First Principles Investigation of Nanomaterials for ... · First Principles Investigation of Nanomaterials for Hydrogen Generation and Hydrogen Storage Shwetank Yadav Masters of Applied

First Principles Investigation of Nanomaterials for Hydrogen

Generation and Hydrogen Storage

by

Shwetank Yadav

A thesis submitted in conformity with the requirements

for the degree of Masters of Applied Science

Graduate Department of Materials Science and Engineering

University of Toronto

c© Copyright 2015 by Shwetank Yadav

Abstract

First Principles Investigation of Nanomaterials for Hydrogen Generation and Hydrogen Storage

Shwetank Yadav

Masters of Applied Science

Graduate Department of Materials Science and Engineering

University of Toronto

2015

Ab initio computational modelling was used to examine nanoscale materials for renewable energy appli-

cations. Hydrogen production from water splitting was investigated on three edges of two-dimensional

monolayer molybdenum disulfide by studying active sites, reaction pathways, activation energies and

rates of reaction. The Mo-edge termination was found to adsorb and spontaneously dissociate water

at room temperature conditions. Hydrogen storage through adsorption was studied on metal decorated

graphene, defective graphene and metal decorated non-graphene 2-D carbon allotropes. Nickel was found

to produce the best hydrogen gravimetric density for metal decorated graphene at 6.12 wt.%, lower than

previous studies which neglected van der Waals forces. Defect engineered graphene produced a maximum

gravimetric density of 7.02 wt.% while the lithium decorated 2-D carbon allotropes produced a best of

7.12 wt.%.

ii

Acknowledgements

I would like to express thanks to my supervisor Professor Chandra Veer Singh. He has displayed tremen-

dous patience in guiding me through my research, greatly enhanced my learning experience and provided

with me valuable technical, career and personal advice. I would also like to extend my gratitude to the

members of the Computational Materials Engineering Laboratory, especially Kulbir Kaur Ghuman, for

their collobaration and advice throughout my time with them. I would also like to thank the Connaught

Research Fund, NSERC and the Department of Materials Science and Engineering for funding this re-

search. Finally I would like to acknowledge SciNet, Calcul Quebec and Compute Canada for providing

the computing resources for carrying out this research.

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Contents

1 Introduction 1

1.1 Background Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.1 Hydrogen production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.2 Hydrogen storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Computational atomistic modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Thesis objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.5 Thesis organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Atomistic Modeling 7

2.1 Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Born-Oppenheimer approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.2 Hartree-Fock and the variational principle . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.3 Hohenberg-Kohn theorems and Kohn-Sham equations . . . . . . . . . . . . . . . . 9

2.1.4 Plane-wave periodic systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.5 Pseudopotentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 Nudged Elastic Band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3 Ab Initio Molecular Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.1 Metadynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Water Dissociation on Two-dimensional Molybdenum Disulfide Edges 15

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.3 Computational Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.3.1 Ab Initio Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.3.2 Structure Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.4.1 Adsorption of H, OH and H2O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.4.2 Dissociation of H2O on MoS2 edges . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.4.3 Free Energy with Vibrational and Entropic Contributions . . . . . . . . . . . . . . 28

3.5 Finite temperature ab initio molecular dynamics . . . . . . . . . . . . . . . . . . . . . . . 29

3.6 Metadynamics biased finite temperature ab initio molecular dynamics . . . . . . . . . . . 29

3.6.1 Mechanism 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.6.2 Mechanism 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

iv

3.7 Surface Processes Subsequent to Water Dissociation . . . . . . . . . . . . . . . . . . . . . 34

3.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4 Hydrogen Storage on Metal Decorated Graphene 36

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36



4.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.4.1 Metal anchoring over graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.4.2 Hydrogen adsorption on metal-decorated graphene . . . . . . . . . . . . . . . . . . 42

4.4.3 Optimal hydrogen storage on Ni-decorated graphene . . . . . . . . . . . . . . . . . 45

4.4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5 Hydrogen Storage on Defective Graphene 53

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53



5.4 Hydrogen Binding over Individual Defect Systems . . . . . . . . . . . . . . . . . . . . . . 56

5.4.1 Pristine Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.4.2 Stone-Wales Defect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.4.3 Single Vacancy Defect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.4.4 585 Double Vacancy Defect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.4.5 555-777 Double Vacancy Defect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.4.6 5555-6-7777 Double Vacancy Defect . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.4.7 Bilayer Graphene with Single Vacancy Defect . . . . . . . . . . . . . . . . . . . . . 62

5.5 Hydrogen Binding over Multiple Defect Systems . . . . . . . . . . . . . . . . . . . . . . . 62

5.5.1 Grain Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.5.2 Mixed Stone-Wales and Single Vacancy . . . . . . . . . . . . . . . . . . . . . . . . 63

5.5.3 Single Vacancy with Metal Decoration . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.5.4 Single Vacancy Maximum Hydrogen Density (SVMD) System . . . . . . . . . . . . 64

5.5.5 Stone Wales Single Vacancy Maximum Hydrogen Density (SWSVMD) System . . 66

5.6 Discussion: General Trends Towards Defect Engineering of Graphene for Hydrogen Storage 67

5.6.1 Individual Defect Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.6.2 Mixed Defect Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6 Hydrogen Storage on Two-Dimensional Carbon Allotropes 78

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78



6.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.4.1 Metal Adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.4.2 Hydrogen Adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

v

6.4.3 Maximum Gravimetric Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

7 Conclusion and Future Work 90

7.1 Summary and overall contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

7.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

Bibliography 92

vi

List of Tables

1.1 Energy content by mass for hydrogen and conventional fuels. . . . . . . . . . . . . . . . . 2

3.1 Calculated structural parameters and adsorption energies of H2O, OH and H for the most

stable site on S100-edge, S-50-edge and Mo-edge. Eads (eV) represents the adsorption

energy, h(A) represents the vertical height of the H2O, OH and H species from the surface,

dO−H represents the OH bond lengths for OH and H2O molecules and αHOH represents

the H-O-H angle for H2O molecule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.1 Binding energies (eV), vertical adatom distance with respect to graphene sheet (A) and

literature values (Lit.) for single sided metal decoration. The adatom positions over

graphene are indicated in brackets, where H stands for adatom at the hollow, B stands

for adatom on the bridge between two carbon atoms and T stands for adatom above a

carbon atom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.2 Binding energies per atom (eV), vertical adatom distance with respect to graphene sheet

(A) and literature values (Lit.) for double sided metal decoration. The adatom positions

over graphene are indicated in brackets, where H stands for adatom at the hollow, B

stands for adatom on the bridge between two carbon atoms and T stands for adatom

above a carbon atom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.3 Average hydrogen binding energy (eV/H2) for metal graphene system. The adatom posi-

tions over graphene are indicated in brackets, where H stands for adatom at the hollow,

B stands for adatom on the bridge between two carbon atoms and T stands for adatom

above a carbon atom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.4 Average hydrogen binding energy (eV/H2) for increasing number of adsorbed hydrogen

molecules and different substrate sizes (in terms of number of carbon atoms). Dashed lines

indicate a simulation was not conducted, due to low chance of adsorption for 6C or low

gravimetric density for 32 C. The 16C substrate represents the best balance of substrate

size and binding energy which allows it to meet the DOE’s goal of 5.5% gravimetric density. 47

5.1 Binding energies of a hydrogen molecule placed over individual topological defects in

graphene. Multiple positions, shown in Figure 5.1, were tested for each defect type. Both

PBE-GGA and vdW-DF2 functionals were utilized to ascertain differences in binding

energies due to choice of density functional. The vdW-DF2 results all demonstrated

stronger binding and a smaller range of values among sites within a defect than the PBE-

GGA results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

vii

6.1 Average lithium adsorption energy (eV) for each two-dimensional carbon allotrope and

adsorption position. Note the bulk cohesive energy for lithium is 1.63 eV. All structures

except C31 posses lithium binding energy greater than the cohesive energy and this should

prevent metal atom agglomeration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

6.2 Average hydrogen adsorption energies (eV/H2) for each two-dimensional carbon allotrope

and adsorption position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

viii

List of Figures

1.1 Global carbon dioxide emissions from fossil fuels . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Hydrogen production methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Hydrogen storage technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1 Basic Molecular Dynamics (MD) algorithm. [1]. . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1 (a) Top and (b) side view of the perfect basal plane of 2D MoS2. Blue, red and green dotted

lines show the location of the three most thermodynamically stable surface terminations.

These terminations, along with the their simulation supercells, are shown in the following:

(c) S-edge with 100 percent (S100-edge) sulfur coverage, (d) S-edge with 50 percent (S50-

edge) sulfur coverage and, (e) S-edge with 0 percent (Mo-edge) sulfur coverage. The yellow

and the purple spheres represent S and Mo atoms, respectively. . . . . . . . . . . . . . . . 18

3.2 Locations of H, OH and H2O adsorption sites on (a) S100-edge, (b) S50-edge and (c)

Mo-edge. The view of the edge with the MoS2 plane oriented perpendicular to the page

is shown in (d) with sites A and B. Mo atoms are in purple, S atoms are in yellow, and

sites A and B are represented by pink spheres. . . . . . . . . . . . . . . . . . . . . . . . . 19

3.3 Isosurfaces of the charge density difference ∆ρ for H2O molecule adsorbed on the most

stable site for (a) S100-edge, (b) S50-edge and (c) Mo-edge. The purple, yellow, blue and

red spheres are Mo, S, H and O atoms, respectively. The positive and negative isosurfaces

are in pink and blue, indicating regions of charge gain and loss respectively. . . . . . . . . 21

3.4 Reaction pathway and reaction barrier of single water dissociation on S100-edge from

Climbing Image Nudged Elastic Band (CI-NEB) simulation. Purple atoms represent Mo;

yellow atoms represent S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.5 Reaction pathway and reaction barrier of single water dissociation on S50-edge from

Climbing Image Nudged Elastic Band (CI-NEB) simulation. Purple atoms represent Mo;

yellow atoms represent S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.6 Reaction pathway and reaction barrier of single water dissociation on Mo-edge from Climb-

ing Image Nudged Elastic Band (CI-NEB) simulation. Purple atoms represent Mo; yellow

atoms represent S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.7 Reaction mechansim of H2O dissociation reaction on Mo-edge of MoS2 during unbiased

ab-intio molecular dynamics simulation at 300K. The reaction roughly follows the same

path as CI-NEB simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

ix

3.8 Free energy surface of Mechanism 1 in terms of collective variables for metadynamics

biased AIMD simulation at 300K with corresponding atomic configurations at specific

energy minima. The dissociation reaction proceeds from point A to B. However, the

deepest energy well and largest activation barrier corresponds to adsorption of the water

molecule at point C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.9 Free energy surface of Mechanism 2 in terms of collective variables for metadynamics

biased AIMD simulation at 300K with corresponding atomic configurations at specific

energy minima. The dissociation reaction proceeds from point A to B and then C, leaving

behind a lone adsorbed O atom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.1 Possible adsorption sites for metal atoms. From left to right, the adatom is at the hollow

site, the top site and the bridge site respectively. . . . . . . . . . . . . . . . . . . . . . . . 38

4.2 Isosurfaces of charge density and charge density difference for (a) Ni and (b) Al adatoms

adsorbed on graphene. In the charge density difference isosurfaces, yellow indicates regions

of charge gain and blue indicates regions of charge loss. The Al atoms, a light metal, show

greater charge loss and a smaller region of remaining charge density than the heavy metal

Ni atoms. This might be one reason for heavier metal atoms possessing stronger hydrogen

binding energy as they have greater charge which can interact with hydrogen molecules. . 41

4.3 PDOS of Ni-graphene system simulations with (a) GGA functional alone and (b) GGA

functional with vdW-DF2 corrections. The greater number of peaks and width of the Ni

d-shell orbital for (a) indicates more distinct localized energy states and stronger potential

for interaction with a hydrogen molecule. . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.4 Examples of the hydrogen-metal complexes formed by transition metals, palladium on the

left and copper on the right. The hydrogen molecule has dissociated and moved towards

a chemisorbed state, producing stronger hydrogen binding energies for transition metals. . 45

4.5 Supercells used for differing Ni metal coverage simulations: (a) 6 carbon atoms (b) 16

carbon atoms (c) 32 carbon atoms (d) 72 carbon atoms . . . . . . . . . . . . . . . . . . . 46

4.6 Average hydrogen binding energy (eV/H2) for Ni-decorated graphene systems at different

substrate sizes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.7 Average hydrogen binding energy (eV/H2) for increasing number of adsorbed hydrogen

molecules and different substrate sizes (in terms of number of carbon atoms) . . . . . . . 48

4.8 Maximum theoretical hydrogen gravimetric density (wt.%) for different number of ad-

sorbed hydrogen molecules and substrate sizes (in terms of number of carbon atoms).

Note that not all of the systems successfully adsorbed the hydrogen molecules (see Figure

4.7). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.9 Configurations of adsorbed hydrogen on the 16 carbon Ni decorated supercell, with in-

creasing numbers of hydrogen molecules: (a) 2, (b) 4, (c) 6, (d) 8 & (e) 10. . . . . . . . . 49

4.10 Correlation between hydrogen gravimetric density (wt.%) and average binding energy

(eV/H2) for the 16 carbon substrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.11 PDOS of 16 carbon Ni decorated supercell system with increasing numbers of adsorbed

hydrogen molecules: (a) 2, (b) 4, (c) 6, (d) 8, & (e) 10. The Fermi level is indicated by a

dashed line. The charge density difference of the system with 2 hydrogen molecules (red

colored atoms) adsorbed is shown in (f), where yellow indicates regions of charge gain and

blue indicates regions of charge loss and carbon atoms are black colored. . . . . . . . . . . 51

x

5.1 Supercells for hydrogen binding over individual defect systems depicting different initial

positions for the adsorption of a hydrogen molecule: (a) Pristine (b) SW (c) SV (d) DV

585 (e) DV 555-777 (f) DV 5555-6-7777. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.2 Top view of charge density for studied defective graphene systems (except for SV, found

in Fig. 5.10. The highest amount of charge can be seen to concentrate around the carbon

atoms arranged in rings. Conversely, the lowest amount of charge is present in the hollow

regions of these rings. The very high charge density around the carbon atoms make

the top and bridge positions unfavourable for adsorption. Among hollow positions, the

pentagon rings seem to have the most optimum charge density for favourable hydrogen

adsorption, whearas the lower charge densities of the larger rings leads to slightly weaker

binding energies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.3 A side cross-section of the single vacancy defect: (a) prior to and (b) after adsorption of

hydrogen molecule. Adsorption of the hydrogen molecule clearly distorts the graphene

sheet, pushing the atoms adjacent to the vacancy out of the plane away from the hydrogen

molecule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.4 Grain boundary defect consisting of 5-7 rings, analogous to Σ7 defect, and adsorbed

hydrogen molecules. Two adjacent supercells are shown to visualize the grain boundaries

indicated by the dashed lines. Note the different orientations of the graphene lattice on

each side of a grain boundary, indicating different grains. . . . . . . . . . . . . . . . . . . 63

5.5 Mixed defect system showing single vacancy at the top-left and Stone-Wales in the center.

The hydrogen molecule is adsorbed at the penta position in the Stone-Wales defect. The

hydrogen binding energy is significantly higher in this mixed defect system than for either

defect in isolation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.6 Single vacancy defect system with double-sided nickel metal decoration and hydrogen

molecule adsorption: (a) top view and (b) side view. The nickel atoms are anchored over

a single vacancy, while the adjacent vacancy is left undecorated. Although the hydrogen

molecule binding energy is still within the preferred range for hydrogen storage, it is

weaker than that of the corresponding system without vacancies. . . . . . . . . . . . . . 65

5.7 Defect engineered systems for hydrogen stroage: (a) SVMD system prior to hydrogen

adsorption, (b) SVMD system subsequent to hydrogen adsorption top view and (c) side

view. A total of 11 hydrogen molecules were adsorbed to yield a gravimetric density of

5.81%. Nine of the hydrogen molecules dissociated into individual atoms. The underly-

ing graphene sheet itself has undergone significant structural distoration subsequent to

hydrogen adsorption. The SWSVMD system prior to adsorption (d) is also shown, and

subsequent to hydrogen adsorption (b) top view and (c) side view. . . . . . . . . . . . . . 66

5.8 Change in average hydrogen binding energy of high defect density systems with increasing

number of hydrogen molecules: (a) single vacancy (SVMD) system (b) Stone-Wales and

single vacancy (SWSVMD) system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.9 The effect of interlayer spacing on the average hydrogen binding energy of high defect

density systems: (a) single vacancy (SVMD) system (b) Stone-Wales and single vacancy

(SWSVMD) system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

xi

5.10 Top view charge density plot for the single vacancy defect. The three carbon atoms

adjacent to the vacancy can be observed to have lower charge density around them in

comparison to the rest of the carbon atoms in the graphene sheet. The carbon atom with

a dangling bond is located just above the vacancy in the figure. The other two adjacent

atoms have a greater amount of charge between them than the amount of charge between

either of them and the dangling bond atom, giving these two adjacent atoms slightly

higher stability than the dangling bond atom. . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.11 Projected Density of States (PDOS) of graphene systems prior to hydrogen adsorption:

(a) pristine graphene (b) single vacancy defect (SV). The Fermi level is represented by

the dashed vertical line. The dangling bond carbon atom in the SV defect has less co-

ordination than atoms in the pristine graphene. Hence, its orbitals have a lower extent of

overlap and hybridization, leaving them more distinct and localized. This is visible from

the higher number of peaks in the PDOS for the SV defect at all energies. The unshared

charge in the more localized SV defect makes it more attractive for adsorpting a hydrogen

molecule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.12 Side view of single vacancy (SV) charge density: (a) relaxed SV prior to adsorption and

(b) relaxed SV with adsorbed hydrogen molecule. Black filled circles represent carbon

atoms, while white filled circles represent hydrogen atoms. Regular hexagons of high

charge density usually found in graphene sheets can be seen on the left and right edges

of either diagram. In (a), the dangling bond carbon atom has a samller region of lower

charge than the hexagons and the low charge density of the vacancy region is also visible.

In (b), the dangling bond carbon atom has higher charge density equivalent to that of the

hexagons and the vacancy region also has visibly increased charge density. This increased

charge density is likely due to the charge supplied by the hydrogen molecule. . . . . . . . 74

5.13 Charge density plots of the mixed Stone-Wales and single vacancy system: (a) prior

to hydrogen adsorption and (b) subsequent to hydrogen adsorption. Single vacancies are

visible at the top left and right of the figures, while the Stone-Wales defect is in the center.

There is large redistribution of charge after adsorption of the hydrogen molecule (blue

atoms), with the regions around the pentagons of the Stone-Wales defect losing charge

to the single vacancies. This lower region of charge then strongly binds the hydrogen

molecule, leading to higher hydrogen binding energies than was the case for either defect

by itself. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

6.1 Substrate structures and hydrogen adsorption sites of the six studied two-dimensional

carbon allotropes with double-sided lithium decoration: a) C31; b) C41; c) C62; d) C63

hexa; e) C63 tri; f) C64 hexa; g) C64 square; h) C65 hexa; i) C65 penta. . . . . . . . . . . 81

6.2 Average metal binding energies (eV/atom) at multiple sites for the six studied two-

dimensional carbon allotropes with double-sided lithium decoration . . . . . . . . . . . . . 82

6.3 Projected density of states (PDOS) for the lithium decorated two-dimensional carbon

allotropes from simulations using the vdW-DF2 functional: a) C31; b) C41; c) C62; d)

C63; e) C64; f) C65. There is evidence of sp hybridization within the carbon sheet and

hybridization between the lithium and carbon atoms. The C65 structure displays the

greatest degree of hybridization and electron sharing while the C31 structure displays the

highest localization of electrons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

xii

6.4 Average hydrogen binding energies (eV/H2) at multiple sites for double sided lithium

decorated carbon allotrope systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

6.5 Charge density difference isosurfaces for (a) C64-hexa and (b) C63-hexa systems. Yellow

indicates regions of charge gain, blue indicates regions of charge loss, green indicates

lithium atoms and red indicates hydrogen atoms. The isosurfaces show clear polarization

around the hydrogen molecules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

6.6 Configuration of C64 system with maximum number of adsorbed hydrogen molecules.

Each lithium atom binds two hydrogen molecules to give eight molecules in the system

and a hydrogen gravimetric density of 2.6 wt%. . . . . . . . . . . . . . . . . . . . . . . . . 87

6.7 Configuration of C41 system with maximum number of adsorbed hydrogen molecules.

Each lithium atom binds three hydrogen molecules to give twenty four molecules in the

system and a hydrogen gravimetric density of 7.1 wt%. . . . . . . . . . . . . . . . . . . . . 88

xiii

List of Acronyms and Symbols

Acronym DescriptionAIMD ab initio molecular dynamicsCV collective variableDFT density functional theoryFS final stateGGA generalized gradient approximationIS initial stateLDA local density approximationMEP minimum energy pathNEB nudged elastic bandPDOS projected density of statesTISE time independent Schrodinger equationTS transition state

Symbol Units Descriptionr spatial coordinates of electronsR spatial coordinates of nuclein(r) - electron density

H - Hamiltonian operatorΨ - eigenvector term representing wavefunctionsE - eigenfunction term representing system energyExc - exchange-correlation functional, component of system energy EEsubscript eV DFT obtained ground state energy for subscript specified system or

process (activation, adsorption), representing potential energy for afixed configuration of atoms

Gsubscript eV free energy of subscript specified system or process (activation, ad-sorption)

xiv

Chapter 1

Introduction

The extensive use of fossil fuels for energy production in the world economy is of concern with regards

to the pollution and carbon dioxide emissions produced during energy extraction processes. Climate

change as a result of rising global temperatures is predicted to have serious negative impacts on human

societies and is only expected to rise in the future with current technologies and increasing growth in

the developing world [2]. Indeed, atmospheric carbon dioxide concentrations have risen drastically over

the last century to around 400 ppm [3], while it is suggested by scientists that concentrations should be

reduced to 300 ppm [4]. The majority of this increase is widely considered to be from human activities,

particularly burning of fossil fuels [5] (see Figure 1.1).

Figure 1.1: Global carbon dioxide emissions from fossil fuels. [6].

Hence, a replacement for conventional fossil fuels which does not increase carbon dioxide emissions

is required. Hydrogen is considered a good candidate for such an alternative clean fuel as it can used

to produce energy with no carbon dioxide emissions. This is accomplished through the following overall

1

Chapter 1. Introduction 2

reaction, where the only byproduct is water:

2H2(g) +O2(g) → 2H2O(l) (1.1)

Hydrogen also has a high energy content by mass compared to conventional fossil fuels such as gasoline

(Table 1.1). Furthermore, hydrogen provides flexibility in that it can produce energy through combustion

Fuel Energy Content (MJ/kg)Hydrogen 120Liquefied natural gas 54.4Propane 49.6Automotive gasoline 46.4Automotive diesel 45.6Ethanol 29.6

Table 1.1: Energy content by mass for hydrogen and conventional fuels. Adapted from Ni et al.[7]

(via internal combustion engines or gas turbines) or electrolytic reaction (via fuel cells) and can be used

in both stationary and transportation applications. However, there are several technical challenges,

such as high cost and low efficiency, [8, 9] facing the practical implementation of a widespread hydrogen

energy system which consists of clean and renewable hydrogen production, storage and usage. Novel

nanomaterials such as two-dimensional substances and nanoparticles offer the possibility of overcoming

these technical challenges which current solutions are unable to satisfactorily solve.

1.1 Background Information

1.1.1 Hydrogen production

One of the problems associated with using hydrogen as a fuel is that it is not easily found in nature and

so must be extracted from other compounds. There are currently multiple possible routes for hydrogen

production (Figure 1.2), however the majority of current global hydrogen is produced from fossil fuels

[8] through steam reformation of natural gas or from crude oil fractions in refineries. This defeats the

purpose of using hydrogen to reduce fossil fuel use and so there is a focus on renewable methods of

production. Hydrogen from water splitting is particularly attractive as it uses an abundant feedstock

present in much higher quantities and requiring less processing than biomass.

The splitting of water itself presents several challenges due to the high energy input required for

traditional electrolytic dissociation. As such, there are numerous thermochemical, photochemical and

electrochemical approaches proposed which utilize energy from renewable sources and catalysts to reduce

the energy needed to drive the water dissociation reaction forward [9]. Photocatalytic materials are

interesting as they split water powered by passive sunlight and thus have greatly reduced greenhouse

gas emissions [10]. Many studied photocatalytic materials are heterogeneous metal compounds such as

metal oxides, nitrides and sulfides [11].


Figure 1.2: Hydrogen production methods. Reprinted from [9] with permission from Elsevier.

1.1.2 Hydrogen storage

One major issue facing deployment of hydrogen fuel systems is that of easy storage and transportation,

which is not possible with current technologies [12]. Despite having a high energy content by mass,

hydrogen has very low volumetric densities compared to fossil fuels. Conventional systems such as high

pressure compressed gas storage or low temperature cryogenic gas storage present problems as they

operate under extreme and unsafe conditions [13]. As a result, a variety of storage methods have been

proposed and adsorption of hydrogen on solid substrates has received intense research focus [14], looking

at high specific area substrates such as metal organic frameworks [15], carbon nanotubes [16] and boron

nitride sheets [17] and fullerenes [18]. Figure 1.3 showcases many of the hydrogen storage technologies

being currently looked at.

Adsorption based technologies also have to deal with providing sufficient hydrogen gravimetric den-

sity due to the added mass of the substrate and low relative mass of hydrogen. The United States

Department of Energy (DOE) has set an initial hydrogen gravimetric density target [19] of 5.5 wt.%

for light transportation applications and this is often the goal for adsorption based hydrogen storage

solutions.

1.2 Computational atomistic modeling

This study primarily consists of first principles based modeling of material properties at the atomic scale.

