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A Computational Study of Surface Adsorption and Desorption

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Title:
A Computational Study of Surface Adsorption and Desorption
Creator:
WANG, LIN-LIN ( Author, Primary )
Copyright Date:
2008

Subjects

Subjects / Keywords:
Adsorption ( jstor )
Electron density ( jstor )
Electronics ( jstor )
Electrons ( jstor )
Hexagons ( jstor )
Ions ( jstor )
Potential energy ( jstor )
Pseudopotentials ( jstor )
Simulations ( jstor )
Work functions ( jstor )

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Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright Lin-Lin Wang. Permission granted to University of Florida to digitize and display this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Embargo Date:
4/30/2004
Resource Identifier:
55802505 ( OCLC )

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Full Text











A COMPUTATIONAL STUDY OF SURFACE ADSORPTION AND DESORPTION


By

LIN-LIN WANG

















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2004


























Copyright 2004

by

Lin-Lin Wang


































To my parents.
















ACKNOWLEDGMENTS

I have benefited from numerous people and many facilities during my graduate

study at the University of Florida. First, I would like to acknowledge my advisor,

Professor Hai-Ping Cheng, whose enthusiasm and expertise were greatly appreciated. I

would also like to thank Professors James W. Dufty, Arthur F. Hebard, Jeffery L. Krause

and Samuel B. Trickey for serving on my supervisory committee.

I am very grateful for many current and former members of the Quantum Theory

Project for their support. Of special note are Dr. Ajith Perera, Dr. Magnus Hedstroim, and

Dr. Andrew Kolchin. I spent a wonderful student life in the University of Florida with

numerous friends. They are Dr. Mao-Hua Du, Mr. Chun Zhang, Dr. Rong-Liang Liu, Dr.

Lin-Lin Qiu, Dr. Zhi-Hong Chen, Mr. Xu Du, Mr. Ling-Yin Zhu, Mr. Wu-Ming Zhu, Mr.

Chun-Lin Wang and many others. At last, I would like to thank my loving parents, Xue-

Ping Li and Xiang-Jin Wang, and my beautiful wife, Dr. Yi Wu, for their endless support.

This work has been supported by DOE/Basic Energy Science/Computational

Material Science under contract number DE-FGO2-97ER45660



















TABLE OF CONTENTS


page

ACKNOWLEDGMENT S .............. .................... iv

LIST OF T ABLE S ............ ..... ._ .............. vii...

LI ST OF FIGURE S ............ ..... ._ .............. viii..

AB STRAC T ................ .............. xi

CHAPTER


1 OVERVIEW ................. ................. 1...............


2 DENSITY FUNCTIONAL STUDY OF THE ADSORPTION OF A C60
MONOLAYER ON NOBLE METAL (111) SURFACES ................... ...............6

2. 1 Introducti on .................. ......__ ........._ ............
2.2 Theory, Method, and Computational Details ............_......__ ................11
2.2. 1 DFT Formulism with a Plane Wave Basis Set............_ .........._ .....11
2.2.2 Computational Details ....._ .....___ ........__ ............1
2.3 Results and Discussion............ .............__ ............._ ........1
2.3.1 Adsorption of a C60 ML on Cu(l111) Surface............_ ........._ .......16
2.3.1.1 Energetics and Adsorption Geometries............... ...............1
2.3.1.2 Electronic Structures .............. .. ............. .. ............1
2.3.1.3 Electron Density Redistribution and Work Function Change..........24
2.3.2 Adsorption of a C60 ML on Ag (1 11) and Au( 111) Surfaces ................... ..30
2.3.2.1 Energetics and Adsorption Geometries............... ...............3
2.3.2.2 Electronic Structure and Bonding Mechanism............... ................3
2.3.2.3 W ork Function Change .............. ...............40....
2.3.2.4 Simulated STM Images .................._...... ............... 45.....
2.3.2.5 Difference in Band Hybridization ....._____ .........__ ..............47
2.3.3 Adsorption of C60 ML on Al(1 11) and Other Surfaces .............. ................48
2.3.4 Adsorption of SWCNT on Au(111) Surface ................. ......................51
2.4 Conclusion ................ ...............57.................


3 MOLECULAR DYNAMICS SIMULATION OF POTENTIAL SPUTTERING ON
LiF SURFACE BY SLOW HIGHLY CHARGED IONS ................. ............... ....59

3 .1 Introducti on ................. ...............59........... ...












3.2 Modeling and Simulation .............. ..... ... ..............6
3.2.1 Calculations of Potential Energy Functions .............. ....................6
3.2.2 Two-body Potentials for MD Simulation ......___ ..... ...._ ..............71
3.2.3 Simulation Details .............. ...............75....
3.3 Results and Discussion .............. ...............76....
3.3.1 Initial Condition............... ...............7
3.3.2 Surface M odification ........._. ....._...... ...............77...
3.3.3 Sputtering Yield............... ...............80.
3.3.4 Profile of Dynamics ..............__......._. ...............85...
3.4 Conclusion .............. ...............89....


4 AN EMBEDDING ATOM-JELLIUM MODEL ................. ................. ........ 90


4. 1 Introducti on ................. .. ...... ..... ...... ........... ........ .......9
4.2 DFT Formulism for Embedding Atom-j ellium Model............ ............_ ...92
4.3 Results and Discussion .............. ...............95....


5 FRACTURE AND AMORPHIZATION IN SiO2 NANOWIRE STUDIED BY A
COMBINED MD/FE METHOD ....._ .....___ .........__ ............9


5 .1 Introducti on ............ .......__ ...............98.
5.2 M ethodology .............. ... ... ........ ... ............10
5.2. 1 Summary of Finite Element Method ............ ..... ._ ...............100
5.2.2 Hybrid MD/FE: New Gradual Coupling ............ ..... ._ ..............104
5.3 R esults................ .. ..............10
5.3.1 Interface Test .............. ...._... ...............107..
5.3.2 Stretch Simulation ........._.._.._ ...._.._....._. ....... .....1


6 SUMMARY AND CONCLUSIONS ...._.._.._ ..... .._._. .....__.............1



APPENDIX


A TOTAL ENERGY CALCULATION OF SYSTEM WITH PERIODIC
BOUNDARY CONDITIONS ........._._. ...._... ...............115....


B REVIEW OF DEVELOPMENT IN FIRST-PRINCIPLES PSEUDOPOTENTIAL125


B. 1 Norm-Conserving Pseudopotential ................ ...............125...............
B.2 Ultrasoft Pseudopotential and PAW ................. ...............131........... ...


LI ST OF REFERENCE S ................. ...............143................


BIOGRAPHICAL SKETCH ................. ...............156......... ......

















LIST OF TABLES


Table pg

2-1. Structural and energetic data of an isolated C60 mOlecule ................. ................ ...15

2-2. Structural and energetic data for bulk Cu, Ag, Au, clean Cu(111), Ag(1 11) and
A u(111) surfaces. ............. ...............15.....

