Quantum simulation of the adsorption of toxic gases on the surface of borophene

Comparison among gases of the shortest distance between gas molecules and substrate (dz), the distance from the massed center of gas molecules to the substrate (dc), and the adsorption[r]

VIETNAM NATIONAL UNIVERSITY, HANOI VIETNAM JAPAN UNIVERSITY

TA THI LUONG

QUANTUM SIMULATION OF THE ADSORPTION OF TOXIC GASES ON

THE SURFACE OF BOROPHENE

MASTER'S THESIS

VIETNAM NATIONAL UNIVERSITY, HANOI VIETNAM JAPAN UNIVERSITY

TA THI LUONG

QUANTUM SIMULATION OF THE

ADSORPTION OF TOXIC GASES ON THE SURFACE OF BOROPHENE

MAJOR: NANOTECHNOLOGY CODE: PILOT

RESEARCH SUPERVISOR: Dr DINH VAN AN

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ACKNOWLEDGMENT

First of all, I sincerely appreciate the great help of my supervisor, Dr Dinh Van

An Thank you for all your thorough and supportive instructions, your courtesy, and

your encouragement This thesis absolutely could not be conducted well without your dedicated concerns

Second of all, I would like to show my gratefulness to Prof Morikawa Yoshitada, my supervisor during my internship time at Osaka University Your guidance helps me a lot to get a more profound insight into my research topic as well as research-related works

Third of all, I want to express my warm thanks to my classmate, Pham Trong Lam Thanks to you, I got acquaintance more easily with computational material science Thank you for your willingness to help; it means a lot to me

Last but not least, I also would like to thank Vietnam Japan University and the staff working here for their necessary supports

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CONTENTS

Page

Acknowledgment i

CONTENTS ii

LIST OF TABLES iv

LIST OF FIGURES v

LIST OF ABBREVIATIONS vii

ABSTRACT viii

Chapter INTRODUCTION

1.1 Background of the research

1.2 Objectives and subjects of the research

1.2.1 Adsorbent material: Borophene

1.2.2 Gas molecules

1.3 Toxic gases adsorption on two-dimensional materials

1.3.1 Gas adsorption on other two-dimensional materials

1.3.2 Adsorption application of borophene

1.4 Thesis outline

Chapter THEORETICAL BASICS AND METHODS 11

2.1 Density Functional Theory 11

2.2 Vasp 15

2.3 Bader charge analysis 16

2.4 Calculation scheme 17

Chapter RESULTS AND DISCUSSION 20

3.1 Adsorbent characteristics 20

3.2 Energetically favorable configurations 21

3.2.1 CO - borophene 21

3.2.2 CO2 - borophene 22

3.2.3 NH3 - borophene 23

3.2.4 NO2 - borophene 24

3.2.5 NO - borophene 25

3.3 Adsorption energy and reaction length 26

3.3.1 Adsorption energy and adsorption distance in comparison of vdW-employed functionals 26

3.3.2 Comparison of adsorption energy among gases 30

3.4 Potential energy surface 31

3.5 Electronic characteristic 36

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3.6.1 Charge analysis of the (CO – borophene) system 39

3.6.2 Charge analysis of the (CO2 - borophene) system 40

3.6.3 Charge analysis of the (NO - borophene) system 42

3.6.4 Charge analysis of the (NO2 - borophene) system 43

3.6.5 Charge analysis of the (NH3 - borophene) system 44

CONCLUSION 47

FUTURE PLANS 48

iv

LIST OF TABLES

Page Table 1.1 The adsorption energy of CO, CO2, NO2, NO, and NH3 on different

two-dimensional materials (eV)

Table 3.1 Calculated lattice constants of β12 borophene vs experimental data 20

Table 3.2 Bader charge analysis of the (CO - borophene) system 39

Table 3.3 Bader charge analysis of the (CO2 – borophene) system 41

Table 3.4 Bader charge analysis of the (NO – borophene) system 42

Table 3.5 Bader charge analysis of the (NO2 – borophene) system 43

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LIST OF FIGURES

Page Figure 1.1 Elements predicted to be precursors of synthetic elemental 2D materials

and their synthetic methods

Figure 1.2 Borophene assumed to be synthesized on Ag (111) substrate (a) buckled triangular borophene, (b) β12 borophene, and (c) χ3 borophene

Figure 2.1 The flow chart of gas absorbing calculations 19

Figure 3.1 The calculated supercell of β12 boron sheet after optimization 20

Figure 3.2 Band structure and DOS of the unit cell of β12 borophene 21

Figure 3.3 Top view and side view of the most stable configurations of CO on borophene 22

Figure 3.4 Top view and side view of the most stable configurations of CO2 on borophene 23

Figure 3.5 Top view and side view of the most stable configurations of NH3 on borophene 23

Figure 3.6 Top view and side view of the most stable configurations of NO2 on borophene 24

Figure 3.7 Top view and side view of the most stable configurations of NO on borophene using different vdW functionals 25

Figure 3.8 Adsorption energy change accordingly to the distance of the (a) CO and (b) CO2 molecule and borophene in comparison 26

Figure 3.9 Adsorption energy change accordingly to the distance of the (a) NH3 and (b) NO2 molecule and borophene 28

Figure 3.10 Adsorption energy change accordingly to the distance between NO molecule and borophene 29

Figure 3.11 Comparison among gases of the shortest distance between gas molecules and substrate (dz), the distance from the massed center of gas molecules to the substrate (dc), and the adsorption energy (Ea) using optPBE-vdW functional 30

Figure 3.12 Potential energy surface of CO adsorbed borophene 31

Figure 3.13 Potential energy surface of CO2 adsorbed borophene 32

Figure 3.14 The projected binding energy of NH3 along the surface of borophene 33