Computational modeling complements experimental investigations by probing processes inaccessible or

unfavorable to experimental study or by speeding up and providing direction to experimental discovery

of materials. In the latter role, it can screen materials and rank them according to a specific property,

yielding the most suitable materials for further experimental testing. This process can be potentially

much faster and cheaper than experimental based screening and more logically directed than the trial

and error approach often used in experimental discovery [20]. Computational simulations can predict the

stable phases, structural properties, thermal properties and electronic properties such as band structure

of these materials and greatly contribute to optimization of a material for a particular application. These

abilities are especially useful for the study of nanoscale materials such as graphene, a two-dimensional


Figure 1.3: Hydrogen storage technologies. Reproduced from [13] with permission of The Royal Societyof Chemistry.

material with a single atomic length thickness, which can be easily simulated computationally but are

quite cumbersome to handle and analyze experimentally.

Techniques such as Density Functional Theory (DFT), which incorporates electronic behavior of

atoms into its model, allow the investigation of specific atoms and bonds in a system. For example,

some of the work as part of thesis looked at the interaction of a single hydrogen molecule with a single

metal atom adsorbed on a graphene surface and obtained electron charge distribution for the system and

information on its thermodynamic stability. Such powerful abilities are particularly useful in the study of

complex systems such as heterogeneous catalysts in which multiple factors affect performance and it can

be challenging to experimentally isolate the effect of a particular variable. Furthermore, it is also difficult

to study reaction mechanisms where transition species cannot always be determined or intermediate steps

happen very quickly and often cannot be observed directly. In such cases, computational investigations

can provide excellent insights as they can simulate the evolution of a reaction at femtosecond scale

time lengths using techniques such as Ab Initio Molecular Dynamics (AIMD) and obtain information on

charge transfer, transition state configurations, adsorption energies and activation barriers while tightly

controlling the conditions of the simulation and composition of the substances involved.

Atomistic scale modeling deals with a large amount of model information and has become more

widespread in recent years due to the increase in available computational power. Typically such calcula-

tions are done on supercomputer systems as desktop machines would not produce results in a reasonable

time frame. The calculations for this work were carried out on the SciNet [21] supercomputer cluster and

the Briare and Guillimin clusters of Calcul Quebec operated under the Compute Canada Consortium.


1.3 Motivation

Nanomaterials provide exceptional properties, such as very high specific surface area, and an unprece-

dented ability to modify and tune such characteristics. Hence, they make very promising candidates

for overcoming the technical challenges related to the very important sustainable energy issues outlined

in Section 1.1. For example, the atomic layer thick two-dimensional material called graphene has been

labeled a wonder material which has phenomenal properties and possible applications across an enor-

mous number of fields [22]. Since the discovery of graphene there have been a large number of further

two-dimensional materials, both synthesized and theoretically proposed, which also display exceptional

properties [23]. Nanoparticles have also been the focus of intense research activity and optimism in

producing superior materials properties [24, 25]. Such nanoscale materials make ideal candidates for in-

vestigation through DFT modeling and there has been an explosive growth in research papers with such

studies over the last two decades. Hence, DFT was used to explore graphene and other two-dimensional

carbon allotropes such as graphyne for their use in hydrogen storage applications, two-dimensional MoS2

as a photocatalyst for water splitting as part of hydrogen production and In2O3 nanoparticles as pho-

tocatalysts for hydrogenation of carbon dioxide into methanol. Each of these materials shows great

promise in improving on the performance of the best currently available technologies for each of these

applications.

1.4 Thesis objectives

The use of nanoscale materials, consisting of two-dimensional materials and nanoparticles, for use in

renewable hydrogen production hydrogen storage and atmospheric carbon dioxide mitigation applications

was evaluated through density functional theory with the following specific objectives:

• Investigate Hydrogen Production from Water on Two-Dimensional Molybdenum Disul-

fide

◦ Determine active sites and binding energies for water adsorption on MoS2-edge terminations

◦ Determine reaction mechanisms and activation barriers for water dissociation on MoS2-edge

terminations

• Investigate Hydrogen Storage on Two-Dimensional Carbon Substrates

◦ Study the hydrogen binding energies of metal decorated graphene with various metal adsor-

bates and accurate van der Waals corrections and determine the maximum possible hydrogen

gravimetric density for such systems

◦ Investigate the effect of point defects and mixed defect regions on hydrogen adsorption ability

of graphene and determine the maximum possible hydrogen gravimetric density for such

systems

◦ Evaluate the hydrogen adsorption ability of lithium decorated two-dimensional carbon al-

lotropes other than graphene and determine their maximum possible hydrogen gravimetric

density


1.5 Thesis organization

The outline of this thesis is as follows: chapter 2 introduces the theoretical concepts behind the atomistic

modeling techniques used for this work; chapter 3 focuses on evaluating water adsorption and dissociation

on MoS2-edge terminations; chapter 4 focuses on hydrogen storage on metal decorated graphene; chapter

5 focuses on hydrogen storage on defective graphene; chapter 6 focuses on hydrogen storage on non-

graphene metal decorated two-dimensional carbon allotropes; and chapter 7 provides conclusions and

possibilities for future work.

Chapter 2

Atomistic Modeling

The research presented in this thesis utilized the computational technique of Density Functional Theory

(DFT) which allows for the atomic scale modelling of materials with the inclusion of electron effects in a

relatively efficient manner. The DFT technique was used to calculate the ground state energies of systems

with various compositions and configurations. The energy difference in system configurations allowed

for the prediction of stability and relative favorability of each configuration. This was then used to find

the adsorption energy of various chemical species on substrates throughout the study. Additionally, the

Nudge Elastic Band (NEB) method was used in conjunction with DFT calculations to find the activation

energy barrier for the water dissociation reaction. Ab Initio Molecular Dynamics (AIMD) was used to

include finite temperature effects in which a system was allowed to dynamically evolve over time while

keeping track of its potential energy. Such AIMD simulations were also biased using a metadynamics

potential which allowed for the calculation of the system’s free energy and the energy barrier for the

water dissociation reaction. The Quantum Espresso [26] software suite was used to carry out all DFT

simulations in this work, with the added PLUMED [27] plug-in to facilitate metadynamics biased AIMD.

The following sections explain the theoretical basis for the mentioned techniques.

2.1 Density Functional Theory

The Schrodinger equation can fully describe the quantum state of a particular set of atoms. However,

solving the partial differential equation for most systems is infeasible as the equation becomes a many-

body problem with an enormous number of dimensions. Building on a number of approximations, DFT

is able solve the non-relativistic time-independent Schrodinger equation (TISE) by greatly reducing the

number of dimensions and can reasonably predict the ground (lowest energy) state quantum properties

for a wide variety of systems in a practical time frame. The TISE is of the basic form:

HΨ = EΨ (2.1)

and consists of a Hamiltonian operator H, eigenvectors Ψ (which represent wavefunctions) and eigen-

values E (which represent system energy). The Hamiltonian in turn is composed of the following terms,

which describe a set of atoms with interacting nuclei (with spatial coordinates represented by R) and

electrons (with spatial coordinates represented by r):

7

Chapter 2. Atomistic Modeling 8

H = Te(r) + TN (R) + VeN (r,R) + VNN (R) + Vee(r) (2.2)

Here, the first term on the right represents the kinetic energy of electrons, the second term represents

kinetic energy of nuclei, the third term represents electron-nuclei interactions, the fourth term represents

nuclei-nuclei interactions and the last term represents electron-electron intereactions. This Hamiltonian

does not include a term for spin-orbit effects which are generally neglected for DFT calculations but

can be added later if desired for a particular system. The simulations in this thesis did not include

spin effects; their effect was tested for particular metal atoms and it was confirmed their effect could

be ignored. Equation 2.2 clearly shows the multiple-body problem inherent in solving the TISE as

there are interacting terms (in terms of both r and R) which must be simultaneously solved. The

Born-Oppenheimer approximation helps to reduce the difficulty in solving this equation.

2.1.1 Born-Oppenheimer approximation

The Born-Oppenheimer (BO) approximation separates an atom’s wavefunctions into components corre-

sponding to nuclei and electrons, in which the wavefunction is expressed as a product of its individual

components, Ψ(r,R) = Ψ(r)χ(R). As nuclei are much more massive than electrons, their velocities are

substantially smaller and electron motion can be considered to be occuring on a timescale where the

nuclei are almost stationary. This fact leads to the computational methodology which takes advantage

of the BO approximation as it allows the solution of two distinct math problems [28]. First positions of

the nuclei are fixed while the wavefunctions describing electronic motion within the field of the nuclei

are determined for their lowest ground state energy. As the nuclei are fixed, R acts as a parameter for

the electronic component of the wavefunction:

Ψ(r,R) = Ψ(r;R)χ(R) (2.3)

The stationary nuclei also mean that the TN (R) term of the Hamiltonian in Equation 2.2 can be

removed and the VNN (R) term can be neglected for further Hamiltonian formulations as it is a constant

and can be grouped with other such terms. The TISE, with expanded terms, is now of the form:

− h2

2m

N∑

i=1

∇2i +

N∑

i=1

V (ri) +

N∑

i=1

∑

j<i

U(ri, rj)

Ψ = EΨ (2.4)

where the the first term on the left represents the kinetic energy of electrons, the second term

represents electron-nuclei interactions and the last term represents electron-electron interactions for a

system with N electrons. Here Ψ essentially consists of the electronic wavefunction (Ψ(r)) alone. All

constants, such as χ(R) have been rolled into the E term.

Next the parameter corresponding to nuclear position (R) can be repeatedly changed and Equation

2.4 solved again for each new value to give system energy as a function of the nuclei position. This

multidimensional energy potential function describes the adiabatic potential energy surface, also known

as the Born-Oppenheimer potential energy surface. Hence, this method effectively separates electronic

and nuclear motion and solves for them independently.


2.1.2 Hartree-Fock and the variational principle

After the Born-Oppenheimer approximation, the electronic wavefunction is still a function of the co-

ordinates of all electrons in the system. The Hartree product assumes that this wavefunction can be

expressed a product of individual electron wavefunctions, which for N electrons is:

Ψ = Ψ1(r1)Ψ2(r2), . . . ,ΨN (rN ) (2.5)

These individual wavefunctions could now be solved independently of each other and again this sepa-

ration of functions would help to greatly reduce mathematical complexity. However, the simple Hartree

product does not always satisfy the antisymmetry principle which states that the wavefunction must

change sign whenever any two electrons are exchanged (from which is derived the Pauli exclusion prin-

ciple). The Hartree-Fock approximation instead approximates the electronic wavefunction with a Slater

determinant to create an anti-symmetric product of non-interacting wavefunctions. The Slater determi-

nant for N electrons is essentially a determinant of a N x N matrix of individual electron wavefunctions

which produces a sum of N! Hartree products each with individual electron wavefunctions in a different

order and has the following form:

Ψ(r1, r2, . . . , rN ) =1√N !

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

Ψ1(r1) Ψ2(r1) · · · ΨN (r1)

Ψ1(r2) Ψ2(r2) · · · ΨN (r2)...

.... . .

...

Ψ1(rN ) Ψ2(rN ) · · · ΨN (rN )

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

(2.6)

This product can be treated in a similar fashion to the Hartree product in that each electron can be

assumed to move independently of other electrons. Next the variational principle helps us to solve for

the energy and eventually wavefunction solutions of the problem. The energy is expressed as a function

of the wavefunction as:

E [Ψ] =< Ψ|H|Ψ >

< Ψ|Ψ >

< Ψ|H|Ψ > =

∫

Ψ∗HΨd−→r(2.7)

The variational principle says that this energy is always an upper bound to the true energy. By varying

the wavefunction parameters, we can minimize the energy for the particular system (find it’s ground

state energy) and better approximate the actual wavefunctions. Therefore, the true wavefunctions will

minimize the energy.

2.1.3 Hohenberg-Kohn theorems and Kohn-Sham equations

Even after the Hartree-Fock method, we are still left with solving for a high number of individual

electron wavefunctions and this remains a computationaly difficult problem. Hohenberg and Kohn

helped to simplify this problem and established DFT by introducing two important theorems which

used the electron density of the system. The electron density of the system is a spatial quantity defined


as a function of individual wavefunctions:

n(r) = 2∑

i

Ψ∗i (r)Ψi(r) (2.8)

The first theorem stated that the ground state energy in the Schrodinger equation of system is a

unique functional of the electron density. This manages to remove the many-body issue by allowing the

expression of the Schrodinger equation in terms of the electron density which only depends on three

spatial coordinates, thereby reducing the electronic description of the system to a three dimensional

problem instead of the 3N dimensions needed previously for N electrons. The second theorem stated

that the electron density which minimizes the energy functional is the true electron density which would

be produced by the exact ground state solution of the Schrodinger equation. Hence, by finding the energy

functional minimum, we can now solve for the exact electron density of the system. Unfortunately, the

Hohenberg-Kohn theorems do not provide the exact form of the energy functional and finding the form

of this energy functional remains the principle challenge in DFT to this day. The energy functional, in

terms of electron density n(r), can be written as:

E(n) = Te(n) + Vext(n) + VH(n) + Exc(n) (2.9)

The terms on the right hand side, other than the Exc [n] term, include electron kinetic energy and

Coulombic interactions between and amongst nuclei and electrons and their exact forms are known. The

remaining Exc [n] term is known as the exchange-correlation functional and includes the effects of ex-

change interaction and correlation between electrons as well any other effects, such as self-interaction cor-

rections, which are not included in the earlier known terms. The exact form of the exchange-correlation

functional for any system other than the free electron gas is not known. Over the years there have been

several approximate forms proposed to represent this term. One of the earliest and simplest functionals

is called the Local Density Approximation (LDA) which uses the local density of the exactly known

uniform electron gas to define the exchange-correlation functional. The next class of functional which is

still very widely used today is the Generalized Gradient Approximation (GGA) which incorporates both

the local density and the local gradient of the electron gas. There are numerous specific implementations

of these functionals as well more complex and hybrid functionals with additional terms available.

The energy functional in Equation 2.9 was then used by Kohn and Sham to reformulate the TISE in

terms of electron density as:

[

− h2

2m∇2 + V (r) + VH(r) + VXC(r)

]

ψi(r) = εiψi(r) (2.10)

This equation contains similar terms to those in Equation 2.4. The second term on the left defines

interaction between an electron and nuclei and the third term describes interaction between an electron

and total electron density with the following form:

VH (r) = e2∫

n(r′)

|r− r′|d3r′ (2.11)

This highlights how Equation 2.10 differs from the original TISE in the key fact that it involves only

electron density and single electron wavefunctions of three spatial variables for the terms on the left hand

side as opposed to the summation terms which included the effects of all other electrons in the original


TISE. The last potential term in the left hand side of Equation 2.10 is related to the exchange-correlation

functional from Equation 2.9 through the following relationship:

VXC (r) =δEXC(r)

δn(r)(2.12)

The Kohn-Sham equations can be then iteratively solved in a self consistent manner to find the

ground state electron density, single-particle wavefunctions and ground-state system energy.

2.1.4 Plane-wave periodic systems

When studying continuous periodic systems, as is common for solid materials and was the case for all

investigations in this work, the solution to Schrodinger’s equation must satisfy the Bloch theorem. Such

systems have a periodically repeating system space known as the supercell. The Bloch theorem states

that the Schrodinger equation solution can be expressed as a sum of terms where the wavefunction has

the following form:

ψk(r) = exp(ik · r)uk(r) (2.13)

where uk(r) is periodic in space with the same periodicity as the supercell. This implies that the

Schrodinger equation can solved for each value of k independently. The k vectors are part of k-space

which is also known as the reciprocal space used in crystallography and solid state physics fields. Solving

the DFT mathematical expressions is easier when working in k-space and this approach is commonly

adopted when working with periodic systems. Such methods are referred to as plane wave calculations as

functions with the form of the exponent on the right hand side of Equation 2.13 are known as plane wave

functions. Many calculations in k-space involve integrating functions of k vectors over the primitive cell

of the system in reciprocal space known as the Brillouin zone. The selection of k values over which to

perform integration in the Brillouin zone is an important parameter that must be specified in most DFT

implementations.

The periodic uk(r) term in Equation 2.13 can be further expanded in terms of a special set of plane

waves:

uk(r) =∑

G

cGexp(iG · r) (2.14)

Combining this equation with Equation 2.13 results in an expression involving summation over an

infinite number of G vector values. However, the functions in this combined expression can be interpreted

as solutions of the Schrodinger equation involving kinetic energy, E = h2m |k+G|2. As such, the lower

energy solutions are more significant physically and the higher energy solutions can be ignored for most

practical applications. Therefore, the infinite sum of the G vector expressions is truncated to solutions

which have kinetic energies below a certain cutoff energy. This then reduces the expression for the

solutions to the following form:

ψk(r) =∑

|G+k|<Gcut

cG+kexp[i(k+G)r] (2.15)

The cutoff energy is an important parameter that must be selected in most DFT implementations.


2.1.5 Pseudopotentials

The core electrons of atoms are often not very important for physical interactions between atoms, such

as those involving chemical bonding or electronic conductivity. Furthermore, such core electrons require

very large energy cutoffs to model in plane wave calculations due to their small length scale oscillations.

As a result the core electrons can be approximated by pseudopotentials. Pseudopotentials make use of

the frozen core approach in which the electron density for core electrons up to a certain radial cutoff is

replaced with an effective density which matches the density calculated from an all electron simulation.

This allows the usage of much lower energy cutoffs as only valence electron plane waves are solved in

each calculation and thus reduces computational expense. The three common types of pseudopotentials

are ultrasoft pseudopotentials (USPP), projected augmented wave (PAW) and norm-conserving. The

USPPs usually require the lowest energy cutoffs but contain more empirical parameters and so can be

less easily used across differing systems and computational setups.

2.2 Nudged Elastic Band

The Nudged Elastic Band (NEB) technique is essentially a method for finding the Minimum Energy

Pathway (MEP) connecting two local minima on a potential energy surface [29]. This is useful for

finding the reaction path and transition states in a proposed chemical reaction. The method works by

linearly interpolating a set of images (each image corresponding to a certain configuration of atoms)

between the initial and final states and minimizing the energy of this set of images. The images are

forced to maintain their distance to neighboring images during energy minimization by adding spring

forces between them along the path or band they form. The component of the potential force parallel

to to the band is also removed from acting on the images, ensuring that only the spring forces act on

images along the path and only potential forces act on the images perpendicular to the path (this is

referred to as the nudging). This prevents the images from relaxing to the energy minima of the initial

and final states. The Climbing Image (CI) implementation of NEB is a method for finding the true

saddle point along the MEP as normal NEB rarely has images present at this point [30]. In CI-NEB,

the highest energy image is driven up to the saddle point by removing the spring forces acting on this

image and inverting the true forces acting on this image along the tangent of the band. This results

in the highest image moving towards the maximum of the potential energy surface in the direction of

the band while minimizing its values on the potential energy surface in directions perpendicular to the

band, which causes it to reach the definition of a saddle point.

2.3 Ab Initio Molecular Dynamics

The previously described DFT methods study essentially static systems at their lowest ground state

energies where the atoms posses zero velocities. Molecular dynamics (MD) allows one to look at the dy-

namic evolution of an atom’s trajectory with atomic velocities assigned at finite temperatures. Classical

MD is described by the general algorithm outlined in Figure 2.1.

The basic premise of MD involves calculating the potential energy field for a particular configuration

of atoms. This potential can be calculated by a large number of available methods and in classical

simulations it is generally based on regarding atoms as spheres with no separation of nuclei and electrons

and taking into account various interatomic interactions. Next the potential is used to calculate the forces


Figure 2.1: Basic Molecular Dynamics (MD) algorithm. [1].

acting on each atom in the system, generally obtained by taking some form of derivative of the potential.

These forces are then fed into equations of motion which are solved for each component of the system

over some time interval. The solutions are used to propagate the positions of each atom. The equations

of motion are generally classical Newtonian or Lagrangian in form and integrated numerically. There

are various numerical schemes for the equation of motion integration and atomic propagation steps, with

one of the most common methods being the velocity verlet scheme [31] which is also used for simulations

in this work. This entire process is repeated iteratively for the desired simulation time interval.

The macroscopic properties of the system, such as temperature, are sampled using various statistical

mechanics ensemble averages, as long as the system obeys the ergodic hypothesis. In fact, MD simulations

are usually constrained based on these ensembles, common examples being the microcanonical ensemble

(in which the total system energy is conserved) and canonical ensemble (in which the system temperature

is kept constant). The latter ensemble allows the system to exchange energy with its surroundings and

is generally more representative of real world experimental conditions in which we are interested. There

are a variety of thermostats available which exchange energy with the system to maintain the canonical

ensemble (and hence maintain the temperature), for instance they often modify the velocities (and hence

kinetic energy) of the atoms in the system. The simulations in this work utilized the Andersen thermostat

[32], in which the system is coupled to a heat bath which modifies the kinetic energies of atoms using

random collision events whose collision frequency is determined stochastically. These collisions produce

new velocities based on the Boltzman distribution of velocity at the set temperature.

Ab initio molecular dynamics (AIMD) differs from classical MD chiefly in that it explicitly includes

electronic effects separately from nuclei instead of considering the whole atom as a single hard sphere

[33]. These electronic effects are then incorporated into the calculation of potentials and forces. In the

simplest form of AIMD, named Born-Oppenheimer molecular dynamics (BOMD) and the method used

for simulations in this work, the electronic and nuclear systems are fully decoupled from each other

in a manner similar to that in DFT. BOMD follows the exact same algorithm as classical MD except

that the potential and force calculation steps are performed with more in-depth calculations. A full

DFT electronic ground state calculation is conducted to obtain the potential energy of the system as


a function of spatial electron density (where as part of a normal DFT calculation following the BO

approximation, the nuclei are fixed). The forces acting on nuclei in the system are then calculated based

on the Hellmann-Feynmann theorem:

~Fi = − dE

d ~Ri

= −d⟨

Ψ∣

∣

∣H∣

∣

∣Ψ⟩

d ~Ri

=

⟨

Ψ

∣

∣

∣

∣

∣

− dH

d ~Ri

∣

∣

∣

∣

∣

Ψ

⟩

=

⟨

Ψ

∣

∣

∣

∣

∣

− dV

d ~Ri

∣

∣

∣

∣

∣

Ψ

⟩

(2.16)

These forces are then used in the normal MD algorithm to solve classical equations of motion and

then propagate the atomic nuclei as if they were classical particles. This ensures that as the system

evolves with time, it follows the Born-Oppenheimer or adiabatic potential energy surface.

2.3.1 Metadynamics

Metadynamics is a technique that can accelerate rare events in molecular dynamics simulations (both

classical MD and AIMD) by adding an extra potential to the system and can also reconstruct the free

energy of the simulation [34, 35]. The metadynamics algorithm relies on selecting a number of collective

variables (CV) to describe the system, where the collective variables are functions of spatial coordinates

(S(r)) and represent degrees of freedom analogous to reaction coordinates in other approaches. The

equilibrium probability distribution of these variables is given by :

P (s) =exp(−(1/T )F (s))

∫

ds exp(−(1/T )F (s))(2.17)

where s denotes the d dimenionsional vector representing values of the d CVs describing the system.

Here F(s) represents the free energy as a function of CVs through the following relationship:

F (s) = −T ln

(∫

dx exp

(

− 1

TV (r)

)

δ(s− S(r))

)

(2.18)

The metadynamics algorithm adds a history dependent potential to the Hamiltonian describing the

system, where the potential is built from a sum of Gaussians centered along the trajectory of the CVs.

The form of the external potential added by the metadynamics algorithm at time t is the following:

VG(S(r), t) = ω∑

t′=τG, 2τG, ... for t<t′

exp

(

− (S(r)− s(t′))2

2δs2

)

(2.19)

Here τG is the frequency of Gaussian deposition, ω is the Gaussian height and δs is the Gaussian

width. This potential helps to accelerate rare events which would take excessive simulation times to occur

in normal MD simulations. By biasing the simulation trajectory it helps to push the system out of local

free energy minima and discourages the system from returning to energy minima it has already escaped.

This is especially useful for exploring reaction pathways as the system will usually escape energy minima

through the lowest saddle points, the system can sample a wide variety of possible configurations if the

CVs are chosen well and knowledge of the final state of the system is not required (unlike in NEB).

Additionally the recorded history of the deposited Gaussians can be used to reconstruct the free energy

surface of the evolving system as the metadynamics potential eventually mirrors the free energy, after a

sufficient period of time, through the following relation:

limt→∞

VG(s, t) ∼ −F (s) (2.20)

Chapter 3

Water Dissociation on

Two-dimensional Molybdenum

Disulfide Edges

3.1 Introduction

The interaction of water molecules with solid surfaces and their possible subsequent dissociation is of

particular interest [36], especially as this is a process which serves as a precursor to various important

reactions, including the renewable generation of hydrogen from water through the hydrogen evolution

reaction (HER) and the syntheis of methanol through the water gas shift (WGS, CO + H2O→ CO2+H2)

reaction. Due to the high energetic costs of water splitting, there are many catalysts being investigated

to facilitate this process [37, 11, 38]. This work looks at two-dimensional MoS2 as one such possible

catalyst in promoting water dissociation, which has been suggested to be the rate limiting step for

hydrogen production for a variety of metals [39]. The geometries and active sites for water adsorption

were studied for three edge terminations of MoS2. Next, the activation energies for the water dissociation

reaction on each edge were determined using climbing image nudged elastic band (CI-NEB) methodology.

Finally, finite temperature effects were included through ab initio molecular dynamics (AIMD) and

metadynamics to study the water dissociation reaction on the most favorable edge. The activation

barriers were then used to estimate the rate of reaction for water dissociation.