2-3. Work function change of a C60 ML adsorbed on a Cu(l111) surface............._..._.. .......28

2-4. Adsorption energies of a C60 ML on Ag( 111) and Au( 111) surfaces ........................3 1

2-5. The relaxed structure of a C60 ML adsorbed on Ag( 111) and Au( 111) surfaces with
its lowest energy configuration. ............. ...............33.....

2-6. Work function change of a C60 ML adsorbed on Cu(l111), Ag( 111) and Au( 111)
surfaces ................. ...............41.................

3-1. Sputtering yields of ten MD simulations with different initial conditions. ...............83


















LIST OF FIGURES


Figure pg

2-1. Surface geometry and adsorption sites for a C60 ML on a Cu(111) surface ...............17

2-2. Adsorption energies as functions of rotational angle for a C60 ML on a Cu(l111)
surface. ............. ...............18.....

2-3. Total density of states and partial DOS proj ected on the C60 ML and the Cu(l111)
surface. ............. ...............19.....

2-4. Band structure for the adsorption of a C60 ML on a Cu(l111) surface. .......................20

2-5. DOS of an C60 ML before and after its adsorption on a Cu(l111) surface. ................21

2-6. Partial DOS of different adsorption configurations for a C60 ML on a Cu(l111)
surface. ............. ...............23.....

2-7. Iso-surfaces of electron density difference for a C60 ML on a Cu(l111) surface.. ......25

2-8. Planar averaged electron density differences and the change in surface dipole
moment for the adsorption of a C60 ML on a Cu(l111) surface. ............. ................26

2-9. Work function change and electronic charge transfer as functions of the distance
between a C60 ML and a Cu(111) surface. ............. ...............29.....

2-10. Surface geometry and adsorption sites for a C60 ML on Ag(1 11) and Au(111)
surfaces............... ...............31

2-11i. Adsorption energies as functions of rotational angle of C60 ML on Ag( 111) and
A u(111) surfaces. ............. ...............32.....

2-12. Density of states of a C60 ML on Ag(1 11) and Au(111) surfaces. ...........................35

2-13. Iso-surfaces of electron density difference for the adsorption of a C60 ML on
Ag( 111) and Au(111) surfaces. .............. ...............36....

2-14. Partial DOS of different adsorption configurations for a C60 ML on Ag( 111) and
A u(111) surfaces. ............. ...............39.....

2-15. Planar averaged electron density differences and the change in surface dipole
moment of a C60 ML on Ag( 111) and Au( 111) surfaces. ............. ....................42










2-16. Work function change and electronic charge transfer as functions of the distance
between the C60 and the metal surfaces ................. ...............45........... ..

2-17. Simulated STM images of a C60 ML on Ag( 111) and Au( 111) surfaces. ................46

2-18. Difference in electronic structures for the adsorption of a C60 ML on noble metal
(111) surfaces. ............. ...............47.....

2-19. Density of states for the adsorption of a C60 ML on a Al(1 11) surface ................... .49

2-20. Electron density difference and change in surface dipole moment for a C60 ML on a
Al(111)surface ................. ...............50........... ...

2-21. Density of states for the adsorption of a (5,5) SWCNT on a Au( 111) surface. .......54

2-22. Electron density difference and change in surface dipole moment for a (5,5)
SWCNT on a Au(111)surface. ............. ...............55.....

2-23. Density of states for the adsorption of a (8,0) SWCNT on a Au( 111) surface. .......56

2-24. Electron density difference and change in surface dipole moment for a (8,0)
SWCNT on a Au(111)surface. ............. ...............56.....

3-1. Calculated ground state potential energy function for (Li Li ) from CCSD[T]. .......64

3-2. Calculated ground state potential energy function for (F ) from CCSD[T].......... .65

3-3. Calculated potential energy functions for (Li F ) and (LioFo) from CCSD[T]..........66

3-4. Calculated potential energy functions for (Li Lio) from CCSD[T].............._._..........67

3-5. Calculated potential energy functions for (LioF ) from CCSD[T]. ............................67

3-6. Calculated potential energy functions for (LioLio) from CCSD[T]............._.._. .........68

3-7. Calculated potential energy functions for (Li Fo) from CCSD[T]. ............................68

3-8. Calculated potential energy functions for (FoF )from CCSD[T]. ........._.... .............69

3-9. Calculated potential energy functions for (FoFo) from CCSD[T] ........._..... .............69

3-10. Potential energy functions for ground state (Li+ ). ............. .....................7

3-11i. Four sets of potential energy functions for each species in LiF surface used in the
M D simulations. ............. ...............73.....

3-12. Snapshot of the LiF surface at t = 0 for simulation 6. ............. .....................7

3-13. Snapshot of the LiF surface at t = 1.2 ps for simulation 6 ................... ...............77










3-14. Snapshot of the the LiF surface at t = 1.2 ps for simulation 9. ............. .................78

3-15. Distribution functions of the number of particles and potential energy along the z
direction at t =1.2 ps for simulation 6............... ...............79...

3-16. Distribution functions of the kinetic energy along the z direction at t = 1.2 ps for
sim ulation 6. ............. ...............84.....

3-17. Normalized angular distribution functions of the neutral particles averaged over
simulations 3, 6, 7, and 8 at t =1.2 ps. ............. ...............85.....

3-18. Distribution functions of the number of particles and potential energy along the z
direction of Lio at different time instants for simulation 6..........._.._.. ........._.._... .86

3-19. Distribution functions of the number of particles and potential energy along the z
direction of Fo at different times for simulation 6. ........._.._.. ......._.._........._..87

4-1. A jellium surface modeled by a seven-layer Al slab with 21 electrons. ....................95

4-2. The quantum size effect of jellium surfaces, (a) Al and (b) Cu. ............. .................96

4-3. Partial density of states projected on atomic orbitals. ................ ............ .........97

5-1. Geometry of the a-cristobalite (SiO2) HanOwire............... ...............10

5-2. Energy conservation test with respect to time for (a) FE only, (b) MD only, and (c)
both FE and MD. ........... ..... ._ ...............108..

5-3. Distributions of force and velocity in the y direction during a pulse propagation test
for the MD/FE interface. ............. ...............109....

5-4. The stress-strain relation for a uniaxial stretch applied in the y direction of the
nanowire at speed of 0.035 ps' ......__ ....._____ ......___ ...........1

5-5. Five snapshots from the tensile stretch applied in the y direction of the nanowire at
speed of 0.035 ps ..........__ ...............111.___ ....

5-6. Pair correlation functions of the nanowire during the uniaxial stretch simulation...1 12
















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

A COMPUTATIONAL STUDY OF SURFACE ADSORPTION AND DESORPTION

By

Lin-Lin Wang

May 2004

Chair: Hai-Ping Cheng
Major Department: Physics

In this work, the phenomena of surface adsorption and desorption have been

studied by various computational methods. Large-scale density functional calculations

with the local density approximation have been applied to investigate the energetic and

electronic structure of a C60 mOnolayer adsorbed on noble metal (111) surfaces. In all

cases, the most energetically preferred adsorption configuration corresponds to a hexagon

of C60 adsorbing on an hcp site. A small amount of electronic charge transfer of 0.8, 0.5

and 0.2 electrons per molecule from the Cu(111), Ag(1 11) and Au(111) surfaces to C60

has been found. We also find that the work function decreases by 0.1 eV on Cu(111)

surface, increases by 0.1 eV on Ag(1 11) surface and decreases by 0.6 eV on Au(111)

surface upon the adsorption of a C60 mOnolayer. The puzzling work function change is

well explained by a close examination of the surface dipole formation due to electron

density redistribution in the interface region.

