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

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 related works

research-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

This research is funded by National Foundation for Science and Technology Development (NAFOSTED) under grant number 103.01-2018.315

CONTENTS

Page

Acknowledgment i

CONTENTS ii

LIST OF TABLES iv

LIST OF FIGURES v

LIST OF ABBREVIATIONS vii

ABSTRACT viii

Chapter 1 INTRODUCTION 1

1.1 Background of the research 1

1.2 Objectives and subjects of the research 2

1.2.1 Adsorbent material: Borophene 2

1.2.2 Gas molecules 5

1.3 Toxic gases adsorption on two-dimensional materials 7

1.3.1 Gas adsorption on other two-dimensional materials 7

1.3.2 Adsorption application of borophene 7

1.4 Thesis outline 9

Chapter 2 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 3 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

3.6 Charge transfer characteristic 39

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

REFERENCES 49

LIST OF TABLES

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

two-dimensional materials (eV) 7

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

Table 3.6 Bader charge analysis of the (NH3 – borophene) system 44

LIST OF FIGURES

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

and their synthetic methods 3

Figure 1.2 Borophene assumed to be synthesized on Ag (111) substrate (a) buckled triangular borophene, (b) β12 borophene, and (c) χ3 borophene 4

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 3 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

Figure 3.18 Band structure and DOS of CO2 - borophene 37

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

isosurface (isosurface level = 0.00054) 42

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

0.003) 43

Figure 3.25 Charge density difference after NO2 adsorption illustrated using

isosurface (isosurface level = 0.01) 44

Figure 3.26 Charge density difference after adsorbing NH3 (isosurface level = 0.0012) 45

Figure 3.27 Charge transfer of CO, CO2, NH3, NO, NO2, and SO2 and borophene 45

LIST OF ABBREVIATIONS

DFT Density Functional Theory

VASP Vienna Ab initio Software Package

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

Keywords: 12 – borophene, DFT, adsorption, toxic gases

CHAPTER 1 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 1 in 9 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 do 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

Overall, low-dimensional materials are potential adsorbents on gas adsorbing applications due to their high surface-to-volume ratio Borophene is a new noble two-dimensional material, which is newly successfully synthesized [28] Borophene

is expected to have intriguing characteristics like graphene, initially expresses the outstanding mechanical and electronic performance such as existing spin gapless

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

As the rising of graphene after the Nobel Prize in Physics to Andre Geim, Konstantin Novoselov in 2010, 2D materials intrigue many interests of scientists worldwide because of their superlative physiochemical characteristics Moreover, there still exists much unexplored promising information about such nanomaterials 2D materials are atomically thin sheets that exhibit unique electronic, optical, and mechanical properties with remarkable potential for technological applications and

a plethora of unknown fundamental science [29] Regarding adsorption related problems, 2D materials express as one of the most prospective candidates due to their unique characteristics and its high specific surface area With tremendous attention from researchers, more and more new 2D materials are synthesized

recently Figure 1.1 shows elements able to form synthetic elemental 2D materials

and synthesis methods

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 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]

three-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]

Recently, borophene has been successfully synthesized by two independent groups

Mannix et al (2015) and Feng et al (2016) by chemical vapor deposition method in

ultrahigh vacuum conditions on silver (111) substrate [31][12] From these empirical data, borophene expresses as a metallic material which agrees with

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

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 dimensional boron: Structures, properties and applications‖, by Zhang, Penev, &

―Two-Yakobson, 2017, Chemical Society Reviews, 46(22), 6746-6763 Copyright [2017]

by The Royal Society of Chemistry

Initially, these existences of borophene are controversial; some argued that buckled triangular borophene was experimentally synthesized The difference between these polymorphs is the number of vacancies in the lattice of theirs Defining η as the vacancy density, then η is the ratio of the number of vacant sites to the total number

of sites (consisting boron sites and vacancies) in one unit cell; it is the number specifying the boron-sheet type from global and local points of view Accordingly,

η is 1/6 in the β12 lattice and 1/5 in the χ3 lattice, while η is zero in buckled borophene The complex chemical properties accompanying with various geometries, lets borophene become one of the most unpredictable two-dimensional materials However, borophene itself has an aura of irresistible intriguing properties, which attracts great attention of both theoretical and experimental study groups, so that scientists go to an agreement that 12 and 3 are two kinds of borophene grown

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

Outdoor air pollution is the result of natural and anthropogenic sources Adverse health consequences of air pollution can occur as a result of short- or long-term exposure [46] Herein, this work investigates the adsorbability of 5 pollutants which

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

- Nitrogen monoxide (NO): In the atmosphere environment, NO is easily oxidized

into NO2 Nitrogen oxides are produced in combustion processes, partly from nitrogen compounds in the fuel, but mostly by direct combination of atmospheric oxygen and nitrogen in flames Nitrogen oxides are produced naturally by lightning, and also, to a small extent, by microbial processes in soils [3]