Figure 3.15 Potential energy surface of borophene-NO 34

Figure 3.16 Potential energy surface of NO2 – borophene 35

Figure 3.17 Band structure and DOS of CO - borophene 36

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Figure 3.19 Band structure and DOS of NH3 - borophene 38 Figure 3.20 Band structure and DOS of NO - borophene 38 Figure 3.21 Band structure and DOS of NO2 - borophene 39 Figure 3.22 Charge density difference after CO adsorption illustrated using

isosurface (isosurface level = 0.00034) 40 Figure 3.23 Charge density difference after CO2 adsorption illustrated using

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LIST OF ABBREVIATIONS

2D Two-dimensional

DFT Density Functional Theory

VASP Vienna Ab initio Software Package

vdW van der Waals

DOS Density of state

KS Kohn-Sham

MO Molecular orbital

HF Hartree-Fock

3D Three-dimensional

viii ABSTRACT

2D materials have attracted significant research interest due to their excellent characteristics Borophene, a new member of the 2D material family, was proven that it has a unique structure and promising properties by both empirical and theoretical studies In this study, the adsorption configuration, adsorption energy of toxic gas molecules (CO, NO, CO2, NH3, and NO2) on 12 – borophene was investigated by first – principle calculations using three van der Waals correlation functionals: revPBE-vdW, optPBE-vdW, and vdW-DF2 The most stable configurations and diffusion possibilities of the gas molecules on the 12 – borophene surface were determined visually by using Computational DFT-based Nanoscope [10] The nature of bonding and interaction between gas molecules and 12 – borophene are also disclosed by using the density of states analysis and Bader charge analysis The obtained results are not only considerable for understanding gas molecules on borophene but also useful for technological applications of borophene in very near future

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CHAPTER INTRODUCTION

1.1 Background of the research

In the present society, when industrialization and urbanization are increasing sharply, air pollution becomes a severe global problem Air pollution can affect human health directly or indirectly

According to WHO (2017) data, air pollution causes in deaths worldwide while ambient air pollution caused 7.6% deaths over the world in 2016, which is included 4.2 million premature deaths Air pollution might lead to stroke, lung cancer, stroke, chronic obstructive, heart disease and acute respiratory infections in children

Worldwide ambient air pollution accounts for:

 29% of deaths and diseases caused by lung cancer

 17% of all patients related to acute lower respiratory infection  24% of all deaths from stroke

 25% of all deaths and disease from ischaemic heart disease

 43% of all deaths and disease from chronic obstructive pulmonary disease [46]

To decrease the impacts of air pollution, detecting pollutants is the first work needed to before carrying out the processing procedure [46] Hence, the things here is discovering good material which has high sensitivity and selectivity with poisonous gases, which are the significant pollutants causing air pollution, toward creating an effective sensor to detect these pollutants effectively

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Dirac cone, and supposed to be metallic for most phases [11] Beside those promising properties, borophene also has a high surface-to-volume ratio due to its two-dimensional existence Borophene thus is a promising candidate for adsorption of poisonous applications

1.2 Objectives and subjects of the research

Toward developing gas sensor materials, pollutants absorbability of potential materials is investigated by using quantum simulation This research aims to discover a potential material for filtering or sensing toxic gases in the ambient atmosphere contributing to air pollution mitigation and enhancing community health As follows, borophene as a potential candidate will be investigated the gas adsorbing performance The obtained results will be not just for understanding of borophene, a new material, but for the development of gas sensor at the nanoscale as well Hence, the research subject here is the complex system of toxic gas molecules on the adsorbent material

1.2.1 Adsorbent material: Borophene

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Figure 1.1 Elements predicted to be precursors of synthetic elemental 2D materials and their synthetic methods Adapted from ―Synthesis and chemistry of elemental 2D materials‖, by A J Mannix et al., 2017, Nature Reviews Chemistry, 1, 1-15, Copyright [2017] by Macmillan Publishers Limited

Boron is one of the most complicated elements in terms of chemical bond in three-dimensional structure due to its 3-electron outer shell configuration This fact prevents the fulfillment of the octet rule, leading to irregular ‗electron poor‘ bonding configurations [41] A striking feature of boron is that B12 icosahedral cages occur as the building blocks in bulk boron and many boron compounds [1]

Regarding its two-dimensional existence, boron also expresses its diversity of polymorphs on different substrates or cultivation conditions [26][13] Boron 2D sheets, which is so-called borophene, is predicted by first principle calculations to have various allotropes Notably, these polymorphs of borophene have been predicted to be metallic or semi-metallic where boron in 3D bulk phase is an insulator [27]

4

previous theoretical predictions From STM images and LEED diffraction, borophene structures are confirmed to have two main polymorphs when using Ag (111) as a substrate: 12 and 3 (also called as 1/6 and 1/5, respectively) as shown in

Figure 1.2

(a) (b) (c)

Figure 1.2 Borophene assumed to be synthesized on Ag (111) substrate (a) buckled triangular borophene, (b) β12 borophene, and (c) χ3 borophene Adapted from ―Two-dimensional boron: Structures, properties and applications‖, by Zhang, Penev, & Yakobson, 2017, Chemical Society Reviews, 46(22), 6746-6763 Copyright [2017] by The Royal Society of Chemistry

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on Ag (111) substrate such as Zhang et al (2016) [50], Campbell et al (2018) [8] , Peng et al (2017) [35] and Shukla et al (2017) [37]

In an attempt to enhance the potential of such unusual material, many experiments and theoretical works related to borophene synthesis and borophene characterization have been conducted recently As a result, structure and many physiochemical properties are revealed gradually In 2018, Campbell et al found out that two types of borophene polymorph (i.e 12 and 3) can be discrete They claimed that 12 is dominant in lower temperature (300 C) whereas 3 is mostly formed in higher temperature (400 C) [30]