Potential sputtering on the lithium fluoride (LiF) (100) surface by slow highly

charged ions has been studied via molecular dynamics (MD) simulations. A model that is









different from the conventional MD is formulated to allow electrons to be in the ground

state as well as the low-lying excited states. The interatomic potential energy functions

are obtained by a high-level quantum chemistry method. The results from MD

simulations demonstrate that the so-called defect-mediated sputtering model provides a

qualitatively correct picture. The simulations provide quantitative descriptions in which

neutral particles dominate the sputtering yield by 99%, in agreement with experiments.

An embedding atom-j ellium model has been formulated into a multiscale

simulation scheme to treat only the top metal surface layers in atomistic pseudopotential

and the rest of the surface in a j ellium model. The calculated work functions of Al and Cu

clean surfaces agree well with the all-atomistic calculations. The multiscale scheme of

combining finite element (FE) and MD methods is also studied. A gradual coupling of

the FE and MD in the interface region is proposed and implemented, which shows

promising results in the simulation of the breaking of a SiO2 HanOwire by tensile stretch.















CHAPTER 1
OVERVIEW

The importance of understanding surface phenomena stems from the fact that for

many physical and chemical phenomena, a surface plays a key role. A better

understanding and, ultimately, a predictive description of surface and interface properties

is vital for the progress of modern technology, such as catalysis, miniaturization of

electronic circuits, and emerging nanotechnology.

The richness of physical and chemical properties of surfaces finds its fundamental

explanation in the arrangement of atoms, the distribution of electrons, and their response

to external perturbations. For examples, the processes of surface adsorption and

desorption are the results of the interplay between geometric structure and electronic

structure of the adsorbate and substrate. The ground state electronic structure fully

determines the equilibrium geometry of the adsorption system. The ground state

electronic structure also largely determines the chemical reaction and dynamics on the

surface, such as transition states and reaction barriers. Nevertheless, more severe

processes of surface dynamics, such as surface desorption stimulated by external laser

fields, electron and charged ion bombardments, always involve electronic excited states

and energy exchange between electronic and ionic degree of freedom. To study these

processes, the electronic structure of excited states must be included.

Computer simulation has been proved to be a powerful tool, besides experiment

and theory, to study surface science in recent decades. There are two categories of

simulation, which are characterized by the degrees of freedom they consider and the










implemented scales. One is molecular dynamics (MD) [1], which treats atoms and

molecules as classical particles and omits the degrees of freedom from the electrons. The

other is quantum mechanical methods, which treats electrons explicitly. Although the two

kinds of simulation are different, they are strongly connected and compose a hierarchy of

knowledge of the system studied. In MD, classical particles move according to the

coupled Newton's equations in force fields. Although no electron is included in such

simulations, the force fields have input in principle from electronic information. In

quantum mechanical methods, the Schroidinger equation is solved to include the many-

body interaction among electrons explicitly. Once the electronic structure is known, the

total energy of the system can be calculated. Molecule dynamics can be done with the

force calculated from first-principles.

To solve a many-body Schroidinger equation, two categories of methods are

available. Traditionally, in quantum chemistry [2], wave-function-based methods are

pursued, such as the Hartree-Fock method, which only treats the exchange effect of

electrons explicitly. The omitted correlation effect of electrons is included by many post

Hartree-Fock methods, such as configuration interaction (CI) and various orders of many-

body perturbation theory (MBPT). The coupled-cluster method is closely related, in that

the correlation effect of electrons can be improved systematically by considering the

single, double, triple, etc, excitations.

Recently, the electron-density based method, i.e., density functional theory

(DFT) [3, 4], has become popular because it can reach intermediate accuracy, comparable

to single CI, at relatively low computational cost. According to the Hohenberg-Kohn

theorem [5, 6], the ground state total energy of an electronic system is a unique functional









of the electron density. The exchange-correlation (XC) energy from the many-body

effects can be treated as a functional of electron density. Thus, DFT in the Kohn-Sham

approach maps the many-body problem for interacting electrons into a set of one-body

equations for non-interacting electrons subj ected to an effective potential. The proof of

the Hohenberg-Kohn-Sham theorems and related development of XC functional of

electrons are not the focus of this work. The remaining one-particle Kohn-Sham (KS)

equation still poses a substantial numerical challenge. Among the various strategies,

plane wave basis sets with pseudopotentials stands out as a popular choice because of its

efficiency. In the past decade, new developments in pseudopotential formalism, more

efficient algorithm in iterative minimization, and faster computer hardware have made

large-scale, first-principles DFT simulation treating hundreds of atoms a reality.

In this dissertation, we use all of these methods to study the phenomenon of surface

adsorption and desorption. In Chapter 2, the ground state properties of a C60 mOnolayer

(ML) adsorbed on noble metal (Cu, Ag and Au) (111) surfaces are studied by large-scale

DFT calculations. The adsorption energetic, such as the lowest energy configuration,

translational and rotational barriers are obtained. Electronic structure information, such as

density of states, charge transfer, and electron density redistribution, are also studied.

With the detailed information on electronic structure, we explain very well the opposite

change of work function on Cu and Au surfaces vs. Ag surface, which has been a

puzzling phenomenon observed in experiments.

In Chapter 3, we study a surface dynamical process, the response of a LiF(100)

surface to the impact of highly charged ions (HCI) via MD simulation. We extend the

conventional MD formalism to include the forces from electronic excited states









calculated by a high-level quantum chemistry method. Within this new model, the so-

called potential sputtering mechanism is examined by MD simulations. Our results agree

well with the experimental results on the sputtering pattern and the observation of

dominant sputtering yield in neutral particles. We found that the potential sputtering

mechanism can be well-explained by the two-body potential energy functions from the

electronic excited states.

We will also address the issues of multiscale simulation in Chapter 4 and 5. There

are two maj or reasons for multiscale simulations. One is the compromise between

accuracy and efficiency. Only a crucial central region needs to be treated in high accurate

method; the surrounding region can be treated in less accurate, but more computationally

tractable approximation. In Chapter 4, we consider using j ellium model as a simplified

pseudopotential together with the atomistic pseudopotential to study the properties of

metal surfaces in DFT calculation. The other reason to do multiscale simulation, which is

more important, is that some phenomena in nature are intrinsically scale-coupled in

different time, length and energy scales. For less scale-coupled phenomena, a sequential

multiscale scheme usually works Eine. One such example is the potential sputtering on

LiF surface by HCI studied in Chapter 2. In that study, first, a highly accurate quantum

chemistry method is used to calculate the potential energy functions. Then this

information is fed to the MD simulation to study the dynamical processes. For strongly

scale-coupled phenomena, only an intrinsic multiscale model can capture all the relevant

physical processes, for example, material failure and crack propagation. The stress Hield,

plastic deformation around the crack tip, and bond breaking inside the crack tip all

depend on each other. These three different length scales are coupled strongly. In Chapter






5


5, we construct a combined finite element and molecule dynamics method to investigate

the breaking of a SiO2 HanOWife.