3.2 Literature Review

Recently, various experimental studies have reported the synthesis of chalcogenide MX2 monolayers,

such as MoS2, WoS2, MoSe2, MoTe2, TiS2, TaS2, TaSe2, NiTe2, and ZrS2 [40, 41] and they have

attracted attention for a broad range of applications including electronics, optoelectronics, photovoltaics

and photocatalysis. As two-dimensional (2D) materials, they possesses a high specific surface area ideal

for catalysis and a small band-gap which allows them to be strong visible light absorbers and possibly

promote photocatalytic reactions [42]. In fact, both MoX2 and WX2 have indirect band-gaps as bulk

materials while their monolayers posses direct bandgaps [43, 44], highlighting the interesting properties

15

Chapter 3. Water Dissociation on Two-dimensional Molybdenum Disulfide Edges 16

of 2D materials. Furthermore, out of these monolayeres, only molybdenum disulphide (MoS2) has its

band positions aligned with the water oxidation and reduction potentials [45], which combined with its

stability against photocorrosion [46], make it an interesting material for use as a photocatalyst for water

splitting. Additionally, MoS2 might serve as a possible cheaper and more abundant future replacement

for precious metal catalysts (such as the optimally performing but expensive platinum).

MoS2 itself has been previously studied for potential applications as an electrocatalyst for hydrogen

evolution. While large scale bulk MoS2 is a poor catalyst [47], nanoparticles of MoS2 have shown high

activity [48, 49, 50, 51]. The HER activity for these nanoparticles is strongly associated with exposed

edge sites that have a local stoichiometry, physical structure and electronic structure that differs from

the catalytically inert basal planes of MoS2 [52, 53, 54]. Similar investigations of 2D MoS2 are critical

for designing and developing 2D MoS2 based catalytic materials. A recent theoretical study reported

that, similar to the inert basal planes of bulk MoS2, the surface of pristine 2D MoS2 is not very favorable

for water adsorption and dissociation due to the repulsive interaction between free H2O and the perfect

surface [55]. The study looked at triple vacancy defects as a way of disrupting the perfect surface and

found that they lead to exothermic adsorption and dissociation of water molecules. Another theoretical

has found that 2D MoS2 edges are potentially favorable for proton reduction [56]. However, despite

the excellent activity of bulk MoS2 edges, there is no available theoretical or experimental investigation

of the catalytic activity of 2D MoS2 monolayer edges for water adsorption and dissociation (H2O →OH + H) mechanisms in terms of thermodynamic stability, active sites, activation barriers and rates of

reactions.

3.3 Computational Details

3.3.1 Ab Initio Techniques

IIn order to understand the electronic structure and photocatalytic properties of MoS2, density functional

theory (DFT) was utilized. The Quantum Espresso [57] software package within the plane-wave basis

set approach was utilized throughout this study. Interactions between the valence electrons and the

ionic core were represented by the projector augmented wave (PAW) [58] method with Perdew-Burke-

Ernzerhof (PBE) formulation[59]. Kinetic energy cutoffs of 680 eV and 6800 eV were used for the

wave functions and the charge density, respectively. Brillouin zone integrations were performed using

a Monkhorst-Pack [60] grid of 4× 4× 1 k-points. To obtain better equilibrium separations, structural

parameters (like bond length, bond angle) and adsorption energies, long range non-local effects such as

van der Waals (vdW) forces were taken into account by applying van der Waals corrections through the

vdW-DF2 functional [61]. The structures were relaxed using a conjugate gradient minimization algorithm

until the magnitude of the residual Hellman-Feynman force on each atom was less than 0.025 eVA−1.

The evaluation of the minimum energy reaction paths (MEPs) and Transition states (TS) has been

done using the climbing image nudged elastic-band (CI-NEB) method [62, 63, 64]. Finite temperature

analysis of the system at 300 K was conducted through ab-initio molecular dynamics (AIMD) on the

Born-Oppenheimer surface which maintained temperature through the Andersen thermostat. A time

step of 2.5 fs was employed for the AIMD and Brillouin zone integrations were performed on the Γ point

in order to decrease simulation times. Biased AIMD simulations were conducted using the metadynamics

[34, 35] technique applied through the PLUMED [27] plugin with the same timestpe and temperature.


3.3.2 Structure Model

The basal plane of 2D MoS2 consists of two hexagonal planes of sulfur (S) atoms and an intercalated

hexagonal plane of molybdenum (Mo) atoms bonded to the S atoms in a trigonal prismatic arrangement,

as indicated in Fig. 3.1(a, b). A single MoS2 sheet cut along the dotted lines (Fig. 3.1(a) is terminated

by three different 1D edge terminations Fig. 3.1(c-e). The first edge termination consists of two S

atoms per Mo atom (100% S coverage) shown in Fig. 3.1(c), the second consists of single S atoms

(50% S coverage) shown in Fig. 3.1(d) and finally the third consists of Mo atoms only (0% S coverage)

as shown in Fig.3.1(e). The present study was restricted to these sulfur coverages as previous slab

calculations [65] indicate that only these coverages are thermodynamically stable. In agreement with

previous studies [65], the 100% S coverage or S100-edge exhibits S2 dimers after relaxation and the outer

Mo atoms are sixfold coordinated. Furthermore it should be noted that a slight pairing of the S2 dimers

is observed. Reducing the S coverage to 50% leads to a zigzag configuration, where the S monomers

are in a bridging position and the Mo atoms again have sixfold coordination. The S-edge with 0% S

coverage (Mo-edge) is subjected to reconstructions due to the very low coordination (twofold) of the Mo

atoms.

3.4 Results and discussion

3.4.1 Adsorption of H, OH and H2O

As a first step, active sites for the adsorption of the H2O, OH and H species were investigated. A water

coverage of 0.25 ML (i.e. one water molecule per unit cell) was used. The adsorption energy of an

adsorbate on the surface was calculated as:

∆Eads = Etot − Ebare − Ead, (3.1)

where Etot, (Ebare) are the energy of the slab with (without) adsorbate and Ead is the energy of the

isolated adsorbate species calculated in the same supercell. Hence, a negative ∆ Eads indicates stable

adsorption whereas a positive value indicates unstability. To check the advantage of the edge termina-

tions we first investigated the possibility of water dissociation on the stoichiometric 2D MoS2 surface

(basal plane). We considered various high-symmetry sites and found that the configuration of the water

molecule remains intact with it possessing a postive adsorption energy. This indicates a repulsive inter-

action between free H2O and the perfect surface of MoS2. The ∆ Eads values for H and OH were also

positive which suggests that dissociation of water on the MoS2 basal plane will not take place. This is

likely because the O atom cannot receive sufficient electrons in order to release H and is in agreement

with previous study [55].

Next, the adsorption of H, OH and H2O on the three MoS2 edges was investigated. Although each

edge had different surface configurations, they were all composed of the same basic pattern of a plane

of Mo atoms sandwiched between two planes of S atoms and thus had similar types of adsorption sites.

These common adsorption site types are shown in Fig. 3.2(a) for the S50-edge, Fig. 3.2(b) for the

S100-edge and Fig. 3.2(c) for the Mo-edge. They consisted of the following: on top of a S atom (marked

S1); on top of a Mo atom (marked Mo1); a bridge site (labelled A) between two S atoms (marked S2

and S3), above a S atom (marked S4), a bridge site (labelled B) between two S atoms (marked S1 and


Mo S

(a) Top view of Basal Plane

(b) Side view of Basal Plane

(c) S100-edge (d) S50-edge

(e) Mo-edge

Figure 3.1: (a) Top and (b) side view of the perfect basal plane of 2D MoS2. Blue, red and greendotted lines show the location of the three most thermodynamically stable surface terminations. Theseterminations, along with the their simulation supercells, are shown in the following: (c) S-edge with100 percent (S100-edge) sulfur coverage, (d) S-edge with 50 percent (S50-edge) sulfur coverage and, (e)S-edge with 0 percent (Mo-edge) sulfur coverage. The yellow and the purple spheres represent S and Moatoms, respectively.


S1

Mo1

S2

B

S3

S4

A

Mo2

(a)

S1

Mo1

A

S2

B

S3

S4

Mo2

(b)

S2 Mo1

S1

B

S3

S4

A

Mo2

(c)

A

B

(d)

Figure 3.2: Locations of H, OH and H2O adsorption sites on (a) S100-edge, (b) S50-edge and (c) Mo-edge. The view of the edge with the MoS2 plane oriented perpendicular to the page is shown in (d) withsites A and B. Mo atoms are in purple, S atoms are in yellow, and sites A and B are represented by pinkspheres.


S2) and above a Mo atom (marked Mo2). In Fig. 3.2(d) a different perspective further displays the two

bridge sites.

S100-edge

Most stable species Eads (eV) h(A) dO−H αHOH

H2O(on site Mo1) 0.15 2.989 0.9796, 0.9797 103.85OH(on site S1) -0.215 0.251 0.988 -H (on site S1) -0.155 0.206 - -

S50-edgeH2O (on site A) 0.23 2.848 0.9783,0.9838 103.55OH (on site S1) -0.275 1.682 0.995 -H (on site S1) -0.199 1.304 - -

Mo-edgeH2O (on site Mo1) -0.55 2.274 0.9905, 0.9768 108.82OH (on site B) -3.863 1.630 0.983 -H (on site B) -4.921 1.346 - -

Table 3.1: Calculated structural parameters and adsorption energies of H2O, OH and H for the moststable site on S100-edge, S-50-edge and Mo-edge. Eads (eV) represents the adsorption energy, h(A)represents the vertical height of the H2O, OH and H species from the surface, dO−H represents the OHbond lengths for OH and H2O molecules and αHOH represents the H-O-H angle for H2O molecule.

Table 3.1 gives the most stable adsorption energies and sites for each species on the three edges and

also contains the corresponding structural parameters (OH bond lengths and H-O-H bond angle). It was

found that the H2O molecule was energetically most stable on top of a Mo atom (marked Mo1) for both

S100-edge and Mo-edge whereas it was most stable at site A for S50-edge. For all the edges, the water

molecule oriented itself to have the O atom closest to the MoS2 surface with the H atoms located further

at roughly similar distances and seemingly facing away from the surface as seen in Fig. 3.3. This also

indicated that the O atom possesses a greater affinity for the surface than the H atoms. The distance of

the O atom from S100-edge, S50-edge and Mo-edge surfaces was 2.989, 2.848 and 2.274 A respectively.

The O-H bond lengths for S100-edge, S50-edge and Mo-edge were 0.980 and 0.980 A 0.978 and 0.984 A

and 0.991 and 0.977 A respectively which are slightly larger than that of a free H2O molecule (0.958 A) in

vacuum. This indicates that the O-H bond is slightly weakened when the molecule is adsorbed on MoS2

edges. The magnitudes of the most stable adsorption energies on S100-edge, S50-edge and Mo-edge are

0.15, 0.23 and -0.55 eV respectively. The difference in energy between the most stable site and the next

most stable site on S100-edge, S50-edge and Mo-edge was only 0.016, 0.004, 0.380 eV respectively.

The H2O molecule demonstrated a stable negative adsorption energy favourable for binding only on

the Mo-edge, while both the S100-edge and S50-edge produced positive adsorption energies unfavourable

to adsorption. This is likely related to the interaction of the O atom with the surface atoms on the

edges. In the normal 2D MoS2 structure, the Mo atoms have sixfold coordination and the S atoms have

threefold coordination. Amongst the investigated edge terminations, the S100-edge and S50-edge also

have surface Mo atoms with sixfold coordination as discussed. However, the Mo-edge has surface Mo

atoms with twofold coordination and hence its Mo atoms are less stable than those of the other two

edges and more likely to interact with adsorbate species. Furthermore, the O atom is more likely to be

attracted to Mo atoms whose electronegativity differs from its own more than that for the S atoms and

this plays a role in charge transfer as discussed later. For this reason, sites above Mo atoms were more

favourable than those above S atoms for the edge systems.


(a) (b)

(c)

Figure 3.3: Isosurfaces of the charge density difference ∆ρ for H2O molecule adsorbed on the most stablesite for (a) S100-edge, (b) S50-edge and (c) Mo-edge. The purple, yellow, blue and red spheres are Mo,S, H and O atoms, respectively. The positive and negative isosurfaces are in pink and blue, indicatingregions of charge gain and loss respectively.


Another factor which likely affected adsorbate binding ability conisted of geometrical constraints.

For the Mo-edge surface, the Mo1 site atoms are well exposed in isolation allowing free interaction with

the H2O molecule, whereas access to Mo atoms for the S100-edge and S50-edge is blocked by S atoms to

a certain degree. For both the S100-edge and S50-edge, the most favored site provides the best access to

a Mo atom while maintaining a greater distance from S atoms than the other sites. Hence, the S atoms

actually seem to be repulsive to the H2O molecule and this is in line with similar results found by Ataca

et. al where the layer of S atoms in the perfect non-terminated structure is repulsive to the O atom [55].

This repulsion makes sense in terms of electonegativities and the usually negative partial charges of both

O and S atom species, as discussed later. The S50-edge seems to provide slightly better access to the

underlying Mo atom due to greater spacing between overlying S atoms than the S100-edge, however the

latter is slightly more stable for adsorption due to opposite acting charge based factors discussed later.

It should be noted that even for the Mo-edge, although there is adsorption and attraction between the

H2O molecule and surface, the adsorption energy is still weaker than typical covalent bond energies (for

example, the bond energy of O-H bond in water is about 5.0 eV).

The electrostatic repulsions and charge transfer interactions between the H2O molecule and edge

surfaces were further confirmed by Bader charge analysis. The surface S atoms for each edge had

negative effective charges, while the Mo atoms had positive effective charges. This helps to explain the

previously noted repulsion felt by the O atom in the H2O molecule from the surface S atoms as the O

atom has an effective negative charge as well. On the other hand, the positive effective charge of Mo

atoms in the MoS2 systems attracts the O atom in H2O molecules and provides an opportunity for the

strongly electronegative O atom to strip away charge from the weakly electronegative Mo atoms. This

is one reason that the pristine MoS2 surface does not strongly interact with H2O molecules as the layer

of negatively charged S atoms shields the inner Mo atoms and the more highly coordinated Mo atoms

have less charge available to donate to interacting molecules. For the edge terminations, charge analysis

was focused on the atoms of the H2O molecule and the nearest surface atoms at the adsorption location.

The free H2O molecule was found to have effective charges of -1.18e for the O atom and 0.59e for the

H atoms. For adsorption on the S50-edge, the effective charges had almost no change, with O atom now

having a charge of -1.17e and the H atoms have charges of 0.53e and 0.58e. The four surface S atoms

closest to the H2O molecule changed from having charges of -0.51e each to charges of -0.47e, -0.50e,

-0.47e & -0.49e. This demonstrates the repulsion felt between the O and S atoms as they seem to push

charge away from each other, with the O atom transferring charge to the H atoms and the S atoms likely

transferring charge to surrounding Mo atoms. For the S100-edge, there is a stronger degree of interaction

as expected. The O atom now gains additional negative charge going to an effective charge of -1.22e

while the H atoms have charges of 0.59e and 0.60e. The four surface S atoms closest to the H2O molecule

changed from having charges of -0.11e and -0.25e to charges of -0.14e, -0.16e, -0.15e & -0.19e, thus going

from an average effective charge of -0.18e to -0.16e. The two underlying Mo atoms bonded to these four

S atoms go from charges of 1.27e and 1.28e to 1.30e each. Hence, there is a charge redistribution within

the H2O molecule and the closest surface MoS2 atoms, with the effect that the more negative O atom

has greater attraction to the more positive Mo atoms and experiences reduced repulsion from the less

negative S atoms. It should be also noted that the surface S atoms for S100-edge were less negatively

charged than the S50-edge atoms, possibly due to less number of bonds to Mo atoms from which they

can draw charge. This helps explain why there is stronger interaction with the H2O molecule for the

S100-edge than S50-edge as their is less repulsion from the overlying negative S atoms and this factor


overcomes the geometrical advantages which should make S50-edge more favorable for interaction as

discussed previously. The Mo-edge displayed the greatest charge redistribution with the H2O molecule’s

O atom possessing an effective charge of -1.30e and the H atoms having charges of 0.68e and 0.62e. The

Mo atom closest to the molecule went from a charge of 0.97e to 1.22e. This demonstrates a clear increase

in the polarization of the H2O molecule. There does not seem to be a transfer of charge from Mo to O

as the overall charge on the H2O molecule remains zero. Instead the charge on the Mo atom was likely

pushed away further into the surface. Hence, the adsorption of the H2O molecule appears to take place

through electrostatic attraction.

In order to further study the interaction between the H2O molecule and edge terminations and any

possible charge transfer, we plotted the charge density difference ∆ρ for the best adsorption site of each

edge as shown in Fig. 3.3. Here ∆ρ = ρ (edge+H2O) - ρ (edge) - ρ (H2O), where ρ (edge + H2O)

and ρ (edge) are the charge densities of the edge with and without H2O adsorbed on the terminated

surface respectively, and ρ (H2O) is the charge density of the isolated H2O molecule. With this definition,

isosurfaces of positive values (pink) indicate charge gain, while negative values (blue) indicate charge loss.

As expected, the greatest charge redistribution occurs for the Mo-edge, indicating a strong interaction

between the H2O molecule and nearest neighboring Mo atom. Both the O atom and the nearest Mo

atom seem to be polarized and this points to a electrostatic attraction between them as proposed earlier.

The increase in negative charge below the Mo atom, away from the surface, further confirms that there

is likely no charge transfer from the Mo atom to the O atom and instead charge polarization as proposed

earlier based on Bader analysis. The stronger interaction is also likely responsible for the elongation of

OH bond lengths in the H2O molecule for the Mo-edge system. The large regions of charge loss between

the H2O molecule and the nearest two S atoms for the two S-edges points to the repulsion felt between

the O and S atoms. On all the edges the charge gets redistributed within the H2O molecule, indicating

there atleast some level of interaction for each system and this occurs the most for the Mo-edge.

Unlike H2O, both H and OH species were able to stably adsorb with negative adsorption energies

on all edges, as expected since the latter two are no longer part of the stable water molecule. The most

stable absorption energies for the H and OH species were -0.155 and -0.215 eV for S100-edge, -0.199

and -0.275 eV for S50-edge and -4.921 and -3.863 eV for Mo-edge. For the two S-edges, OH had a

stronger adsorption energy than the H atom, while the H atom had stronger adsorption for the Mo-edge.

Furthermore, the adsorption energies for the Mo-edge are significantly stronger than for S-edges and are

into typical covalent bond energy ranges. The most stable adsorption position for both species on the

S-edges was on an S atom (marked S1) while it was at bridge site B for both species on the Mo-edge.

Hence, both H and OH seemed to have formed covalent bonds on the Mo-edge due the strong adsorption

energies and the fact that they seem to be equally spaced between adjacent Mo atoms which suggests a

charge sharing arrangement. The distances of the H and OH species were 0.206 and 0.251 A from the

S100-edge, 1.304 and 1.682 A from S50-edge and 1.346 and 1.630 A from Mo-edge surfaces respectively.

The O-H bond lengths for the most stable adsorbed OH species were 0.988, 0.995 and 0.983 A for

S100-edge, S50-edge and Mo-edge respectively. As the Mo-edge is also most favourable for adsorption of

the OH and H species in addition to the H2O molecule, it can be considered most likely to successfully

participate in the dissociation reaction of water.


-1

-0.5

0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1 1.2

Ene

rgy

(eV

)

Reaction coordinate (arb. units)

2.31 eV

Figure 3.4: Reaction pathway and reaction barrier of single water dissociation on S100-edge from Climb-ing Image Nudged Elastic Band (CI-NEB) simulation. Purple atoms represent Mo; yellow atoms repre-sent S.


-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2

Ene

rgy

(eV

)


0.82 eV

Figure 3.5: Reaction pathway and reaction barrier of single water dissociation on S50-edge from ClimbingImage Nudged Elastic Band (CI-NEB) simulation. Purple atoms represent Mo; yellow atoms representS.


3.4.2 Dissociation of H2O on MoS2 edges

To understand the mechanism of water dissociation on the 1D MoS2 edges, we performed NEB calcu-

lations with 11 images in order to evaluate the MEP and the TS energy. For each edge, the initial

state (IS) and final state (FS) were obtained from the adsorption simulations discussed in section 3.4.1,

with the IS corresponding to H2O adsorption (whole water molecule) and the FS corresponding to OH

and H adsorption (dissociated water molecule). Fig. 3.4, 3.5 and 3.6 present the energy profiles that

represent MEP between IS and FS for S100-edge, S50-edge and Mo-edge respectively along with their IS,

TS and FS geometries and activation energy barriers. The chosen TS configuration corresponds to the

highest energy point along the MEP. All the reaction paths have similar TSs where the H2O molecule

has dissociated into OH and H species. The OH group has then bonded to a surface atom for all the

edges, while the H atom has bonded to a surface atom for the S100-edge but remains unbonded for

the remaining two edges. Eventually the H atoms do draw close to the surface and form bonds in the

FS for each edge. For the Mo-edge FS, the H atom remains in a position roughly equidistant between

two adjacent surface Mo atoms, which suggests it shares bonds with both surface atoms. For the two

S-edges, the H atoms form bonds with a single surface atom in the FS configrations.

The TSs can be used to find the activation energies for the dissociation reactions. The activation

energy barriers are defined as Ea = ETS - EIS , where ETS is the energy of the transition state and EIS is

the energy of the IS. The calculated activation energy barrier Ea for water dissociation on S100-edge was

a relatively high value of 2.31 eV. The S50-edge had a significantly lower barrier of 0.82 eV while the Mo-

edge had the lowest barrier at 0.54 eV. The activation energy barriers for all the edges were significantly

lower than that for water splitting in free space (∼5eV). The energy barriers for S50-edge and Mo-edge

were even lower than water splitting in liquid water (∼1eV) [36, 66] and on the surfaces of Cu, Ni, and

Pd (∼1 eV) [37]. The activation energy barrier for water splitting on Mo-edge was comparable with

that of water dissociation over a semiconducting (8,0) CNT (∼0.48 eV) and on a metallic (5,5) CNT

(∼0.41eV) [67]. In particular, this compares favorablly with platinum surface, which is often regarded as

the best performing catalyst for such reactions. A recent DFT based study found a minimum activation

energy of 0.44 eV for Pt(110) surface but higher than 0.54 eV for the other four crystal surfaces tested

[39]. Thus, the magnitude of the activation barriers for the S50-edge and Mo-edge can likely be overcome

with relatively low energy inputs (thermal, electric or photonic).

The reaction energy is defined as ∆E = EFS - EIS , where EFS is the energy of the FS, so that

a negative ∆E indicates an exothermic reaction and a positive ∆E represents an endothermic one.

The H2O dissociation on S100-edge was endothermic with positive reaction energy difference of 1.4 eV

(Fig. 3.4). On the other hand, both S50-edge (Fig. 3.5) and Mo-edge ( 3.6) had exothermic negative

reaction energies of -0.22 eV and -1.29 eV respectively. This beats the best reaction energy obained

for Pt surfaces, with a figure of -0.20 eV [39]. The much larger magnitude of the Mo-edge reaction

energy in relation to the S-edges is likely in relation to its superior water adsorption ability, whereas

the S-edges did not even favorably adsorb H2O molecules in their ISs. The negative reaction energies

for both edges point to thermodynamic favourbility and the low activation barriers point to favourable

kinetics. On the other hand, water dissociation on the S100-edge is energetically less favorable due to

its comparatively higher activation barrier and large positive reaction energy and thus the S100-edge is

not a good candidate for water splitting.


-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Ene

rgy

(eV

)


0.54 eV

Figure 3.6: Reaction pathway and reaction barrier of single water dissociation on Mo-edge from ClimbingImage Nudged Elastic Band (CI-NEB) simulation. Purple atoms represent Mo; yellow atoms representS.


3.4.3 Free Energy with Vibrational and Entropic Contributions

Although NEB analysis revealed the Mo-edge as highly active for water dissociation, the reaction energy

results only provided potential energy differences at ground state. In order to get a more complete

picture of behaviour at room temperature conditions, it is typical to consider quantum corrections to

the activation barrier in order to account for the discreteness of vibrational modes at room tempera-

ture (300K). Therefore, the entropic contribution as well as zero point energy (ZPE) correction were

incorporated by computing Gibbs free energy ∆G between IS and TS.

∆G = Ea +∆ZPE − T∆S, (3.2)

where Ea is activation energy barrier obtained by subtracting total energies of IS and TS as defined

in Section 3.4.2 and obtained from NEB, ∆ZPE is the difference of zero point energies between IS and

TS, ∆S is the change of entropy of water between IS and TS and T is the temperature. The ∆ZPE was

computed through the phonon frequencies obtained within linear response [68] and found to be -0.404

eV. The entropic contribution (T∆S) can be considered to be very low for adsorbate species as they are

already bound to a surface with little configurational freedom [69]. The entropy of adsorbed molecules

is elmost entirely in the vibrational partition with little translational or rotational contributions, with

most of the freedom related to vibration of the molecule normal to the surface and so largely dependent

on bond length and strength between between adsorbate and surface [70]. Both the water molecule

in the IS and OH species in the TS are bound to the surface at similar distances (2.23 and 2.12

respectively) and can be considered to have zero entropy difference. The dissociated H atom in the

TS might produce an entropy difference depending on how strongly it is bound to the surface; if it is

considered to have strong adsorption like the other species then the entropy difference remains zero as

a lower bound estimate. An upper bound for the entropy difference term can be obtained if the H atom

in the TS is considered to be fully free of the surface and act as a free gas, in which case the T∆S value

is 0.20 eV/H2O at room temperature [69]. After considering these corrections, we calculated the free

energy change ∆G of activation for the reaction to be from 0.14 eV (T∆S=0) to -0.06 eV (T∆S=0.20)

on Mo-edge which suggests that the Mo-edge has not only excellent catalytic activity but that water

dissociation on Mo-edge could be spontaneous at finite temperature.