12, as a main existence of borophene, has a flat and special symmetry structure which has an alternate arrangement between vacant boron hexagonal row and boron-centered hexagonal row in its lattice This configuration is assumed that is similar to the honeycomb flat geometry of graphene However, the alternating of vacant and boron-centered hexagonal even expresses more attractive unique properties It is the first pure 2D material able to emit the visible and near – infrared light by activating its plasmon [16][4] Under the microscope, it also exhibits undulations on the STM image, demonstrating its wavy nature [50] Thus, it can be highly stretched once removed from the substrate, or reattached to a soft on other substrates, which facilitates favorable conditions to borophene applying on electronic devices [14] Also, this polymorph of borophene has been depicted to have unusual mechanical, electronic, and chemical properties, materializing its potential in practical applications [50] For example, β12 borophene appears Dirac-fermions or Dirac cones independently explored by both prediction [45] and experiment [11]

1.2.2 Gas molecules

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have strong impacts on human health as well as the earth climate, i.e., global warming

- Carbon monoxide (CO): In normal condition, CO exists as an odorless and colorless gas At high concentration, CO has severe negative impacts on human health by decreasing the level of oxygen in the blood circulation system High concentrations of CO are critical for both indoor and outdoor air quality, particularly in developing countries Moreover, new evidence shows that long-term exposure to low concentrations is also associated with a wide range of health effects [46] The main sources of ambient CO include motor vehicle exhaust and machinery that burn fossil fuels

- Carbon dioxide (CO2): is the main greenhouse gas affecting global warming and climate change This gas is emitted from the combusting of fossil fuel originated from vehicles and industrial processes Accompanying with industrialization and urbanization, the concentration of CO2 in the atmosphere is increasingly higher, contributing to ambient air pollution

- Nitrogen dioxide (NO2): is an important component of particulate matter and ozone depletion This gas is a by-product of power generating and industrial processes, as well as traffic activities It affects seriously human health i.e, symptoms of bronchitis, asthma, and lead to respiratory infections and reduced lung function and growth Evidence also suggests that NO2 may be responsible for a large disease burden, with exposure linked to premature mortality and morbidity from cardiovascular and respiratory diseases

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- Ammonia (NH3): a colorless gas with a pungent smell Ammonia is one of the major components of particulate matter which affects more people than any other pollutant [46]

1.3 Toxic gases adsorption on two-dimensional materials

1.3.1 Gas adsorption on other two-dimensional materials

There are many studies on gas adsorption application of 2D materials carried out previously Overall, these materials have a good sensitivity toward CO, CO2, NO2, NO, and NH3 The adsorption energy of all those gases on buckled borophene, graphene, silicone, phosphorene, germanene, and molybdenum sulfide are summarized in Table 1.1

Table 1.1 The adsorption energy of CO, CO2, NO2, NO, and NH3 on different two-dimensional materials (eV)

CO CO2 NO2 NO NH3

Buckled borophene [24]

-1.38 -0.36 -2.32 -1.79 -1.75

Graphene [22, 25]

-0.01 -0.05 -0.07 -0.03 -0.03

Silicene [18] -0.18 -0.04 -1.37 -0.35 -0.60

Phosphorene [21]

-0.32 -0.41 -0.60 -0.86 -0.50

Germanene [47]

-0.16 -0.10 -1.08 -0.51 -0.44

MoS2 [52] -0.44 -0.33 -0.14 -0.55 -0.16

1.3.2 Adsorption application of borophene

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Regarding the gas adsorption on borophene, Valadbeigi, Farrokhpour, and Tabrizchi (2015) utilized DFT with B3LYP functional to investigate the adsorption of small gases (CO, N2, H2O, O2, and NO) on B36 borophene, in which the vacancies to boron atoms ratio is 1:36 They found that the edge of B36 is more active than the area closer to the vacancy However, this type of borophene B36 has not proved its existence in reality by experiment [44]

Liu et al studied the adsorption of popular harmful gases (CO, CO2, NH3, NO, NO2 and CH4) on buckled borophene using first principle calculations They found that all these gases apart from CH4 have a moderately strong interaction with buckled borophene In particular, CO and CO2 are chemically adsorbed; NH3, NO and NO2 are chemisorbed through covalent bonds; while CH4 physically adsorbed on borophene [24]

Also doing study related to gas adsorption, Shukla et al researched CO, NO, NO2, NH3 and CO2 adsorbability of buckled borophene monolayer using DFT and non-equilibrium Green‘s function calculations [38] Similar to Liu‘s group, they found that all buckled borophene has a good adsorbability toward all these gases The adsorption energy of these gases on borophene are given by 0.18, 0.35, 0.04, -0.06, -1.37 eV for CO, NO, CO2, NH3 and NO2, respectively These figures are considerably higher than most of the other 2D materials Besides, in this case, CO, CO2, NO, and NO2 gas are electron withdrawers; while NH3 gas is electron acceptor

Newly, Hao, Xiaoxing, and Dachang accomplished a study to consider whether buckled borophene has a good adsorbability to SO2 gases using DFT calculation [9] The SO2 adsorption capacity also was calculated and found to be one supercell of borophene can adsorb maximum SO2 molecules

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band gap were investigated Similar to previous studies worked on buckled borophene, this research found that both borophene nanosheets and nanotubes can be used as a chemiresistor to detect NH3 in the ambient atmosphere, in which adsorption energy is -0.951 eV and the charge transfer is 0.494 e

As for gas adsorption on β12 borophene, there exists few studies published related to this topic Recently, Tan, Tahini, and Smith implemented theoretical research to analyze the capacity of borophene to capture as well as to release CO2 controlled via switching on/off the charges carried on boron sheets [42] At neutral condition, β12 borophene physically adsorbs CO2 with comparatively small adsorption energy varied from -0.15 to -0.19 eV Accordingly, the shortest distance from borophene to CO2 is 3.3 Å This adsorption performance is neither too strong nor too weak facilitating borophene a good sensing material to CO2

