ĐẠI HỌC QUỐC GIA HÀ NỘI
Trường Đại học Khoa học Tự nhiên
Quantum-Mechanical Study of H₂ Adsorption of Ca
Atoms Decorated on Doped Graphene Using Density
Functional Theory
Student: Nguyen Hoang Son
Supervisor: Dr. Nguyen Thuy Trang
Hanoi, 2025
1
1, Introduction
•
Problem statement
Property
H₂ Value
Gravimetric density
120 MJ/kg
2.7× higher than gasoline
Fossil fuel
44 MJ/kg (gasoline)
50 MJ/kg (diesel)
Combustion product
H₂O only
Zero emissions
CO₂, CO, NOₓ, SOₓ
Particulate matter
Availability
Abundant (from water)
Renewable production
Limited reserves
Depletion risk
[1] https://www.axios.com/2024/11/13/carbon-emissions-fossil-fuels-record-high
[2] https://www.researchgate.net/figure/Predicted-rates-of-global-fossil-fuel-depletion-The-depletion-of-total-fossil-fuels_fig1_45286735
1, Introduction
•
H2 storage methods and limitations Method
[3] Lavanya Mulky et.al, An overview of hydrogen storage technologies – Key challenges and opportunities
Advantages
Major Limitations
Liquid H₂ (253°C, 20-30 bar)
- Extreme
- High density (70.85 temperature (-253°C)
g/L)
- High energy cost
- Energy density (8.5 (30-40%)
MJ/L)
- Continuous boil-off
- Efficient large(1-3%/day)
scale transport
- Very high
infrastructure cost
Compressed H₂
(700 bar)
- High pressure
safety risks
- Low density (39.75
kg/m³ max)
- Heavy tanks (10 kg
CF/1 kg H₂)
- Tank cost (3.5×
metal tanks)
- Fast refueling (3-5
min)
- Room temperature
operation
- Lower energy
penalty (10%)
→ Solid hydrogen storage based on hydrogen absorbing or
adsorbing materials has attracted attention from scientists.
1, Introduction
•
H2 storage methods and limitations
Storage Method
Advantages
Major Limitations
Physisorption
•Fast kinetics (seconds)
Examples:MOFs
•Fully reversible
(MOF-5, NU-100), •Room temperature operation
Zeolites (NaX, CHA)
•Large surface area (>3000
m²/g)
•Low pressure requirements
• Weak binding energy
• Low RT capacity (<2 wt%)
• Need 77K for adsorption
• MOF-5: 4.5 wt% (78K) → 1.0 wt%
(RT)
• Zeolite NaX: 2.55 wt% (77K) → <0.1
wt% (RT)
Chemisorption
•High capacity (up to 7.6
Examples: LaNi₅H₆, wt%)
MgH₂ ,TiFe, NaAlH₄ •Safe operation
•No high pressure needed
•Long-term stability
•MgH₂: meets DOE target (6
wt%)
• High desorption temp (100-400°C)
• Slow kinetics (minutes-hours)
• Heavy materials (metals)
• LaNi₅H₆: 25-80°C to release H₂
• MgH₂: 300-400°C for desorption
[4] Nesrin et.al, Comparative Study of Hydrogen Storage and Metal Hydride Systems: Future Energy Storage Solutions, 2025
[5] Lena Marie Funke et.al Metal–Organic Frameworks: Challenges Addressed via Magnetic Resonance Spectroscopy, 2023
[6] https://www.linkedin.com/posts/manar-alruwaili_difference-between-physical-adsorption-and-activity-7163957280978247682-gSGB
1, Introduction
•
H2 storage methods and limitations
→ Carbon based materials have attracted special
attention from the scientific community due to their
outstanding advantages
Property
Advantage
Value
Surface area
Extremely large
>3000 m²/g
Chemical stability
High durability
Long lifetime
Structural
tunability
Design flexibility
Customizable
Binding energy too weak: 4-8 kJ/mol
→ Need 15-25 kJ/mol for practical use
[7] Maryam Rezaie et.al, Carbon nanomaterial-based sensors for wearable health and environmental
monitoring, 2022
1, Introduction
•
Research Objective
- Enhance hydrogen storage capacity of carbon-based materials using Ca-decorated graphene
- Investigate H₂ adsorption mechanisms on Ca-functionalized graphene via DFT calculations
- Address Ca-graphene binding challenges by doping graphene with heteroatoms (Al, Si, Ga, Ge)
atom X
Ca
2, Research method
•
DFT calculation
Effective potential
External potential (from nuclei)
Electron density
Exc: exchangecorrelation potential
PAW-PBE
Ehatree: Hartree potential
(electron-electron
Coulomb interaction)
Cutoff energy:
550 eV
[8] Andy Paul Chen, Magnetism and Spin Transport at the Interface of Ferroelectric
and Ferromagnetic Materials, PhD Thesis, National University of Singapore, 2018.