The kinetic rate constant can be estimated by the transition-state theory expression:

k =kBT

hexp−∆G/kBT , (3.3)

where kB and h denote Boltzmanns and Planks constant, respectively. From the formula above, we

derived a rate constant range from k = 2.8 × 1010 s−1 (T∆S=0) to k = 6.4 × 1013 s−1 (T∆S=0.14)

at 300 K. A change of 0.06 eV in activation barrier produces an approximate rise or fall in reaction rate

by one order of magnitude. However, even with a few orders of magnitude change in value, this would

still be a very high rate constant. This very clearly suggests that the Mo-edge is very favourable for

the water dissociation reaction not only thermodynamically but kinetically as well and the reaction is

likely to occur spontaneously and quickly at room temperature. Hence, this dissociation step is likely

not going to be rate limiting as part of an overall set of reactions.


3.5 Finite temperature ab initio molecular dynamics

Water dissociation on the Mo-edge, the best performing of the MoS2 surfaces, was selected to be simu-

lated with finite temperature AIMD to observe temperature effects in dynamic evolution of the system.

The system was initialized with the H2O molecule oriented so as to have the O atom facing the MoS2

surface (see Fig. 3.7(a)) and then allowed to evolve along the Born-Oppenheimer energy surface at 300K.

As the simulation progressed, the H2O molecule started to move towards the MoS2 surface and tilt to

allow the O atom to decrease its distance to the nearest Mo atom and eventually started to form a bond

between the O and Mo atoms (see Fig. 3.7(b)) at around 0.37 ps in the dynamics. Next, one of the

H atoms in the H2O molecule started to detach from the O atom and form a bond with the Mo atom

adjacent to the O bonded Mo atom (Fig. 3.7(c)). By 1.07 ps, the first H atom to detach had moved to

a postion intermediate between two Mo atoms and seemed to form slight bonds with both of them in a

manner similar to that observed for the adsorption simulations in Section 3.4.1, while the remaining H

atom moved further away from the O atom (see Fig. 3.7(d)). This configuration continued to be stable

for the remaining simulation time upto 1.48 ps at which point the simulation was stopped as complete

dissociation had been achieved and there was little change in the atomic configurations.

The quick and straight forward dissociation of the H2O molecule into OH and H in under 1.5ps

indicates that the energy barrier for dissociation is not larger than the thermal energy available at 300K.

This confirms the spontaneous nature of H2O molecule dissociation on the Mo-edge surface and that it

strongly favors this reaction even at room temperature. This also correlates with the earlier calculated

rate constants as it falls within the range of prediction of a dissociation happening once every 0.02-36.0ps

on average, with it falling closer to the lower bound which corresponds to a free H atom and bound

OH species. The initial H2O adsorption took place at the same active site found most favorable in the

adsorption simulations (marked Mo1 in Fig.3.2(c)). The overall evolution of the reaction is generally

similar to the adsorption and NEB based results, especially the final configuration of the dissociated

water molecule. The O atoms first forms a bond to the nearest Mo atom while the H2O molecule is

still intact in both approaches. The first H atom to detach from the water molecule stabilizes roughly

intermediate between two Mo atoms in both the AIMD and adsorption results. Hence, the dissociation

proceeds in a roughly similar manner even with entropic and temperature effects.

3.6 Metadynamics biased finite temperature ab initio molecu-

lar dynamics

The water dissociation AIMD simulation conducted on the Mo-edge in section 3.5 was repeated with a

metadynamics based bias and the same timestep of 2.5 fs in order to obtain a free energy surface of the

reaction and explore possible alternate reaction mechanisms. Two schemes of collective variables were

tested in two different biased simulations and each resulted in a different reaction mechanism, both of

which are presented in the following sections. Once an energy surface was obtained for a mechanism,

specific regions of the surface corresponding to important energy barriers were explored with a smaller

timestep of 1.25 fs in order to obtain a more detailed and accurate estimate of free energy barriers.


(a)t=0.37 ps (b)t=0.45 ps

(d) t=0.58 ps (c)t=1.07 ps

Figure 3.7: Reaction mechansim of H2O dissociation reaction on Mo-edge of MoS2 during unbiasedab-intio molecular dynamics simulation at 300K. The reaction roughly follows the same path as CI-NEBsimulations


3.6.1 Mechanism 1

In the first simulation, two collective variables were biased, the first (CV1) representing coordination

number between the O atom in the H2O molecule and the nearest Mo atom and the second (CV2)

representing coordination number between the O atom in the H2O molecule and a H atom in the

same molecule (see Supporting Information for coordination number collective variable definitions).

The reaction proceeds according to the same mechanism as found from NEB and the unbiased AIMD

simulations, namely the H2O molecule dissociates into OH and H species which both adsorb on Mo

atoms on the Mo-edge surface. During the dissociation, the H2O molecule’s O atom first forms a bond

with a Mo atom and then a H atom splits from the molecule, leaving the OH species adsorbed initially,

and eventually the H also adsorbs to surface Mo atoms.

The resulting free energy surface for the first biased simulation is described in Figure 3.8. The free

energy minima corresponding to the IS (representing the adsorbed H2O molecule) and FS (representing

the fully dissociated representing the adsorbed H2O molecule) from the NEB simulations are labelled A

and B respectively. The free energy barrier for escaping from the free energy well at A, which corresponds

to the activation energy barrier from the NEB calculations, is roughly 0.014 eV (0.33 kcal/mol). This

energy well was then further explored with a smaller timestep of 1.25 fs, which yielded an activation

energy barrier of 0.061 eV (1.4 kcal/mol). This value falls within the range of free energy barriers

calculated from the NEB calculations (-0.06 to 0.14 eV) and lies closer to the lower bound which was

associated with the intermediate transition state (TS) consisting of a bound OH and free H atom (while

the upper bound consisted of both OH and H species bound to the surface with practically no freedom of

movement). This also matches the results of the non-biased AIMD simulation in which the dissociation

also happened with a time closer to that predicted by the lower bound of a free H atom. Hence, the TS

probably has an H atom loosely attracted to and held by the surface which is not fully adsorbed and

possesses more freedom of movement than the final bound state but less than in free gas state.

The free energy surface also confirms that the water dissociation step is not the rate limiting step

in the overall water to hydrogen process as it does not involve the deepest energy well labelled as C in

Figure 3.8. Instead, the deepest energy well corresponds to the unadsorbed free water molecule and the

barrier for escaping from this well is 0.023 eV or 0.17 eV when simulated with a 1.25 fs timestep. This

demonstrates that, even for the Mo-edge which is thermodynamically favorable for water adsorption,

the water adsorption step is a candidate for the rate limiting step for the hydrogen production process.

3.6.2 Mechanism 2

The second biased simulation also utilized two collective variables, the first (CV1) representing coordi-

nation number between the O atom in the H2O and the nearest two surface Mo atoms and the second

(CV2) representing coordination number between an H atom and the two nearest Mo atoms to which

it was bound in the final state of the unbiased AIMD simulation. The dissociation of this reaction

proceeded by a different mechanism than for the first biased simulation. The common process for gen-

eration of hydrogen from water on catalyst surfaces involves water dissociation in which both species

resulting from water splitting eventually adsorb to the surface (as was the case for our NEB and AIMD

simulations) and then adsorbed hydrogens eventually combine to form a hydrogen molecule (through

the simple route 2H* → H2 or more complex intermediates), leaving behind the adsorbed OH species;

giving an overall reaction of (H2O + * → OH* + 1/2H2) [69]. However, an alternate mechanism involves


ΔG

(kcal/m

ol)

CV1CV2

B A

C

C

Figure 3.8: Free energy surface of Mechanism 1 in terms of collective variables for metadynamics biasedAIMD simulation at 300K with corresponding atomic configurations at specific energy minima. Thedissociation reaction proceeds from point A to B. However, the deepest energy well and largest activationbarrier corresponds to adsorption of the water molecule at point C.


C B A

Figure 3.9: Free energy surface of Mechanism 2 in terms of collective variables for metadynamics biasedAIMD simulation at 300K with corresponding atomic configurations at specific energy minima. Thedissociation reaction proceeds from point A to B and then C, leaving behind a lone adsorbed O atom.


the hydrogen atoms of the water molecule directly combing to form a hydrogen molecule while leaving

behind only the O atom adsorbed (H2O + * → O* + H2). The second simulation seems to follow

this second mechanism. This demonstrates the utility of metadynamics in exploring different possible

reaction mechanisms and also the importance and influence of collective variable selection.

Figure 3.9 describes the free energy surface for the second biased simulation. The free energy minima

corresponding to the whole water molecule which is attracted and loosely bound to the MoS2 surface

is labelled A. The O atom proceds to adsorb strongly to the nearest Mo atom while the H atoms are

starting to break free of the O atom by point B. At point C, the two H atoms have fully broken away

from the O atom and are moving away from the MoS2 surface while drawing closer to each other to

form what looks like an H2 molecule. The free energy barrier for the H atoms to escape the O atom

and go from point B to C was roughly 0.024 eV (0.56 kcal/mol). This energy well was then further

explored with a smaller timestep of 1.25 fs, which yielded an activation energy barrier of 0.360 eV (8.3

kcal/mol). This is significantly higher than the energy barrier for breaking the O-H bond in Mechanism

1, which is to be expected as there now two bonds being broken at roughly the same time. This means

that this mechanism will occur far less frequently than Mechanism 1 at room temperature. However,

the activation barrier is not particularly high and can be overcome with a slight energy input. It should

be noted that the barrier is also greater than that for water adsorption in Mechanism 1.

3.7 Surface Processes Subsequent to Water Dissociation

Following the splitting of the water molecule into OH and H species in Mechanism 1, there are several

additional steps required for hydrogen gas production. A prelimanary examination of these was done

by studying the further dissociation of the OH species into O and H, the migration of H atoms across

the Mo-edge surface and the possible formation of hydrogen by the simple route of the Tafel reaction

(2H* → H2) at ground state conditions. The OH splitting reaction was found to be thermodynamically

favorable with a reaction energy ∆E of -1.58 eV but had a significant activation energy Ea of 2.00 eV.

The migration of individual H atoms across the Mo-edge surface atoms was found to have a barrier of

1.15 eV. The desorption of two adjacent H atoms adsorbed on the same Mo-atom to then form an H2

molecule was found to have an equivalent Ea and ∆E of 1.07 eV, indicating there is not an intermediate

transition state. The activation energy for these post-dissociation processes are higher than that for the

water splitting step, hinting that one of these steps is likely the rate-limiting step for a full hydrogen

evolution reaction. The hydrogen desorption step is especially troublesome as even the overall reaction

seems to be thermodynamically unfavorable with a positive potential energy change. However, it should

also be noted that for desorption processes, where the gas phase transition or final state can have

significantly greater freedom of movement than the initial adsorbed state, entropy can be a significant

factor and greatly lower the free energy of activation or reaction for the step [70]. Furthermore, the

hydrogen evolution step might proceed by a more complex route with several intermediate species than

the simple Tafel mechanism tested.

The prelimanary simulations demonstrate that the hydrogen desorption mechanism needs to be

studied in greater detailed with finite temperature entropy effects and exploration of multiple possible

reaction pathways. Additionally, this work was restricted to studying a single H2O molecule on the edge

surface and did not consider the impact of multiple H2O molecules. Other H2O molecules can affect

reaction mechanisms due to their polar nature, although this is much more significant in liquid phase


reactions where they can protonate H atoms. Another important factor for surface catalytic reactions

involves surface coverage effects where adsorbed molecules can interact with each other and even form

surface layers. Surface layers themselves can interfere with adsorption of reactants and affect reaction

rates. This also brings up the issue of the O atom which is left adsorbed to the surface and whether it

is removed by some reaction such as O2 evolution, otherwise this might result in the poisoning of the

catalytic surface. Such considerations will have to be properly investigated before the MoS2 monolayer

material can be used for practical applications. As such these should be investigated in future studies

and are out of the current study’s scope.

3.8 Summary

This work looked at the three edge terminations (S100, S50 and Mo) of MoS2 for their water adsorption

and dissociation abilities. The S100 and S50 edges were found to be thermodynamiclly unfavorable for

H2O adsorption, with the S100 being slightly more stable than the S50-edge. The Mo-edge was found

to bind the H2O molecule in a stable configuration which the O atom of the H2O forms a bond with a

surface Mo atom. All edges were able strongly bind the individual OH and H species on their surface.

Next the water dissociation mechanism was simulated for all edges using nudged elastic band method,

with all followeing roughly the same path during which an H atom split from the H2O molecule to leave

an adsorbed OH and eventully adsorbed itself onto the surface. The S100-edge turned out to have a very

high activation potential energy barrier of 2.31 eV, while the S50-edge had a barrier of 0.82 eV and the

Mo-edge had the lowest barrier of 0.54 eV. The Mo-edge free energy activation barrier was then found

using zero-point energy and entropy corrections to produce a barrier in the range of -0.06 eV to 0.14

eV and a very high rate constant which indicated that the water dissociation reaction would proceed

spontaneously on the Mo-edge at room temperature. Water dissociation was then further studied on the

Mo-edge using the alternative technique of ab initio molecular dynamics with metadynamics to study

the reaction when the system was allowed to evolve freely at finite temperature with no fixed final state.

These simulations confirmed that the reaction occurs very quickly and produced a free energy activation

barrier of 0.014 eV. Furthermore, they also demonstrated that the reaction can occur via an alternate

pathway in which the H atoms of the H2O molecule directly form a hydrogen molecule while leaving

behind an adsorbed O atom. This latter mechanism was also found to have a very favorable, albeit

higher, free energy activation barrier of 0.024 eV.

Chapter 4

Hydrogen Storage on Metal

Decorated Graphene

The material in this chapter has been published as a journal article under the title of “A van der Waals

density functional theory comparison of metal decorated graphene systems for hydrogen adsorption”. Text

and figures are reprinted from “Journal of Applied Physics” [71], Copyright 2014, AIP Publishing LLC.

4.1 Introduction

In the past few years, there has been an increasing interest in using hydrogen as a clean alternative fuel

[72]. Presently, one of the main issues associated with hydrogen fuel technology is its energy storage

capacity, which is still far from being able to compete with fossil fuels [73, 12]. For hydrogen storage

systems in transportation applications, the US DOE has set a target of achieving a hydrogen gravimetric

capacity of 5.5 wt% and a volumetric capacity of 0.04 kg/m3 by 2015 [74]. One approach for room

temperature storage is through the adsorption of hydrogen on substrate materials. Among proposed

substrates, including hydrides, zeolites, and metal organic frameworks, porous carbon structures are

some of the most appealing [75]. These substrates are low in weight and have the potential to be the

most economically viable. Within this class of materials is graphene, a single layer of carbon atoms with

a unique 2D structure which gives it a large specific surface area and great mechanical strength. These

properties make graphene an ideal material for hydrogen adsorption citeSun2011.

This study compares the hydrogen binding ability of several metal adatoms (Al, Li, Na, Ca, Cu,

Ni, Pd, Pt) on graphene and evaluates the importance of including van der Waals (vdW) interactions,

incorporated using the vdW-DF2 functional. This should help provide a more accurate prediction for

the hydrogen binding ability of each atom in comparison to earlier studies. In total, four light metals and

four transition metals were investigated. The best overall metal system for reversible storage was used

to study changes in binding ability for varying metal decoration coverage. The gravimetric density for

these varying metal coverage systems was also investigated by adsorbing multiple hydrogen molecules.

36

Chapter 4. Hydrogen Storage on Metal Decorated Graphene 37


Molecular hydrogen, as found in its gaseous form for practical storage devices, adhers to graphene

through physisorption. However, for the case of pristine graphene, this process is too weak for it to stably

bind enough hydrogen molecules to reach the DOE hydrogen density targets [13]. Metal decoration of

graphene sheets shows potential in increasing their hydrogen adsorption ability to levels required for

the DOE targets [76, 77]. In such cases, the hydrogen molecules generally bind to the metal atoms

through physisorption, although they may dissociate and chemisorb due to the infuence of some metals

[13]. Theoretical studies conducted on metal decorated graphene systems predict very high gravimetric

densities which easily surpass the DOE target. For instance, it has been claimed that a Li decorated

system can achieve 16 wt.% hydrogen storage [77], Al decoration can achieve 13.8 wt.% [78] and Ca

decoration can achieve 8.4 wt.% [79]. Contrary to these theoretical studies, the experimental results for

metal decorated graphene have fallen far short of these numbers and none have been able to achieve

greater than 2 wt.% at room temperature [80, 81, 82, 83]. Theoretical predictions are generally made with

density functional theory (DFT) calculations using local density approximation (LDA) and generalized

gradient approximation (GGA) functionals. It should be noted that this can cause inaccuracies associated

with hydrogen binding energy values as generally they can be overestimated by LDA or underestimated

by GGA. The LDA functional is usually inaccurate for interactions in such complex systems, while the

GGA functional is accurate for strong covalent type forces but neglects van der Waals (vdW) interactions.

For metal decorated graphene systems, vdW interactions are significant for describing the physisorption

of hydrogen and the interaction between neighboring metal atoms, especially at higher coverages [76, 77]

and this might be one reason as to why experimental results fall short of theoretical assertions. A

recent study which attempted to consider the effect of vdW forces in Ca decorated graphene [76] hints

at this as it concluded that the system could only achieve a gravimetric density of 2.6 wt.%, a marked

decrease from previous claims. Amongst theoretical studies, the highest gravimetric densities have been

generally achieved for light metals. However, it is difficult to compare different metal predictions as

various studies use widely varying exchange-correlation functionals, pseudopotentials and simulation

parameters. Therefore, a comprehensive understanding of the realistic hydrogen binding ability of metal

decorated systems is currently lacking.


The hydrogen storage capacity of a metal decorated graphene sheet was studied using first princi-

ples methods based on density functional theory (DFT). The DFT calculations were performed with

Quantum-Espresso [26] which uses the plane-wave pseudopotential approach. The generalized gradient

approximation (GGA) functional described by Perdew-Burke-Ernzerhof (PBE) [84] was used to describe

the exchange-correlation of electrons. Ultrasoft pseudopotentials were used for all calculations. Van der

Waals interactions were modeled by adding a correction to the GGA functional, when applied, through

the vdW-DF2 functional [85]. This functional was used instead of the earlier vdW-DF [86] for increased

accuracy in estimating the equilibrium separation, H2 bond strengths and van der Waals attractions at

intermediate separation longer than equilibrium ones [85]. The kinetic energy cutoff value was set to

60 Ry for the wave functions and to 600 Ry for the charge density. The supercell and atomic positions

were optimized using the conjugate gradient algorithm. The convergence threshold was set to 7E-7 Ry


Figure 4.1: Possible adsorption sites for metal atoms. From left to right, the adatom is at the hollowsite, the top site and the bridge site respectively.

for self consistency in energy and to 8E-3 a.u. for forces. The total energy convergence was maintained

at ≤ 5 meV/atom.

The metal-graphene systems for comparing different metals were modeled with 1 × 1 supercells (6

C atoms) and a vacuum layer thickness ≥ 20 A. The Brillouin zone was sampled using a 8 × 8 × 1

Monkhorst-Pack [60] k-point grid and Methfessel-Paxton [87] smearing of 0.01 Ry [88]. In addition, each

metal adatom was placed at its most stable adsorption site on the graphene sheet according to literature.

Based on previous work by Wang et al. [76] and Sigal et al. [89, 90], the most favorable adsorption site

for Al, Ca, Li, Na, and Ni on graphene is at the “hollow” position, while Pd and Pt prefer the “bridge”

position and Cu prefers the “top” position. See Figure 4.1 for the schematic diagram of the different

binding sites. Simulations investigating metal coverage and gravimetric density were conducted with a

single metal adatom placed on each side of the graphene sheet (to give a total of two metal adatoms in

the entire supercell) and varying the number of surrounding carbon atoms.

The binding energy of a metal atom on graphene was calculated as:

Eb = −[Egraphene+nmetal − (Egraphene + nEmetal)]/n (4.1)

where Egraphene+nmetal is the total energy of the graphene sheet with either single- or double-sided metal

decoration, Egraphene is the total energy of the pristine graphene sheet, Emetal is the total energy of the

free metal adatom and n corresponds to the number of metal adatoms.

The average binding energy per hydrogen molecule was calculated with the following equation:

Eb = −[Emetal−graphene+iH2− (Emetal−graphene + iEH2

)]/i (4.2)

where Emetal−graphene+iH2is the total energy of the hydrogen adsorbed on the metal-graphene system,

Emetal−graphene is the total energy of the metal-graphene sheet, EH2is the total energy of the free H2

molecule and i corresponds to the number of H2 molecules.

4.4 Results and Discussion

In this section, we first report the adsorption energy of metal adatoms over graphene sheets for eight

metals and consider both single and double sided metal decoration. Thereafter, adsorption of hydrogen

molecules over different metal-decorated systems is described, considering the same substrate size among

the investigated metals. A careful analysis of these hydrogen adsorption studies pointed to Ni as the

most promising metal adatom. Thus, a more thorough investigation was conducted for the Ni deco-

rated graphene system to understand the effect of substrate size, and determine its optimum hydrogen

adsorption capability.


The effect of spin polarization was determined by comparing the binding energies of metal decora-

tions on graphene using only GGA with and without spin polarization. Spin polarization has not yet

been implemented for the vdW-DF method in Quantum Espresso. Therefore, all simulations with the

vdW-DF2 functional were performed without spin polarization. For the GGA simulations, it was deter-

mined that spin polarization had no significant effect on the metal binding energy of any of the metals.

For hydrogen adsorption, only Ni, Pd and Pt demonstrated a small sensitivity to spin polarization.

Therefore, these three metal systems had both spin and no-spin calculations conducted while studying

hydrogen adsorption with the GGA functional alone. There was a less than 0.01 eV difference due to

spin polarization for Ni and Pd and less than 0.6 eV difference for Pt in these results.

4.4.1 Metal anchoring over graphene

The overall stability of each metal-graphene system, prior to hydrogen adsorption, was analyzed by

calculating the binding energy of the metal adatom on graphene for both the single- and double-sided

decoration cases. According to Eq. (5.1), a positive binding energy indicates that the metal adatom is

stably bound to graphene in its ground state. The binding ability results for the single- and double-sided

metal decoration are listed in Tables 4.1 and 4.2 respectively, along with the equilibrium distances of

each adatom from the graphene sheet. In both cases, the vdW-DF2 results show that all metal atoms

bind to graphene, while all metals with the exception of Li and Na do so for the GGA simulations. The

transition metals generally show stronger binding than light metals with the exception of Ca, which has

quite strong binding, and Cu, which has relatively weak binding. The metals with strong binding metals

all have unfilled d-shells (including the non-transition Ca), suggesting that this may be a possible cause

for a stronger bond as their less stable nature may cause them to be more likely to share charge with

the graphene electrons. This would also explain the lower binding energy for Cu, despite it being a

transition metal, as it has a filled d-shell. Figure 4.2 points to another difference between the graphene

anchored light and transition metals by comparing the charge densities of Al and Ni. Both the charge

density difference for metal adatom adsorption and charge density isosurface at a value of 0.14 (number

of charge/Bohr-3) are shown for each metal type. The figure indicates that there is a greater charge loss

from around the Al atoms (Fig. 4.2(b)), especially at the ends facing away from the graphene sheet

which are most likely to interact with hydrogen molecules, than from around the Ni atoms (Fig. 4.2(a)).

Furthermore, the Ni atoms have greater charge density around them, whereas the Al atoms show no

noticeable charge surrounding them. This indicates that the Ni atom will have more charge available

for interaction with hydrogen atoms.

There are four additional trends observed from both Tables 4.1 and 4.2. First, going from single-

sided to double-sided decoration generally increased the binding energy of each metal adatom. The

exceptions, Na and Pd, showed insignificant decreases of less than 0.1 eV which can be ignored when

considering the advantages gained by having the ability to bind hydrogen on both sides of the graphene

sheet. Hence, double sided decoration is preferred for hydrogen adsorption. Second, for single sided

decoration, light metals (Al, Li, Na, Ca) generally show an increased binding energy with vdW-DF2

functional as compared to GGA only simulations, while transition metals depict the opposite trend. For

double sided decoration this trend holds except for Ca and Pt, perhaps reflecting the particular nature of

each metal and the manner in which its valence shells interact. The tables also present literature values

for the metal binding energies. Our GGA and vdW-DF2 metal binding values are consistently lower

than both LDA and GGA results found in literature. The higher literature LDA values are expected as


System Eb (eV) d⊥ (A) Literature NotesGGA vdW-DF2 Lit. GGA vdW-DF2 Lit.

AlC6 (H) 0.03 0.22 0.82 2.06 3.49 2.08 System was C8 with 18 A c-axis using LDAPP [78]

LiC6 (H) -0.43 0.17 1.00 5.99 1.91 1.88 System was C6 with 16 A c-axis using PBE-GGA and PAW PP [77]

NaC6 (H) -0.01 0.04 0.59 2.70 2.81 – System was C60 with 20 A c-axis usingGGA-PBE, localized basis sets and norm-conserving PP [89]

CaC6 (H) 0.52 0.50 2.19,1.53,1.60

2.33 2.49 – (LDA,GGA & vdW-DF respectively) Sys-

tem was C6 with 20 A c-axis with indicatedfunctionals [76]

CuC6 (T) 0.15 0.17 0.39 2.14 3.21 – System was C60 with 20 A c-axis usingGGA-PBE, localized basis sets and norm-conserving PP [89]

NiC6 (H) 1.27 0.48 1.99 1.59 1.77 1.65 System was C24 with 20 A c-axis usingGGA-PBE, localized basis sets and norm-conserving PP [90]

PdC6 (B) 0.76 0.48 1.08 2.12 2.34 2.25 System was C24 with 20 A c-axis usingGGA-PBE, localized basis sets and norm-conserving PP [91]

PtC6 (B) 1.13 0.66 1.73 2.03 2.15 – System was C60 with 20 A c-axis usingGGA-PBE, localized basis sets and norm-conserving PP [89]

Table 4.1: Binding energies (eV), vertical adatom distance with respect to graphene sheet (A) andliterature values (Lit.) for single sided metal decoration. The adatom positions over graphene areindicated in brackets, where H stands for adatom at the hollow, B stands for adatom on the bridgebetween two carbon atoms and T stands for adatom above a carbon atom.

