findings of both theoretical
and experimental studies [35, 36]. It shows the dependence between adsorption energy and the coverage,
which can be explained by the increase of hydrogen atoms on the adsorbing surface. This results in a
greater number of hydrogen atoms being pushed out by the palladium surface, which then bond with
each other, thereby increasing the hydrogen binding energy. From our computations, Pd-H bonding at
the top site of the Pd surface is inherently unstable and the least favourable site in comparison to the
hollow site and bridge site [37].

Table 2: The bond length of the adsorbent atom (dP d−P d , Å) with the H atom on top of the surface
(dP d−H , Å), the vertical displacement of the adsorbent atom compared to their relaxed position (h, Å),
and the hydrogen adsorption energy (Eads , Å):

surface coverage site dP d−H (Å) dP d−P d (Å) h (Å) Eads (eV) Eads (eV/atom)
1/18 TP d 1.5983 2.77 0.098 0.14 0.14
1 TP d 1.5878 2.76 0.088 3.51 0.19
Figure 4: The top view of the optimized H/Pd(100) Figure 5: The side view of the optimized H/Pd(100)
system with out-of-plane distortion at the neighbors system with out-of-plane distortion at the neighbors
of the adsorbent atom in TP d adsorption configura- of the adsorbent atom in TP d adsorption configura-
tions. Displacements of the Pd atom and its local tions. Displacements of Pd atoms along the z-axis
neighbors are shown by the red numbers. (Å) are shown by the red numbers.

4 CONCLUSIONS

The hydrogen adsorption on the Pd(100) surface was investigated using a first-principles DFT-GGA
calculation using the SIESTA package. It was shown that the total energy of the 3 × 3 lateral unit cell of
the Pd is dependent on the number of k-points and the energy, ET OT , was observed to remain constant
at -44360.404 eV. Further simulation of Pd surface with hydrogen adsorption shows good agreement in
Pd-H length with other studies. From the results, it shows an endothermic reaction of hydrogen atoms
onto the top site of Pd surface which causes unstable bonding between Pd and H atoms. This study
leaves an important note in the future for any investigation of hydrogen adsorption sites such as bridges
and hollows.

ACKNOWLEDGMENTS

This research received no specific grant from any funding agency in the public, commercial, or not-for-
profit sectors. We acknowledge Ho Chi Minh City University of Technology (HCMUT) and VNU-HCM
for supporting this study.

