<<

A STUDY OF , PORPHYRIN AND THEIR DYAD ON

GRAPHENE

A Thesis

Presented to

The Graduate Faculty of The University of Akron

In Partial Fulfillment

of the Requirements for the

Master of Science

Navin Kumar Kafle

August, 2016 A STUDY OF FULLERENE, PORPHYRIN AND THEIR DYAD ON

GRAPHENE

Navin Kumar Kafle

Thesis

Approved: Accepted:

Advisor Dean of the College Dr. Alper Buldum Dr. John Green

Faculty Reader Dean of the Graduate School Dr. Robert R. Mallik Dr. Chand Midha

Faculty Reader Date Dr. Graham S. Kelly

Department Chair Dr. David Steer

ii ABSTRACT

Molecular devices employing hybrids of graphene, acting as electron acceptor, with

C60 and porphyrin, acting as electron donors are promising for the . The models of fullerene (C60), zinc-tetraphenylporphyrin (ZnTPP) and their dyad on sin- gle layer graphene (SLG) were designed and their structural and electronic properties were studied using classical and computational modeling. First- principles density functional theory (DFT) calculations were carried out in quantum calculations. Our study shows that the C60ZnTPP dyad and SLG interact more strongly than the other two with SLG. We also found that van der Waals in- teraction was an important factor for non-covalent interactions between our molecules and SLG. The HOMO-LUMO gap of the ZnTPP-SLG model structure was smaller than C60-SLG model structure. Density of states (DOS) calculations shows that

C60ZnTPP-SLG had a high value of DOS at Fermi level and it has number of par- tially filled orbitals above Fermi level. This showed that our C60ZnTPP had metallic character. We believe that such properties of our model structures would encourage experimentalists to examine them for their practical applications in electronic devices and energy conversion.

iii ACKNOWLEDGEMENTS

My deepest gratitude goes first to Professor Alper Buldum, who expertly guided me throughout my graduate research and gave me the freedom to work independently.

It was a pleasure working with him.

I would like to thank Dr. Robert R. Mallik and Dr. Graham S. Kelly for being on my thesis defense committee and for reading my thesis and offering great suggestions.

Further, I would like to thank Dr. Mahesh Dawadi and Sudip Adhikari whose continuous support and ideas with regards to programming were invaluable to my work.

I would also like to thank my family and friends for all their encouragement, and I am especially thankful to my lovely wife Sabita Kafle for her continuous care, support and motivation during my research.

iv NOMENCLATURE

SLG Single Layer Graphene

C60 Fullerene

ZnT P P Zinctetraphenylporphyrin

DFT Density Functional Theory

HOMO Highest Occupied

LUMO Lowest Occupied Molecular Orbital

DOS Density Of States

2D Two Dimentional

TPP Tetraphenylporphyrin

M − TPP Metallo-Tetraphenylporphyrin

H Hamiltonian

GP W Gaussian and Planewave

MD

UFF Universal

R Separation between and SLG

C − R Resonant

N − 2 Trigonal

v PBE Perdew-Burke-Erznerhof

FFT Fast Furier Transform

GT H Gredecker-Teter-Hutter

GAP W Gaussian and Agumented plane wave

STO Slater Type Orbitals

DZ Double Zeta

EAd Adsorbtion energy

EC60 Energy of optimozed C60

EGr Energy of optimized graphene

ET ot Total energy

vi TABLE OF CONTENTS

Page

LIST OF TABLES ...... ix

LIST OF FIGURES ...... x

CHAPTER

I. INTRODUCTION ...... 1

II. BACKGROUND ...... 3

2.1 Atomic Structure and Properties of Graphene ...... 3

2.2 Atomic Structure and Properties of Fullerene (C60)...... 7

2.3 Atomic Structure and Properties of Porphyrins ...... 8

2.4 Computational Methods ...... 11

2.5 CP2K ...... 14

2.6 Material Studio ...... 15

III. MODELS ...... 17

3.1 C60-SLG Model ...... 17

3.2 ZnTPP-SLG Model ...... 18

3.3 C60ZnTPP-SLG Model ...... 20

IV. CLASSICAL MOLECULAR MECHANICS SIMULATIONS ...... 21

4.1 Methods ...... 21

vii 4.2 Result and Discussion ...... 24

V. QUANTUM MECHANICS SIMULATION ...... 37

5.1 Method ...... 37

5.2 Results and Discussion ...... 40

VI. CONCLUSION ...... 53

BIBLIOGRAPHY ...... 54

viii LIST OF TABLES

Table Page

4.1 Parameters used in geometrical optimization calculations ...... 24

4.2 Initial Parameters used for energy minimization and geometrical optimization of C60-SLG...... 26 4.3 Parameters used in the energy calculation and geometrical optimiza- tion of ZnTPP-SLG...... 30 4.4 Parameters used in the energy calculation and geometrical optimiza- tion of C60ZnTPP-SLG...... 33 5.1 The energies of optimized structures...... 43

ix LIST OF FIGURES

Figure Page

2.1 The derived from graphene. Figure extracted from Ref. [13]...... 4

2.2 Graphene sheet with the unit cell, where Lx = 2.4592 Aand˚ Ly = 4.26 A.˚ 5

2.3 Structure of buckyball (C60)...... 8

2.4 Structure of Porphyrin...... 9

2.5 Structure of zinc tetraphenylporphyrin (ZnTPP), where cyan repre- sents C , red is Zinc, blue is Nitrogen and orange is Hydrogen. . . 10

3.1 Side view of the structure of C60-SLG ...... 18

3.2 Structure of ZnTPP-SLG with (a) a Zn of ZnTPP on the top of a carbon atom of SLG (b) a Zn atom of ZnTPP in the middle of a hexagonal ring of SLG ...... 19

3.3 Side view of the structure of C60ZnTPP-SLG ...... 20

4.1 Changes in the molecule’s geometry and energy stepwise by geome- try optimization from point 1 to 4...... 23

4.2 Snapshot of C60-SLG model with periodic boundaries...... 25

4.3 The variation of total energy as a function of C60 and SLG separation in C60-SLG. One kilocalorie per mole is 0.0433eV...... 27 4.4 Forcite Geometrical Optimization- Convergence, purple; Grad.Norm (kcal/mol/A),˚ blue; Energy Change (kcal/mol)...... 28 4.5 Forcite Geometrical Optimization- Energy minimization...... 28

x 4.6 Snapshot of ZnTPP-SLG model with periodic boundaries ...... 29

4.7 The variation in total energy of the ZnTPP-SLG with changes the separation between ZnTPP and SLG with (a) a Zn atom of ZnTPP in the middle of hexagonal ring of SLG (b) a Zn atom of ZnTPP on the top of a carbon atom of SLG...... 31