DOI: 10.13140/RG.2.2.35323.95529
+ Total energy, electron density,
Kohn-Sham orbitals
+ Other physical observables
2, Research method
•
Bader charge
- Determine the charge of atoms by partitioning a molecule into adjacent atomic domains from the electron
density [9]
- Apply the partitioning method along the charge density gradient from one point to another until the maximum
charge density is achieved.
- The result is close to the actual charge state of an atom.
[9] https://theory.cm.utexas.edu/henkelman/research/bader/
2, Research method
•
Research model
Top
Edge/Bridge
Hollow
Figure 2: Typical sites of Ca adsorption on
graphene surface
Figure 1: Graphene structure research
3, Result and discussion
•
Doped
Atom
Electronic interactions between impurities and graphene
Table 1: The free atomic radius and the integer charge at the doping site as well as of the C atoms in the
nearest and second nearest neighbourhood of the doping site.
Free
atomic
radius
(Å)
Energy
Atomic
difference charge (e)
between
pxpy and s
(eV)
Charge of C atoms around the impurity center
Nearest Neighbors
Next nearest neighbors
C6
C7
C11
C10
C22
C27
Al
1,25
2,3
+3,0
-0,647
-0,853
-0,630
-0,032
+0,031
+0,031
Ga
1,3
2,27
+3,0
-0,78
-0,850
-0,805
-0,015
+0,023
+0,023
Si
1,1
2.88
+4,0
-1,344
-1,233
-1,341
+0,036
-0,033
-0,033
Ge
1,25
2.6
+4,0
-1,227
-1,378
-1,225
+0,020
+0,048
+0,048
Figure 3: The nearest (red circle) and next nearest
(blue circle) neighboring Carbons with the impurity
center located at the center of the circle
3, Result and discussion
•
Electronic interactions between impurities and graphene
- After doping, the electron density decreases
on the dopant atom and increases in the
symmetry region of the sp2 hybrid orbitals of
the C atoms in the nearest neighborhood of the
dopant center.
Figure 4. The charge density differences for relaxed graphene doped
with: (a) Al (Gra_Al) (The inset corresponds to the 3D structure), (b)
Ga (Gra_Ga), (c) Si (Gra_Si) and (d) Ge (Gra_Ge) (isovalue of 0.01
e/Å3). The yellow and cyan regions correspond to electron
accumulation and depletion, respectively.
3, Result and discussion
•
Electronic interactions between impurities and graphene
Figure 5. (a) Total density of states (TDOS) and (d) (PDOS) of C element in undoped graphene. (b) PDOS of C element
and (e) Al in Al-doped graphene (Gra_Al). (c) PDOS of C element and (f) Si in Si-doped graphene (Gra_Si). The Fermi
level EF is set to zero and is represented by the vertical dashed line.
3, Result and discussion
•
Interaction of Ca atoms with doped graphene
Figure 6. Optimized structures of decorated Ca graphene: a) Aldoped (Gra_Al+Ca), b) Si-doped (Gra_Si+Ca), c) pure
(Gra+Ca), d) B-doped (Gra_Ga+Ca), e) Ge-doped
(Gra_Ge+Ca). The values ​indicated next to the Ca and B atoms
are the corresponding atomic charges.
Figure 7. Charge density differences for decorated Ca graphene
a) Al-doped (Gra_Al+Ca), b) Si-doped (Gra_Si+Ca), c) pure
(Gra+Ca), d) Ga-doped (Gra_Ga+Ca), e) Ge-doped
(Gra_Ge+Ca) (isosurface value 0.002 e/Å3). The yellow and
cyan regions correspond to electron accumulation and depletion,
respectively. . The insets correspond to the structures at different
views
3, Result and discussion
•
Interaction of Ca atoms with doped graphene
Table 2: The characteristics of the decorated Ca structure
X
dCa-Gra (Å)
dX-Gra (Å)
QCa (e)
QX (e)
Eb(Ca) (eV)
Bulk
cohesive
energy (eV)
Al
1.326
1.568
+1.394
+2.503
-5.683
3,3
Ga
1.314
1.645
+1.391
+2.077
-5.966
2.4
Si
1.465
1.429
+1.365
+2.788
-3.395
4,6
Ge
1.382
1.654
+1.390
+2.197
-5.241
4,7
+0,817
-
-0,72
-
Pure
2.293
graphene
-
3, Result and discussion
•
Interaction of Ca atoms with doped graphene
- Fermi level shifted above Dirac point
- Shows graphene p-state gains electrons
- Confirms electron addition from Ca
Figure 8. PDOS results of 2s and 2p C a) Al-doped decorated
Ca, b) Si-doped decorated Ca, c) Ga-doped decorated Ca, d)
Ge-doped decorated Ca. The Fermi level EF is set to 0
indicated by the dashed line
3, Result and discussion
•
Interaction of Ca atoms with doped graphene
Figure 9. PDOS results of 4s, 3p Ca and PDOS of 3d Ca TH a,b) Al-doped decorated Ca, c,d) Sidoped decorated Ca, e,f) Ga-doped decorated Ca, g,h) Ge-doped decorated Ca. The Fermi level EF
is set to 0 indicated by the dashed line.