System Eb (eV) d⊥ (A) Literature NotesGGA vdW-DF2 Lit. GGA vdW-DF2 Lit.

Al2C6 (H) 0.15 0.21 0.96 2.26 3.55 2.14 System was C8 with 18 A c-axis using LDAPP [78]

Li2C6 (H) -0.37 0.18 0.99 6.05 1.86 1.85 System was C6 with 16 A c-axis using PBE-GGA and PAW PP [77]

Na2C6 (H) -0.01 0.03 – 2.08 2.16 – –Ca2C6 (H) 0.66 0.64 2.33,

1.63,1.69

2.31 2.39 (LDA,GGA & vdW-DF respectively) Sys-

tem was C6 with 20 A c-axis with indicatedfunctionals[76]

Cu2C6 (T) 0.14 0.18 – 2.26 3.35 – –Ni2C6 (H) 1.18 0.49 – 1.63 1.83 – –Pd2C6 (B) 0.64 0.43 – 2.18 2.46 – –Pt2C6 (B) 0.84 1.00 – 2.16 2.17 – –

Table 4.2: Binding energies per atom (eV), vertical adatom distance with respect to graphene sheet(A) and literature values (Lit.) for double sided metal decoration. The adatom positions over grapheneare indicated in brackets, where H stands for adatom at the hollow, B stands for adatom on the bridgebetween two carbon atoms and T stands for adatom above a carbon atom.


(b)

(a)

Figure 4.2: Isosurfaces of charge density and charge density difference for (a) Ni and (b) Al adatomsadsorbed on graphene. In the charge density difference isosurfaces, yellow indicates regions of chargegain and blue indicates regions of charge loss. The Al atoms, a light metal, show greater charge loss anda smaller region of remaining charge density than the heavy metal Ni atoms. This might be one reasonfor heavier metal atoms possessing stronger hydrogen binding energy as they have greater charge whichcan interact with hydrogen molecules.


Eb (eV)System GGA

(no-spin)

GGA(spin)

vdw-DF2(no-spin)

Literature Value Literature Notes

Al2C6-2H2 (H) 0.004 - 0.044 Eb = 0.2 eV [78] System was C8 with 18 A c-axis using LDA PP

Li2C6-2H2 (H) 0.356 - 0.118 Eb = 0.10 eV [77] System was C6 with 16 A c-axis using PBE-GGA and PAW PP

Na2C6-2H2 (H) 0.021 - 0.000 Eb = 0.02 eV [89] System was single-side decorated C60 with 20 Ac-axis using GGA-PBE, localized basis sets andnorm-conserving PP

Ca2C6-2H2 (H) 0.007 - 0.025 Eb=0.03 eV (LDA),0.01 eV (GGA), 0.06eV (vdW-DF) [76]

System was C6 with 20 A c-axis with indicatedfunctionals

Cu2C6-2H2 (T) 0.506 - 0.262 Eb = 0.04 eV [89] System was single-side decorated C60 with 20 Ac-axis using GGA-PBE, localized basis sets andnorm-conserving PP

Ni2C6-2H2 (H) 0.268 0.267 0.171 Eb = 1.21 eV [90] System was single-side decorated C24 with 20 Ac-axis using GGA-PBE, localized basis sets andnorm-conserving PP

Pd2C6-2H2 (B) 0.843 0.842 0.510 Eb = 1.86 eV [91] System was single-sided C24 with 20 A c-axisusing GGA-PBE, localized basis sets and norm-conserving PP

Pt2C6-2H2 (B) 1.75 1.15 1.02 Eb = 1.65 eV [89] System was single-side decorated C60 with 20 Ac-axis using GGA-PBE, localized basis sets andnorm-conserving PP

Table 4.3: Average hydrogen binding energy (eV/H2) for metal graphene system. The adatom positionsover graphene are indicated in brackets, where H stands for adatom at the hollow, B stands for adatomon the bridge between two carbon atoms and T stands for adatom above a carbon atom.

the functional is known to overestimate binding. The reasons for the difference between our GGA results

and those from literature are likely due to very different metal coverage and simulation parameters such

as vacuum spacing, pseudopotential and software implementation, partially described in the Literature

Notes section of Tables 4.1 and 4.2. We have tried to produce highly accurate GGA simulations by

using vacuum spacing much larger than previous studies as we found interlayer interactions even at the

spacing level of the previous studies, as well as stringent energy cutoffs and a high number of k-points.

As a third trend, there is a distinct pattern observed for transition metal vdW-DF2 results that is

less apparent in the calculations made using only GGA. The binding energy tends to increase as the

number of d-electrons increases. However, when the number of d-electrons increases to more than half

occupancy, the binding energy starts to decrease. Finally, the distance of the adatom from the graphene

sheet is greater for vdW-DF2 results than GGA only results for all cases. This trend may be due to the

presence of stronger long range interactions allowed in vdW-DF2, which allows the metal atom to be

energetically stable at a farther distance from the graphene sheet. On the other hand, GGA simulations

without vdW corrections would require greater proximity to feel the same level of attractive force. It

should be pointed out that while the earlier vdW-DF functional tended to overestimate distances, the

vdW-DF2 functional has improved distance estimation [85] and hence we expect the present results to

be more accurate.

4.4.2 Hydrogen adsorption on metal-decorated graphene

The binding energy for the adsorption of a single hydrogen molecule on each metal adatom is summarized

in Table 4.3. Since previous calculations showed that double-sided metal decoration is more stable in most

cases, the hydrogen adsorption energies were calculated for that configuration only. GGA calculations


with and without spin polarization are also included for the transitions metals Ni, Pd and Pt. These

GGA results confirmed that spin polarization can be ignored for Ni and Pd, while Pt does show a

difference of 0.6 eV in binding energy owing to its inclusion. However, this difference in energy for Pt

is not large enough to affect its comparison to other metals and our conclusions from the simulations

remain unaffected. As stated earlier, the vdW-DF2 functional has not been be implemented with spin-

polarization in Quantum Espresso at present and so only unpolarized simulations were conducted for this

functional. For the light non-transition metal adatoms (Al, Ca, Na, Li), the vdW-DF2 results produced

higher binding energies than GGA results by an order of magnitude but were still much weaker than

those of the transition metals. For the heavier transition metals, the GGA results produced stronger

binding energies than vdW-DF2 results; although the difference was not an order of magnitude. The

difference occuring due to the vdW-DF2 correction can be analyzed by looking at the partial density of

states (PDOS) of the Ni system, as shown in Figure 4.3. The PDOS for the GGA simulation shows a

greater number of peaks and wider distribution for the Ni d-shell compared to the plotted PDOS after

including the vdW-DF2 functional. This indicates that the GGA Ni has more localized distinct energy

states which are likely to more strongly interact and share charge with hydrogen molecules. On the other

hand, the reduced number of peaks in the vdW-DF2 Ni indicates that its d-shell is filled due to greater

charge sharing with the graphene substrate. It is thus more stable and less likely to strongly interact

with a hydrogen molecule. Consequently, the vdW-DF2 simulated Ni will have a weaker hydrogen

binding energy than the GGA simulated Ni. The increased sharing of charge between the Ni atoms

and the graphene substrate when vdW corrections are included also helps to explain why the vdW-DF2

simulation showcased a stronger metal binding energy than the GGA simulation. These results reinforce

that vdW interactions can affect the charge distribution in a metal decorated system and its hydrogen

binding ability and should be taken into account when modelling such systems. Amongst the considered

metals, Pt possessed the strongest hydrogen binding ability, while Na possessed the weakest.

After system relaxation, both the GGA and vdW-DF2 simulations displayed the formation of a

complex involving a hydrogen molecule and metal adatoms for the transition metals (Cu, Ni, Pd and Pt),

as can be seen from Figure 4.4. This complex, involving the dissociation of the H-H bond, corresponds

to structure III described previously by Lopez-Corral [91] for their H2-Pd-graphene system. The H-

H distance after adsorption for our Pd-graphene system was about 0.80 A. The H-H distance after

adsorption for Lopez-Corral’s Pd-graphene system with single-sided metal decoration ranges from 0.85

to 0.87 A. The formation of the complex is likely the cause for the much stronger binding energies of

the transition metals as the hydrogen atoms move towards a more chemical type of adsorption.

Optimal binding energies for reversible hydrogen storage should lie within the range of 0.2 to 0.6

eV per H2 molecule [78]. If the binding energy is too high, then releasing the hydrogen molecules will

be difficult at moderate operating conditions. If the converse occurs, then the storage of hydrogen will

be minimal. Based on our results, three metal-graphene systems fulfill this optimal criterion. The Cu-

graphene system displayed a hydrogen binding energy of 0.51 eV for GGA only results and 0.26 eV for

vdW-DF2 results. The Ni-graphene system had a hydrogen binding energy of 0.27 eV for GGA only

results and 0.17 eV for vdW-DF2 results. Lastly, the Pd-graphene system demonstrated a hydrogen

binding energy of 0.84 eV for GGA only results and 0.51 eV for vdW-DF2 results. The GGA binding

energy value for Pd is too high and outside of the optimal range of values 0.2 to 0.6 eV, while the

vdW-DF2 value for Ni is just lower than the lower limit of preferred values. The vdW-DF2 result of Ni

is outside of the needed range of values by only 0.03 eV, which is a small enough difference to effectively


0

5

10

15

20

-14 -12 -10 -8 -6 -4 -2 0 2 4

DO

S

Energy (eV)

Ni 4sNi 4dC 2sC 2pH 1s

(a)

0

5

10

15

20

-14 -12 -10 -8 -6 -4 -2 0 2 4

DO

S

Energy (eV)

Ni 4sNi 4dC 2sC 2pH 1s

(b)

Figure 4.3: PDOS of Ni-graphene system simulations with (a) GGA functional alone and (b) GGAfunctional with vdW-DF2 corrections. The greater number of peaks and width of the Ni d-shell orbitalfor (a) indicates more distinct localized energy states and stronger potential for interaction with ahydrogen molecule.


Figure 4.4: Examples of the hydrogen-metal complexes formed by transition metals, palladium on theleft and copper on the right. The hydrogen molecule has dissociated and moved towards a chemisorbedstate, producing stronger hydrogen binding energies for transition metals.

still consider Ni suitable for reversible storage. The slight improvement needed in binding ability may

be provided by moderately increased gas pressure or other techniques.

As the goal of the studied metal-graphene systems is to maximize hydrogen gravimetric density, a

heavy metal mass is disadvantageous as it would reduce the relative mass percentage of hydrogen in

the system. Among the three selected metals best suited for reversible hydrogen storage, the increased

binding energies of Pd and Cu compared to Ni will allow them to bind more hydrogen molecules.

However, Pd and Cu are also heavier than Ni and this offsets any advantage offered by the few additional

hydrogen molecules they can adsorb. Hence, binding more hydrogen molecules does not necessarily lead

to higher hydrogen mass percentage in the system. Nickel provides the best balance by still having a

fairly strong hydrogen binding ability while possessing the lowest mass of the studied transition metals.

The nickel-graphene system also showed the strongest binding to the graphene substrate among the three

selected candidates, making it the most stable among the three. Furthermore, investigations conducted

by Sigal et al. [90] observed that chemical treatment can be used to deposit nickel compounds onto a

graphene surface, suggesting experimental feasibility of a nickel-graphene system. In the same study,

nickel was determined to be less easily oxidized than other metal decorations. Oxidation may occur in

real world situations where the system is exposed to air, and acts as a strong inhibitor for hydrogen

adsorption. The combination of strong hydrogen binding ability suited to reversible storage, relatively

low mass and increased practical feasibility due its highly stable metal-graphene system and resistance

to oxidation make nickel the best candidate for use in a metal decorated graphene hydrogen storage

system. Therefore, nickel was selected for use in all subsequent simulations looking at metal coverage

and maximum gravimetric density.

4.4.3 Optimal hydrogen storage on Ni-decorated graphene

Effect of Varying Ni Coverage

The effect of metal coverage, described by the relative density of or equivalently the distance between

metal adatoms on the graphene sheet, can be quite significant due to the complex mix of attractive

and repulsive forces acting within each system. As observed by Wang et al. [76], changes in metal

adatom distance result in variations in interaction energy between adatoms, thus influencing their binding


(a) (b) (c) (d)

Figure 4.5: Supercells used for differing Ni metal coverage simulations: (a) 6 carbon atoms (b) 16 carbonatoms (c) 32 carbon atoms (d) 72 carbon atoms

0 20 40 60

0.5

1

Carbon atoms in supercell

Bindingenergy(eV)permolecule

GGA

vdW-DF2

Figure 4.6: Average hydrogen binding energy (eV/H2) for Ni-decorated graphene systems at differentsubstrate sizes.

abilities with the hydrogen molecules. Since each simulation uses a repeating supercell with a single metal

adatom on each side of the graphene sheet, the size of the graphene substrate supercell determines the

metal coverage of the system. The small 6 carbon supercell used for the simulations comparing different

metal systems represents the highest metal coverage where metal adatoms have the shortest distance

between them. Four supercells of increasing size (6, 16, 32 and 72 carbon atoms as seen in Figure 4.5)

were simulated with GGA alone and with vdW-DF2 included. The results are presented in Figure 4.6.

In general, an increase in supercell size yielded an increase in hydrogen adsorption binding energy.

The 32 carbon atom graphene substrates provided the highest binding energy for GGA only results

(just slightly higher than 72 atoms) while the 72 carbon atom supercell provided the highest energy

for vdW-DF2 results. This suggests that at close range, the proximity of metal atoms has a negative

effect on hydrogen binding ability. This might be due to the increased stability felt by the closer metal

atoms, making the hydrogen molecule less attractive to them for achieving stability. There might also be

repulsive forces between hydrogen molecules at such close range, as they become partially charged after


Graphene Substrate Number of Hydrogen molecules2 4 6 8 10

6 C 0.171 -2.148 Not converged -0.956 –16 C 1.119 0.470 0.323 0.260 0.232

32 C 1.157 0.638 0.160 0.261 –

Table 4.4: Average hydrogen binding energy (eV/H2) for increasing number of adsorbed hydrogenmolecules and different substrate sizes (in terms of number of carbon atoms). Dashed lines indicate asimulation was not conducted, due to low chance of adsorption for 6C or low gravimetric density for 32C. The 16C substrate represents the best balance of substrate size and binding energy which allows itto meet the DOE’s goal of 5.5% gravimetric density.

donating electronic charge towards the metal adatoms. The finding that increased supercell size leads

to higher binding energy suggests that lower metal coverage might be beneficial for hydrogen storage.

However, an increased supercell size also increases the number of carbon atoms and this will very quickly

outweigh any gains from additional adsorbed hydrogen. Hence, a balance must be found between the

need for fewer carbon atoms per metal adatom to decrease non-hydrogen mass and for larger supercells

to increase hydrogen binding energies. It should be noted that the lower metal cover simulations all

produce strong hydrogen binding energies outside the range of -0.2 to -0.6 eV preferred for reversible

storage.

Maximum Gravimetric Density for Ni Graphene Systems

The gravimetric density for each varying metal coverage system studied in the previous section was

investigated by adding increasing numbers of hydrogen molecules to each metal adatom. The results

of the gravimetric density simulations and average hydrogen molecule binding energy are presented in

Table 4.4 and Figure 4.7, while Figure 4.8 presents the theoretical gravimetric density numbers for each

system if the hydrogen molecules successfully adsorbed. The 6 carbon atom supercell fails to bind more

than two hydrogen molecules, with higher numbers of molecules producing negative binding energies or

failing to converge in their simulations which would suggest unstable configurations. This is caused by

the relatively lower binding energy for this metal coverage as discussed in the previous section, which

prevents the binding of large numbers of hydrogen molecules and hence simulations were stopped after

attempting to adsorb 8 molecules. Note that the 6 carbon substrate also has the highest theoretical

gravimetric density for each number of hydrogen molecules, indicating it is preferable to have higher

metal adatom coverage. The 16 carbon atom supercell is the next smallest substrate and has a high

enough binding density to adsorb up to 10 hydrogen molecules. This is also the point at which this

substrate is able to surpass the DOE goal of 5.5% gravimetric density, achieving 6.2 wt %. Hence, the

16 carbon substrate is able to provide a good balance between having a supercell size which allows high

gravimetric densities and binding energies strong enough to adsorb multiple hydrogen molecules. The

configurations for the increasing numbers of hydrogen molecules can be seen in Figure 4.9.

A correlation between the gravimetric density and average binding energy for the 16 carbon substrate

is shown in Figure 4.10, where a rapid drop of binding strength with increasing number of hydrogen

molecules shows the importance of vdW interactions as the binding strength moves away from the

chemisorption type of binding towards weaker physisorption strengths. The final data point for the

maximum 10 hydrogen molecules is just within the desired range of -0.2 to -0.6 eV. The PDOS of the 16

carbon substrate with the different number of hydrogen molecules adsorbed are shown in Figure 4.11.

The distance of the hydrogen from the Fermi level and the lack of overlap between hydrogen and Ni


2 4 6 8 10

−2

−1

0

1

Hydrogen Molecules

Bin

din

gen

ergy

(eV)per

molecu

le

6C

16C

32C

stable

unstable

Figure 4.7: Average hydrogen binding energy (eV/H2) for increasing number of adsorbed hydrogenmolecules and different substrate sizes (in terms of number of carbon atoms)

2 4 6 8 100

2

4

6

8

10

Hydrogen Molecules

GravimetricDensity%

6C

16C

32C

Figure 4.8: Maximum theoretical hydrogen gravimetric density (wt.%) for different number of adsorbedhydrogen molecules and substrate sizes (in terms of number of carbon atoms). Note that not all of thesystems successfully adsorbed the hydrogen molecules (see Figure 4.7).


(a) (b) (c) (d) (e)

Figure 4.9: Configurations of adsorbed hydrogen on the 16 carbon Ni decorated supercell, with increasingnumbers of hydrogen molecules: (a) 2, (b) 4, (c) 6, (d) 8 & (e) 10.

peaks indicates that the hydrogen is not binding through a Kubas type interaction [92], despite the fact

that Ni has unfilled d-shells. This would then suggest that the hydrogen binds by a weak electrostatic

dipole mechanism. This is further confirmed by looking at the charge density difference for two adsorbed

hydrogen molecules in Figure 4.11(f), where sharp charge accumulation and depletion zones around the

hydrogen atoms indicate polarization of the hydrogen molecule. As expected, the number of states

for hydrogen increase as the number of adsorbed hydrogen molecules increases. Another interesting

aspect is the interaction between hydrogen molecules which is visible as the peaks of hydrogen change

in number and spread with different numbers of molecules. The system with 6 hydrogen molecules has

the most distinct peaks, demonstrating a broad range of occupancies for quite differently configured

hydrogen molecules. For the 10 molecule system, the number of peaks goes down again to two while the

number of states at these two peaks’ energies increases, indicating overlap and stabilization in the more

symmetrically configured molecules.

The 32 carbon atom substrate initially showed the highest binding energy as expected but surprisingly

produced lower average binding energies than the 16 carbon substrate for increasing numbers of hydrogen

molecules. This might be because the increased distance between hydrogen molecules adsorbed to

different metal adatoms allows them to interact and stabilize each other to a lower extent, whereas

this distance seems to be closer to optimal for the 16 carbon substrate and too small for the 6 carbon

substrate. The 32 carbon substrate also has very low theoretical gravimetric densities and hence no

simulations were attempted beyond 8 hydrogen molecules as they would not be able to meet the DOE’s

target. By the same reasoning, the 72 carbon atom supercell would have had particularly low gravimetric

densities due to the large number of carbon atoms and was thus excluded from the gravimetric density

simulations altogether. This addresses the point discussed in the previous section, where the increased

binding energy of larger supercells comes at the price of more carbon atoms which negate any gains of

additional hydrogen adsorption as a greater number of heavier carbon atoms actually decreases the mass

fraction of hydrogen.


1 2 3 4 5 6

0.2

0.4

0.6

0.8

1

1.2

Gravimetric Density %


Figure 4.10: Correlation between hydrogen gravimetric density (wt.%) and average binding energy(eV/H2) for the 16 carbon substrate

4.4.4 Discussion

The disjointed set of previous studies cannot be used to confidently evaluate the comparative performance

of metal-graphene systems. This is because these earlier studies used different types of pseudopotentials,

exchange-correlation functionals, DFT simulation package implementations, metal coverages and calcu-

lation parameters such as number of k-points, vacuum spacing and energy cutoffs. This points to the

motivation for and one of the advantages of this paper’s investigations, where the simulation of a large

number of metals using the same consistent conditions allows the proper comparison of these systems.

Our results on the whole show less spectacular performance for metal decorated systems with regards to

hydrogen storage as opposed to some earlier studies which have claimed very high hydrogen binding ener-

gies and gravimetric densities which easily exceed the DOE target of 5.5% wt. The lack of consideration

of vdW forces, the use of small vacuum spacings and the use of the LDA functional, which is known to

overpredict binding energies, likely all lead to earlier studies overestimating the hydrogen binding ability

of metal decorated systems. In fact, several of the metal systems which previously reported studies claim

can exceed the DOE’s target (such as Al and Li) have been found in our investigations to be unable to

meet this goal. On the other hand, even our best case result for Ni barely manages to surpass the DOE

target in its theoretical gravimetric density. This value will likely decrease in real life conditions as part

of a larger contained system and may turn out to be below the target value. This suggests that metal

decoration alone will be unlikely to meet the DOE gravimetric density targets, although it can get us

there most of the way. This is also likely one of the reasons that experimental results are not able to

replicate the spectacular values claimed by earlier studies. Therefore, additional methods for increasing

hydrogen adsorption abilities of graphene will have to be explored together with metal decoration. These

could include manipulating the curvature or interlayer distance of the graphene substrate as suggested

by Tozzini et al.[13] or defect engineering some of the graphene substrate as suggest by Yadav et al.[93].

The combination of both approaches would lead to a higher hydrogen storage capacity than either one

by itself and metal decoration would continue to play an important role in significantly increasing the

hydrogen binding ability of graphene systems.


0

5

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25

-10 -8 -6 -4 -2 0 2 4

DO

S

Energy (eV)

NiHC

0

5

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15

20

25

-10 -8 -6 -4 -2 0 2 4

Energy (eV)

NiHC

0

5

10

15

20

25

-10 -8 -6 -4 -2 0 2 4

DO

S

Energy (eV)

NiHC

0

5

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-10 -8 -6 -4 -2 0 2 4

DO

S

Energy (eV)

NiHC

0

5

10

15

20

25

-10 -8 -6 -4 -2 0 2 4

Energy (eV)

NiHC

(a) (b)

(c) (d)

(e) (f)

Figure 4.11: PDOS of 16 carbon Ni decorated supercell system with increasing numbers of adsorbedhydrogen molecules: (a) 2, (b) 4, (c) 6, (d) 8, & (e) 10. The Fermi level is indicated by a dashed line.The charge density difference of the system with 2 hydrogen molecules (red colored atoms) adsorbed isshown in (f), where yellow indicates regions of charge gain and blue indicates regions of charge loss andcarbon atoms are black colored.


4.5 Summary

The atomic adsorption ability of eight metals on graphene, four light metals and four transition metals,

was investigated using the PBE-GGA functional first and then with the addition of the vdW-DF2

functional. The use of vdW-DF2 generally led to stronger binding of the metal adatom for lighter

metals and weaker binding for heavier metals in comparison to GGA only simulations. Both single and

double-sided decoration were found to obey the same trends and double sided decoration did not decrease

system stability. Therefore, all subsequent simulations were carried out using double-sided decoration.

The hydrogen binding ability of these metals was then investigated through the adsorption of a single

hydrogen molecule over each adatom. The light metals were found to weakly bind hydrogen, whereas

the transition metals displayed an order of magnitude stronger binding. The transition metals produced

hydrogen-metal complexes where the hydrogen molecule had dissociated into individual atoms over a

metal atom. Similar to metal atom binding, it was found that hydrogen binding ability was increased

with the use of vdW-DF2 for light metals but decreased for transition metals.

Three metals (Cu, Ni, Pd) demonstrated hydrogen binding energies close to the range of 0.2 to 0.6

eV considered useful for practical reversible hydrogen storage. Among these, Ni was selected as the best

candidate for a metal-graphene hydrogen storage system due to its low mass and stability in practical

systems. The effect of varying metal coverage on a graphene sheet was investigated for four different

sized (6-72 carbon atoms) supercells. It was found that decreasing metal coverage by increasing the

supercell size (thereby increasing the number of carbon atoms per Ni atom) generally improved the

hydrogen binding ability of the metal. Next, the gravimetric density of the three smallest supercells

was studied as additional hydrogen molecules were adsorbed onto the system. The 16 carbon supercell

displayed the best balance of small supercell size and ability to bind several hydrogen molecules (up to

10), giving it the highest produced gravimetric density of 6.12 wt.%.

Our investigations show that vdW forces can have a significant impact on simulation results. Correc-

tions to better represent such forces should be applied with functionals such as vdW-DF2, particularly

as vdW forces play an important role in hydrogen interactions and adsorption. The inclusion of vdW

forces was also found to decrease the hydrogen binding ability of transition metals, which means that

earlier studies which neglected such effects might have overestimated the usefulness of metal adatoms

for hydrogen adsorption. This could be a reason for the inability of experimental studies to replicate the

phenomenal hydrogen storage results of theoretical metal decoration studies. Our results suggest that

even the best case scenario would produce a gravimetric density of 6.12 wt.%, just above the DOE target

of 5.5 wt.%. This means that additional techniques for enhancing hydrogen storage, such as graphene

sheet curvature and defect engineering, should be investigated to be used in conjunction with metal

decoration to produce a truly feasible real world hydrogen storage system.

Chapter 5

Hydrogen Storage on Defective

Graphene

The material in this chapter has been published in the journal “International Journal of Hydrogen En-

ergy” under the title of “Defect engineering of graphene for effective hydrogen storage“ [93]. Text and

figures are reproduced with permission from the International Association of Hydrogen Energy.