4.8 (a) Forcite Geometrical Optimization- Convergence, purple; Grad.Norm (kcal/mol/A),˚ blue; Energy Change(kcal/mol) (b) Forcite Geometrical Optimization- Energy minimization...... 32

4.9 Snapshot of the C60ZnTPP-SLG model with periodic boundaries . . . . 34

4.10 The variation in total energy of the C60ZnTPP-SLG with change separation between C60ZnTPP and SLG...... 35 4.11 Forcite Geometrical Optimization- Convergence, purple; Grad.Norm (kcal/mol/ A),˚ blue; Energy Change (kcal/mol)...... 36 4.12 Forcite Geometrical Optimization- Energy minimization...... 36

5.1 The variation of total energy as a function of C60 and SLG separation in C60-SLG. One atomic unit of energy is 27.211 eV...... 41

5.2 (a) The optimized structure of the fullerene (C60) molecule. (b) The optimized structure of the supercell of graphene monolayer with 240 carbon atoms on it. (c) Side view of the optimized structure of C60-SLG structure...... 42 5.3 Energies of five HOMO and five LUMO along with the HOMO- LUMO energy gap...... 44

5.4 Electronic profiles of LUMO of C60-SLG structure. The isosurface value is ± 0.01 (distinguished by blue/red) in atomic unit...... 45 5.5 The variation of total energy as a function of the separation of ZnTPP and SLG in the ZnTPP-SLG structure. One atomic unit of energy is 27.211 eV...... 46 5.6 The variation of total energy as a function of the separation of C60ZnTPP dyad and SLG in the C60ZnTPP-SLG structure...... 47

5.7 DOS for the C60-SLG. The Fermi energy is shifted to zero...... 49

5.8 DOS for the ZnTPP-SLG. The Fermi energy is shifted to zero...... 50

xi 5.9 DOS for the C60ZnTPP-SLG. The Fermi energy is shifted to zero. . . . 51

5.10 DOS for the SLG. The Fermi energy is shifted to zero...... 52

xii CHAPTER I

INTRODUCTION

Carbon of low like (C60), carbon nanotubes

(CNT) and single layer graphene (SLG) have attracted great research interest in recent years. They offer novel properties and they can be potential building block materials for future nano-electronics structure [1]. Graphene is a mono atomic (2D) sheet of carbon. Due to its outstanding structural, electronic and mechanical proper- ties, it is a promising material for advanced technological applications. By controlling its size, shape, carrier types, one can control graphene’s electronic and magnetic prop- erties [2]. It is a zero band gap semiconductor and shows ballistic conductance [3].

2 C60 is a soccer ball shaped carbon allotrope with sixty sp -hybridized carbon atoms.

It can be treated as a semiconductor or conductor depending upon its size [3]. In a broad range of fields like solar cells, superconductors, and C60 is applied [4]. Porphyrins are micro cyclic compounds with four mod- ified pyrrole rings linked through a methine bridge [5]. Metals can be inserted into the central region of a macrocyclic ring. This gives the derivative of porphyrin called

Metallo-porphyrin. These are more stable and significant natural compounds that play an important role in respiration, electron transfer and photosynthesis [6]. They are mostly taken as the potential materials for photovoltaic devices [7].

1 The study and fabrication of hybrid carbon nanostructures has been an in- tense research subject over the past few years. Chemically functionalized graphene with fullerene which has an electron-accepting behavior, has been studied [8]. Ex- perimentally, C60 molecules on graphene are prepared epitaxially on SiC [9]. Energy transfer has been observed between porphyrin-graphene complexes [10].

Here, we designed three hybrid models containing graphene. Models of C60, porphyrin and their dyad on graphene were created. Classical and quantum simula- tions were carried out by using Material Studio and CP2K software respectively. The total energy and geometry optimization calculations of our models were performed by classical simulation. We employed DFT in quantum calculations to find the non- covalent interactions between C60, porphyrin and their dyad with graphene. It was found that the dyad of C60 and porphyrin on graphene was more strongly bonded than other structures. The electronic structures of our models were calculated. Our results showed that some of the model structures were metallic.

In chapter II, a brief review of the important properties of graphene, C60 and porphyrin is given. In addition, simulation softwares are introduced. The model structures are described in chapter III. Classical simulation methods and their results are given in chapter IV. In chapter V, quantum simulation methods and their result and discussions are provided. Finally chapter VI, is for the conclusion of our work.

2 CHAPTER II

BACKGROUND

2.1 Atomic Structure and Properties of Graphene

Graphene is a two dimensional mono-atomic sheet of carbon atoms [11]. It is one of the allotropes of carbon. It is taken as the building block of other carbon al- lotropes. The carbon atoms are sp2-hybridized and packed in a honeycomb crystal lattice forming a one atom-thick planer sheet [11]. Some of the graphene sheets have ridges because of the thermal fluctuation [12]. The other allotropes like carbon nan- otubes, fullerene and can be formed from graphene by rolling, wrapping and stacking graphene sheets together as shown in Figure 2.1 [13].

Previous studies for two dimensional graphene had indicated that the exis- tence of graphene in pristine form is not possible due to thermal fluctuations that destroy the long range crystallinity [12]. In 2004 Andre Geim and Kosty Novoselov disproved this theoretical prediction with their experimental proof of graphene sheets by using the tape peeling method [13]. They won a Nobel Prize for their work in 2010.

After this discovery, scientists from all around the globe have been showing enormous interest in graphene and devices based on it [14]. Due to its outstanding mechanical, electrical, thermal and optical properties, it has became one of the most attractive

3 nano materials in the world of nano science[15]. It has good electrical conductivity

[16], high carrier mobility ( (2 − 5)x 103 cm2V−1S−1) [17], high surface area (2630 m2g−1) [18], (500 Wm−1K−1) [16] and high Young’s modulus

(1 TPa ) [19]. Because of these extraordinary properties, it has wide technological applications in sensors, batteries, photo-detectors, bioscience, ultra-capacitors, etc.