3, Result and discussion
•
Adsorption of H2 molecules
Figure 10. Optimized structure of decorated Ca graphene for adsorption of 1 H2 and 4 H2
of the following phases a,b) Al doped, c,d) Si doped, e,f) Ga doped, g,h) Ge doped.
3, Result and discussion
•
Adsorption of H2 molecules
Table 3. Adsorption energy for each H2 molecule during adsorption with Ca center
Structure
Eads(H2) (eV)
H2_1
H2_2
H2_3
H2_4
Gra_Al+Ca
-0.136
-0.283
-0.194
-0.196
Gra_Ga+Ca
-0.138
-0.282
-0.228
-0.138
Gra_Si+Ca
-0.131
-0.277
-0.197
-0.192
Gra_Ge+Ca
-0.140
-0.281
-0.203
-0.180
+, 1 H₂ molecule: Binding energy around 0.13–0.14
eV → suitable for electrostatic adsorption.
+, 2 H₂ molecules: Binding energy increases to
~0.28 eV → ideal for maintaining the bond at room
temperature.
+, 3–4 H₂ molecules: Binding energy decreases but
is still higher than the first molecule, except for the
Gra_Ga+Ca sample.
The binding enhancement >0.20 eV indicates the
influence of Kubas-type interactions, beyond purely
electrostatics.
3, Result and discussion
•
Adsorption of H2 molecules
There is a significant similarity between the four
Gra_Al/Ga/Si/Ge+Ca samples.
+, 1 H₂ molecule: The electron density moves from
the outside to between H₂ and Ca → response
polarization of H₂ under the effect of Ca electric
field.
Figure 11. Charge density differences for the optimized structures of Gra_Al+Ca/nH2 (n +, 2–4 H₂ molecules: The electron density shows
= 1-4): (a) 1 H2, (b) 2 H2, (c) 3 H2, (d) 4 H2 (isosurface value is 0.001 e/Å3). The
Kubas-type orbital interactions, in which:
yellow and cyan regions correspond to electron accumulation and depletion, respectively.
+, H₂ transfers electrons from the bonding σ orbital
to the empty 3d orbitals of Ca.
+, Ca transfers electrons from the filled 3d orbitals to
the antibonding σ orbital* of H₂.
→ Consequence: Increase in H–H bond length from
0.75 Å → 0.76 Å.
Figure 12. Changes in (a) Bader charge of Ca (Q₍Ca₎) and (b) total Bader charge of
adsorbed H2 molecules during adsorption of n H2 on graphene (n = 1-4).
3, Result and discussion
•
Adsorption of H2 molecules
+, 1 H₂ molecule: There is a small
contribution of the Ca 3d state to the PDOS
peak of H₂ at ~ -9 eV → indicating dz² – σ
interaction.
+, 2–4 H₂ molecules:
+, The PDOS peak of H₂ has contributions
from the Ca 3d states (in the range of -7 to -9
eV) → electron transfer from H₂ to Ca.
+, There is also a contribution from the H₂
state at higher energy → indicating reverse
electron transfer from Ca to H₂.
Figure 13. Partial charge densities (PDOS) of 2p C, 1s H, 4s Ca and 3d Ca orbitals in H2
adsorption structures: a,b) Gra_Al+Ca/nH2, c,d) Gra_Si+Ca/nH2, e,f) Gra_Ga+Ca/nH2, g,h)
Gra_Ge+Ca/nH2 with n = 1, 4 corresponding to 2 characteristic stages in the adsorption
process. The Fermi level EF is set to 0 represented by the dashed line.
3, Result and discussion
- All 4 structures stably adsorb 4 H₂ molecules with an average energy of ~ –0.2 eV/H₂ → suitable for
the ideal physical adsorption region according to DOE standards.
- Maximum mass storage density (4 H₂):
+ Gra_Al+Ca: 1.79 wt%
+ Gra_Ga+Ca: 1.633 wt%
+ Gra_Si+Ca: 1.786 wt%
+ Gra_Ge+Ca: 1.623 wt%
→ Not meeting DOE standards (6.5 wt%) for transport applications.
- Conclusion: Gra_X+Ca materials have the potential to store H₂, especially through electrostatic
interactions with Ca.
- Development direction: Increase the density of Ca centers or add more elements to improve storage
efficiency.
Thank you for your
listening