5.1 Introduction

Hydrogen is considered to be a promising environmentally friendly fuel for the future as it possesses

a very high energy content by mass compared to conventional fuels and can cleanly produce energy

with no harmful by-products. However, it is impractical to store and transport hydrogen using existing

methods. Therefore, research efforts in recent years have focused on finding systems which can store

hydrogen through adsorption on various media [14], with an initial goal of 5.5wt% gravimetric capacity

targeted by the US Department of Energy (DOE) [74]. A class of materials that can act as effective

adsorption media for hydrogen molecules are carbon-based nanostructures, due to their relative low

weight and high surface areas [75, 94]. Amongst these, graphene is considered particularly promising

as a one atom thick two-dimensional structure gives it the highest specific surface area among these

materials [73].

This study looked at the effect of individual Stone-Wales (SW), single vacancy (SV) and double

vacancy (DV) 585, 555-777 and 5555-6-7777 defects on the hydrogen binding ability of graphene. Based

on the individual defect simulation results, a combined SW and SV defect system was created to inves-

tigate mixed defect regions. Similarly, a system consisting of SV anchored metal atoms with adjacent

undecorated SVs was created to investigate the effect of undecorated vacancies on the hydrogen binding

ability of metal atoms. A grain boundary structure, commonly created during graphene synthesis [95],

was also investigated for hydrogen adsorption. Finally, the results of the individual and mixed defect

simulations were utilized to engineer two high defect density structures to evaluate the maximum pos-

sible hydrogen molecule adsorption in graphene systems modified solely using defects. The first system

consisted of closely spaced SVs, named the single vacancy maximum hydrogen density (SVMD) system.

The second system consisted of half SW and half SV defects, named the Stone Wales single vacancy

maximum hydrogen density (SWSVMD) system.

53

Chapter 5. Hydrogen Storage on Defective Graphene 54


The need for reversible storage, where hydrogen can be both easily stored and released under near-

ambient conditions, requires that hydrogen binding should be neither too strong nor too weak. Based

on this practical need, the ideal binding energy range for reversible hydrogen adsorption is considered to

be between -0.2 to -0.6 eV [96]. Pristine graphene, with a hydrogen binding energy in the range of -0.01

to -0.09 eV, does not meet this requirement [97, 13]. Consequently, several modifications to graphene

have been proposed to improve its storage capacity. They include metal decoration [76, 98], doping

with hetero-atoms such as nitrogen and oxygen [99, 100], and the introduction of strain, curvature and

edges [13]. An important issue with these studies is that they analyze idealized graphene structures

and usually ignore the effect of defects on hydrogen adsorption, even though commercially prepared

graphene sheets would typically contain topological defects [95]. When they are considered in some

studies, defects are looked at for the sole purpose of anchoring metal atoms over defect sites [101]. To

the best of our knowledge, the direct interaction of defects with hydrogen molecules and their modifying

role in hydrogen adsorption has not been characterized thus far in the literature.

Furthermore, the metal-decorated systems studied so far have not been reproduced experimentally,

rendering these theoretical results less useful in practice. There are additional concerns to these proposed

systems. For instance, metal-decorated systems require the challenging task of isolating and placing

single metal atoms at exact locations over the graphene layer, which might prove difficult to achieve

under experimental conditions. On the other hand, the creation and control of topological defects

over graphene layers has already been demonstrated experimentally [102]. Importantly, defect control

would still be required for many proposed metal-decorated systems. Thus, it is necessary to understand

the fundamental role of defects in graphene with respect to its hydrogen storage ability. Moreover, if

defective graphene is shown to have sufficient binding ability, a system modified solely with defects would

be potentially easier to implement in practice than the current proposed approaches.

In this paper, the hydrogen molecule binding ability of a graphene sheet with the Stone-Wales (SW),

single vacancy (SV) and double vacancy (DV) 585, 555-777 and 5555-6-7777 defects is investigated.

These five point defects were chosen as they have been observed experimentally and are known to be

stable at room temperature. They are usually formed during manufacturing processes such as chemical

vapor deposition, or can be induced by irradiation with electrons or ions [95]. The hydrogen binding

ability in each case was evaluated using density functional theory (DFT) with the generalized gradient

approximation (GGA) functional. The GGA functional is good at modeling covalent type bonding but

poorly represents van der Waals (vdW) forces. Although vdW forces are negligible in covalent bonding

dominated systems, they are a significant component in hydrogen molecule adsorption [103, 104]. Hence,

all systems were also studied with the recently implemented vdW-DF2 functional [105] which better

accounts for vdW forces.


The simulations were performed using plane wave based DFT as implemented in the Quantum Espresso

software [26]. The exchange-correlation functional was represented using GGA as described by Perdew-

Burke-Ernzerhof (PBE) [84]. Interactions between the valence electrons and the ionic core were rep-

resented by Vanderbilt Ultra-Soft Pseudopotentials [106]. The kinetic energy cutoff for wavefunction


expansion was set at 60 Ry (1 Ry = 13.61 eV) and for the charge density it was set at 600 Ry. Each self

consistent field calculation had a convergence threshold of 1E-5 Ry for the total system energy. Each

system was relaxed with variable cell size using conjugate gradient minimization until the magnitude

of the residual Hellman-Feynman force on each atom was less than 1E-3 Ry/Bohr. The total system

energy during relaxation was minimized to within 1E-3 Ry. Brillouin zone integrations were performed

using a Monkhorst-Pack grid with 8× 8× 1 k-points [60].

All simulations, except for the SVMD and SWSVMD systems, were performed with a vacuum spacing

of 30 A to sufficiently isolate the graphene layer and remove interactive effects between layers. All such

simulations also allowed variable cell dimensions during system relaxation. The SVMD and SWSVMD

systems were first simulated using a vacuum spacing of 6 A and variable cell dimensions to allow for

enhanced hydrogen adsorption through interaction effects between graphene layers. Subsequently, the

effect of interlayer spacing effects was investigated for both SVMD and SWSVMD systems using fixed

cell dimensions and vacuum spacings ranging from 2 to 7 A. For the individual defect simulations, the

graphene sheet size varied in proportion to the defect size so as to minimize interaction energies between

periodic defect images. Specifically, the pristine graphene and SW supercells were modeled using 50

carbon atom 4× 4 graphene sheets, while the SV used a 49 atom 4× 4 sheet. The supercell containing

the 585 DV was modeled using a 58 atom 4× 5 sheet; the 555-777 DV using a 72 atom 5× 5 sheet; and

the 5555-6-7777 DV using a 82 atom 5× 6 sheet. Bilayer graphene was modelled using a 24 atom sheet

stacked with a 23 atom sheet in an AB stacking configuration. The mixed SV and SW system and the

SWSVMD system were modeled using a 49 carbon atom 4 × 4 graphene sheet. The metal decorated

system and SVMD system simulations used 30 atom 3× 3 sheets. The semi-metallic nature of graphene

was represented using Methfessel-Paxton [87] smearing with a degauss value of 0.01. The binding energy

of a hydrogen molecule for each system was calculated as :

Eb = (Esystem+iH2− Esystem − iEH2

)/i (5.1)

where Esystem+iH2is the total energy of the modified graphene system with hydrogen adsorbed, Esystem

is the total energy of the modified graphene system without hydrogen, EH2is the total energy of the

free H2 molecule and i corresponds to the number of H2 molecules. In order to accurately obtain

energy changes, the three simulations required to produce values for the terms on the right hand side of

the equation used the same supercell size and parameters. The hydrogen molecule was placed in several

starting configurations for each individual defect system by varying its position laterally across the sheet.

Its orientation with regards to the plane of the sheet (perpendicular or parallel) was also analyzed.

It was recognized that in addition to the above, the PBE-GGA functional is only good at accounting

for localized effects and describing strong bonds, but is not good at describing long-range nonlocal effects

such as vdW forces which have long decay tails. There have been several functionals proposed to help

better model such weak interactions, and among them the vdW-DF approach provides a generalized

truly nonlocal functional independent of system geometry [86]. The vdW-DF2 functional is a further

improvement over the originally proposed vdW-DF functional [105], and provides better equilibrium

separations, hydrogen bond lengths and more accurate vdW interactions at intermediate distances longer

than equilibrium ones. More importantly, for our purpose at hand, when compared with several DFT

functional approaches, the vdW-DF2 functional has been found to most closely match experimental data

for adsorption of a hydrogen molecule on copper surfaces [103], as well as molecular adsorption on metal

surfaces [104]. All individual defect simulations were repeated with van der Waals corrections to the


PBE-GGA through the vdW-DF2 functional while keeping all other simulation parameters the same.

This allowed for comparison with previous literature and investigation of the effect of different density

functionals. The remaining simulations were all performed solely with the vdW-DF2 correction since it

probably models complex hydrogen systems more accurately.

5.4 Hydrogen Binding over Individual Defect Systems

In this section, the five individual defect simulation results are presented and their binding energy values

are available in Table 5.1. It was found that the orientation of the hydrogen molecule with regards to the

plane of the sheet (perpendicular or parallel) had a negligible impact on binding energies and so only the

differences in energy at different locations over the defect are reported in the table. The corresponding

plots of charge density variation around each defect are found in Figure 5.2. According to Eq. (5.1),

a negative binding energy indicates favorable conditions for hydrogen adsorption, with a more negative

value indicating stronger binding.

Binding Energy (eV)PBE-GGA vdW-DF2

Pristine -0.0102 -0.0618Stone-Wales (SW)

top -0.0100 -0.0610hepta 0.0011 -0.0620penta -0.0136 -0.0727

Single Vacancy (SV) -0.3282 -0.4020Double Vacancy (DV)

585octa -0.0082 -0.0624penta -0.0156 -0.0646

555-777bridge57 -0.0080 -0.0592bridge77 -0.0091 -0.0571top -0.0037 -0.0542hepta -0.0020 -0.0655penta -0.0051 -0.0678

5555-6-7777hepta 0.0009 -0.0614hex -0.0067 -0.0618penta -0.0127 -0.0656

Table 5.1: Binding energies of a hydrogen molecule placed over individual topological defects in graphene.Multiple positions, shown in Figure 5.1, were tested for each defect type. Both PBE-GGA and vdW-DF2functionals were utilized to ascertain differences in binding energies due to choice of density functional.The vdW-DF2 results all demonstrated stronger binding and a smaller range of values among sites withina defect than the PBE-GGA results.

5.4.1 Pristine Graphene

To establish a baseline for binding energy results, in comparison to which modifications of graphene

should offer an advantage, hydrogen adsorption over pristine graphene was studied first. Previous


h��

�t�

octa

��p��

��p��

bridge57

hepta

bridge77

top

hepta hex

penta

(a) (b)

(c)(d)

(e)

(f)

Figure 5.1: Supercells for hydrogen binding over individual defect systems depicting different initialpositions for the adsorption of a hydrogen molecule: (a) Pristine (b) SW (c) SV (d) DV 585 (e) DV555-777 (f) DV 5555-6-7777.


literature [107] has shown that the hollow position, as shown in Figure 5.1(a), has the lowest adsorption

energy with a binding value of -0.011 eV using the PBE-GGA functional and -0.054 eV using the

vdW-WF functional (another functional used to better represent vdW forces). In the current paper,

the hydrogen binding energy of pristine graphene layer was found to be -0.010 eV using PBE-GGA

(consistent with literature value) and -0.062 eV with vdW-DF2 (slightly different from [107] due to a

different functional used for vdW interactions). These values indicate a very weak binding of hydrogen on

pristine graphene, far from the preferred -0.2 to -0.6 eV range, and demonstrates that pristine graphene

cannot fulfill the requirements for a practical hydrogen storage medium.

5.4.2 Stone-Wales Defect

For the SW defect, the hydrogen molecule was placed over three positions as indicated in Figure 5.1(b).

For the top position, the PBE-GGA binding energy was found to be identical to that of the pristine

graphene case and seemed to offer no additional advantage for hydrogen binding. The penta position,

however, offered a small improvement while the hepta position was unfavorable with a positive binding

energy. The non-existent binding in the hepta position is likely due to the hydrogen molecule’s increased

distance from the surrounding carbon atoms, resulting in weaker covalent interactions as represented

by PBE-GGA. The reason for the better penta binding energy was likely due to the closer equilibrium

distance of the H2 molecule to the surrounding ring atoms leading to a stronger interaction of the

electrons in the hydrogen molecule with those of the carbon atoms. For the top position, there was a

high density of electrons near the carbon atom, as shown in Figure 5.2. This resulted in a relatively

stronger repulsive force being felt by the hydrogen molecule, making this a less stable position.

For the vdW-DF2 calculations, the binding energy at top position was found to be very similar to

that of pristine graphene. The hepta position was also found to have a virtually identical binding value,

while the penta position offered slightly stronger binding. A previous study, using atomic orbital basis

sets with GGA and Double Zeta Polarization (DBZ) for this system, has reported a binding value of

-0.082 eV at the penta position and a binding value of -0.090 eV at the hepta position [108]. These are

closest to the vdW-DF2 results in our study (-0.073 eV for penta and -0.0620 eV for hepta), suggesting

the DBZ can provide corrections similar to those of vdW-DF2 for atomic basis sets, at least for this

type of defect. These somewhat better values in the cited study could be due to differences in the DFT

approach and simulation parameters, although in both cases the penta position is found to be slightly

stronger than the hepta position. The stronger binding energy of the hepta position for vdW- DF2

compared to PBE-GGA is likely due to vdW interactions which act over the increased distance of the

hydrogen molecule from surrounding atoms. As can be seen, the SW binding values were still outside

the preferred range of -0.2 to -0.6 eV. Yet, since the SW defect had a better binding ability than pristine

graphene, it is expected that the presence of SW defects will increase the ability of a graphene system

to draw hydrogen molecules closer to the surface even though it will not bind them strongly enough for

practical purposes.

5.4.3 Single Vacancy Defect

The supercell for this defect system is shown in Fig. 5.1(c). The single vacancy defect was observed to

have binding energy values much stronger than those for any of the other single layer individual defect

systems. They fall comfortably within the desired range required for practical reversible adsorption.


Pristine SW

DV 585DV 555-777

DV 5555-6-7777

Figure 5.2: Top view of charge density for studied defective graphene systems (except for SV, found inFig. 5.10. The highest amount of charge can be seen to concentrate around the carbon atoms arrangedin rings. Conversely, the lowest amount of charge is present in the hollow regions of these rings. Thevery high charge density around the carbon atoms make the top and bridge positions unfavourable foradsorption. Among hollow positions, the pentagon rings seem to have the most optimum charge densityfor favourable hydrogen adsorption, whearas the lower charge densities of the larger rings leads to slightlyweaker binding energies.


The vacancy has three carbon atoms adjacent to it, which were found to undergo significant movement

after adsorption of the hydrogen molecule. This is quite different than the other studied individual

defects, for which the carbon atoms did not undergo any appreciable movement after introduction of

the hydrogen molecule. The change in the carbon atom configurations is shown in Figure 5.3 (a), a side

cross-section of the graphene sheet prior to adsorption. From the figure, it is clear that the atoms were

more or less contained within a single plane of the graphene sheet. However, after adsorption of the

hydrogen molecule, as depicted in Figure 5.3(b), the adjacent atoms have moved out of the plane of the

sheet away from the hydrogen molecule. This configuration was found to be the most optimal in helping

to share electronic charge between the hydrogen molecule and the atoms around the vacancy as further

discussed in section 5.6.

Figure 5.3: A side cross-section of the single vacancy defect: (a) prior to and (b) after adsorption ofhydrogen molecule. Adsorption of the hydrogen molecule clearly distorts the graphene sheet, pushingthe atoms adjacent to the vacancy out of the plane away from the hydrogen molecule.

A variable which might also affect hydrogen binding is the distance between defects in the graphene

sheet. As the SV defect was found to be the most promising of the single layer individual defects, the

effect of defect density was briefly investigated for this defect using different sized supercells. Both 31

carbon atom and 71 carbon atom supercells with a SV in each were simulated to observe the effect of

higher and lower defect density respectively. The 31 atom supercell exhibited a hydrogen binding energy

of -0.494 eV while the 71 atom supercell showed a hydrogen binding energy of -0.323 eV. This indicates

a monotic increase in hydrogen binding strength with increasing defect density (created by decreasing

supercell size) and was a motivation for creating the very high defect density structures studied in


sections 4.4 and 4.5.

5.4.4 585 Double Vacancy Defect

Two positions were investigated for the 585 defect for H2 adsorption, as displayed in Figure 5.1(d). While

PBE-GGA showed large differences in binding energies between the two locations, with the penta position

found to have the lower energy of the two, this positional difference was observed to be inconsequential

in the case of the vdW-DF2 functional. This is similar to the case of the SW defect where the hepta

(or octa here) position was at the center of a large region of very low electron density and far from the

surrounding atoms, causing it to experience a lower amount of interaction with them (see Fig. 5.2). The

use of vdW-DF2, on the other hand, allowed for interactions to occur over larger distances. The vdW-

DF2 results displayed a much stronger binding of the hydrogen molecule than the PBE-GGA results,

although they were only marginally better than the pristine graphene case and weaker than the preferred

range of values.

5.4.5 555-777 Double Vacancy Defect

The 555-777 defect had the most unique available positions for the adsorption of the hydrogen molecule,

a total of five as shown in Figure 5.1(e). For PBE-GGA simulations, the hepta position produced the

weakest binding energy, followed by the top position, penta position and the two bridge positions. On

the other hand, for vdW-DF2, the top position displayed the weakest binding energy, followed by the two

bridge positions, the hepta position and then the penta position. The vdW-DF2 results followed expected

trends, similar to those seen for the SW and 585 defects, where the top and bridge positions possessed

weaker binding energies due to the repulsion felt by the hydrogen molecule from close proximity to high

electron density (see Fig. 5.2). The hepta and penta positions in the hollow of the rings both exhibited

better binding energies as the hydrogen molecule can easily fill a region previously devoid of charge and

interact well with electrons belonging to the surrounding carbon atoms. Once again, the penta position

demonstrated slightly stronger binding than the larger hepta position, indicating that the penta position

is closest to an optimal distance from the surrounding carbon atoms. For the PBE-GGA simulations,

the strange order of binding energies was likely due to the poor ability of the functional to account for

vdW forces. The distance of the H2 molecule was greater from surrounding atoms in hollow positions in

the center of rings and this produced low stability due to the absence of long-range interactions. This

caused the penta and hepta positions to have weaker binding energies relative to other positions. In fact,

PBE-GGA results for all positions in this defect demonstrated weaker binding energies than the pristine

graphene case. The vdW-DF2 results were only marginally better than the pristine graphene case and

still weaker than the preferred range of values. As was the case in other individual defect systems, the

spread in the binding energy values for vdW-DF2 cases was observed to be much smaller than that for

the PBE-GGA calculations.

5.4.6 5555-6-7777 Double Vacancy Defect

As depicted in Figure 5.1(f), three positions were analyzed as potential sites for H2 adsorption for the

5555-6-7777 defect. Both PBE-GGA and vdW-DF2 showed the hepta position with the weakest binding

energy and the penta position with the strongest binding, following the same trends as SW, 585 and

555-777 defects. The PBE-GGA hepta position binding energy was exceptionally weak and actually the


lowest binding energy of the individual point defect simulations in this paper. Once again, the vdW-DF2

simulations had similar binding values for all locations while the PBE-GGA showed a much wider spread.

Again the vdW-DF2 binding energies were found to be much stronger than the PBE-GGA values but

still offered no significant improvement over the vdW-DF2 pristine graphene results and do not lie in

the preferred range of values.

5.4.7 Bilayer Graphene with Single Vacancy Defect

During graphene manufacturing, a particular form of graphene produced is bilayer graphene which has

a specific interlayer spacing. In an attempt to study the effect of defects on hydrogen adsorption in

this structure, bilayer graphene in an AB stacking with a SV defect on one of the layers was simulated

for two cases. In the first case, the hydrogen molecule was placed above the defect and between the

two carbon layers and in the second case the hydrogen molecule was placed above the defect as well

as the entire bilayer structure. For the first case, the hydrogen binding energy turned out to be 0.505

eV while the second case resulted in a hydrogen binding energy of -2.824 eV. The first case was clearly

unfavourable for hydrogen adsorption. The second case had a very strong binding energy which was

well outside the preferred range of values and thus would be impractical in creating a reversible storage

process. Furthermore, the bilayer structures consist of two carbon layers in which only one of the layers

participates in hydrogen adsorption on one of its surfaces. This is quite inefficient and drastically reduces

hydrogen density of the overall system. Finally, a bilayer structure with AA stacking falls within the

range of interlayer spacings investigated for the high defect density structures explored in sections 4.4

and 4.5.

5.5 Hydrogen Binding over Multiple Defect Systems

5.5.1 Grain Boundary

Large scale graphene sheets, such as those synthesized from chemical vapor deposition, are usually poly-

crystalline and contain one dimensional defects along grain boundaries. These defects are generally tilt

boundaries and can be thought of as a line of individual point defects [95]. Several such defects consisting

of arrangements of pentagons and heptagons, found to be the most thermodynamically stable among

possible ring structures, have been previously simulated to obtain mechanical properties [109]. One such

system, shown in Figure 5.4 and analogous to the Σ7 grain boundary defect, was selected to simulate the

hydrogen adsorption ability of grain boundaries in graphene. This defect is likely representative of other

similar grain boundary defects which also consist of ring structures. Our previous simulations suggest

that these structures would have hydrogen adsorption abilities similar to other ring structure defects

such as double vacancies. This was confirmed as the resulting binding energy of -0.081 eV was barely

stronger than that of graphene and the point defects (beating the SW penta position by just 0.008 eV)

and similarly outside of the range of values preferred for reversible storage. Thus, it can be reasonably

concluded that while grain boundaries are not detrimental to hydrogen adsorption ability in graphene

sheets, they do not offer much benefit either.


Figure 5.4: Grain boundary defect consisting of 5-7 rings, analogous to Σ7 defect, and adsorbed hydrogenmolecules. Two adjacent supercells are shown to visualize the grain boundaries indicated by the dashedlines. Note the different orientations of the graphene lattice on each side of a grain boundary, indicatingdifferent grains.

5.5.2 Mixed Stone-Wales and Single Vacancy

Both the SW and SV defects were modeled in the same supercell to study the effect of mixed defect

regions. They were placed in close proximity and only separated by a hexagon ring of carbon atoms, as

shown in Figure 5.5. The SW defect penta position was studied, as this position presented the strongest

binding energy after that of the SV in all individual point defect simulations. The binding energy of -

0.545 eV at the penta position showed a significant improvement in binding ability, by a factor of 7.5 over

the same position in the isolated SW defect, due to the presence of the single vacancy. This represents

the highest H2 binding energy amongst all 30 A vacuum spacing single layer simulations. This system

shows that the mixture of single vacancies with other point defects, unlike the mixture of only ring

structure defects found in the grain boundary system, is very beneficial to hydrogen adsorption ability.

5.5.3 Single Vacancy with Metal Decoration

A structure consisting of closely spaced SVs was modeled with double sided metal decoration. Only

half the vacancies anchored nickel atoms as seen in Figure 5.6, thereby ensuring each metal atom had

an adjacent empty vacancy. The SVs themselves were separated from each other by at least a hexagon

of carbon atoms. A hydrogen molecule was in turn adsorbed on each of the nickel atoms. The binding

energy of -0.238 eV for each hydrogen molecule was found to be within the preferred range of values

for practical hydrogen storage. However, it is lower than the value of -1.157 eV found for a similar

system sans defects, simulated in a separate study by Wong et al. [71] . This suggests that the presence

of adjacent SVs decreases the hydrogen binding ability of metal atoms. This is despite the fact that

the metal atoms were anchored in vacancies, which in earlier studies have been shown to increase the

hydrogen binding ability of metal atoms when there are no empty adjacent vacancies [110].


Figure 5.5: Mixed defect system showing single vacancy at the top-left and Stone-Wales in the center.The hydrogen molecule is adsorbed at the penta position in the Stone-Wales defect. The hydrogenbinding energy is significantly higher in this mixed defect system than for either defect in isolation.

5.5.4 Single Vacancy Maximum Hydrogen Density (SVMD) System

A structure with a very high density of SVs, where the vacancies are separated by a minimum of only

one hexagon of carbon atoms, was chosen to represent a defect engineered system for use in hydrogen

storage as shown in Figure 5.7(a). This structure was then packed with the maximum number of

hydrogen molecules which were still able to produce a negative binding energy. In total 11 H2 molecules

were accommodated, which represents 5.81% gravimetric density for hydrogen storage. The change

in the average H2 binding energy with successive addition of molecules to the structure is shown in

Figure 5.8(a). The binding ability of the system rapidly drops after the first four hydrogen molecules,

indicating that each vacancy is quickly stabilized and saturated by about two hydrogen molecules each.

The lowest binding energy of -0.1 eV is just below the preferred range of values for reversible hydrogen

storage. After relaxation, the interlayer spacing had decreased to 2.65 A from the initial 6 A. Nine

of the hydrogen molecules had been split apart and their individual hydrogen atoms were observed to

move closer to carbon atoms, as can be seen in Figure 5.7(b). Most of these individual hydrogen atoms

were now positioned over carbon atoms in the top position but stayed out of chemical bonding range.

The exception was around the vacancy sites, where three hydrogen atoms appear to have moved into

chemical bond range with the three carbon atoms surrounding each vacancy. The graphene structure

itself underwent significant distortion from its flat planar shape as can be seen from Figure 5.7(c).

This suggests that the carbon and hydrogen atoms formed a complex network stable at the decreased

interlayer spacing.

The effect of interlayer spacing was further explored by calculating the average hydrogen binding

energy with different vacuum spacing in the supercell, going from 3A to 7A, the results of which are

presented in Figure 5.9(a). The strongest binding energy was found to be at 3 A, a sharp drop from the

energy at 2.65 A which had been achieved when the supercell dimensions were allowed to vary during

relaxation. There is also a sharp rise in energy when going to 4 A, which displays an unstable positive

average binding energy. Thereafter, the binding energy once again starts to decrease and become stable

upto 7 A, at which point it has even stronger than the energy at 2.65 A.