[20].

Figure 2.1: The allotropes of carbon derived from graphene. Figure extracted from Ref. [13].

Sp2-hybridized carbon atoms are arranged in a hexagonal closed packed struc- ture in graphene where 2s state mixes with two of the 2p orbitals to form orbitals. 4 The orbitals of graphene are oriented in an xy-plane with an angle of 120 degrees

[21]. The nearest carbon atoms are separated from each other by the distance of 1.42

A.˚ The unit cell was chosen in such a way that it contains four electrons, which is shown in the Figure 2.2.

Figure 2.2: Graphene sheet with the unit cell, where Lx = 2.4592 Aand˚ Ly = 4.26 A.˚

Each carbon atom is bonded with three carbon atoms. As we know a carbon atom has four valence electrons, three of which are strongly bonded with three elec- trons of other carbon atoms by sigma bonds while the fourth electron is bonded with a weak which is responsible for the charge transport in graphene.

Although single layer graphene has great industrial applications, the mass production of quality sheets is more challenging to researchers. The most common 5 methods of graphene synthesis include mechanical exfoliation [14], chemical vapor deposition (CVD) on metallic catalysts, chemical reduction of exfoliation graphene oxide [14] and of SiC [13]. Here some of them are discussed briefly.

Mechanical exfoliation is the earliest method used to produce graphene on a small scale [14]. Mainly experimental research groups use this method to study. The graphene layer can be isolated from graphite by peeling it several times using Scotch tape, then the tape is pressed on a suitable substrate like Si/SiO2, where we can get single or multiple layer graphene. The thickness of the film obtained by this method ranges from 10 to 100 nm [22].

The most common and large scale production method for high quality graphene is CVD.The graphene films are grown onto a transition metal substrate, mainly Ir

[23], Ru [24], Ni [25] and Cu [26]. This can be achieved when essential chemical materials in gaseous states decompose onto the substrate after reacting under high temperature. Among transition metals, films grown on (Cu) substrate are rel- atively good [26]. Since the thickness of film is controlled by the solubility of carbon atoms onto the heated substrate, the Cu has the lowest solubility compared to others.

Films grown on Cu substrates have 97.4 % optical transmittance and resistance 125

Ω/sq [26].

6 2.2 Atomic Structure and Properties of Fullerene (C60)

2 Fullerene (C60) is a carbon allotrope. It is made up of sixty sp hybridized carbon atoms, commonly known as buckyball. In 1970, Osawa reported C60, which had a structure and shape like a soccer ball [27]. Later in 1985, Kroto and Smalley accidently discovered C60 during their study of refractory clusters generated by a by using mass [28]. The name was given after an American architect Buchminster Fuller, which had the shape of a . Here,

Figure 2.3 shows the atomic structure of C60. It has 32 faces, including 20 and 12 pentagons [29]. The pentagons are isolated by the hexagons and the bond lengths at the junction of the and pentagon are longer than the bond lengths at the junction of two hexagon. Double bonds are only located in hexagonal rings alternately. There are no double bonds in pentagon rings. The diameter has been found to be 7.10 ± 0.07 A.˚ The outer diameter with the consideration of π electron clouds with carbon atoms is 7.10 ± 3.35 A[30].˚

The common methods of C60 preparations are arc process, thermal evap- oration, combustion and CVD [31,32,33]. It can withstand high temperature and pressure since it is extremely stable. It is soluble in many organic . It can react with other species of carbon by maintaining its spherical geometry [34]. By doping it can be electrically insulating, conducting, semi-conducting or even super- conducting. It can be used as an optical device, photovoltaic, antioxidant, lubricant, etc [35].

7 Figure 2.3: Structure of buckyball (C60).

In our work, one of the models is a hybrid structure of graphene and C60. We have studied the structural and electronic properties of this structure.

2.3 Atomic Structure and Properties of Porphyrins

Porphyrins are a large group of macrocyclic compounds. They are naturally occurring molecules with an important role in biological systems and . Hemoglobin and

8 chlorophyll are examples of them. They have great importance in different fields of study, like biology, medicine, material science, geology and many others [36].

The parent compound is called the porphyrin. It consists of four nitrogen atoms and twenty carbon atoms, as shown in Figure 2.4. It has four modified pyrrole rings linked through a methine bridge [37]. In two of the rings nitrogen atoms are of the pyridine type. Their unshared electron pairs are oriented towards the inside of the macrocycle. A symmetrical dianion is formed when nitrogen-hydrogen bonds are ionized, then all become the same because of the delocalization of negative charges [38]. In this condition, different kind of metals are allowed to fix within the macrocycle, forming co-ordination bonds with the four N-atoms. This type of porphyrin is stable and called metalloporphyrin. These porphyrins are also natural compounds and they are involved in photosynthesis, respiration and electron transfer

[39]. In Figure 2.4, the atomic structure of porphyrin is presented.

Figure 2.4: Structure of Porphyrin.

9 A porphyrin with four phenyl rings attached at the meso position is called tetraphenylporphyrin (TPP). In 1936, Rothemund synthesized TPP for the first time from the reaction of benzaldehyde and pyrrole at 150 0C for 24 hours but the produc- tion was too slow [40]. Later, in 1967, Adler and Longo performed the same reaction with some improvements, which increased the product and the efficiency of the reaction [41].

A Tetraphenylporphyrin with a metal atom accommodated inside core is called Metallo-Tetraphenylporphyrin (M-TPP). These compounds provide building blocks for the control of properties of nano materials. They have strong absorption bands and they can be used as photo sensitizers [42]. The atomic structure of Zinc-

Tetraphenylporphyrin (ZnTPP) is presented in Figure 2.5.

Figure 2.5: Structure of zinc tetraphenylporphyrin (ZnTPP), where cyan represents C atoms, red is Zinc, blue is Nitrogen and orange is Hydrogen.

10 2.4 Computational Methods

Density Functional Theory [DFT] is a quantum mechanical modeling method used to determine the ground-state properties of many-body electronic structures [43]. This method has been a popular quantum calculation method since the 1970s.

Mathematically, it uses the functional of electron density instead of many body wave function and expresses the total energy of the system as a functional of electron density. Instead of dealing with 3N variables of many-electron wave functions it deals with the three variables of a density functional which makes the problem more simple.