CHAPTER 2
DENSITY FUNCTIONAL STUDY OF THE ADSORPTION OF A C60 MONOLAYER
ON NOBLE METAL (111) SURFACES

2.1 Introduction

Ever since its discovery [7], C60 has attracted much research attention because of its

extraordinary physical properties and potential application in nanotechnology. The

adsorption of the C60 mOlecule on noble metal surfaces has been studied intensively in

experiments over the last decade [8]. Due to the high electron affinity of the C60 mOleCUle

as well as the metallic nature of the surfaces, the interaction has been understood in terms

of electronic charge transfer from noble metal surfaces to the adsorbed C60 mOnolayer

(ML). According to the conventional surface dipole theory, all noble metal surfaces

should have an increase in work function upon the adsorption of a C60 ML. However, a

small decrease in work function on Cu surfaces [9] and Au surfaces [10], and a small

increase in work function on Ag surfaces [l l] have been observed in experiments with

the adsorption of a C60 ML. Electronic charge transfer alone can not explain this

phenomenon [9, 10, 12]. Furthermore, the most preferred adsorption site and orientation

of the C60 ML on Ag( 111) and Au( 111) surfaces are still unclear [13-16]. All these basic

issues require additional insight to understand the fundamental nature of the interaction.

Evidence for electronic charge transfer from noble metal (111) surfaces to C60 has

been observed in various experiments. The C60-Cu film is ai system in which fascinating

phenomena have been observed in studies of conductance as a function of the thickness

of Cu film [17]. Experiments indicate that when a C60 mOnolayer is placed on top of a










very thin Cu film, the resistance of the monolayer is measured about 8000 02, which leads

to resistivity corresponding to half of the three-dimensional alkali-metal-doped

compounds A3 60 (A=K, Rb). When the C60 iS beneath the Cu film, the ML also

enhances the conductance. It is suggested from experimental analysis that the

enhancement of conductance in the C60-CU Systems is due to charge transfer from Cu to

C60 at the interface. Further experimental measurements indicate that when the thickness

of the Cu film increases, the resistance curves cross. As the thickness of the Cu film

increases, the conductance of the film increases to approach the bulk Cu limit, which is

much higher than the conductance of the electron-doped C60. When the thick Cu film is

covered with a C60-ML, the resistance of the system is increased. This effect is

understood as a result of the diffusive surface scattering process.

More direct evidence for electronic charge transfer from noble metal (111) surfaces

to an adsorbed C60 mOnolayer come from photon emission spectroscopy (PES). In

valence band PES [9, 10, 18-25], a small peak appears just below the Fermi level due to

the lowest unoccupied molecule orbital (LUMO) derived bands of the C60, which cross

the Fermi level and are partially filled upon adsorption. In carbon 1s core level PES [9,

10, 18, 19, 21, 24, 26], the binding energy shifts toward lower energy and the line shape

becomes highly asymmetric due to the charge transfer. Modification in the electronic

structure of the molecules is also found to be responsible for the enhancement in Raman

spectroscopy [19, 27-3 1]. A substantial shift of the Ag(2) pentagonal pinch mode to lower

frequency for C60 mOlecule adsorbed on noble metal surfaces has a pattern similar to that

from the alkali metal doped C60 COmpound.









In regard to the magnitude of electronic charge transfer from noble metal surfaces

to an adsorbed C60 mOnolayer, different techniques give different results. By comparing

the size of the shift of the Ag(2) mode in Raman spectroscopy between C60 adsorbed on

polycrystalline noble metal surfaces and that for K3 60, a charge transfer of less than

three electrons per molecule can be derived [19]. In valence PES studies, the intensity of

the C60 LUMO-derived bands is compared to the intensity of the C60 HOMO-derived

bands or the intensity of the C60 LUMO-derived bands co-adsorbed with alkali metals.

These studies indicate that 1.6, 0.75 and 0.8 electrons per molecule are transferred from

Cu(111) [10], Ag(1 11) [22] and Au(111) [10] surfaces to the C60 mOnolayer. Another

study shows that 1.8, 1.7 and 1.0 electrons per molecule are transferred from

polycrystalline Cu, Ag and Au surfaces, respectively, to the C60 mOnolayer [20]. Based

on the observed electronic charge transfer, the interaction between the C60 and the noble

metal surfaces is assigned as ionic in nature.

The geometry of an adsorbed C60 mOnolayer on noble metal (111) surfaces has

been studied in numerous STM experiments [13-16, 32-42] as well as by x-ray diffraction

experiments [43-46]. At the beginning of the adsorption on these surfaces, C60 iS mobile

on the terrace and occupies initially the step sites to form a closely packed pattern. After

the first monolayer is complete, C60 forms a commensurate hexagonal (4x4) structure on

the Cu(111) surface. On the Ag(1 11) surface, C60 forms a commensurate hexagonal

(22/ x 2 )R30o structure, and some additional structures rotated by 14o or 46o from the

foregoing structure [16]. Then after annealing, only the (2J x 2 5)R30o structure

remains, which indicates that this is the most energetically favored structure. On the

Au(111) surface, the adsorption configuration is more complicated, due to reconstruction









of the free Au( 111) surface. In addition to the commensurate hexagonal

(2J x 2 S)R30o structure and the rotated structures, C60 Can alSo form a (38x38) in-

plane structure [13-15, 36, 37]. After annealing, only the well-ordered (2J x 2l~ )R30o

structure remains. The reconstruction of the free Au( 111) surface is lifted. Recently,

another commensurate close-packed (7x7) structure was proposed [39].

Considering the adsorption site and the orientation of the C60 mOnolayer in the

(4x4) structure on the Cu(1 11) surface, the Sakurai group [33] found that C60 adsorbs on

a threefold hollow site with a hexagon parallel to the surface. They observed clearly a

threefold symmetric STM image of C60 with a ring shape and a three-leaf shape for

negative and positive bias respectively. So it must be a hexagon of C60 parallel to the

Cu(l111) surface. With this orientation, because of the nonequivalent 600 rotation, there

should be only two domains in the well-ordered (4x4) structure if C60 Occupies the on-top

site. Their observation shows four domains, which indicates that C60 Occupies the

threefold hollow sites, both hcp and fcc sites. For the ( 2J x 2J )R30O" structure of C60

on the Ag(1 11) and Au(111) surfaces, Altman and Colton [13-15] proposed, on the basis

of experimental STM images, that the adsorption configuration is a pentagon of C60 On an

on-top site for both surfaces. However, Sakurai et al. [16], again based on interpretations

of experimental STM images, proposed that the adsorption site is the threefold hollow

site for the Ag( 111) surface, in analogy to the (4x4) structure of C60 mOnolayer adsorbed

on the Cu(l111) surface [33]. But they did not specify the orientation of the C60 mOleCUleS

on the Ag(1 11) surface.