Lately, Rana, Meysam, and Sahar studied to analyze how halogen atoms interact with β12 borophene They found that the electronegativity and the mass of halogen atoms affect to the adsorption behaviors [43] Thereby, the adsorption energy of all these halogen atoms on borophene is significant high varied from 2.71 to 5.22 eV, increase accordingly to the electronegativity As follows, the distances from the adsorbent to F, Cl, Br, and I are 1.39, 1.99, 2.18, 2.38 Å, respectively

Also, Alvarez-Quiceno, Schleder, Marinho, and Fazzio (2017) studied the electronic and magnetic characteristics of d-block metals adsorbed on β12 borophene monolayer as well as on silver-supported β12 borophene They found out that all these transition metals are stably adsorbed on borophene and this stability increased from 3d to 5d elements Notably, the Ag(111) substrate shows a slight impact on borophene behaviors [2]

1.4 Thesis outline

This thesis ―Quantum simulation of the adsorption of toxic gases on the surface

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Chapter 1: Introduction – This chapter includes the research background indicating why we need to conduct this work It also mentions the research objectives and the research subjects As a result, the scope of work will be made clear

Chapter 2: Theoretical basics and methods – This chapter presents logically and systematically the brief of theoretical basics related to this work, which are DFT, VASP, and Bader charge analysis Thereby, the proper foundation of knowledge is built toward being able to understand this work Also, the framework towards solving the problems of this thesis, the specific utilized method and tools are mentioned carefully in this section

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CHAPTER THEORETICAL BASICS AND METHODS

2.1 Density Functional Theory

In 1964, Pierre Hohenberg and Walter Kohn proved that for molecules with a nondegenerate ground state, the ground-state molecular energy, wave function, and all other molecular electronic properties are uniquely determined by the ground-state electron probability density ( ), a function of only three variables One says that the ground-state electronic energy is a functional of and writes

[ ], where the square brakets denote a functional relation [23]

Hohenberg and Kohn proved their theorems only for non-degenerate ground states Subsequently, Levy proved the theorems for degenerate ground states [23]

If we know the ground-state electron density ( ), the Hohenberg-Kohn theorem tells us that it is possibe in principle to calculate all the ground-state molecular properties from without having to find the molecular wave function The Hohenberg-Kohn theorem does not tell us how to calculate from , nor does it tell us how to find without first finding the wave function A key step toward these goals was taken in 1965 when Kohn and Sham devised a practical method for finding and for finding from Their method is capable, in principle, of yielding exact results, but because the equations of KS method contain an unknown functional that must be approximated, the KS formulation of DFT yields approximate results [23]

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( ) is defined for the reference system, the external potential ( ) in the reference system is determined uniquely, although we might not know how to actually find it The electrons not interact with one another in the reference system, so the Hamiltonian of the reference system is

̂ ∑ [ ( )] ∑ ̂

(2.1)

̂ is the one-electron KS Hamiltonian [23]

Since the reference system s consists of non-interacting particles, the ground-state wave function of the reference system is the Slater determinant of the lowest-energy KS spin-orbitals of the reference system | |,

( )

Kohn and Sham rewrote the Hohenberg-Kohn equation as follows Let ̅ be defined by

̅[ ] ̅[ ] ̅[ ] (2.2)

̅ is the difference in the average ground-state electronic kinetic energy between the molecule and the refence system of noninteracting electrons with electron density equal to that in the molecule Let

̅ [ ] ̅ [ ] ∬ ( ) ( )

(2.3)

The Hohenberg-Kohn equation now becomes

[ ] ∫ ( ) ( ) ̅[ ] ∬ ( ) ( )

̅[ ] ̅ [ ]

(2.4)

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[ ] ∫ ( ) ( ) ̅[ ] ∬ ( ) ( )

[ ] (2.5)

This formula expresses [ ] in terms of three quantities, the first three terms on the right side, that are easy to evaluate from and that include the main contributions to the ground-state energy, plus a fourth quantity , which, though not easy to evaluate accurately, will be a relatively small term They key to accurate KS DFT calculation of molecular properties is to get a good approximation to The electronic energy including nuclear repulsion is found by the addition of the internuclear repulsion [23]

The Kohn-Sham orbitals are found as follows The Hohenberg-Kohn variational theorem tells us that we can find the ground-state energy by varying (subject to the constraint ) so as to minimize the functional [ ] Equivalently, instead of varying , we can vary the KS orbitals , which determine In doing

so, we must constrain the ‘s to be orthonormal, since orthonormality was assumed when we evaluated ̅

One can show that the KS orbitals that minimize the energy for the molecular ground-state energy satisfy

[ ∑

∫

( )

( )]

( ) (2.6)

where the exchange-correlation potential is found as the functional derivative of the exchange-correlation energy :

( )

[ ( )]

( ) (2.7)

If [ ] is known, its functional derivative is readily found from the above formula, and so is known

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and are unknown Various approximations to will be discussed shortly [23] The Kohn-Sham orbitals are orbitals for the fictitious reference system of noninteracting electrons, so, strictly speaking, these orbitals have no physical significance other than in allowing the exact molecular ground-state to be calculated The density-functional molecular wave function is not a Slater determinant of spin-orbitals In fact, there is no density-functional molecular wave function However, in practice, one finds that the occupied Kohn-Sham orbitals resemble molecular orbitals calculated by the Hartree-Fock method, and the Kohn-Sham orbitals can be used (just as Hartree-Fock MOs are used) in qualitative MO discussions of molecular properties and reactivity Note that, strictly speaking, Hartree-Fock orbitals also have no physical reality, since they refer to a fictitious model system in which each electron experiences some sort of average field of the other electrons [23]