Hamiltonian H, for a system of interacting electrons and nuclei can be ex- pressed as

1 X 2 X ZI 1 X 1 H = ∇i − + 2 |ri − RI | 2 |ri − rj| i i,I i6=j (2.1) 1 X 2 1 X ZI Zj − ∇I + 2MI 2 |RI − RJ | I I6=J

H = Te + Vne + Vee + Tn + Vnn, (2.2) where upper case subscripts refer to nuclei with a charge of Z and a mass of M and lower case subscripts refer to the electrons. In eq. (2.2), Te refers to the kinetic energy of the electrons,Vne is the potential energy acting on the electrons due to the nuclei,Vee is the electron-electron interaction, and Vnn is for the interaction between the nuclei. The Fermi velocity of the electrons is much larger than the ionic velocity, such that we can assume that at any instant of time, the electrons are at their ground state for that particular ionic configuration [44]. The Born-Oppenheimer

11 approximation is the best approximation in most cases, for example, the calculation of the phonon dispersion of a crystal [45].

The many-body Schrodinger equation is:

H |Ψi = (Te + Vne + Vee + Vnn) |Ψi = E |Ψi (2.3) where |Ψi is the eigenstate of the Hamiltonian and it depends on the 3N electronic coordinates ri, i.e.(r1, r2;.....,rN ). The time independent solution of equation (2.1) is obtained by solving equation (2.3) within the Born-Oppenheimer approximation. A set of eigenfunctions and eigenvalues, E, the total energy are obtained as the solution of eq. (2.3). All ground-state properties can be obtained from the ground state energy

E0 which include the cohesive energies of solids, their equilibrium crystal structure and the transition between different structures, the nuclear motion, etc.[44].

It is impossible to solve eq. (2.3) exactly for a real system. But one can obtain approximate solutions by using the Kohn-Sham density functional theory [43].

Density functional theory (DFT) is the most widely used quantum mechanical tool in physics and chemistry for finding properties of materials from single molecule to condensed phase systems. The first Hohenberg-Kohn theorem states that in the presence of an external potential Vext(r) in a system of interacting electrons, the Vext(r) is determined from the ground state electron density n0(r), except for a constant shift in the energy.

Thus by knowing n0(r), the ground state electron wave function Ψ0(r1, r2,....,rN ) can be obtained. Similarly, other ground state properties of a material can be ob-

12 tained from the density. The second Hohenberg Kohn theorem states that there exists a universal functional of the electron density (F[n(r)]) for any given external potential Vext(r) [45]. From the minimization of this functional at n0(r), the ground state energy E0 for any vext(r) can be obtained as:

E0 = E[n0(r)] ≤ E[n(r)] (2.4)

Both Hohenberg Kohn theorems try to find a solution to the complicated many body problem in terms of n(r) alone instead of the much more complex many body wave function that depends on 3N degrees of freedom.

A more successful approach to solve the many-body problem has been intro- duced by Kohn and Sham [46]. The electron kinetic energy and the electron-electron interaction of the interacting electron system are reformulated in terms of a non- interacting one by using the idea of Khon and Sham. All the problems associated with the quantum mechanical many-body interactions are then reestablished into a term called the exchange-correlation functional, Exc[n(r)].

Under the Kohn-Sham idea, the Hamiltonian can be rewritten in terms of a system of non-interacting particles, using a single-particle approach. Now, n(r) can

σ be expressed as the sum of the squares of the non-interacting orbitals ψi for each spin σ:

N σ X X X σ 2 n(r) = n(r, σ) = |ψi (r)| (2.5) σ σ i=1

13 2.5 CP2K

In this project, a computer programming package called CP2K is used for the simu- lations. CP2K was developed based on the theories needed real systems in a practical way. CP2K is a free open-source project written in Fortran 95.

This package provides many different methods of quantum chemistry and molecular modeling, such as DFT, molecular dynamics, ab-initio etc. The DFT part of CP2K is called Quickstep [47].The DFT calculations are based on the hybrid Gaussian and plane waves (GPW) method. The wave functions are described by an atom-centered

Gaussian-type basis, while the density is described in terms of an auxiliary plane wave basis sets. In CP2K input, the general format section system is:

&SECTION

......

......

&END SECTION

This implies that we can use different sections of input files to describe dif- ferent parameters that are needed for the calculation. For example, the coordinates of the system under study may be in the COORDS section. Global, Force Eval and

Motion are three mandatory sections of each CP2K input. We can keep any section, one after another.

The Global Section consists of different commands as below:

&GLOBAL

14 PROJECT

RUN TYPE

PRINT LEVEL

&END GLOBAL

We introduce the name of project in the project line. Run Type provides the type of calculation that is going to be done e˙g˙molecular dynamics (MD), Geometry

Optimization (GEO OPT) or single point calculation (Energy Force). Print Level defines the amount of information that we desire to see in the output file.

The Force Eval, which is the heart of calculation defines how forces and energy will be calculated.The motion section is to contain the information for the calculation in which the atoms move for instance during a geometry optimization or a molecular dynamic calculation.

CP2K is used to find the minimum energy structure by calculating the energy of the system with changes in atomic structure. Total electron density and density of states (DOS) of the system were calculated.

2.6 Material Studio

Material studio is a comprehensive environment for computational .

It allows us to do both quantum and classical calculations. It has different components that help to investigate periodic and modified crystal structure and crystal growth.

We can find the most stable state of a molecule, electronic, optical and structural properties. Accelrys’ comprehensive range of software combines quantum mechanics, 15 molecular mechanics, mesoscale modeling, analytical instrument simulation and sta- tistical correlations into an easy-to-use modeling environment. These techniques are supported by structural building and visualization capabilities and tools to analyze and present scientific data. For our project, it is used in the classical calculation of energy of the system, as well as for the geometrical optimization of our system.

16 CHAPTER III

MODELS

The graphical representations of our models were created using C programming and they were studied using Material Studio 4.0 Visual software and the CP2K pack- age. We created three different models. All are nano composites of graphene. The

first model contains structures of fullerene (C60) and Single Layer Graphene (SLG),

(C60-SLG). The second model has zinc-tetraphenylporphyrin (ZnTPP) and SLG,

(ZnTPP-SLG) and the third model is the hybrid structure of C60-ZnTPP and SLG,

(C60ZnTPP-SLG).