- 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

1.3.2 Adsorption application of borophene

Recently, there are several studies related to sensing application of borophene However, most of them examined on buckled borophene, which is proven not to be the main existence of borophene

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, NO2and 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 NO2are 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 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,

non-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 8 SO2 molecules

Nagarajan and Chandiramouli also carried on a theoretical study to predict the interaction of ammonia gas and buckled borophene nanosheets and nanotubes [34] The Bader charge transfer, the density of state, adsorption configuration, and energy

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

of borophene‖ includes three chapters

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

Chapter 3: Results and discussion – This chapter presents and illustrates significant

results of this work The detailed discussions of the adsorption mechanism are given

CHAPTER 2 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]

Kohn and Sham considered a fictitious reference system (denoted by the subscript

and often called the non-interacting system) of noninteracting electrons that each

experience the same external potential-energy function ( ), where ( ) is such

as to make the ground-state electron probability density ( ) of the reference system equal to the extact ground-state electron density ( ) of the molecule we are interested in; ( ) ( ) Since Hohenberg and Kohn proved that the ground-state probability-density function determines the external potential, once

( ) 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 do 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 energy KS spin-orbitals of the reference system | |,

[ ] ∫ ( ) ( ) ̅[ ] ∬ ( ) ( )

[ ] (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 :

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 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]

Kohn-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]

In a ―true‖ DFT, one would deal with only the electron density (a function of three variables) and not with orbitals and would search directly for the density that minimizes [ ] Because the functional is unknown, one instead uses the KS

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

The Vienna Ab initio Simulation Package (VASP) is a computer program for atomic scale materials modeling, e.g., electronic structure calculations and quantum-mechanical molecular dynamics, from first principles VASP computes an approximate solution to the many-body Schrödinger equation, either within DFT, solving the KS equations, or within the Hartree-Fock (HF) approximation, solving the Roothaan equations Hybrid functionals that mix the HF approach with DFT are

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]

Richard Bader, from McMaster University, developed an intuitive way of dividing molecules into atoms His definition of an atom is based purely on the electronic charge density Bader uses what are called zero flux surfaces to split atoms A zero-flux surface is a 2D surface on which the charge density is a minimum perpendicular to the surface Typically in molecular systems, the charge density

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) = 0 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

First-principles DFT calculations will be implemented using the Vienna Ab initio Software Package [32] The calculations employed periodic boundary conditions and plane-wave expansion of the wave function The generalized gradient approximation in the scheme of the Perdew–Burke–Ernzerhof function was used to calculate the exchange-correlation potential and the PAW pseudopotential was applied to describe electron-ion interactions Dispersion vdW-corrected revPBE-vdW [49], optPBE-vdW [19] and vdW-DF2 [20] methods are implemented to calculate the interaction energies for small molecules adsorbed on borophene The internal coordinates and lattice constants were optimized until the Hellman–

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:

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]

The calculations conducted to investigate adsorption characteristics are summarized

in Figure 2.2

Figure 2.2 The flow chart of gas absorbing calculations

- From the most stable position,

scan along z-direction

structure

Calculate adsorption energy

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

- Bader charge analysis

- Obtain charge transfer

CHAPTER 3 RESULTS AND DISCUSSION

Table 3.1 Calculated lattice constants of β12 borophene vs experimental data

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

CO gas at the freedom state has bond length of 1.128 Å After relaxation, CO on borophene has a longer bond of 1.145 Å with revPBE-vdW, and 1.144 Å with optPBE-vdW and vdW-DF2 correlation functionals The adsorption site of CO on borophene is the hollow site of the vacant boron hexagonal The energetically

favorable configurations are presented in Figure 3.3; in which, the red bubble refers

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

Figure 3.3 Top view (1) and side view (2) of the most stable configurations of CO

on borophene optimized by using 3 different vdW functionals (a) revPBE-vdW, (b) optPBE- vdW, and (c) vdW-DF2

3.2.2 CO 2 - borophene

In isolation, CO2 has a flat structure with the bond length of 1.162 Å Because of the interaction with the adsorbent, these bonds are lengthened to 1.179 Å with revPBE-vdW, and 1.177 Å with optPBE-vdW or vdW-DF2 Besides, the molecule is bent a little from 179.5 to 179.8 depending on the correlation functionals The stable

configuration of this gas when being adsorbed on borophene is illustrated in Figure 3.4 Therein, CO2 molecule energetically prefers to locate at the hollow site of vacant boron hexagon The orientation of this gas molecule is parallel with the surface of borophene Generally, the different vdW correlation functionals give the similar geometries