For a closed-shell molecule, each Hartree-Fock occupied-orbital energy is a good approximation to the negative of the energy needed to remove an electron from that orbital (Koopmans‘ theorem) However, this is not true for KS orbitals energies The one exception is for the highest-occupied KS orbital, which can be proved

to be equal to minus the molecular ionization energy With the currently used approximations to , ionization energies calculated from KS highest-occupied-orbital energies agree poorly with experiment [23]

Various approximate functionals [ ] are used in molecular DFT calculations To study the accuracy of an approximate [ ], one uses it in DFT calculations and compares calculated molecular properties with experimental ones The lack of a systematic procedure for improving [ ] and hence improving calculated molecular properties is the main drawback of the DFT method [23]

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method, which calculated an orbital for each electron Thus, the KS method represents something of a compromise with the original goals of DFT [23]

The procedure of DFT can be summarized as in the below diagram

Figure 2.1 Flow chart of the solution procedure of DFT 2.2 VASP

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implemented as well Furthermore, Green's functions methods (GW quasiparticles, and ACFDT-RPA) and many-body perturbation theory (2nd-order Møller-Plesset) are available in VASP

In VASP, central quantities, like the one-electron orbitals, the electronic charge density, and the local potential are expressed in plane wave basis sets The interactions between the electrons and ions are described using norm-conserving or ultrasoft pseudopotentials, or the projector-augmented-wave method

To determine the electronic ground state, VASP makes use of efficient iterative matrix diagonalization techniques, like the residual minimisation method with direct inversion of the iterative subspace (RMM-DIIS) or blocked Davidson algorithms These are coupled to highly efficient Broyden and Pulay density mixing schemes to speed up the self-consistency cycle [32]

2.3 Bader charge analysis

Atomic charges in molecules or solids are not observables and, therefore, not defined by quantum mechanical theory The output of quantum mechanical calculations is continuous electronic charge density, and it is not clear how one should partition electrons amongst fragments of the system such as atoms or molecules [40]

Many different schemes have been proposed, some based on electronic orbitals (Mulliken population analysis, Density matrix based normal population analysis), and others found on only the charge density (Bader analysis, Hirshfeld analysis) [40]

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reaches a minimum between atoms, and this is a natural place to separate particles from each other [15]

Besides being an intuitive scheme for visualizing atoms in molecules, Bader's definition is often useful for charge analysis For example, the charge enclosed within the Bader volume is a good approximation to the total electronic charge of an atom The charge distribution can be used to determine multipole moments of interacting atoms or molecules Bader's analysis has also been used to define the hardness of atoms, which can be used to quantify the cost of removing charge from an atom [15]

The ideas behind Bader charge analysis are as follows [40]

 The electron density, ρ(x, y, z), of materials are analyzed  Critical points of ρ(x, y, z) are determined and classified

 The 3D space is divided into subsystems, each usually containing one nucleus (but sometimes none)

 ―zero-flux‖ surfaces separate the subsystems:

∇ρ(rs) • n(rs) = for every point rs on the surface S(rs) where n(rs) is the unit vector normal to the surface at rs

 The electron density can either be from experimental data (e.g., X-ray crystallography) or theoretical data (e.g., ab initio calculations) 2.4 Calculation scheme

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Feynman forces acting on each atom were less than 0.01 eV/Å The energy convergence was chosen as 10-5 eV between two steps, and a vacuum of 20 Å was employed along the z-direction of the borophene sheet to eliminate interactions between borophene sheets The energy cut-off was determined to be 500 eV by using the fixed K-point at 12121 Then the K-point mess in the Brillouin zone was investigated and optimized at 331 at cut-off energy 500 eV for the 43 supercell

The Computational DFT-based Nanoscope [10] was applied to determine the most stable configurations, diffusion possibilities, and electronic attributes of the gas molecules on the 12 – borophene surface visually

The Bader charge analysis was executed using the code developed by Henkelman group from the University of Texas at Austin [15] The following equation calculates the charge density difference:

(2.8)

While is the total charge of the system, AB is the complex system, A and B are two separated systems Note that in calculation two latter quantities, the atomic positions are fixed as those have in the AB system

The visualization using in this work is VESTA developed by K Momma and F Izumi [17]

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Figure 2.2 The flow chart of gas absorbing calculations

Optimization employing vdW correlation functionals

- Initial relaxation

- Scan xy plane to find the most stable position

- From the most stable position, scan along z-direction

 get the final optimized

structure

Calculate adsorption energy

Ea = Egas-borophene – (Egas + Eborophene) (2.9)

Calculate electronic structure - Band structure

- Density of State

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CHAPTER RESULTS AND DISCUSSION

3.1 Adsorbent characteristics

Figure 3.1 The calculated supercell of β12 boron sheet after optimization The lattice crystal of β12 borophene shown in Figure 3.1 has a flat structure Along zigzag direction, there exists a mixture of boron-centered and empty hexagons The unit cell includes five boron atoms marked by the dashed line Accordingly, three different types of boron atom B1, B2, and B3 are marked by orange dots in Figure 3.1 The lattice constants of borophene are totally in agreement with empirical data [31, 7, 12] and previous theoretical studies [35, 48, 33], as shown in Table 3.1

Table 3.1 Calculated lattice constants of β12 borophene vs experimental data

a (Å) b (Å)  () β ()  ()

GGA 2.92126 5.08306 90 90 90

RevPBE-vdW 2.92752 5.10578 90 90 90

OptPBE-vdW 2.93095 5.07477 90 90 90

vdW-DF2 2.91287 5.07054 90 90 90

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The calculated band structure along the high-symmetry paths and density of state of a unit cell of β12 borophene are shown in Figure 3.2