3.1 C60-SLG Model

The 2D SLG sheet with a 10 x 6 periodic layer in both the a and b directions was taken such that we could keep C60 at the middle of graphene, leaving space, equal to the diameter of C60 on both sides of it. The SLG had 240 atoms on it. A fullerene

(C60) with a single atom at the bottom was placed directly atop a carbon atom of

SLG.The separation between the lowest height carbon atom of C60 and SLG was 3.1

A.˚ The periodic supercell with dimensions 24.5952 x 25.56 x 35 A˚ was created in the calculations. Fig.3.1 shows the side view of the C60-SLG model.

17 Figure 3.1: Side view of the structure of C60-SLG

3.2 ZnTPP-SLG Model

Fig 3.2 shows the top view of the ZnTPP-SLG model. A graphene sheet of 14 x 8 unit cells containing 448 carbon atoms was created and a ZnTPP molecule (77 atoms) was placed at equilibrium distance of 4.3 A˚ from the substrate (graphene). The total number of atoms in this model is 525. The size of the supercell was 34.4288 x 34.08 x 35 A.˚ The periodic boundary condition had been used in all three directions. We have studied two different ZnTPP-SLG structures. In one, the Zn atom of ZnTPP was kept at the top of the central atom of the SLG, and in another Zn was in the middle of the central hexagonal ring of the SLG.

18 (a)

(b) Figure 3.2: Structure of ZnTPP-SLG with (a) a Zn atom of ZnTPP on the top of a carbon atom of SLG (b) a Zn atom of ZnTPP in the middle of a hexagonal ring of SLG

19 3.3 C60ZnTPP-SLG Model

For this model, we created a graphene sheet of 15 x 9 unit cells with 540 atoms on it, and C60ZnTPP, which has 144 atoms, was placed at the equilibrium distance 5.3 A˚ above the graphene. This separation was taken between the Zn atom of C60ZnTPP and the substrate (SLG). The total number of atoms in this model was 684. A super cell of size the 36.888 x 38.34 x 40 A˚ was created to perform energy calculations and geometrical optimization. Figure 3.3 represents a side view of C60ZnTPP-SLG model.

Figure 3.3: Side view of the structure of C60ZnTPP-SLG

20 CHAPTER IV

CLASSICAL MOLECULAR MECHANICS SIMULATIONS

4.1 Methods

In order to study the model structures and their stable configurations, classical molec- ular mechanics simulations were performed using Material Studio 4.0 Visualizing

Software [48]. Forcite tools, which is a molecular mechanics tool to perform single point energy calculations and geometry optimization, was used to perform energy calculation and geometry optimization of our systems.

4.1.1 Total Energy Calculations

The variations in total energy of all the model structures for different molecule- graphene separations were studied. Equilibrium heights for the minimum energy structures were found.

For the total energy calculation Universal Force Field (UFF) was applied.

UFF was developed for all the elements of the since the other popu- lar force fields were limited to specify the combination of atoms.The parameters of

UFF mainly depend on the elements and in their connectivity. These parameters are atomic bond radii, van der Waals interaction, torsional and inversion barriers and effective nuclear charges [49]. UFF can be used for linear, resonant, trigonal, tetra-

21 hedral, square planar, trigonal bipyramidal and octahedral geometries [49].The sum of the valence or bonded interaction and non-bonded interaction gives the energy of a molecule in UFF.

The Ewald method was used for the electrostatic and van der Waals force calculation. It is a method for determining the electrostatic potential and energy of an system having both positive and negative charges.This method is also used to calculate the repulsive inter-nuclear electrostatic energy in an electronic structure [50].

While simulating a system of and molecules in a cube of length L with periodic boundary conditions, the interaction between the and all its periodic images can be calculated using the Ewald electrostatic potential Φ (r). The electrostatic potential energy of the system is given by the following equation.

N N N X X ξ X U = q q Φ(r ) + q2 (4.1) i j ij 2L i i=1 j=1 i=1

Here qi and qj are charges interacting, rij = ri + rj + n is a vector in the unit cell and ξ/L is self correction term.

The convergence criteria of energy was 0.001 kcal/mol and force was 0.5 kcal/mol/A.˚

4.1.2 Geometrical Optimization

The study of properties and behavior of a molecule based upon its structure can be done from its stable and low energy structure, but a molecule created in a compu- tational software package may have high energy. Therefore, energy minimization is carried out to find a stable low energy structure via geometry optimization. Geom- 22 etry optimization is a numerical method for finding a minimum on potential energy surface beginning with high energy structure. This method works in a stepwise fash- ion, such that the energy of the molecule is reduced in each step and finally the local or global minimum on potential energy surface is reached [51].

Figure 4.1 presents the process of energy minimization. The label 1 represents the initial high energy structure. The energy and geometry goes on changing as the process moves forward and eventually it reaches a minimum energy structure at step

4.

Figure 4.1: Changes in the molecule’s geometry and energy stepwise by geometry optimization from point 1 to 4.

23 The initial energy parameters that were used in our geometry optimization calculations are listed in Table 4.1.

Table 4.1: Parameters used in geometrical optimization calculations

Parameters Specification

Algorithm Smart

Forcefield Universal

Van der Waals Summation methods Ewald

Charges Current

Convergence tolerance Energy - 0.001 kcal/mol

Force - 0.5 kcal/mol/A˚

Maximum number of iterations 500

4.2 Result and Discussion

The minimum energy structures of our models were studied from energy and geomet- rical optimization calculations.

4.2.1 C60-SLG System

In this model, the lowest height carbon atom (x = 12.2637 A,˚ y = 13.0216 A,˚ z =

3.1000 A)˚ of C60 was placed atop of the carbon atom (x = 12.2975 A,˚ y = 12.7800 A,˚ z = 0.0000 A)˚ of the middle region of SLG. This geometry of C60-SLG was found to

24 be the most stable one [52]. In simulation, SLG was fixed while the C60 molecule was set for free movement. The periodic boundary conditions were applied. The C60-SLG model is shown in Figure 4.2.

Figure 4.2: Snapshot of C60-SLG model with periodic boundaries.

25 Parameters used in simulation are presented in Table 4.2.

Table 4.2: Initial Parameters used for energy minimization and geometrical optimiza- tion of C60-SLG.