Despite the large amount of experimental data on electronic, transport, and optical

properties, many basic issues remain unanswered. Although electronic charge transfer









from the noble metal substrates to the C60 OVer-layer is evident, the work function

actually decreases on the Cu(111) surface by 0.08 eV [9], decreases on the Au(111)

surface by 0.6 eV [10], and increases on the Ag(110) surface by 0.4 eV [1l], which

cannot be understood at all within the simple description of surface dipole layer

formation due to charge transfer that is ionic in nature. Furthermore, the adsorption site

and orientation of the C60 mOnolayer on Ag( 111) and Au( 111) surfaces are still in

debate [13-16]. All these basic issues require additional insight to understand the

fundamental nature of the interaction between the noble metal (1 11) surfaces and the

adsorbed C60 mOnolayer.

On the theoretical side, very few first-principles calculations of C60-metal

adsorption systems have been performed. Such calculations involve hundreds of atoms,

and so the calculations are computationally demanding. There were density functional

calculations treating a C60 mOlecule immersed in a jellium lattice to mimic the presence

of the metal surface [47]. Only recently, a system consisting of an alkali-doped C60

monolayer and an Ag(1 11) surface has been calculated fully in first-principles to study

the dispersion of the C60 LUMO-derived bands [48]. In addition, the (6x6) reconstruction

phase of a C60 mOnolayer adsorbed on an Al(1 11) surface has been studied by first-

principles density functional calculations [49].

In this work, we study the adsorption of a C60 mOnolayer on noble metal (1 11)

surfaces using large-scale first-principles DFT calculations. We address a collection of

issues raised in a decade of experimental work, such as C60 adsorption sites and

orientation, barriers to translation and rotation on the surface, surface deformation,

electronic structure, charge transfer and work function change. The chapter is organized









as follows. In Section 2.2, the basics of DFT total energy calculations using a plane wave

basis set and pseudopotential are outlined, and the computational details described. In

Section 2.3, we present calculated results and discussion. The adsorption of C60 On the

Cu(111) surface is presented in Section 2.3.1. In Section 2.3.2, we show results for C60

adsorbed on Ag(1 11) and Au(111) surfaces. As a comparative study, we also show

results for a C60 ML adsorbed on Al(111) surface in Section 2.3.3 and a single wall

carbon nanotube (SWCNT) adsorbed on Au(111) surface in Section 2.3.4.

2.2 Theory, Method, and Computational Details

2.2.1 DFT Formalism with a Plane Wave Basis Set

In this work, DFT [5, 6] total energy calculations have been used to determine all

structural, energetic and electronic results. The Kohn-Sham (KS) equations are solved in

a plane wave basis set, using the Vanderbilt ultrasoft pseudopotential [50, 51] to describe

the electron-ion interaction, as implemented in the Vienna ab initio simulation program

(VASP) [52-54]. Exchange and correlation are described by the local density

approximation (LDA). We use the exchange-correlation functional determined by

Ceperly and Alder [55] and parameterized by Perdew and Zunger [56].

According to the Hohenberg-Kohn theorem [3-6], the ground state total energy of

an electronic system is a unique functional of the electron density


E= F n(r) +V n', (r)]
(2-1)



where To is the kinetic energy of non-interacting electrons, Exe is the exchange-

correlation energy, which includes all the many-body effects, and Es is the electrostatic









energy due to the Coulombic interaction among electrons and ions. They are all

functionals of the electron density


n(r)= [wkf n,k 2,k (2-2)


which has been expressed in Bloch wave functions r/2,k, () for electrons in a system with

period boundary condition (PBC). The index of i and k are for the state and k-point,

respectively. The integral in the first Brillouin zone has been changed to a summation

over the weight of each k-point wk The symbol of J;,k is the occupation number. The

total energy can be written as


E = Cw ",kII d3r rl,k i~( _I2 I,k E n(r)+x lr>
I,k 21 (2-3)
+Ez n(r)l +En nl(r)1 +E no((R, )


where Ez, is the Hartree energy, Elon is the energy due to Coulombic interaction between

electrons and ions, and Elon-zon is the Coulomb energy among ions. The evaluation of

these energies for a system with PBC is nontrivial and is discussed in detail in Appendix



Applying the variational principle to the total energy with respect to electron

density, the Kohn-Sham equation is obtained,






HKS 2,,k = 2,k 2,,k (2-5)


where 2,~k iS the eigenvalue of the Kohn-Sham Hamiltonian HKS. The Kohn-Sham

Hamiltonian is










HKS__2,
(2-6)




where the effective potential yF consists of three parts,



V, [n] r) =(2-7)
Sn(r)


SE, n1(r)]
V7, [n],r) =(2-8)
Sn (r)



IFo (.) = (2-9)
.." an (r )


They are the exchange-correlation potential, Hartree potential and potential due to ions.

The KS equation is a self-consistent equation because the effective potential

depends on the electron density. To solve the KS equation, it is natural to expand the

Bloch wave function in a plane wave basis set as

pt,k(> 7,~k+ Ce(k+G)-r (2-10)
1. _.
I,--k+GT Ect

where G is a reciprocal lattice vector and Ec is the kinetic energy cutoff, which controls

the size of the basis set. The advantages of using a plane wave basis set is its well-

behaved convergence and the use of efficient Fast Fourier Transform (FFT) techniques.

However, a huge basis set is needed to include the rapid oscillation of radial wave

function near the nuclei. Since the chemical properties of atoms are mostly determined by

the valence states, a frozen core approximation is usually used to avoid the rather inert

core states. In addition, the valence states can be treated in a pseudopotential, which









smooths the rapid oscillation of valence wave function in the core region and reproduces

the valence wave function outside a certain cutoff radius. Thus the size of the basis set

can be reduced dramatically. With the developments of first-principles pseudopotentials

in recent years, the plane wave basis set plus pseudopotential has become a very powerful

tool in DFT total energy calculations. The details of the developments of first-principles

pseudopotentials are reviewed in Appendix B.

2.2.2 Computational Details

The kinetic energy cutoff for the plane wave basis set is 286 eV. For the calculation

of a single C60 mOlecule, a 20 A+ simple cubic box is used with sampling only of the r k-

point. A Gaussian smearing of 0.02 eV is used for the Fermi surface broadening. For all

other calculations, we use the first-order Methfessel-Paxton [57] smearing of 0.4 eV. In

the calculation of the bulk properties of Cu, Ag and Au, a (14 x 14 x 14) Monkhorst-

Pack [58] k-point mesh is used, which corresponds to 104 irreducible k points in the first

Brillouin zone. All metal surfaces are modeled by a seven-layer slab with the bottom

three layers held fixed. For a C60 ML adsorbed on Cu(111) surface, we use the (4x4)

surface unit cell, which consists of 60 carbon atoms, 1 12 copper atoms, and 1472

electrons in total. For a C60 ML adsorbed on Ag(1 11) and Au(111) surfaces, the

(2J x 2 S)R30o surface unit cell is used, which includes 60 carbon atoms, 84 metal

atoms, and 1 164 electrons. The thickness of the vacuum between the adsorbate and the

neighbor metal surface is larger than 15 A+. The first Brillouin zone is sampled on a

(3 x3 x 1) Monkhorst-Pack k-point mesh corresponding to 5 irreducible k points.