Figure 3.2 Band structure and DOS of the unit cell of β12 borophene

β12 borophene has line defects, which is the expression of the existence of parallel hollow hexagons together with filled hexagons It facilitates favorable condition for β12 borophene to have various adsorption sites, classified to the hollow sites, the top of B1, B2, and B3 sites, and the bridge of boron atoms [36] The electronic structure of β12 borophene is a metallic structure with no band gap (shown in Figure 3.2), empowering borophene to be one of the most intriguing two-dimensional materials 3.2 Energetically favorable configurations

3.2.1 CO - borophene

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to the oxygen atom, the brown bubble is carbon atom, and green bubbles represent to boron atoms The CO molecule lies parallel to the surface of adsorbent when employing revPBE-vdW functional The carbon atom, however, is slightly closer to the surface when utilizing optPBE-vdW or vdW-DF2

(a1) (b1) (c1)

(a2) (b2) (c2)

Figure 3.3 Top view (1) and side view (2) of the most stable configurations of CO on borophene optimized by using different vdW functionals (a) revPBE-vdW, (b) optPBE- vdW, and (c) vdW-DF2

3.2.2 CO2 - borophene

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(a1) (b1) (c1)

(a2) (b2) (c2)

Figure 3.4 Top view (1) and side view (2) of the most stable configurations of CO2 on borophene using three different vdW functionals (a) rev-PBE-vdW, (b) opt-PBE- vdW, and (c) vdW-DF2

3.2.3 NH3 - borophene

(a1) (b1) (c1)

(a2) (b2) (c2)

24

NH3 at isolated state has a bond length of 1.012 Å; however, the bond is lengthened after this gas being adsorbed on borophene to 1.022 Å The energetically favorable geometries are shown in Figure 3.5, in which, green bubbles refer to boron atoms, light blue bubble indicates nitrogen atom, and small white bubbles represent hydrogen atoms Different from CO and CO2, the adsorption site, in this case, is the top of the B2 boron atom The nitrogen atom tends to be closer to boron sheet while one of three hydrogen atoms tends to be repulsed off it Remarkably, revPBE-vdW and optPBE-vdW seem to give more reasonable geometries, because NH3 locates at higher symmetrical site rather than in the case employing vdW-DF2 functional Hence, revPBE-vdW and optPBE-vdW becomes the more preferable employed functionals

3.2.4 NO2 - borophene

(a1) (b1) (c1)

(a2) (b2) (c2)

Figure 3.6 Top view (1) and side view (2) of the most stable configurations of NO2 on borophene using three different vdW functionals (a) revPBE-vdW, (b) optPBE- vdW, and (c) vdW-DF2

25

124 with revPBE-vdW and vdW-DF2, which indicates that borophene provides electrons to NO2 molecule to repulse two rich-electron areas surrounding oxygen atoms Accordingly, it can be predicted that employing optPBE-vdW functionals enables the charge transferred to the molecule in a higher amount than when employing the other methods The geometries of stable configurations are presented in Figure 3.6 Other than CO, CO2, and NH3, the NO2 molecule is favorable to be adsorbed on the top of B1 boron atom In all of three cases used these vdW functionals, NO2 molecule orients along the zigzag direction However, in case of using optPBE-vdW functional, one of two oxygen atoms moves closer to the boron sheet until N-O bond being parallel to boron sheet while the other cases show that both oxygen atoms are expelled from borophene

3.2.5 NO - borophene

(a1) (b1) (c1)

(a2) (b2) (c2)

Figure 3.7 Top view (1) and side view (2) of the most stable configurations of NO on borophene using different vdW functionals (a) revPBE-vdW, (b) optPBE- vdW, and (c) vdW-DF2

26

oxygen atom with respect to boron sheet Besides, the positions of the gas molecule are similar when applying optPBE-vdW and vdW-DF2 functionals

3.3 Adsorption energy and reaction length

3.3.1 Adsorption energy and adsorption distance in comparison of vdW-employed functionals

(a)

(b)

27

The comparison of the adsorption energy of CO among three vdW correlation functionals is shown in Figure 3.8(a) In this figure, the lowest peak corresponds to the most stable position of CO molecule along the z-direction Thereby, revPBEvdW and optPBErevPBEvdW functional give higher adsorption energy at 0.145 and -0.174 eV, respectively; while the distance between CO and the substrate is more than Å with revPBE-vdW and optPBE-vdW as well as vdW-DF2 The reaction length here is defined by the distance from where gas molecule starts to react with the adsorbent to the surface of the adsorbent Hence, in this case, the reaction length of CO is around Å

In an analogy with CO, these vdW correlation functionals have the same order of impacts on the binding energy and the distance of CO2 molecule, illustrated in

Figure 3.8(b) In particular, optPBE-vdW gives the highest adsorption energy, while vdW-DF2 provides the lowest one In all three methods, the binding energy is around -0.2 eV and the distance between the gas molecule and the substrate is approximately Å The reaction length herein is also about Å

In the case of NH3, all three methods give the adsorption energy lower than 0.2 eV shown in Figure 3.9(a) Similar to CO and CO2, the closest distance between the NH3 molecule and borophene is around Å The reaction length is about Å

28

(a)

(b)

29

Figure 3.10 Adsorption energy changes accordingly to the distance between NO molecule and borophene in comparison of using revPBE-vdW, optPBE-vdW, and vdW-DF2 functionals

In the case of NO, among three employed functionals, optPBE-vdW estimates the highest adsorption energy while the others give similar results at smaller values Plus, the distance between gas molecule and the adsorbent is expected to be independent to employed vdW correlation functional