Parameter Specification

Forcefield Type Carbon Resonance (C R)

Hybridization Trigonal

Bond-length 1.42 A˚

Chemical type Aromatic

Supercell dimensions a = 24.5952 A˚

b = 25.56 A˚

c = 35.0 A˚

In the energy calculation, the C60 molecule and SLG separation (R) was changed within a range (2 - 4.6 A).˚ Energy of the system changed with a change in

R. We found that with R equal to 3.1A,˚ the structure had minimum energy. The energy of the model structure with equilibrium R was 622.3974 kcal/mol. The change in energy with a change in R is presented in Figure 4.3. This structure was used to perform geometrical optimization.

The geometrical optimization was performed with the same parameters as shown in Table 4.1. The convergence and energy minimization graphs were repre- sented in the Figures 4.4 and 4.5 respectively.

26 Figure 4.3: The variation of total energy as a function of C60 and SLG separation in C60-SLG. One kilocalorie per mole is 0.0433eV.

The graph of convergence from forcite geometry optimization clearly depicts that the convergence criteria of energy (0.001 kcal/mol) and the force requirement

(0.5 kcal/mol/A)˚ are met. From the energy minimization graph, we found that, at the

final optimization step 63, if log10 = -3, then anti log(-3) = 10−3 kcal/mol, which is

0.001 kcal/mol. Again the gradient norm became smaller than 0.5 kcal/mol/A˚ as re- quired. Thus, the convergence requirements were fulfilled and energy was minimized.

The graph of energy minimization depicts that the total enthalpy of the system at optimization step 20 became a constant value, i.e. 500 kcal/mol.

27 Figure 4.4: Forcite Geometrical Optimization- Convergence, purple; Grad.Norm (kcal/mol/A),˚ blue; Energy Change (kcal/mol).

Figure 4.5: Forcite Geometrical Optimization- Energy minimization.

28 .

4.2.2 ZnTPP-SLG System

The variation in total energy of the ZnTPP-SLG structure with change separation be- tween the ZnTPP molecule and SLG was studied. We assigned individual force field types for all atoms of the model. The force filled type of carbon atoms was carbon res- onant (C R), for Nitrogen atoms, it was nitrogen, trigonal (N 2), zinc,tetrahedral, +2 oxidation state (Zn3+2) for Zinc and hydrogen(H ) for Hydrogen atoms.The ZnTPP-

SLG model is shown in figure 4.6.

Figure 4.6: Snapshot of ZnTPP-SLG model with periodic boundaries

The different parameters used for the calculation of energy are presented in

Table 4.3. We studied two different models: one with the Zn atom of ZnTPP in the middle of a hexagonal ring of SLG, and another with the Zn atom on the top of the 29 Table 4.3: Parameters used in the energy calculation and geometrical optimization of ZnTPP-SLG.

Parameters Specification

Forcefield Types Carbon atoms - C R

Nitrogen atoms - N 2

Zinc atom - Zn3+2

Hydrogen atoms - H

Supercell dimensions a = 34.4288 A˚

b = 34.08 A˚

c = 35.0 A˚

carbon atom of SLG. The equilibrium height for the first model was from Zn atom

(15.98424 A,˚ 16.33 A,˚ 4.6 A)˚ of ZnTPP to SLG, which was 4.6 A.˚ For the second model the equilibrium height was 4.5 A,˚ from Zn atom (17.214 A,˚ 17.04 A,˚ 4.5 A)˚ to the carbon atom (17.21659 A,˚ 17.04 A,˚ 0.0 A)˚ of SLG. The energy of the first model was 394.547 kcal/mol and the second model was 393.713 kcal/mol. We performed geometry optimization of the second model. Variation in total energy as a function of separation between ZnTPP molecule and graphene for both models are shown below.

The figure of convergence, 4.8 (a) clearly depicts that the convergence criteria of energy (0.001 kcal/mol) was met because at the final optimization step, log10 = -3, then antilog(-3) = 0.001 kcal/mol, which was the required value. Again the gradient

30 (a)

(b) Figure 4.7: The variation in total energy of the ZnTPP-SLG with changes the sep- aration between ZnTPP and SLG with (a) a Zn atom of ZnTPP in the middle of hexagonal ring of SLG (b) a Zn atom of ZnTPP on the top of a carbon atom of SLG.

norm is smaller than 0.5 kcal/mol/A˚ as required. Thus the convergence criteria was fulfilled and energy was minimized.The total enthalpy of the system at optimization

31 step 110 became a constant value, i.e., 160 kcal/mol, while external pressure term was set to 0.0 GPa, which is shown in Figure 4.8 (b).

(a)

(b) Figure 4.8: (a) Forcite Geometrical Optimization- Convergence, purple; Grad.Norm (kcal/mol/A),˚ blue; Energy Change(kcal/mol) (b) Forcite Geometrical Optimization- Energy minimization.

32 4.2.3 C60ZnTPP-SLG System

The computational design and total energy calculations of C60ZnTPP-SLG were per- formed. Energies of this model structure were calculated by keeping the C60ZnTPP dyad at various separations from the SLG. This separation was in between the Zn atom of the C60ZnTPP dyad and SLG.The equilibrium separation was between Zn atom at position ( 15 A,˚ 15 A,˚ 5.1 A)˚ to SLG. Force fields were assigned for different kinds of atom groups. This structure with separation 5.1 A˚ was found with minimum energy and it was 1926.566 kcal/mol.

Geometry optimization calculation of this structure was done using a smart algorithm. The van der Waals force was very small between the C60ZnTPP dyad and SLG. Table 4.4 has the parameters that are used to calculate the energy and geometrical optimization.

Table 4.4: Parameters used in the energy calculation and geometrical optimization of C60ZnTPP-SLG.

Forcefield Types carbon atoms - C R

Nitrogen atoms - N 2

Zinc atom - Zn3+2

Hydrogen atoms - H

Supercell dimensions a = 36.888A˚

b = 38.34 A˚

c = 40 A˚

33 Figure 4.9: Snapshot of the C60ZnTPP-SLG model with periodic boundaries

Figure 4.10 represents the variation in total energy of the C60ZnTPP-SLG system with changes in separation between the C60ZnTPP dyad and SLG. The graph of convergence from forcite geometry optimization clearly shows that the convergence

34 Figure 4.10: The variation in total energy of the C60ZnTPP-SLG with change sepa- ration between C60ZnTPP and SLG.

criteria of energy (0.001 kcal/mol) are met because at the final optimization step, log10 = -3, then antilog(-3) = 0.001 kcal/mol. Again the gradient norm is smaller than 0.5 kcal/mol/A.˚

The graph of energy minimization depicts that the total enthalpy of the system at the optimization step 20 became a costant value, i.e., 662 kcal/mol, while the external pressure term was set to 0.0 GPa.