(a)

(b)

Figure 5.6: Single vacancy defect system with double-sided nickel metal decoration and hydrogenmolecule adsorption: (a) top view and (b) side view. The nickel atoms are anchored over a singlevacancy, while the adjacent vacancy is left undecorated. Although the hydrogen molecule binding en-ergy is still within the preferred range for hydrogen storage, it is weaker than that of the correspondingsystem without vacancies.


(a) (b) (c)

(d) (e) (f)

Figure 5.7: Defect engineered systems for hydrogen stroage: (a) SVMD system prior to hydrogen ad-sorption, (b) SVMD system subsequent to hydrogen adsorption top view and (c) side view. A totalof 11 hydrogen molecules were adsorbed to yield a gravimetric density of 5.81%. Nine of the hydro-gen molecules dissociated into individual atoms. The underlying graphene sheet itself has undergonesignificant structural distoration subsequent to hydrogen adsorption. The SWSVMD system prior toadsorption (d) is also shown, and subsequent to hydrogen adsorption (b) top view and (c) side view.

5.5.5 Stone Wales Single Vacancy Maximum Hydrogen Density (SWSVMD)

System

The mixed SW and SV system investigated previously, seen in Figure 5.7(d), was considered for use

in a defect engineered hydrogen storage system in a manner similar to that of the SVMD system. In

total, 22 H2 molecules were successfully adsorbed, leading to 7.02% gravimetric density for hydrogen.

The change in average H2 binding energy with successive addition of molecules to the structure is shown

in Figure 5.8(b). The energy follows a more linear pattern than the SVMD system and displays fairly

strong hydrogen binding. After relaxation, the interlayer spacing had decreased to 2.65 A from the initial

6 A, similar to the SVMD structure. Twenty of the hydrogen molecules had been dissociated and the

substrate structure of carbon atoms itself was heavily distorted, as can be seen in Figure 5.7(e). Several

of the carbon rings, especially the heptagons in the SW defect, have broken up and carbon atoms have

moved out of their standard sp2 bond range to open up vacancy like gaps. Unlike the SVMD system,

the individual hydrogen atoms did not seem to prefer the top position over carbon atoms and were more

randomly distributed, with most not positioned directly over a carbon atom. The majority of hydrogen

atoms were also well out of covalent bonding range of carbon atoms and positioned in the space between

graphene layers, as seen in Figure 5.7(f). Hence, the whole system consisting of carbon and hydrogen

atoms appears to have rearranged itself to form a stable complex.

The effect of interlayer spacing was further explored by calculating the average hydrogen binding

energy with different vacuum spacing in the supercell, going from 3A to 7A, the results of which are

presented in Figure 5.9(b). This range was selected as these provide a relatively practical range, with


2 4 6 8 10

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

Number Adsorbed Hydrogen Molecules

Bin

din

gen

ergy

(eV

)per

mole

cule

(a)

0 5 10 15 20−14

−12

−10

−8

−6

−4

−2

Number Adsorbed Hydrogen Molecules

Bin

din

gen

ergy

(eV

)per

mole

cule

(b)

Figure 5.8: Change in average hydrogen binding energy of high defect density systems with increasingnumber of hydrogen molecules: (a) single vacancy (SVMD) system (b) Stone-Wales and single vacancy(SWSVMD) system.

3 A being just below spacing for graphite and spacings beyond 7A reducing volumetric density. The

strongest binding energy was found to be at 7 A, while 3A provides the weakest binding energy.

5.6 Discussion: General Trends Towards Defect Engineering of

Graphene for Hydrogen Storage

In this section, we discuss the general trends in hydrogen binding over individual and mixed defect

systems, identify important parameters which affect hydrogen adsorption ability and suggest a way

towards defect-engineering of graphene for effective hydrogen storage.


3 4 5 6 7

−0.

− .

− .

Interlayer Spacing Å


(a)

3 4 5 6 7−1

−0.9

−0.8

−0.7

Interlayer Spacing Å


(b)

Figure 5.9: The effect of interlayer spacing on the average hydrogen binding energy of high defect densitysystems: (a) single vacancy (SVMD) system (b) Stone-Wales and single vacancy (SWSVMD) system.


5.6.1 Individual Defect Systems

Choice of Exchange Functional

The vdW-DF2 results consistently showed stronger binding values and a smaller range of these val-

ues among different sites within a defect than the PBE-GGA results. The adsorption of the hydrogen

molecule itself appeared to be in the form of physisorption, which is typified by the molecule not disso-

ciating and the lack of strong covalent character bonds between the hydrogen and carbon atoms. This

kind of adsorption is dominated by weak interactive van der Waals forces. The vdW-DF2 functional

captures such interactions much better than the plain PBE-GGA. Since van der Waals forces are mostly

attractive except at very close range (at which point Pauli repulsion dominates), their inclusion generally

results in a stronger binding of the hydrogen molecule to the graphene surface. Furthermore, since they

act over a long-range, molecules experience similar levels of interactions regardless of their location in the

studied ring structures. Conversely, the short-range covalent bond forming forces, modeled well by PBE-

GGA, are highly localized and thus small changes in molecule position can cause large changes in the

amount of interaction felt by the molecule and hence a larger variation in binding values for the same

defect. As the vdW-DF2 results are more accurate for physisorbed systems, the following discussion

summarizes key trends based on the this functional’s simulations.

Ring Structure Defects

The SV defect differs from other defective systems because all the other structures consist of convex

polygon rings where the atoms have rearranged themselves to provide each carbon atom with bonds to

three surrounding carbon atoms. On the other hand, the SV defect consists of a non-convex polygon

in which atoms adjacent to the vacancy have bonds to only two other atoms. These differences lead

to different hydrogen binding trends between the two types of defects. For non-SV structures, binding

energy seems to be determined primarily by the distance of the hydrogen molecule from regions of

charge. The highest electron density is found to concentrate around the carbon atoms arranged in rings,

as can be seen from the top-view of charge density for each of the simulated systems (prior to hydrogen

adsorption) in Figure 5.2. These diagrams all display contours of charge density from 0.0015 to 0.35

(number of charge/Bohr-3). The trends for binding energies in relation to the position of the hydrogen

molecule on the defect can be qualitatively understood by carefully analyzing these contours. It can be

observed that top and bridge positions over regions of very high charge have weak binding ability, likely

due to the appreciable Pauli repulsion felt by the hydrogen molecule. This is in fact opposite to the

case of chemisorption of a single hydrogen atom over graphene, where the top position would be most

preferable as it helps stabilize the charge deficient atom [111].

For ring structures (ranging in size from pentagons to octagons), the charge density is observed to

decrease towards the center of the ring. This suggests that hydrogen binding improves in going from

hollow positions in octagons to heptagons to hexagons and finally pentagons, with the last position

showing the most optimal distance from surrounding charge among ring structures. These binding

energy trends hold true within the same defect for different hydrogen molecule positions, but not across

different defect types. For instance, the octagon ring in the DV 585 defect displayed a weaker binding

energy than the pentagon ring in the same defect as expected, yet it showed a stronger binding energy

than the hexagonal and heptagonal positions in the DV 5555-6-7777 defect and in pristine graphene.

This could be due to the different sizes of the same type of ring found in different defects and also due to


the nature of the surrounding rings. Each ring is somewhat distorted from its regular geometric shape,

depending on the type and arrangement of rings around it. All the binding energies for the ring positions

were found to lie between -0.06 and -0.07 eV, with the exception of the pentagon in the SW defect which

produced a slightly lower energy of -0.0727 eV. The 5555-6-7777 defect was the most complex and largest

area defect studied, with regions of several unsymmetrical non-hexagonal rings. Yet the fact that its

binding value results were similar to that of the smaller area defects suggests that the binding energy

in carbon rings is not influenced by the nature of the surrounding rings and the size of the defect area.

Hence, it can be speculated that larger and more complex defects that have been discovered or theorized

in graphene sheets, consisting of arrangements of rings ranging in size from octagons to pentagons and

sp2 bonded carbon atoms, will likely have binding energies similar to those found for the DV defects in

this paper. Binding energies thus seem to be size independent for ring defects.

Single Vacancy Defect

The SV defect on the other hand has quite different characteristics as seen in Figure 5.10. Even though

the range of charge found to be preferable for binding in ring structures is found around the edges of

the vacancy region, the much lower and uneven charge distribution on the carbon atoms adjacent to

the vacancy means that the same kind of trend analysis is not applicable. The missing carbon atom

in the vacancy leaves behind three dangling bonds on its three adjacent atoms. This causes the defect

to undergo a Jahn-Teller distortion which allows two of the adjacent atoms to form a new albeit weak

bond between them, replacing two of the dangling bonds. However, one of the dangling bonds remains

unable to attach to a second atom and leaves the last adjacent atom with a coordination number of two.

As a result, this defect is quite different compared to the other defects studied in this paper, none of

which have dangling bonds. The carbon atom with the dangling bond has a dearth of negative electronic

charge. This is demonstrated in Figure 5.10, which also shows the stronger electron density representing

a weak bond between the other two adjacent atoms. This leads to an expectation that the vacancy defect

will attract the hydrogen molecule strongly so that it can share in the molecule’s cloud of negative charge,

making it the preferred adsorption position for the molecule. The dangling bond nature of the SV defect

can also be observed by examining PDOS graphs of the defect prior to adsorption and comparing it to

that of pristine graphene, as shown in Figure 6.3. When the carbon atoms in a ring are able to bond to

three adjacent atoms, two of their px and py orbitals participate in sp2 hybrid orbitals formed within

the plane of the sheet, while the remaining pz orbitals, oriented perpendicular to the sheet, overlap and

share charge amongst themselves above and below the plane of the sheet. However, when a carbon atom

is not able to bond with three other atoms, its p-orbitals are unable to hybridize or overlap to the same

extent and are more distinctly localized on the atom as a result. This can be seen in Figure 6.3(b), where

the greater number of peaks for the p-orbitals indicates more distinct localized states when compared to

the much smoother curves for pristine graphene in Figure 6.3(a). The unshared charge in these localized

orbitals is then more likely to interact with the hydrogen molecule in comparison to charge on more

highly co-ordinated atoms in ring structures.

The dangling bond atom would prefer to be close to the hydrogen molecule to share in its increased

electronic charge. This could be accomplished by the atom moving out of the plane towards the hydrogen

molecule on the side from which the molecule approached or moving in the opposite direction as was

observed in our simulation. The first option would cause the dangling bond atom to move further

away from its surrounding carbon atoms and give up sharing of charge with them. On the other hand,


Figure 5.10: Top view charge density plot for the single vacancy defect. The three carbon atoms adjacentto the vacancy can be observed to have lower charge density around them in comparison to the rest ofthe carbon atoms in the graphene sheet. The carbon atom with a dangling bond is located just abovethe vacancy in the figure. The other two adjacent atoms have a greater amount of charge betweenthem than the amount of charge between either of them and the dangling bond atom, giving these twoadjacent atoms slightly higher stability than the dangling bond atom.


0

5

10

15

20

25

30

35

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6

DO

S

Energy (eV)

C 1sC 2p

(a)

0

5

10

15

20

25

30

35

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6

DO

S

Energy (eV)

C 1sC 2p

(b)

Figure 5.11: Projected Density of States (PDOS) of graphene systems prior to hydrogen adsorption: (a)pristine graphene (b) single vacancy defect (SV). The Fermi level is represented by the dashed verticalline. The dangling bond carbon atom in the SV defect has less co-ordination than atoms in the pristinegraphene. Hence, its orbitals have a lower extent of overlap and hybridization, leaving them more distinctand localized. This is visible from the higher number of peaks in the PDOS for the SV defect at allenergies. The unshared charge in the more localized SV defect makes it more attractive for adsorptinga hydrogen molecule.


the latter option allows it to still share in the charge of the graphene sheet while being closer to the

hydrogen molecule and is thus the most stable configuration. Figure 5.12(a) depicts a side-view of the

charge density variation of the vacancy defect. Regular hexagons in pristine graphene, when looked at

from the side, have an elongated bright purple region indicating high charge density, as seen at the left

and right ends of the figure. On the other hand, the single dangling-bond carbon atom has a smaller

circular region of slightly lower and less evenly distributed charge. Furthermore, there is a large gap with

moderately low charge between the dangling bond atom and the regular hexagon at the right end of the

figure, indicating the electronically deficient vacancy region. Figure 5.12(b), shows the cross-sectional

charge density after adsorption of the hydrogen molecule. The dangling bond carbon atom possesses

a larger region of increased electronic density around the atom. Furthermore, the region between the

dangling bond atom and the regular hexagon at the right of the figure and adjacent to the hydrogen

molecule clearly shows greatly increased charge density which was probably drawn from the hydrogen

molecule.

5.6.2 Mixed Defect Systems

Single Hydrogen Molecule Adsorption

The binding ability of the mixed SW and SV defect was found to be surprisingly strong. Since the two

defects individually had the two highest binding energies, mixing them seems to have resulted in an

additive effect. Figure 5.13(a) shows the charge density plot of this system prior to hydrogen adsorption.

The low electron density regions at the single vacancies at the top left and right of the figure (the right

vacancy being part of the next repeating unit of the supercell) and the center of the two heptagons of the

SW defect are clearly visible. The hexagons towards the bottom of the figure have the greatest amount

of high charge (purple color) regions while the hexagons towards the top of the figure, between the two

vacancies and adjacent to a SW heptagon, have greatly reduced regions of low charge. Presumably some

of the charge from the latter hexagons has been transferred to the single vacancies to better stabilize

them. Figure 5.13(b) shows the charge density plot of the system after hydrogen adsorption. The

redistribution of electronic density is now found to be more acute. The region around the pentagon

where the hydrogen molecule is adsorbed has significantly lower charge as does the region around the

other pentagon towards the bottom of the figure (although to a lesser extent). The single vacancies now

show higher charge densities, suggesting that there has been charge transfer from the regions around the

pentagons to the single vacancies. The relatively lower charge density around the hydrogen molecule’s

location would cause it to strongly attract the hydrogen molecule to share in its charge density and would

help explain the high hydrogen binding energy for the system. Therefore, the addition of the hydrogen

molecule has allowed a greater amount of charge redistribution which has made the single vacancy and

hence the entire system more stable.

The results of the mixed SW-SV system and grain boundary system demonstrate that mixed topolog-

ical defect regions are not detrimental to hydrogen adsorption ability and actually have higher hydrogen

binding ability than each isolated individual defect. Yet the mixture of only ring defects, such as that

found in the grain boundary system, provide only a modest improvement which is still below levels of

desired binding ability. The single vacancy on the other hand seems to greatly enhance the binding

ability of ring defects to the required levels. However, its presence is not always beneficial. The reduced

binding ability of the nickel atoms when compared with a defect free system might be due to the adja-


(a)

(b)

Dangling Bond Carbon Atom

Vacancy Region

Dangling Bond Carbon Atom

Vacancy Region

Figure 5.12: Side view of single vacancy (SV) charge density: (a) relaxed SV prior to adsorption and(b) relaxed SV with adsorbed hydrogen molecule. Black filled circles represent carbon atoms, whilewhite filled circles represent hydrogen atoms. Regular hexagons of high charge density usually found ingraphene sheets can be seen on the left and right edges of either diagram. In (a), the dangling bondcarbon atom has a samller region of lower charge than the hexagons and the low charge density of thevacancy region is also visible. In (b), the dangling bond carbon atom has higher charge density equivalentto that of the hexagons and the vacancy region also has visibly increased charge density. This increasedcharge density is likely due to the charge supplied by the hydrogen molecule.


(a)

(b)

Figure 5.13: Charge density plots of the mixed Stone-Wales and single vacancy system: (a) prior tohydrogen adsorption and (b) subsequent to hydrogen adsorption. Single vacancies are visible at the topleft and right of the figures, while the Stone-Wales defect is in the center. There is large redistribution ofcharge after adsorption of the hydrogen molecule (blue atoms), with the regions around the pentagonsof the Stone-Wales defect losing charge to the single vacancies. This lower region of charge then stronglybinds the hydrogen molecule, leading to higher hydrogen binding energies than was the case for eitherdefect by itself.


cent vacancy competing with the metal atom for the hydrogen molecule’s charge and creating a more

energetically unfavorable system overall. This indicates that the presence of nearby vacancies might be

detrimental to the hydrogen adsorption ability of anchored metal systems. Furthermore, it suggests that

it might be more beneficial to construct a structure purely from single vacancies, which provided better

binding ability than the investigated nickel adatoms.

High Defect Density Structures and Gravimetric Density

The results of the SVMD and SWSVMD system simulations demonstrate the potential of defect en-

gineered systems for hydrogen storage. The gravimetric density of the SVMD system (5.81%) is just

above the initial DOE goal of 5.5%. This is achieved with an average binding energy (-0.1 eV) slightly

weaker than the lower limit (-0.2 eV) of binding energy values thought to be required for practical room

temperature storage. Therefore, at room temperature conditions, the gravimetric density will likely

decrease somewhat to just below target values. The SWSVMD system, on the other hand, has a higher

gravimetric density of 7.02%, and its average binding energy (-2.52 eV) is actually much stronger than

the higher end (-0.6 eV) of preferred values. With such a strong binding energy, it was surprising that

the SWSVMD system was unable to accommodate even more hydrogen molecules. This might possibly

be due to crowding of hydrogen molecules and a strong repulsion felt by squeezing additional molecules

into the remaining small gaps and destabilizing the carbon-hydrogen complex that had formed. As

discussed, these values will likely decrease at room temperature and probably reach desired values.

The designed SVMD and SWSVMD systems thus will likely be able to store hydrogen to a level

which is within the ballpark of the DOE targets, with the latter providing higher levels of storage. Yet,

they will fall short of the targets in real world conditions as the effects of temperature and fluctuating

environmental conditions which cannot be easily modeled become a factor. Furthermore, it is noted here

that these results are for the material alone and in a practical storage device with a container and various

other components, the hydrogen mass fraction in the whole system will decrease even further. In order

to provide a boost in storage ability and a safety factor beyond the targets, additional modifications

through the utilization of curvature effects and high pressure environments should allow such defect

engineered systems to comfortably meet requirements. This would be achievable without the need for

cumbersome and as yet undemonstrated atomic metal decoration.

Clearly interactive effects between graphene layers have played a role in stabilizing the hydrogen

atoms, which are mostly located in the voids between successive graphene layers. The change in hy-

drogen binding energy with interlayer spacing also points to a possible method for reversible storage

by controlling interlayer spacing. Certain spacings are more favorable to adsorption and could be used

when hydrogen is loaded into and stored in the system. Others are less favorable and likely help cause

association and release of hydrogen molecules which could be used during unloading of hydrogen from

the storage system. For instance, for the SVMD system, the interlayer spacing could be changed to 4

A during unloading to desorb hydrogen and changed to 7 A during loading to help adsorb hydrogen

(although 3 A provides even stronger binding energy useful for adsorption, it is too close to 4 A and it

might be difficult to maintain a 1 A gap). For the SWSVMD system, 7 A would be best for loading and

3 A would be best for unloading. The control of interlayer spacing through the use of spacer molecules or

piezoelectric crystals could be implemented through methods proposed by Tozzini et al. [13]. However,

the stability and behavior of the significantly distorted structures during loading and unloading cycles,

especially the SWSVMD system which seemed to form a new complex with the hydrogen atoms, might


be an issue during practical operation and needs to be further investigated. It should be noted though,

that the out of plane displacements and curvature introduced in the high defect density structures does

not likely impeded hydrogen adsorption ability as curvature as been shown to increase hydrogen binding

ability [?]. Nevertheless, mixed defect graphene sheets will undoubtedly prove to be a useful tool in the

design and implementation of practical hydrogen storage systems.

5.7 Summary

Commercially prepared low cost graphene is bound to contain topological defects. With significant

attention on graphene as a hydrogen storage medium, this paper analyzed the role of topological defects

on its hydrogen binding ability and their possible use in defect engineering a better storage system. The

ability to adsorb a hydrogen molecule was examined for five types of individual point defects: Stone-

Wales, single vacancy and three different double vacancy defects. Two types of density functionals were

utilized for all point defect simulations, PBE-GGA and the more recent vdW-DF2 functional which better

models long range van der Waals forces. The vdW-DF2 simulations in general resulted in a stronger

hydrogen binding ability than PBE-GGA, demonstrating that the vdW forces are a significant factor in

hydrogen molecule adsorption and should be accounted for to accurately model this phenomenon. The

vdW-DF2 results also showed a smaller variation in binding energies for different H2 binding sites than

the PBE-GGA computations. The single vacancy defect had the strongest binding value and had only

value which fell within the range desirable for reversible hydrogen adsorption. The Stone-Wales and

double vacancy defects did not display significant improvement in binding ability over that of pristine

graphene, however they were shown to not have a detrimental effect on hydrogen storage ability. Defects

consisting of various planar carbon rings ranging in size from pentagons to octagons, such as the Stone-

Wales and double vacancy defects, were found to have similar hydrogen binding values and the binding

value for a particular site within such a ring was found to be independent of the nature of the surrounding

rings or defect size range.

Subsequent to investigation of isolated defects, a number of multiple defect systems were modeled

using the vdW-DF2 functional only. A grain boundary system analogous to a Σ7 grain boundary defect

and consisting of pentagon and heptagon rings was found to have a hydrogen binding energy similar

to that of the Stone-Wales and double vacancy ring defects. A metal decorated system, consisting

of vacancy anchored nickel adatoms with an adjacent undecorated vacancy, was simulated and it was

found that the presence of an undecorated vacancy decreased the binding ability of the nickel adatom

when compared to a system with no vacancies. On the other hand, the presence of a single vacancy

was found to significantly enhance the hydrogen binding ability of an adjacent Stone-Wales defect and

move its hydrogen binding energy into the range desirable for reversible hydrogen adsorption. Two

high defect density systems, the first consisting of only closely spaced single vacancies and the second

consisting of closely spaced single vacancies and Stone-Wales defects, were then designed and tested for

their ability to bind a large number of hydrogen molecules. The first system managed to produce a

maximum gravimetric density of 5.81% while the latter achieved 7.02%. These results were achieved

at relatively small graphene interlayer spacings, with both systems showing the best average hydrogen

binding energy at 3A spacing and weaker binding ability for both smaller and larger spacings. Hence,

defect engineering of graphene systems shows great potential in meeting hydrogen storage requirements

while avoiding the need for the potentially more challenging metal decoration that is proposed currently.

Chapter 6

Hydrogen Storage on

Two-Dimensional Carbon Allotropes

6.1 Introduction

In recent years, the numerous environmental issues presented by fossil fuels have acted as a major driving

force for the research community to place focus on greener and more sustainable alternatives. Among

the many energy sources being investigated at the moment are hydrogen fuels as they do not create any

carbon emissions when used to produce energy [112]. One obstacle that researchers face with regards

to hydrogen fuels is finding a method to effectively store hydrogen prior to fuel consumption. The US

Department of Energy has set a target to achieve 5.5 wt% gravimetric density for hydrogen storage in

light-duty vehicles by 2015 [19]. Conventional technologies have been unable to meet these targets in

a safe and practical manner [113]. Hydrogen adsorption on substrates has been explored as a possible

route towards meeting these storage goals [14], including the use of materials such as metal organic

frameworks [15], carbon nanotubes [16] and boron nitride sheets [17] and fullerenes [18]. Among carbon

based substrate materials, two-dimensional graphene has been found to be particularly promising [114].

Graphene’s high specific surface area in addition to its unique mechanical and electronic properties

allow it be an ideal substrate which can be modified through metal decoration for increased hydrogen

adsorption [13]. Since the discovery of graphene several other two dimensional carbon structures, such

as graphyne [115, 116] and graphdiyne [117], have been synthesized or theorized and show promise for

hydrogen adsorption applications. This work looked at the hydrogen adsorption ability of graphyne,

graphenylene and four newly theorized and as yet unnamed two-dimensional carbon allotropes using

the LDA, GGA and vdW-DF2 functionals. The lithium binding ability and hydrogen binding ability

on lithium decorations for each of these structures was investigated, with lithium being selected for

metal decoration as it is the lightest known metal and so would help increase relative hydrogen mass in

the system. Finally, this study tried to maximize hydrogen gravimetric density by adsorbing multiple

hydrogen molecules on the lithium-decorated structures.

78

Chapter 6. Hydrogen Storage on Two-Dimensional Carbon Allotropes 79


In a study by Zhang et al.[109] lithium decorated graphyne was predicted to have a gravimetric density

of 15.15 wt%, higher than that of graphene. In 2013, Lu et al. [118] theoretically predicted four new

two-dimensional carbon structures which they propose will be mechanically stable at room temperature.

These structures, along with graphyne and another proposed carbon allotrope called graphenylene [119],

have different carbon bond hybridizations and electron density distributions than graphene. This may

give them potential to better interact with and bind metal adatoms and hydrogen molecules, as graphyne

has already been predicted to do [109].

The present study investigated the hydrogen storage ability with metal decoration of the six carbon

allotropes discussed by Lu et al. [118], which according to the naming convention followed by them are:

C65, C64 (graphenylene), C63, C62 (graphyne), C31 and C41. The C6n structures consist of hexagons

connected by n-sided polygons, going from a pentagon for n=5 to a triangle for n=3 and a straight

chain of two carbon atoms for n=2. Similarly the C31 and C41 structures consist of triangles and

squares connected by single carbon C1 units. Three of the new structures (C65, C63 and C41) are

considered more stable than graphyne and the fourth (C31) is just barely less stable.