30

3.3.2 Comparison of adsorption energy among gases

Figure 3.11 Comparison among gases of the shortest distance between gas molecules and substrate (dz), the distance from the massed center of gas molecules to the substrate (dc), and the adsorption energy (Ea) using optPBE-vdW functional

To have a closer look to compare the adsorption performance among these poisonous gases, we analyze the distance and the binding energy between these gas and the substrate materials In Figure 3.11, the energetically favorable configuration of NO2 is closest to the surface while CO, CO2, and NH3 remain to be quite far from the adsorbent at approximately Å In addition, the adsorption energy of NO2 is highest; almost double the second-come strongest binding energy of NO Employing the same vdW functionals, MoS2, however, exhibits smaller binding energy for all these gases (< -0.3 eV)[52] Also, the adsorption energies of borophene toward these gases are much higher than those of graphene In the case of graphene, although graphene is likewise borophene, most sensitive to NO2, but the adsorption energy is only 67 meV [22] These values of phosphorene are also smaller than borophene with the adsorption energy for CO, NH3, NO, and NO2 are -0.31, -0.18, -0.32, and -0.5 eV, respectively [6]

0 0.2 0.4 0.6 0.8 1.2 1.4 1.6 0.5 1.5 2.5 3.5 dz (Å) dc (Å) Ea (eV)

31 3.4 The surface of binding energy

32

Figure 3.12 describes how the binding energy of CO and borophene change when we move the CO molecule along the surface of the adsorbent The darker color means the stronger adsorption energy of CO on borophene Thereby, CO tends to move along the vacant-defected lines of borophene In other words, CO prefers to diffuse along x-direction above vacant hexagons

33

Figure 3.13 illustrates the change of binding energy of CO2 along the surface of the adsorbent visually Similar to CO, CO2 molecule tends to accumulate along the armchair direction above the vacant hexagons of boron sheet In contrast, the CO2 molecule will be repulsed if it moves close to the B3-typed boron atoms, i.e., the centered boron atoms As a result, the diffusion direction of CO2 on borophene is x-direction

34

Different from CO and CO2 cases, shown in Figure 3.14, NH3 is easier to be adsorbed on the top of B2-typed boron atoms In this case, this NH3 molecule will be repulsed if it moves closer to the hollow sites

35

In case of NO interacting with borophene, this gas molecule energetically prefers to be adsorbed on the bridge of B1 and B2 typed boron atoms This change of adsorption energy is shown in Figure 3.15 Thereby, this gas is quite localized because of the large gap of binding energy between where the gas molecule is trapped and neighboring areas

36

The gap of binding energy in the case of NO2 is also significant at 600 meV The adsorption of NO2, nevertheless, is comparatively delocalized, which means NO2 might move smoothly along the bonds of B1-B2-B1 typed boron atoms This diffusion is illustrated in Figure 3.16 Besides, in an analogy with other studied gas, NO2 dislikes to close to B3 –typed boron atom proven by a bright color around centered boron atom areas

3.5 Electronic characteristic

Figure 3.17 Band structure and DOS of CO – borophene

37

Figure 3.18 Band structure and DOS of CO2 – borophene

38

Figure 3.19 Band structure and DOS of NH3 – borophene

39

Figure 3.21 Band structure and DOS of NO2 – borophene 3.6 Charge transfer characteristic

3.6.1 Charge analysis of the (CO – borophene) system

The Bader charge analysis shows the change of charge for each atom of the complex system adsorption of CO on borophene, described in Table 3.2

Table 3.2 Bader charge analysis of the (CO - borophene) system Atom

index

Charge of complex system (qe)

Charge of isolated system (qe)

Charge difference (qe)

Charge transfer (qe)

B … … … …

-0.0236

B 12 2.8111 2.8159 -0.0048

B 15 2.5389 2.5373 0.0015

B … … … …

B 35 2.7775 2.7808 -0.0033

B 36 2.7734 2.7779 -0.0045

B … … … …

B 45 3.4036 3.4072 -0.0036

40 Atom

index

Charge of complex system (qe)

Charge of isolated system (qe)

Charge difference (qe)

Charge transfer (qe)

O 7.0940 7.0867 0.0073

+0.0236

C 2.9296 2.9133 0.0163

In general, the borophene substrate donates their electrons to the gas molecule; in other words, electrons transfer from substrate to CO molecule As a result, the substrate is slightly positively charged However, this interaction is not significant; the amount of charge transfer is only the order of 0.02 electrons When gas molecule approaches to the adsorbent, two boron atoms B12 and B36 lose the most electron due to their nearest distance to the two terminals of this gas molecule The charge density different after adsorption is illustrated in Figure 3.22, where the yellow color means the increase of electron density, and the blue color means decreasing electron density It shows that the charge density in the plane of gas molecule declines slightly while the charge accumulation exists in perpendicular direction The reason causing the rise of density in the space between the gas molecule and substrate might be the physical adsorption It is consistent with the quite low adsorption energy (-0.174 eV)

Figure 3.22 Charge density difference after CO adsorption illustrated using isosurface (isosurface level = 0.00034)

3.6.2 Charge analysis of the (CO2 - borophene) system

41

Table 3.3 Bader charge analysis of the (CO2 – borophene) system Atom

index

Charge of complex system (qe)

Charge of isolated system (qe)

Charge difference (qe)

Charge transfer (qe)

B … … … …

-0.0268

B 2.7062 2.6996 0.0067

B 12 2.7045 2.6994 0.0051

B … … … …

B 32 2.9344 2.9324 0.0021

B 35 2.9370 2.9325 0.0045

B … … … …

B 45 3.4215 3.4297 -0.0082

B 56 3.3460 3.3573 -0.0113

B … … …

O 7.0176 7.0045 0.0130

+0.0268

O 7.0383 7.0239 0.0145

C 1.9709 1.9716 -0.0006

In analogy to CO, in the case of adsorbing CO2 on borophene, generally, borophene gives its electrons to the gas molecule In other words, electrons transfer from adsorbent to CO molecule As a result, the adsorbent is slightly positively charged Also, this interaction is not significant, which is somewhat stronger than CO and borophene interaction The charge density different after adsorption is illustrated in Figure 3.23, where the yellow color means the increase of electron density, and the blue color means decreasing electron density