35 Figure 4.11: Forcite Geometrical Optimization- Convergence, purple; Grad.Norm (kcal/mol/ A),˚ blue; Energy Change (kcal/mol).

Figure 4.12: Forcite Geometrical Optimization- Energy minimization.

36 CHAPTER V

QUANTUM MECHANICS SIMULATION

The quantum chemistry computational was performed by the CP2K package. The calculates the structure and properties of molecules by de- veloping the mathematical description of the microscopic behaviour of matter using computer simulation [53]. In our work single point energy and geometry optimization calculations were done. The electron density and density of states calculations were performed.

5.1 Method

The energy, electronic structure and geometrical optimization calculations were per- formed by the Density Functional Theory (DFT) method using the CP2K simulation package. The Quick-step module [47] in the CP2K package was used to investigate the periodic structure. The exchange-correlation term in the Khon-Sham equation was approximated by Perdew-Burke-Erznerhof (PBE) [54]. The basis set DZVP-

MOLOPT [55] were used. The van der Waals interactions were described by using the semi-emperical DFT+D3 dispersion correction term [56].

37 5.1.1 Quickstep

DFT is an advanced technique to perform electronic calculations. It is a highly accurate method. Several properties of systems related to physics, chemistry, material science and biology can be predicted in a parameter-free way. DFT can also tackle large systems. The calculations of coulomb energy and orthogonalization of the wave function of large systems are not scaled linearly with system size, and because of that, these terms dominate cost of computation for large system. The hybrid Gaussian and plane waves (GPW) [57] technique offers an efficient methodology to enhance the computational efficiency as well as accuracy. The Quickstep module of DFT implements this method, which is part of the CP2K package.

In this method, atom-centered Gaussian type basis is used to describe the wave functions while auxiliary plane wave basis is used to describe the density. The efficiency of Fast Fourier Transforms (FFT) can be accomplished in order to solve the

Poisson equation and to get the Hartree energy in a time scale linear to the size of the system with the electron density represented as plane waves. FFT based treatment is also the best way to compute systems which are under periodic boundary conditions such as liquids and solids [58]. Plane wave codes and basis GPW are implemented in

CP2K, and they ensure that the nuclei are described using pseudo potentials. This approximation is highly suitable if Goedecker-teter-Hutter (GTH) pseudopotentials are used. All electron calculations can be performed with the extended GPW method, which is the Gaussian and augmented-plane-wave (GAPW) method (LHP99) [59].

38 5.1.2 Basis Sets

A basis set is a collection of simple functions used to develop complex shapes of molecular orbitals. There are mainly two types of basis functions: Slater type orbitals

(STO) and Gaussian type orbitals (GTO) [60]. The following function defines STOs,

STO η−1 −ζr η = Nr e Υlm(θ, ψ) (5.1)

where r, θ , ψ are spherical co-ordinates, Υlm is the angular momentum part, which defines the shape of orbitals, N is the normalization constant and ζ is the exponent. The n, l and m are principle, angular momentum and magnetic quantum numbers respectively.

Similarly, GTOs can be defined by the following function,

ηGT O = Ne−αrr xlymzn (5.2) where x, y, z are Cartesian co-ordinates and α is the exponent. The shape of STOs can be estimated by taking linear combinations of primitive GTOs with different ex- ponents. GTOs are easy to treat computationally. A basis set formed by a linear combination of three contracted Gaussian functions (CGF) is STO-3G, which is sim- ilar to STO. This type of basis set is called a single-zeta (SZ) basis set. Each type of orbital can be described by two or more functions for accuracy and better under- standing of the system. A basis set with two sets of basis function for each orbital is called double zeta (DZ), and a basis set with three functions is called triple zeta

(TZ). More sets of basis functions (larger zeta) are allocated to the valence electrons

39 in comparison with the core electrons and it makes a distinction between core and valence electrons,

5.1.3 Pseudopotentials

The DFT problem is only solved for the valence electrons in the GPW method, assuming that inner electrons are localized at the nuclei. The contribution of core electrons to the total energy is explained by a pseudopotential, which is taken instead of electron-nuclei coulomb potential of all electron calculation. For the GPW method

GTH pseudopotentials are used. It is an accurate and transferable pseudo potential.

It has an analytic form that permits for an excellent treatment of all the terms associated with the GPW method. GTH in Quick step is divided into a local part

(one-electron system) and a non local part (two-electron term). The valence electrons are described by using the DZVP-MOLOPT-SR basis set [55].

5.2 Results and Discussion

The single point energy calculation of all our atomic models were performed. We studied the electron density, highest occupied molecular orbital(HOMO) and lowest unoccupied molecular orbital (LUMO), density of states (DOS), adsorption energy of the model structures.

5.2.1 C60-SLG System

We calculated the total energies of this system by keeping the C60 molecule and

SLG at different separations (R) within a range of 2.5 to 4 A.˚ We found that the

40 structure had minimum energy at the equilibrium separation of 3.1 A.˚ The potential energy curve is plotted in Figure 5.1 as a function of R. The shape of the curve with negative value of the energy showed that the interaction of C60 with SLG is attractive.

The minimum energy was -1706.86 a.u.. After fully optimizing the structure, the equilibrium R was changed to 3.118 A.˚ The van der Waals interaction was included in our energy calculation to get the correct adsorption geometry of our hybrid structure.

Figure 5.1: The variation of total energy as a function of C60 and SLG separation in C60-SLG. One atomic unit of energy is 27.211 eV.

41 (a) (b)

(c)

Figure 5.2: (a) The optimized structure of the fullerene (C60) molecule. (b) The optimized structure of the supercell of graphene monolayer with 240 carbon atoms on it. (c) Side view of the optimized structure of C60-SLG structure.

42 The adsorption energy (EAd) was calculated by subtracting the energy of

isolated optimized C60 (EC60 ) and the energy of optimized SLG (EGr) from the total energy of the optimized C60-SLG system (ET ot), as given by the equation below.