Another issue associated with most theoretical predictions of hydrogen adsorption on metal-decorated

carbon-based structures is that they utilize density functional theory (DFT) with local density approxi-

mation (LDA) and generalized gradient approximation (GGA) functionals. For example, the previously

mentioned study by Zhang et el. [109] of lithium decorated graphyne utilized LDA. However, the

LDA functional can be quite inaccurate for such complex systems and will often overpredict adsorption

strength. On the other hand, while the GGA functional models covalent type forces well, it poorly rep-

resents van der Waals (vdW) interactions. Such vdW interactions are significant in describing the weak

physisorption type of bonding typical of molecular hydrogen adsorption on carbon substrates [76, 77]

and the interaction between neighboring metal atoms especially at higher coverages [77]. The more

recently implemented vdW-DF2 [85] functional is said to better account for vdW forces [120] and so

should provide more accurate adsorption energies. Hence, this study compares theoretical predictions

for lithium and hydrogen adsorption energies using the LDA, GGA and vdW-DF2 functionals for each

simulation.


The various carbon allotrope systems were studied using first principles calculations through density

functional theory (DFT) as implemented using the plane-wave pseudopotential approach in Quantum

Espresso [26]. In order to ascertain accuracy and the effect of different functionals, three electron

exchange functional types were used. The local density approximation (LDA) functional was described

using the Perdew-Wang method [121]. The generalized gradient approximation (GGA) functional was

described using the Perdew-Burke-Ernzerhof (PBE) [84] method. The vdW-DF2 functional [85] was

used to better describe van der Waals forces. This functional was used instead of the earlier vdW-DF

[86] for increased accuracy in estimating equilibrium separations, H2 bond strengths and van der Waals

attraction at intermediate separations longer than equilibrium ones [85]. Ultrasoft pseudopotentials

were used for GGA and vdW-DF2 calculations, while norm-conserving pseudopotentials were used for

the LDA calculations. The kinetic energy cutoff value was set to 60 Ry (1 Ry∼=13.606 eV) for the


wave functions and to 600 Ry for the charge density. The Brillouin zone was sampled using a 8× 8× 1

Monkhorst-Pack [60] k-point grid and Methfessel-Paxton [87] smearing of 0.01 Ry [88]. The supercell

and atomic positions were optimized using the conjugate gradient (CG) algorithm. The total energy

convergence was converged to within less than 5 meV/atom. Each of the structures were modeled using

periodic supercells of 48 carbon atoms, except for the C65 supercell which had 40 carbon atoms. Each

system had a vacuum layer thickness of more than 30 A.

The average binding energy for a metal atom was calculated through the following equation:

Eb = −[Ecarbon+nmetal − (Ecarbon + nEmetal)]/n (6.1)

where Ecarbon+nmetal is the total energy of the metal decorated carbon allotrope system, Ecarbon is the

energy of the carbon allotrope sheet alone, Emetal is the total energy of the free metal adatom and n

corresponds with the number of metal adatoms.

Consequently, the average binding energy for hydrogen adsorption on the lithium-decorated carbon

allotropes can be calculated through the following equation:

Eb = −[Emetal−carbon+iH2 − (Emetal−carbon + iEH2)]/i (6.2)

where Emetal−carbon+iH2 is the total energy of the metal decorated carbon allotrope system with hydrogen

adsorbed, Emetal−carbon is the total energy of the metal decorated carbon allotrope sheet, EH2 is the

total energy of the free H2 molecule and i corresponds to the number of H2 molecules. A positive binding

energy in the previous two equations indicates a stable system configuration.

The charge density differences were obtained from the following equation:

∆ρ = ρmetal−carbon+iH2 − (ρmetal−carbon + ρiH2) (6.3)

where ρmetal−carbon+iH2 is the charge density of the metal decorated carbon allotrope system with

hydrogen adsorbed, ρmetal−carbon is the charge density of the metal decorated carbon allotrope sheet

and ρiH2 is the charge density of the iH2 molecules in their adsorbed positions.

6.4 Results and Discussion

6.4.1 Metal Adsorption

As previously reported, metal decoration on graphene greatly enhances its limited hydrogen adsorption

ability as the hydrogen molecules bind to the metal atoms rather than the carbon substrate [13]. Hence,

double sided lithium decoration was conducted for each carbon substrate to increase the maximum

possible hydrogen storage ability. Lithium was selected as the metal adatom as it is the lightest metal

and hence it would create a relatively lower non-hydrogen mass fraction in the system. The multiple

adsorption positions and system configurations investigated are illustrated in Figure 6.1. The adsorption

positions are above the center of various polygon shapes formed by carbon atoms in the plane of the

various structures; these include a triangle site for the C31 surface, a square site for C41, a hexagon site

for C62, hexagon and triangle sites for C63, hexagon and square sites for C64 and hexagon and pentagon

sites for C65. Generally positions in the large hollow rings of several of the structures (such as in the


a) b) c) d) e)

f) g) h) i)

Figure 6.1: Substrate structures and hydrogen adsorption sites of the six studied two-dimensional carbonallotropes with double-sided lithium decoration: a) C31; b) C41; c) C62; d) C63 hexa; e) C63 tri; f) C64

hexa; g) C64 square; h) C65 hexa; i) C65 penta.


C31

C41

C62 xa

C64-square

C64-hexa

C65-penta

C65-hexa

1

2

3

4

BindingEnergy(eV)

vdW-DF2

PBE-GGA

LDA

Figure 6.2: Average metal binding energies (eV/atom) at multiple sites for the six studied two-dimensional carbon allotropes with double-sided lithium decoration

C65 C41 C63 C64 C62 C31Hexa Penta Square Hexa Tri Hexa Square Hexa Tri

LDA 3.348 3.341 2.678 2.524 2.261 2.688 2.678 2.462 0.964GGA 2.538 2.526 2.106 2.121 1.869 2.225 2.113 2.015 0.687vdW-DF2 2.203 2.210 1.775 1.791 1.618 1.859 1.798 1.696 0.420

Table 6.1: Average lithium adsorption energy (eV) for each two-dimensional carbon allotrope and ad-sorption position. Note the bulk cohesive energy for lithium is 1.63 eV. All structures except C31 posseslithium binding energy greater than the cohesive energy and this should prevent metal atom agglomer-ation.

center of C64) were not investigated as they were presumed to produce weak lithium binding due to

the large distance from surrounding atoms, based on previous work with graphene systems with similar

large hollow spaces [93]. The lithium binding energies for these systems are displayed in Table 6.1 and

Figure 6.2 for easy comparison. All of the positions show positive stable binding energies, indicating that

double sided lithium decoration is physically feasible. Furthermore, all structures except C31, display

lithium binding energies greater than the cohesive energy for bulk lithium (1.63 eV) and so should

have well dispersed lithium atoms which avoid clustering. The C31 structure stands out by having a

metal binding energies significantly below the others. In fact, its binding energy values (0.964, 0.687

& 0.420 eV for LDA, GGA and vdW-DF2 respectively) are below the bulk cohesive energy, indicating

that lithium atoms are likely to cluster into agglomerates by migrating across the C31 surface. Adatom

clustering due to low metal binding energy has been a problem in previous metal decoration systems

[101]. Therefore, our results show that the studied C31 is not a good candidate for practical hydrogen

storage. Nevertheless, it may still be possible to prevent lithium clustering by anchoring the metal

adatoms on a vacancy, as has been previously suggested for other systems [101]. Overall, these results

suggest that the remaining allotropes are more viable candidates for use in a practical storage device.

The Li binding energies for the C65 allotrope are the highest among the studied structures (from

3.348 eV with LDA at its strongest down to 2.203 eV with vdW-DF2), while the remaining allotropes


show more or less similar binding energies (with the exception of C31 as discussed previously). For all

allotropes, a specific pattern can be observed for the energies produced when using different exchange

correlation functionals. The LDA functional consistently produces the highest lithium binding energy,

followed by the GGA functional and the vdW-DF2 functional produces the lowest binding energy for each

allotrope system. The vdW-DF2 functional is known to have a stronger repulsion for electron exchange

effects than PBE GGA [122] and this is likely contributing to its relative lower metal adsorption energies.

It is interesting to note that all the GGA and vdW-DF2 lithium binding energies are stronger than the

corresponding lithium binding energies for double sided decoration on graphene [71], suggesting metal

decoration for these structures might be more favorable than for graphene.

In order to understand the nature of bonding in the systems, the projected density of states (PDOS)

for each of the metal decorated carbon allotropes simulated with the vdW-DF2 functional are presented

in Figure 6.3. For structures with multiple adsorption positions, only one PDOS diagram is shown for

the position with the strongest binding energy as the other positions are likely to have very similar

states. The carbon substrates clearly show sp hybridization within the carbon sheet where the carbon

s and p shell peaks overlap in each diagram. The lithium atoms have very localized peaks which

overlap with carbon peaks to some degree in all the structures and so there is likely some degree of

hybridization between the lithium orbitals and surrounding carbon orbitals. The C65 structure shows

the highest degree of hybridization as the two lithium peaks line up very well with corresponding carbon

peaks; in fact the red carbon p-orbital peak which overlaps the rightmost green lithium peak is barely

visible. This indicates a strong degree of hybridization for the C65 structure and explains its stronger

lithium binding energies. The C65 structure also has the fewest zero state energy regions or number

of deep valleys which are close to zero value in density of states, indicating it has a greater degree of

delocalization of the electrons which are shared well amongst the system atoms and demonstrates that

the lithium atoms have integrated well into the substrate system. Conversely, the C31 structure displays

the greatest number of deep valleys and has several energy regions with zero or near zero states. This

indicates a greater degree of localization of electrons on atoms and decreased charge sharing within the

system, indicating that the lithium adsorption is less favorable for the C31 system configuration. The

PDOS diagrams also demonstrate that none of the lithium adsorbed structures have a band gap, unlike

the bare substrates where the C62 and C64 structures have small energy band gaps indicating they are

semiconductors [118]. On the other hand, the adsorption of lithium seems to have metalized all the

allotropes which all now display conductor like PDOS.

6.4.2 Hydrogen Adsorption

Following lithium adsorption, a hydrogen molecule was adsorbed on each lithium atom for all the carbon

allotrope structures. The average hydrogen molecule binding energy (eV/H2) results are given in Table

6.2. The optimized configurations of the adsorbed hydrogen molecules for each position can be seen

in Figure 6.1. Unlike the lithium adsorption simulations, there is no clear pattern among the binding

energies produced by the different exchange correlation functionals for hydrogen adsorption. In most

cases (seven out of nine) the LDA functional produces the highest binding energy while the lowest binding

energies are almost equally split between GGA and vdW-DF2 functionals. Overall, the C31 allotrope

displays much stronger binding energy than the other structures, opposite to its behavior for lithium

adsorption, as can be seen in Figure 6.4 for easy comparison. As the Li decorated C31 structure was found

to be relatively less stable (with a lithium binding energy even less than bulk lithium’s cohesive energy),


0

5

10

15

20

25

30

35

-20 -10 0

DO

S

Energy (eV)

C sC p

Li

0

5

10

15

20

25

30

35

-20 -10 0

Energy (eV)

C sC p

Li

0

5

10

15

20

25

30

35

-20 -10 0

DO

S

Energy (eV)

C sC p

Li

0

5

10

15

20

25

30

35

-20 -10 0

Energy (eV)

C sC p

Li

0

5

10

15

20

25

30

35

-20 -10 0

DO

S

Energy (eV)

C sC p

Li

0

5

10

15

20

25

30

35

-20 -10 0

Energy (eV)

C sC p

Li

(a) (b)

(c) (d)

(e) (f)

Figure 6.3: Projected density of states (PDOS) for the lithium decorated two-dimensional carbon al-lotropes from simulations using the vdW-DF2 functional: a) C31; b) C41; c) C62; d) C63; e) C64; f) C65.There is evidence of sp hybridization within the carbon sheet and hybridization between the lithiumand carbon atoms. The C65 structure displays the greatest degree of hybridization and electron sharingwhile the C31 structure displays the highest localization of electrons.


C31

C41

C62

C63-tri

C63-hexa

C64-square

C64-hexa

C65-penta

C65-hexa

0.2

0.4

0.6

0.8

BindingEnergy(eV)

vdW-DF2

PBE-GGA

LDA

Figure 6.4: Average hydrogen binding energies (eV/H2) at multiple sites for double sided lithium deco-rated carbon allotrope systems

C65 C41 C63 C64 C62 C31Hexa Penta Square Hexa Tri Hexa Square Hexa Tri

LDA 0.197 0.192 0.196 0.243 0.237 0.226 0.089 0.434 0.709GGA 0.158 0.161 0.159 0.179 0.179 0.167 0.167 0.194 0.743vdW-DF2 0.188 0.175 0.173 0.182 0.177 0.183 0.173 0.189 0.671

Table 6.2: Average hydrogen adsorption energies (eV/H2) for each two-dimensional carbon allotropeand adsorption position

the addition of the hydrogen molecule’s charge acts as a stabilizing force and makes the molecule’s

charge quite attractive to the lithium-C31 system, thereby enhancing its adsorption energy. Amongst

the remaining structures, the GGA and vdW-DF2 functionals produce roughly similar energies across all

positions. The H2 adsorption energies with LDA functional show greater variability, being fairly high for

the C62 allotrope (0.434 eV) and low for the C64-square position (0.089 eV). The vdW-DF2 functional

displays the smallest variability for non-C31 binding energies, with all of them having values within 0.02

eV of each other.

There also seems to be little relation between the strength of hydrogen adsorption and lithium ad-

sorption behavior for the non-C31 allotropes. Instead, the particular electronic and structural properties

of each structure determine their interaction with the hydrogen molecules and a specific pattern seems to

be difficult to predict a priori. In a broad sense, positions located in larger polygons such as hexagons or

pentagons produced slightly stronger hydrogen binding than those in smaller polygons such as squares

or triangles, although the magnitude of the difference is negligible (especially for vdW-DF2 results as

pointed out). Interestingly, all the vdW-DF2 hydrogen adsorption energies are stronger than that of

graphene with double sided lithium decoration with the same functional, while all the GGA binding

energies are weaker (with the exception of C31) [71]. This once again points to the importance of con-

sidering vdW effects, where their neglect leads to the conclusion that these carbon allotropes are inferior

to graphene for hydrogen adsorption while their inclusion results in the opposite conclusion.

As all of the hydrogen molecules remained intact after adsorption and as all of the average hydrogen


(a)

(b)

Figure 6.5: Charge density difference isosurfaces for (a) C64-hexa and (b) C63-hexa systems. Yellowindicates regions of charge gain, blue indicates regions of charge loss, green indicates lithium atoms andred indicates hydrogen atoms. The isosurfaces show clear polarization around the hydrogen molecules.


Figure 6.6: Configuration of C64 system with maximum number of adsorbed hydrogen molecules. Eachlithium atom binds two hydrogen molecules to give eight molecules in the system and a hydrogengravimetric density of 2.6 wt%.

binding energies were below 1.0 eV, the hydrogen likely bonded with the lithium adatoms through

physisorption. This is further confirmed by the charge density differences (CDD) of the systems for

hydrogen adsorption. For example, this is demonstrated with the CDD for the C64-square position

and C63-hexa position using vdW-DF2 results in Figure 6.5. There are very clear regions of charge

accumulation and depletion on either side of the hydrogen molecules, indicating strong polarization of

the hydrogen. This suggests that the hydrogen binds by a weak electrostatic dipole mechanism for all

of the systems and there is no covalent character bonding or strong hybridization between the hydrogen

and lithium atoms. Such relatively weak binding is actually advantageous as it allows easier release of

the hydrogen molecules from the system while stronger covalent type bonds require significant input of

energy.

6.4.3 Maximum Gravimetric Density

The various structures were next investigated for adsorption of the highest number of hydrogen molecules

they could accommodate. The C31 structure was excluded from this study as it was not considered

practical based on metal anchoring ability as previously discussed. Furthermore, since the vdW-DF2

functional is considered to be more accurate for hydrogen adsorption [71], the simulations were carried

out with this functional alone. The systems analyzed so far had only four hydrogen atoms on two lithium

atoms in 48 or 40 carbon atom substrates, leading to quite low gravimetric density for hydrogen (0.68

to 0.81 wt.%). However, even adding multiple hydrogen molecules to each lithium atom would not be

able to compensate for the large number of carbon atoms which represent a significant non-hydrogen

mass fraction. Indeed, it can be seen from Figure 6.1 that only a small area of the carbon substrate

in each simulation is being used for hydrogen adsorption (assuming all such adsorption only occurs on

lithium atoms). Hence, increasing the number of adsorbed lithium positions within each supercell would

go towards greatly increasing hydrogen mass fraction in the supercell.

Expectedly, increasing the number of lithium atoms in each supercell caused the hydrogen binding

energy to decrease and and eventually made hydrogen adsorption unstable in the system. This is similar

to a trend observed for nickel decorated graphene in our previous work [71], where increased metal

coverage decreased the hydrogen adsorption energies. Several configurations with adsorption of lithium

atoms at different positions were analyzed for different allotropes. The best results were obtained for

the C64 and C41 structures. The C64 was able to adsorb up to four lithium atoms in its 48 carbon

supercell, meaning that it could accommodate double sided lithium decoration at only one additional


Figure 6.7: Configuration of C41 system with maximum number of adsorbed hydrogen molecules. Eachlithium atom binds three hydrogen molecules to give twenty four molecules in the system and a hydrogengravimetric density of 7.1 wt%.

position (another hexa position) compared to the earlier simulation. Each of the lithium atoms was able

to adsorb only two hydrogen molecules to give a total of eight hydrogen molecules in the system, as seen

in Figure 6.6, which produced a hydrogen gravimetric density of 2.6 wt.%. The average binding energy

per molecule for these 8 hydrogen molecules was 0.147 eV, a slight decrease from 0.183 eV binding energy

for the initial system with lithium adsorbed at only one position.

The C41 structure was able to adsorb lithium atoms at three additional positions within its 48 atom

supercell, giving it a total of 8 adsorbed lithium atoms. Each of these in turn were able to adsorb

a maximum of 3 hydrogen molecules, resulting in a total of 24 hydrogen molecules being successfully

adsorbed in the supercell, as seen in Figure 6.7. This produced a hydrogen gravimetric density of 7.12

wt.%, by far the highest of any of the carbon allotrope structures studied and the only one to exceed the

DOE target of 5.5 wt.%. The average hydrogen binding energy per molecule was reduced to 0.087 eV, a

marked decrease from the 0.173 eV energy for the initial single site adsorption case. Although the C41

structure’s gravimetric density is lower than the extremely high density of 15.15 wt% reported by Zhang

et al.[109], it should be noted that the previous study used the LDA functional which is less accurate

than the vdW-DF2 functional we have utilized and often overpredicts binding energies. Indeed, in a

previous study we have reported that using the newer vdW-DF2 functional produces drastically lower

hydrogen gravimetric density for graphene (6.12 wt.% at best) compared to earlier studies which used

LDA (with a value reported up to 16 wt.%) [71]. Hence, the C41 structure demonstrates higher possible

hydrogen gravimetric density than graphene. This also demonstrates the importance of selecting a

proper exchange correlation functional which can represent weak van der Waals interactions for molecular

hydrogen systems.

The geometry of the C41 structure likely plays a role in its outstanding performance. The structure

has less large open hollow spaces compared to the other allotropes, allowing for more efficient packing of


its square lithium adsorption sites within a certain area. Yet the lithium adsorption sites are not too close

to each other, as in the adjacent hexa sites of the C64 structure, which can cause less stable hydrogen

adsorption as well as impose geometrical constraints on hydrogen molecule packing. Hence, the C41

carbon allotrope seems to have a balanced structure with potential to be used in a practical hydrogen

storage device. It should be noted the stated hydrogen gravimetric density is its theoretical best for the

allotrope medium and in real life conditions and as part of a wider system the overall figure will likely

drop somewhat. However, the structure will still likely produce hydrogen density in the ballpark of the

DOE target value. Furthermore, the storage capacity of the structure may be even further enhanced by

effects such as the presence of vacancies and other topological defects, which tend to increase hydrogen

storage capability in graphene systems [93], and would be a good candidate for further investigation.

6.5 Summary

The hydrogen storage capacity of six theorized two-dimensional carbon allotropes (C65, C64, C63, C62,

C31 and C41) was investigated using density functional theory. Multiple positions on the allotrope

structures were tested for double sided lithium decoration using LDA, GGA and vdW-DF2 functionals.

Subsequently, the adsorption energy of a single hydrogen molecule on each lithium atom at these positions

was determined using the same three functionals. All the structures were able to successfully bind

lithium atoms with adsorption energies stronger than bulk lithium cohesive energy, with the exception

of the C31 structure which had lithium adsorption energies significantly lower than the other allotropes.

The remaining allotropes showed roughly similar lithium adsorption energies, with the C65 structure

possessing the strongest binding energies. The vdW-DF2 functional resulted in the lowest lithium

binding energies for all structures followed by the GGA functional, while the LDA functional produced

the highest binding energies for all structures. For hydrogen adsorption, all of the structures were again

able to successfully bind hydrogen molecules. The GGA and vdW-DF2 hydrogen adsorption energies for

all of the allotropes, except C31, were roughly similar, while the LDA functional produced more widely

fluctuating though generally stronger binding energies. In contrast to it’s lithium binding energies,

the C31 structure had significantly stronger hydrogen binding energies than the other allotropes. The

maximum possible hydrogen adsorption capacity of each carbon allotrope, other than C31, was then

examined using the vdW-DF2 functional alone. The C41 allotrope produced the highest hydrogen

gravimetric density at 7.12 wt%, better than that of metal decorated graphene, and was the only one to

exceed the DOE hydrogen storage target.

Chapter 7

Conclusion and Future Work

7.1 Summary and overall contribution

This work aimed to use first princples based Density Functional Theory (DFT) to study the possible

use of nanomaterials in addressing the issues of fossil fuel based energy systems through applications in

sustainable hydrogen production and storage.

Hydrogen production from water was looked at by using two-dimensional (2-D) molybdenum disulfide

(MoS2) as a catalyst for water dissociation in Chapter 3. This was accomplished by locating the active

sites for water (H2O) adsorption on the edge terminations of MoS2, studying the water dissociation

reaction on each edge using nudged elastic band method (NEB) and obtaining activation free energy

barriers and rate constant, studying the behaviour of a water molecule on the most favorable MoS2 edge

using finite temperaturab-initio molecular dynamics (AIMD) and using metadynamics biased AIMD

to explore reaction mechanisms for water adsorption and dissociation on the most favorable edge and

obtain free energy reaction barriers.

Hydrogen storage was looked at through adsorption on carbon substrates in Chapters 4, 5 and 6.

In Chapter 4, metal decorated graphene was studied by finding the adsorption energies of eight metals

(Al, Li, Na, Ca, Cu, Ni, Pd, Pt) on graphene with single and double sided decoration, the adsorption

energies of hydrogen on each double sided metal decoration system, the effect of varying metal coverage

on hydrogen adsorption energies and maximum possible hydrogen gravimetric density. In Chapter 5,

defective graphene was studied by finding hydrogen adsorption energies on five point defects (Stone-

Wales (SW), single vacancy (SV) and 585, 555-77 and 5555-6-7777 double vacancies (DV)), hydrogen

adsorption energies on mixed defect systems (a grain boundary, a metal-decorated SV with adjacent SV

and a mixed SV-SW system) and maximum possible hydrogen gravimetric density on two high defect

density systems (consiting of SW-SV and SV-SV mixtures). In Chapter 6, six two-dimensional carbon

allotropes other than graphene were studied by finding the adsorption energies for lithium for each

system with double-sided decoration, the adsorption energies of hydrogen on each double sided metal

decoration system and the maximum possible hydrogen gravimetric density.

The main conclusions of this work are the following:

• The Mo-edge termination of the 2-D MoS2 sheet is its only edge which successfully adsorbs the

H2O molecule in a stable configuration.

90

Chapter 7. Conclusion and Future Work 91

• The Mo-edge termination of 2-D MoS2 dissociates water spontaneously at a room temperature

with a negligible free energy activation barrier and very high reaction rate constant. The reaction

prefers to proceed through cleaving of the O-H bond in H2O, with both OH and H adsorbing on

the catalyst surface but may also proceed by release of both H atoms of H2O to directly form H2

with only O adsorbing on the catalyst surface.

• The effect of van der Waals forces on adsorption of energies of weakly interacting processes such

as H2 physisorption is significant and GGA functionals utilized in previous first principles are

inadequet for describing these interactions

• Light metals have weak hydrogen binding ability when adsorbed on graphene. Nickel is one of the

best metals for graphene decoration with regards to reversible hydrogen storage.

• Previous metal decorated graphene studies overestimated the maximum hydrogen gravimetric den-

sity. Nickel decorated graphene was able to achieve a maximum hydrogen gravimetric density of

6.12 wt.%.

• Topological defects on graphene are not detrimental to hydrogen storage ability. SV defects and

mixed defects involving SVs significantly enhance hydrogen storage ability of graphene.

• Graphene can be defect engineered to make a high defect density system with a maximum hydrogen

gravimetric density higher than metal decorated graphene at 7.02 wt.%.

• Non-graphene 2-D carbon allotropes show promise as hydrogen storage media and through lithium

decoration can achieve a higher maximum hydrogen gravimetric density than metal decorated

graphene at 7.12 wt.%.

7.2 Future work

The research presented in this thesis has looked at one particular part or step of larger processes.

Specifically, there are additional details which must be obtained to provide a more complete picture at

the practical real-world level for each of the areas studied. Hence, the following avenues of investigation

should be explored further in the future:

• Hydrogen Production from Water on Two-Dimensional Molybdenum Disulfide

• Study mechanism and activation energy barriers of hydrogen desorption and evolution on 2-D

MoS2 and possible use of photoactivation to drive forward reaction.

• Study effects multiple H2O molecules, surface coverage and oxygen atom removal on water disso-

ciation and hydrogen evolution reactions.

• Hydrogen Storage on Two-Dimensional Carbon Substrates

• Study the hydrogen storage ability of graphene and other 2-D carbon allotropes under realistic am-

bient temperature and pressure conditions and look at system level hydrogen loading and unloading

processes.

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First Principles Investigation of Nanomaterials for ... · First Principles Investigation of Nanomaterials for Hydrogen Generation and Hydrogen Storage Shwetank Yadav Masters of Applied