Regarding borophene substrate, two boron atoms B56 and B45 nearest to oxygen atoms of gas molecule lose their charge most considerably Notably, the substrate‘s charge density at the area surrounding and parallel with CO2 molecule increase despite the decreasing trend of the whole substrate It can be explained by Pauli repulsion, when gas molecule approaching borophene surface, electrons under gas molecule is repulsed to the surrounding area

42

interaction may reflect the physical adsorbed behavior It is also in agreement with the quite low adsorption energy of -0.24 eV

Figure 3.23 Charge density difference after CO2 adsorption illustrated using isosurface (isosurface level = 0.00054)

3.6.3 Charge analysis of the (NO - borophene) system

The Bader charge analysis shows the change of charge for each atom of the system after adsorption of NO on borophene described particularly in Table 3.4

Table 3.4 Bader charge analysis of the (NO – borophene) system Atom

index

Charge of complex system (qe)

Charge of isolated system (qe)

Charge difference (qe)

Charge transfer (qe)

B … … … …

+0.7686

B 20 3.4557 3.3522 0.1035

B 29 2.9608 2.8600 0.1009

B … … … …

B 52 2.8771 2.7263 0.1508

B 59 2.7338 2.8163 -0.0825

B … … … …

O 6.2618 6.4792 -0.2174

-0.7686

N 3.9696 4.5208 -0.5512

43

here is electron donator, and borophene acts like electron acceptor As a result, there is a large blue area surrounding the NO molecule illustrated in Figure 3.24 below

Figure 3.24 Charge density difference after NO adsorption (isosurface level = 0.003)

3.6.4 Charge analysis of the (NO2 - borophene) system

The Bader charge analysis shows the change of charge for each atom of the system after the adsorption of NO2 on borophene described particularly in Table 3.5

Table 3.5 Bader charge analysis of the (NO2 – borophene) system Atom

index

Charge of complex system (qe)

Charge of isolated system (qe)

Charge difference (qe)

Charge transfer (qe)

B 3.4382 3.4014 0.0367

-0.7522

B 3.4633 3.3789 0.0844

B … … … …

B 25 2.6375 2.8891 -0.2517

B … … … …

B 51 2.5476 2.7959 -0.2483

B … … … …

O 6.4156 6.3424 0.0732

+0.7522

O 6.5589 6.2653 0.2936

N 4.7777 4.3923 0.3854

44

charge difference visualized in the below Figure 3.25, the accumulation of electron in space between N atom and B25 atom as well as between O2 atom and B51 atom can be considered as an evidence of chemical bond within those atoms It is consistent with the high binding energy, which is almost -1.5 eV

Figure 3.25 Charge density difference after NO2 adsorption illustrated using isosurface (isosurface level = 0.01)

3.6.5 Charge analysis of the (NH3 - borophene) system

The Bader charge analysis shows the change of charge for each atom of the system after the adsorption of NH3 on borophene, described particularly in Table 3.6

Table 3.6 Bader charge analysis of the (NH3 – borophene) system Atom

index

Charge of complex system (qe)

Charge of isolated system (qe)

Charge difference (qe)

Charge transfer (qe)

B 2.8169 2.8112 0.0057

+0.0066

B … … …

B 10 2.8151 2.8096 0.0055

B … … … …

B 46 3.4130 3.4071 0.0059

B 48 3.3924 3.4105 -0.0181

B … … … …

B 60 3.4293 3.4557 -0.0263

H 0.6089 0.6155 -0.0066

-0.0066

H 0.6098 0.6145 -0.0047

H 0.6361 0.6377 -0.0017

45

In the same order of binding energy adsorption with CO and CO2, however, the charge transferring behavior of NH3 with borophene is even weaker than those of CO and CO2 Overall, electrons move from NH3 molecule to borophene; however, the amount of charge is not significant It can be interpreted that borophene is quite inert with ammonia gas This slight interaction is illustrated in Figure 3.26

Figure 3.26 Charge density difference after adsorbing NH3 (isosurface level = 0.0012)

Figure 3.27 Charge transfer between gas molecules and borophene 0.0236 0.0268

-0.0066

-0.7686

0.7522

-1 -0.8 -0.6 -0.4 -0.2 0.2 0.4 0.6 0.8

CO CO2 NH3 NO NO2

Charge transfer to gas molecule ∆Q (e)

46

47

CONCLUSION

In this work, the adsorbability of borophene was examined throughout first-principles calculation of the energy configuration, the adsorption potential energy, the density of state for five poisonous gases i.e., CO, CO2, NO, NH3, and NO2 The charge transfer and Bader charge analysis were also given for analyzing the adsorption mechanism Remarkably, CO, CO2, and NH3 are physically adsorbed on β12 borophene, while NO and NO2 are chemically adsorbed on β12 borophene Regarding charge transferring behaviors, CO, CO2 and NO2 are electron acceptors, whereas NO and NH3 are electron donators when being absorbed on the surface of borophene

48

FUTURE PLANS

There are many rooms to explore in the field of the gas adsorbability of borophene which has huge applications in the future With great potential, β12 borophene as well as other types of boron nanosheets or nanoribbons are worth to be intensively studied

For further works, we want to carry out calculations for gas adsorption on borophene with other research subjects:

- Adsorbates: Volatile Organic Compounds would be examined toward fabricating cancer detector sensors

49

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