Convergence tests have been performed with respect to the k-point mesh, slab thickness

and vacuum spacing. The total energy converges to 1 meV/atom. The ionic structure









relaxation is performed with a quasi-Newton minimization using Hellmann-Feynman

forces. For ionic structure relaxation, the top four layers of the slab are allowed to relax

until the absolute value of the force on each atom is less than 0.02 eV/A.

Table 2-1. Structural and energetic data of an isolated C60 mOlecule. The parameters bC,~
and b ,x are the shorter and longer bonds between two neighboring carbon
atoms, respectively. Ecoh is the cohesive energy per carbon atom.
b () b (A) Ecoh (eV/atom)
Present stud 1.39 1.44 9.74
Experment 1.40a 1.45a
a. [59]

Table 2-2. Structural and energetic data for bulk Cu, Ag, Au, clean Cu(111), Ag(1 11) and
Au(111) surfaces. The parameters ao, Ecoh and Bo are the lattice constant,
cohesive energy per atom and bulk modulus for the FCC lattice, respectively.
The parameters @, Esue-, and Adij are the work function, surface energy, and
interlayer distance relaxation for the clean FCC(111) surfaces, resetvely
ao Ecoh Bo 4 Esurf Adl2 Ad23 Ad34
(A) (eV/atom) (GPa) (eV) (eV/A2) 0(
Cu(111) 3.53 4.75 188 5.24 0.11 -0.92 -0.11 0.17
Exp 3.61a 3.49b 137 4.94" 0.11d -0.7e
Ag(111) 4.02 3.74 133 4.85 0.072 -0.45 -0.22 0.21
Exp 4.09a 2.95b 101b 4.74" 0.078d -0.5'
Au(111) 4.07 4.39 185 5.54 0.071 0.37 -0.36 0.05
Expt 4.08a 3.81b 173b 5.31" 0.094d 0.0'
a. [60], b. [61], c. [62], d. [63], e. [64], f. [65], and g. [66]

The calculated properties of an isolated C60 mOlecule and the relevant experimental

data are listed in Table I. The bond lengths are in very good agreement with experiments.

The calculated properties of bulk Cu, Ag and Au, and the clean Cu(l111), Ag( 111) and

Au(111) surfaces are compared with experimental data in Table II. The calculated fcc

bulk lattice constants of 3.53, 4.02 and 4.07 A+ for Cu, Ag and Au, respectively, are in

very good agreement with experiment. The cohesive energies and bulk modulus are

within the typical error of LDA with pseudopotential. As we derive adsorption energy as

the energy difference or compare adsorption energies among different adsorption sites,









error cancellations further increase the accuracy of LDA. The work function of the (1 11)

surfaces are overestimated compared to the experimental data. Our values are in very

good agreement with other DFT calculations using the Vanderbilt ultrasoft

pseudopotential and LDA [67]. The values for work function are 0.2 eV higher than the

experimental data, a difference due to the ultrasoft pseudopotential. A test has been

performed using a norm-conserving pseudopotential, with which the calculated work

function for a clean Cu(111) surface is 5.0 eV, which agrees very well with the

experimental data. Note that the difference among the work functions calculated using

ultrasoft pseudopotentials for the Cu(111), Ag(1 11) and Au(1 11) surfaces is in error by

only 0.1 eV as compared to experiment. Thus, the calculations reproduce the

characteristic differences among the Cu(111), Ag(1 11) and Au(111) surfaces very well.

For the interlayer relaxation of the Cu(l111) and Ag( 111) surface, our data reproduce the

experimental data well. For the interlayer relaxation of the Au( 111) surface, our data are

in good agreement with previous DFT-LDA calculations [68]. Band structure and the

density of states (DOS) are not sensitive to the level of exchange-correlation

approximations made in this study at all. Maj or conclusions from this study are not

influenced by LDA.

2.3 Results and Discussion

2.3.1 Adsorption of a C6o ML on Cu(111) Surface

2.3.1.1 Energetics and Adsorption Geometries

STM experiments [33] have been interpreted to show that C60 adsorbs on a

threefold on-hollow site of the Cu(l111) surface with a hexagon parallel to the surface, as

seen in Figure 2-1(a). Our calculations first confirm that this orientation of C60 iS more

energetically preferred than the one with a pentagon parallel to the surface. However,









there are two different on-hollow sites, hcp and fcc, which cannot be distinguished

experimentally. Our calculations indicate that the hcp site is slightly favored to the fcc

site, by only 0.02 eV. We further investigated two other potential adsorption sites, bridge

and on-top sites as shown in Figure 2-1(b) for the same orientation. We found that the

hcp site is indeed the most stable one. The calculated adsorption energy on a hcp site is

-2.24 eV, followed by bridge at -2.22 eV, fcc -2.22 eV and on-top -2.00 eV.











(a) (b)

Figure 2-1. Surface geometry and adsorption sites for a C60 ML on a Cu(111) surface. (a)
depicts a C60 mOnolayer on hcp sites in the (4x4) unit cells with the lowest
energy configuration (4 cells are shown); and (b) adsorption sites on a
Cu(111) surface: 1, on-top; 2, fcc; 3 bridge; and 4, hcp. Sites 2 and 4 are not
equivalent because of the differences in lower layers (not shown).

The adsorption energy as a function of various rotational angles of the hexagon on

all four adsorption sites is plotted in Figure 2-2 (the configuration of zero degree rotation

corresponds to Figure 2-1(a)). It can be seen in Figure 2-2 that, at certain orientations, a

C60 mOlecule can easily move via translational motion from one hcp site to another with a

nearly zero barrier (translation from hcp to bridge, to fcc and then to hcp). The 3600 n

site rotational energy barrier on all the adsorption sites is about 0.3 eV. Note that a 600

on-site rotation on hcp and fcc sites is subj ect to a barrier of only 0. 1 eV. These energetic

features determine the diffusion of C60 mOlecules on the Cu(l111) surface. Experiments

have found that C60 iS extremely mobile on a Cu surface, which is a result of the low










energy barrier when the molecule rotates and translates simultaneously. So far, there are

no experimental data reported for C60 adsorption energy on Cu(111) surface, but the

experimental adsorption energy of a C60 ML on an Au( 111) surface is 1.87 eV [10],

which is estimated to be smaller than that from a Cu surface. We conclude that the

adsorption energy of a C60 ML on Cu(l111) surface is between -1.9 and -2.2 eV.