EAd = [ET ot − (EGr + EC60 )] (5.3)

Table 5.1: The energies of optimized structures.

EC60 - 340.956 a.u.

EGr - 1365.894 a.u.

ET ot - 1706.873 a.u.

EAd = −0.023au = −0.625eV (1au = 27.211eV ) (5.4)

The adsorption energy of the structure determines its relative stability. The calculated adsorption energy was - 0.625 eV. This showed that the interaction was weak. Our adsorption energy and geometry obtained was in good agreement with previous experimental and theoretical studies [52]. This value of energy shows that

C60 is not tightly bound but it can move around the surface due to thermal effect.

Moreover, the intrinsic properties of graphene may not change significantly due to this weak interaction strength.

The energy gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of a macro molecule determines its 43 electronic properties and conduction. For the higher conduction, the molecule should have a small HOMO-LUMO energy gap.The difference in energy between HOMO- zero and LUMO + zero states gives the HOMO-LUMO gap. In our work, we found a

0.878 eV HOMO-LUMO gap for the C60-SLG system, which was in good agreement with experimental results [1]. We had calculated the energy of five HOMO and five

LUMO. The energies of all ten molecular orbitals are shown in Figure 5.3.

Figure 5.3: Energies of five HOMO and five LUMO along with the HOMO-LUMO energy gap.

44 In order to study the energy band structure near to the Fermi level, we calculated Khon-sham wave functions. The electronic structure of C60-SLG at LUMO is shown in Figure 5.4. It was found that the electron cloud in LUMO is mostly distributed in C60 than in SLG.

Figure 5.4: Electronic profiles of LUMO of C60-SLG structure. The isosurface value is ± 0.01 (distinguished by blue/red) in atomic unit.

5.2.2 ZnTPP-SLG System

Total energies of this structure was calculated for different separations (R) between the C60 molecule and SLG. The structure had minimum energy at the equilibrium separation of 4.3A.˚ The potential energy curve is plotted in Figure 5.1 as a function of R. The shape of the curve with a negative value of the energy showed that the interaction of ZnTPP with SLG is attractive. The minimum energy was -2915.098 a.u.. The van der Waals interaction was included in our energy calculation to get the correct adsorption geometry of our hybrid structure.

45 Figure 5.5: The variation of total energy as a function of the separation of ZnTPP and SLG in the ZnTPP-SLG structure. One atomic unit of energy is 27.211 eV.

5.2.3 C60ZnTPP-SLG System

By keeping the C60ZnTPP dyad at various separations from SLG, we found a mini- mum energy structure at a separation of 5.3 A.˚ The change in total energy with the separation is shown in Figure 5.6 as a function of R. The shape of the curve with a negative value of the energy showed that the interaction of ZnTPP with SLG is attractive. The minimum energy was -3807.6760 a.u.. The van der Waals interaction was included in our energy calculation to get the correct adsorption geometry of our hybrid structure.

46 Figure 5.6: The variation of total energy as a function of the separation of C60ZnTPP dyad and SLG in the C60ZnTPP-SLG structure.

5.2.4 Density of States

The density of states (DOS) of a system is the number of available states for electrons at a particular energy level, i.e., the number of electronic states per unit volume per unit energy [44]. DOS describes the general distribution of states as a function of energy. A low DOS at a particular energy level means that there are only a few states available for occupation. Similarly there is no states can be occupied if the DOS of that energy level is zero.

If a system has a non-zero DOS at the Fermi level, then at a finite temperature there will always be probability electrons to transfer its state from one just below or

47 above the Fermi level. That means the electrons will have free states available at an small energy difference and hence they will be able to conduct and the system is a metal. In opposition to that, if the DOS is zero at the Fermi level, the electrons will not have any new states available and hence there will be no conduction of electrons and the system is either a semi conductor or insulator.

In our work we compared the DOS of all the models. They had non-vanishing

DOS at Fermi level, which implied that they were capable of conducting electrons at some external electric fields. All systems had a higher DOS at the Fermi level than that of SLG. The availability of states has gradually increased above Fermi level in all the systems.

In the C60-SLG system, the DOS at the Fermi level was less than that of

SLG and all other systems. There was an available state just above and below the

Fermi level, which can be seen in Figure 5.5. Its band gap was 0.87 eV, which was higher than the band gap of all other structures. We believed that this structure is not metallic.

DOS of the ZnTPP-SLG system at Fermi level was less than that of the

C60ZnTPP-SLG system. Figure 5.6 shows that this system has available states just below and above Fermi level but not at Fermi level. Its bandgap was 0.656 eV. This value is less than that of C60-SLG system. It might be due to same partially filled states just above Fermi level.

Finally, the C60ZnTPP-SLG system had more DOS than the other two sys- tem. It also did not have available states just below and above the Fermi Level, but

48 other than that, it had available states. It had number of partially filled energy states above Fermi level, which indicated that it was metallic.

Figure 5.7: DOS for the C60-SLG. The Fermi energy is shifted to zero.

49 Figure 5.8: DOS for the ZnTPP-SLG. The Fermi energy is shifted to zero.

50 Figure 5.9: DOS for the C60ZnTPP-SLG. The Fermi energy is shifted to zero.

51 Figure 5.10: DOS for the SLG. The Fermi energy is shifted to zero.

52 CHAPTER VI

CONCLUSION

In the present work, we created and studied three different atomic models of nano materials, C60-SLG, ZnTPP-SLG and C60ZnTPP-SLG, by classical and quantum molecular mechanics simulations. The classical simulation was carried out using

Material Studio software, while the quantum simulations were done using the CP2K package.

Molecular devices from hybrids of graphene as electron acceptor, with C60 and porphyrin, as electron donors are favorable for the solar cell. Non bonding interaction of C60 and ZnTPP with graphene was found less than their dyad C60ZnTPP. This showed that C60ZnTPP and SLG were more strongly bonded than other molecules with SLG. Also the van der Waals interaction is stronger in C60ZnTPP-SLG. The

HOMO-LUMO gap in ZnTPP-SLG was found less than C60 structures, which was

0.656 eV. But C60ZnTPP shows metallic character. The C60ZnTPP-SLG had a higher

DOS value than the others. It was confirmed that this structure has more available states and better conductivity than the other two structures.

We anticipate that the creation of electrically conducting models in our work may provide insight for the development of help for more efficient material design and they will open up new way for future optical and electronic device applications.

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