REFERENCES

[1] Brian D Adams and Aicheng Chen. “The role of palladium in a hydrogen economy”. In: Materials
today 14.6 (2011), pp. 282–289.
[2] Haibo Gan and Hai Sun. “Methanol Sensor-Less Control Strategy for Direct Methanol Fuel Cell
Startup”. In: Frontiers in Energy Research 10 (2022), p. 827763.
[3] R Govindarasu and S Somasundaram. “Studies on influence of cell temperature in direct methanol
fuel cell operation”. In: Processes 8.3 (2020), p. 353.
[4] Shengfeng Xue et al. “Hexapod PtRuCu nanocrystalline alloy for highly efficient and stable methanol
oxidation”. In: ACS Catalysis 8.8 (2018), pp. 7578–7584.
[5] Kyle Mikkelsen et al. “Block copolymer templated synthesis of core–shell PtAu bimetallic nanocat-
alysts for the methanol oxidation reaction”. In: Chemistry of materials 26.24 (2014), pp. 6928–
6940.
 [6] Xiao Zhao et al. “Recent advances in catalysts for direct methanol fuel cells”. In: Energy & Envi-
ronmental Science 4.8 (2011), pp. 2736–2753.
[7] Ruiyun Guo et al. “Facile Synthesis of PtP2 Nanocrystals as Highly Active Electrocatalysts for
Methanol Oxidation”. In: ACS Applied Materials & Interfaces 16.18 (2024), pp. 23233–23240.
[8] Michel Lefèvre, JP Dodelet, and Patrick Bertrand. “Molecular oxygen reduction in PEM fuel cells:
evidence for the simultaneous presence of two active sites in Fe-based catalysts”. In: The Journal
of Physical Chemistry B 106.34 (2002), pp. 8705–8713.
[9] Paul H Matter, Ling Zhang, and Umit S Ozkan. “The role of nanostructure in nitrogen-containing
carbon catalysts for the oxygen reduction reaction”. In: Journal of Catalysis 239.1 (2006), pp. 83–
96.
[10] Vladimir I Zaikovskii et al. “Synthesis and structural characterization of Se-modified carbon-
supported Ru nanoparticles for the oxygen reduction reaction”. In: The Journal of Physical Chem-
istry B 110.13 (2006), pp. 6881–6890.
[11] Alexey Alexandrovich Serov et al. “Preparation, characterization, and high performance of RuSe/C
for direct methanol fuel cells”. In: Journal of power sources 175.1 (2008), pp. 175–182.
[12] William E Mustain and Jai Prakash. “Kinetics and mechanism for the oxygen reduction reaction
on polycrystalline cobalt–palladium electrocatalysts in acid media”. In: Journal of power sources
170.1 (2007), pp. 28–37.
[13] Rebecca S Sherbo et al. “Accurate coulometric quantification of hydrogen absorption in palladium
nanoparticles and thin films”. In: Chemistry of Materials 30.12 (2018), pp. 3963–3970.
[14] Hiroshi Akiba et al. “Nanometer-size effect on hydrogen sites in palladium lattice”. In: Journal of
the American Chemical Society 138.32 (2016), pp. 10238–10243.
[15] Midori Yamaya, Masatoshi Futakawa, and Hidefumi Date. “Effect of hydrogen absorption on the
mechanical properties of palladium”. In: Key Engineering Materials 297 (2005), pp. 2713–2719.
[16] Yusuke Nanba et al. “Theoretical study of the hydrogen absorption mechanism into a palladium
nanocube coated with a metal–organic framework”. In: The Journal of Physical Chemistry C 121.27
(2017), pp. 14611–14617.
[17] Kazuhiro Namba et al. “Acceleration of hydrogen absorption by palladium through surface alloying
with gold”. In: Proceedings of the National Academy of Sciences 115.31 (2018), pp. 7896–7900.
[18] WP Davey. “Lattice constants of twelve common metals Locality: synthetic Note: lattice parameter
is average of runs 1 & 2”. In: Physical Review 25 (1925), pp. 753–761.
[19] Walter Kohn and Lu Jeu Sham. “Self-consistent equations including exchange and correlation
effects”. In: Physical review 140.4A (1965), A1133.
[20] Pablo Ordejón, Emilio Artacho, and José M Soler. “Self-consistent order-N density-functional cal-
culations for very large systems”. In: Physical review B 53.16 (1996), R10441.
[21] José M Soler et al. “The SIESTA method for ab initio order-N materials simulation”. In: Journal
of Physics: Condensed Matter 14.11 (2002), p. 2745.
[22] John P Perdew, Kieron Burke, and Matthias Ernzerhof. “Generalized gradient approximation made
simple”. In: Physical review letters 77.18 (1996), p. 3865.
[23] Hendrik J Monkhorst and James D Pack. “Special points for Brillouin-zone integrations”. In: Phys-
ical review B 13.12 (1976), p. 5188.
[24] John E Bercaw et al. “Electronic structures of PdII dimers”. In: Inorganic chemistry 49.4 (2010),
pp. 1801–1810.
[25] Claudia M Fafard et al. “Addition of ammonia, water, and dihydrogen across a single Pd- Pd bond”.
In: Journal of the American Chemical Society 129.34 (2007), pp. 10318–10319.
[26] Justin R Walensky et al. “Understanding Pd–Pd bond length variation in (PNP) Pd–Pd (PNP)
dimers”. In: Inorganic chemistry 52.5 (2013), pp. 2317–2322.
[27] Simona E Hunyadi Murph et al. “Controlled release of hydrogen isotopes from hydride-magnetic
nanomaterials”. In: ACS applied materials & interfaces 12.8 (2020), pp. 9478–9488.
[28] Sudhansu Sekhar Das, Gregory Kopnov, and Alexander Gerber. “Resistivity testing of palladium
dilution limits in CoPd alloys for hydrogen storage”. In: Materials 15.1 (2021), p. 111.
[29] Kun Shi et al. “Harvesting PdH Employing Pd Nano Icosahedrons via High Pressure”. In: Advanced
Science 10.4 (2023), p. 2205133.
[30] Tran Thi Thu Hanh, Yoshinari Takimoto, and Osamu Sugino. “First-principles thermodynamic
description of hydrogen electroadsorption on the Pt (111) surface”. In: Surface science 625 (2014),
pp. 104–111.
[31] Phi Minh Nguyen et al. “Ab initio investigation of the hydrogen interaction on two dimensional
silicon carbide”. In: ACS omega 7.51 (2022), pp. 47642–47649.
[32] Yiwen Chen et al. “Hydrogen storage properties of economical graphene materials modified by
non-precious metal nickel and low-content palladium”. In: Inorganics 11.6 (2023), p. 251.
[33] W Dong et al. “Hydrogen adsorption on palladium: a comparative theoretical study of different
surfaces”. In: Surface science 411.1-2 (1998), pp. 123–136.
[34] D Tománek, Z Sun, and Steven G Louie. “Ab initio calculation of chemisorption systems: H on Pd
(001) and Pd (110)”. In: Physical Review B 43.6 (1991), p. 4699.
[35] Linda L Jewell and Burtron H Davis. “Review of absorption and adsorption in the hydrogen–
palladium system”. In: Applied Catalysis A: General 310 (2006), pp. 1–15.
[36] OM Løvvik and RA Olsen. “Adsorption energies and ordered structures of hydrogen on Pd (111)
from density-functional periodic calculations”. In: Physical Review B 58.16 (1998), p. 10890.
[37] Graeme W Watson et al. “A comparison of the adsorption and diffusion of hydrogen on the {111}
surfaces of Ni, Pd, and Pt from density functional theory calculations”. In: The Journal of Physical
Chemistry B 105.21 (2001), pp. 4889–4894.