-0.8 .
Bridge ---o---fcc
-1l.0 ~- hop -+-- on-top-






A-12. *s P. g *
0 0 4 0 8 0 2
Roaioa Anle(dgre
Fiur 2-21.4 Adopto enrisa ucinso oainlagl o 6 Lo
Cu11 ufc.Zr-nleoinaini eie a nFgr -() h
sytmhsatrefl ymer eas fteC ltie hnteagei





frelywit te ecetiona of the on-to site



A on a on-top sie hssqec aall adsorption energy, sfntoso rttoa nl o as expeted. Te C60

Cu(111) lll interacroanl oiettion moiisteudryn ulticas dfollowas: At thge C6-CU(a1).


contactte Cu-Cu bond lnthin the tria nge righ to underneathn thep moeue exands byig






5-% vey iniicnt, n the shrtan lngC- bondslnt in the C60 hexago right unenahtemlcl xaboveb










the Cu surface increase by 3% and 2% (not negligible); the Cu atoms beneath the

molecule lower their positions by 0.14 A+, and the Cu atoms surrounding the molecule rise

by 0.10 A+, with respect to the average atomic position in the surface layer. The

deformation and the perturbation from the molecule cause electrons in the surface to

undergo diffusive reflection when they encounter the interface, thus reducing the

conductance of a relatively thick metal film [17].

60 100
-total total
S500 c----C
S400 ""..... Cu in ii --.-.-. Cu
S300 -
S40
2 00 E


-20 -15 -10 -5 0 5 -3 -2 -1 0 2
Energy (eV) Energy (eV)
(a) (b)

Figure 2-3. Total density of states and partial DOS proj ected on the C60 ML and the
Cu(111) surface. They are plotted in the full energy range and near the Fermi
level in (a) and (b), respectively. The dashed vertical line represents the Fermi
level .

2.3.1.2 Electronic Structures

To analyze electronic structure, the density of states and energy bands are proj ected

onto the C60 mOlecule and the Cu surface via the relationships


k211


and

es, =Z (m, k u 7 k 2 (2-12)


respectively. Here, and r7,k, are the atomic and Bloch wave functions, respectively; 1vk

is the weight of each k point, and the indices pu and (i,k) are labels for atomic orbitals










and Bloch states, respectively. The proj section provides a useful tool for analyzing the

electronic band structure and the density of states.







M'; -2


KF MK -



(a) (b)

1.2 . 0.50
1- c
1. re .. .. ,, .-- -




6 080 700 72 74 70 8
Ban Numbe
(c) (d)
Figure~~~~~ ~~~ 2-.Bn tutuefrteasrpino 6 L naC(1)srfc.()i h
fis rllunzn of the twodmnialscegupfpm.Th





3%and 13%, repcily


Thgue tot. ald desirutyr fof stthes DS adindo patal6 DO poece on Cul an C60 Ofe (a) C60

ML adsorbed on n hc seite with iiahexagon pharale ow the isurfae bare shownr in Fiur 2

3.~~slae T6 Lna he Fermi level is) loaedaoe the rane f hestrngCudbnd as effent in Figue2

3(a. Te sarp eas btelo -80 eVi lindicate that the strates in thte lowe energy rane are









modulated strongly by the features of the C60 ML. It can be seen in Figure 2-3(b) that the

DOS near the Fermi level is dominated by states from the Cu(111) surface.



au- before
30-


a 20 i









-3 -2 -1 0 1 2
Energy (eV)

Figure 2-5. DOS of an C60 ML before and after its adsorption on a Cu(l111) surface. The
solid and dashed line stand for before and after the adsorption, respectively.

The band structure of an isolated C60 ML is shown along the T-M-K-T directions in

Figure 2-4(b) together with the first surface Brillouin zone in Figure 2-4(a). It shows that

an isolated C60 ML is a narrow gap semiconductor, with a gap of 1.0 eV. The threefold

degeneracy in the LUMO (t~u) of a C60 mOlecule is lowered by the two-dimensional

symmetry. The LUMO turns into three bands closely grouped from 0.5 to 1.0 eV.

Proj sections of all bands near the Fermi level on C60 and Cu of the C60-CU(1 11) System are

given in Figure 2-4(b). We found that proj sections on C60 are Small fractions compared to

the metal surface. The band structure of the C60-CU(111) System suggests a strong band

mixing, thus making it difficult to trace the origin of any given band. We identify two

energy bands that cross the Fermi energy in Figure 2-4(d), which are likely to be bands

from the ty,, orbital of the isolated C60-ML. These bands have projections of only 3% and









13% on C60. It can be seen from these curves that the hybridization between molecular

and surface states is significant, indicating strong molecule-surface interactions.

The partial DOS proj ected on a C60 ML adsorbed on the Cu(l111) surface (dashed

line) is compared to an isolated C60 ML (solid line) in Figure 2-5. Relative to the isolated

C60 ML, states near the Fermi energy of the adsorbed C60 ML have shifted to lower

energy as a result of molecule-surface interaction. The LUMO (tlz,)-derived band is now

broadened and partially filled below the Fermi energy because of the surface-to-molecule

electronic charge transfer. The calculated DOS compares nicely with experimental results

from photoemission spectroscopy. This energy shift-charge transfer phenomenon is very

characteristic in molecule-surface interactions. It is a compromise between the two

systems: A strong bond between the molecule and the surface has formed at the cost of

weakening the interaction within both the C60 ML and within the metal surface.

Integration of the partially filled C60 LUMO(tlz,)-derived band leads to a charge

transfer of 0.9 electrons per molecule from the copper surface to the adsorbed C60 M1.

To confirm the magnitude of charge transfer, we also implemented a modified Bader-like

approach [69] to analyze the electron density in real space. The bond critical plane is first

located by searching for the minimum electron density surface inside the C60-metal

interface region using

8p(r)
= 0, (2-13)


where p(r) is the electron density and : is the direction normal to the Cu surface. Then

the electron density between the bond critical plane and the middle of the vacuum is

integrated and the result is assigned as the electrons associated with C60. A charge










transfer of 0.8 electrons per molecule is observed using this analysis from the surface to

the C60 mOlecule, which is in agreement with the analysis of the DOS.


-7 -6 -5 -4 -3 -2 -1 0 1 2


-7 -6 -5 -4 -3 -2 -1 0 1 2


Energy (eV)
(b)


Energy (eV)


iI

10 -I



-7 -6 -5 -4 -3 -2 -1 0 1 2


10-



-7 -6 -5 -4 -3 -2 -1 0 1 2


Energy (eV) Energy (eV)
(c) (d)
Figure 2-6. Partial DOS of different adsorption configurations for a C60 E1 On a Cu(1 11)
surface. Partial DOS is proj ected on the bottom hexagon of C60 (upper panel
in a-d) and on the first surface layer of Cu(l111) surface (lower panel in a-d)









for different adsorption sites and orientations. Panel (a) is hcp (solid line) vs.
fcc (dotted line); (b) hcp (solid line) vs. On-top (dotted line); (c) hcp (solid
line) vs. hcp with a 900 rotation (dotted line); and (d) on-top (solid line) vs.
on-top with a 300 rotation (dotted line).

Furthermore, to understand the energetic preference of different adsorption sites,

we analyze their DOS in Figure 2-6. The DOS is proj ected on the bottom hexagon of C60

and the top Cu surface layer in the upper and lower panel of Figure 2-6, respectively. It

can be seen in Figure 2-6(a) that the DOS of a fcc site differs very little from that of a hcp

site, which explains why they have very close adsorption energy. In Figure 2-6(b), the

DOS of an on-top site has a quite visible population shift, with respect to that of a hcp

site, from the bottom of the Cu d band around -3.5 eV to the top of the Cu d band around

-1.5 eV. It is well known [70] that the Cu bonding states, dr located at the bottom of

the d band and the anti-bonding states, dl2_ 2, lOcated at the top of the d band.

Consequently, an increased population in higher energy states means less bonding, while

an increased population in lower energy states indicate more bonding. This explains why

the on-top site has less binding energy than the hcp site, as reflected in the difference of

DOS. Similar features are also depicted for rotations of a C60 mOlecule on the hcp and the

on-top sites in Figure 2-6(c) and (d), respectively.

2.3.1.3 Electron Density Redistribution and Work Function Change

The electron density difference, Ap (r), is obtained by subtracting the densities of

the clean substrate and the isolated C60 ML from the density of the adsorbate-substrate

system. This quantity gives insight into the redistribution of electrons upon the adsorption

of a C60 ML. In Figure 2-7 (a) and (b), the iso-surfaces of electron density difference are

plotted for binding distances of 2.0 A+ and 2.8 A+ for a C60 ML adsorbed on a hcp site with

a hexagon parallel to the surface. In both panels, the three-fold symmetry of the electron









density redistribution can be seen clearly. When C60 iS at the equilibrium distance, 2.0 A+,

from the surface, the redistribution of electrons is quite complicated especially in the

interface region between the surface and the molecule as seen in Figure 2-7(a). To get a

better view, we plot the planar averaged electron density difference along the : direction,

Ap (z), in the upper panels of Figure 2-8(a).













(a) (b)

Figure 2-7. Iso-surfaces of electron density difference for a C60 ML on a Cu(l111) surface.
Electron density decreases in darker (red) regions and increases in lighter
regions (yellow): (a) depicts the equilibrium position and (b) corresponds to
the C60 being lifted by 0.8 A. The iso-surface values are 11.0 and 10.4
e/(10 xbohr)3 in (a) and (b) respectively. The complexity of the distribution
shown leads to a net charge transfer from the surface to the C60 1VL and a
dipole moment that is opposite to the direction of charge transfer.

Considering the charge transfer of 0.8 electrons per molecule from the surface to

C60, the simple picture of electrons depleting from the surface and accumulating on C60

can not be found in these figures. Instead, it is a surprise to see such complexity in the

electron density redistribution. The maj or electron accumulation is in the middle of the

interface region, which is closer to the bottom of C60 than the first Cu layer. This feature

of polarized covalent bonding results in a charge-transfer from the surface to the C60.

Some electron accumulation also happens around the top two Cu layers and inside the C60

cage. On the other hand, the maj or electron depletion is inside the interface region from









places near either the first Cu layer or the bottom hexagon of C60. There are also

significant contributions of electron depletion from regions below the first Cu layer and

inside the C60 cage. When the C60 iS 0.8 A+ away from the equilibrium distance, this

feature of electron depletion inside the C60 cage becomes relatively more pronounced as

seen in Figure 2-7(a) and the upper panel of Figure 2-8(b). This feature has important

effects on the surface dipole moment and the change of work function.



4-40 -d = 2.0 A 15 d 2.8 A;
5 20 10-




1 '0 -2


S-40 -2 I.... Y j....


Oo-50 -3
S-4 2024681 2 -4- 01



z (A) z (A)
(a) (b)

Figure 2-8. Planar averaged electron density differences (upper panel) and the change in
surface dipole moment (lower panel) for the adsorption of a C60 ML on a
Cu(111) surface. Both are the functions of z, the direction perpendicular to the
surface. The distance between the bottom hexagon of C60 and the first copper
layer is 2.0 A+ in (a) and 2.8 A+ in (b). The solid vertical lines indicate the
positions of the top two copper layers and the dashed vertical lines indicate
the locations, in z direction, of the two parallel boundary hexagons in C60. The
dotted horizontal line indicates the total change in the surface dipole moment.

The measured work functions (WF) of a clean Cu(l111) surface and a C60 ML

covered Cu(111) surface from experiments are 4.94 and 4.86 eV [9], respectively. The

WF actually decreases by a tiny amount of 0.08 eV, although a significant charge transfer









from the substrate to C60 iS observed in both experiments and our calculation. This result

is very puzzling with respect to the conventional interpretation of the relationship

between WF change and charge transfer. According to a commonly used analysis based

on simple estimation of a surface dipole moment, when electrons are transferred from

absorbed molecule to the surface the WF will decrease, while transfer the other way will

result in a WF increase.

To resolve this puzzling phenomenon and to investigate the issue thoroughly, we

employ two methods to calculate the work function change. One is to compute the

difference directly between the work function of the adsorption system and that of the

clean surface. The work function is obtained by subtracting the Fermi energy of the

system from the electrostatic potential in the middle of the vacuum. To calculate the work

function accurately, a symmetric slab with a layer of C60 adsorbed on both sides of the

slab or the surface dipole correction suggested by Neugebauer, et al. [71] have been used.

The results are given in Table V as AR and AW,, respectively. To gain insight on the

origin of the change in the work function, we apply a method suggested by Michaelides,

et al. [72] to calculate the change in the surface dipole moment, Apu, induced by the

adsorption of C60. The quantity Apu is calculated by integrating the electron density

difference times the distance with respect to the top surface layer from the center of the

slab to the center of the vacuum,


Ap = 0 2z -z,) p (~d:(2-14)


In this equation, ze is the center of the slab, z, is the top surface layer and a is the length

of the unit cell in the : direction. The quantity Ap (z) is the planar averaged electron









density difference along the z direction. The work function change, AO, is then

calculated according to the Helmholtz equation.


AO = Ap(2-15)
coA

where so is the permittivity of vacuum and A is the surface area of the unit cell. Both

AO and Apu are listed in Table 2-3.

Table 2-3. Work function change of a C60 ML adsorbed on a Cu(111) surface. AR and
AW2 are calculated directly from the difference of the work functions with the
dipole correction and a double monolayer adsorption, respectively. AO is
calculated from the change in the surface dipole moment, Apu, induced by
adsorption of C60.
Exp (eV) AW1 (eV) AW2 (eV) AQ (eV) AgL (Debye)
2.0 A+ -0.08a -0.10 -0.09 -0.09 -0.21
2.8 A~ -0.37 -0.33 -0.32 -0.73
a. [9]

The calculated WF of a neutral C60-ML is 5.74 eV. The calculated WF of a pure

Cu(111) surface and C60 ML covered surface are 5.24 and 5.15 eV, respectively, which

are in good agreement with experiments (4.94 and 4.86 eV, respectively). The calculated

work function change is -0.09 eV, which agrees very well with the change of -0.08 eV

from experiments. The planar averaged charge density difference is depicted as a

function of z in the upper panels of Figure 2-8 for the equilibrium distance, 2.0 A+ and

the distance of 2.8 A+. In the lower panels, the integration of the surface dipole is shown

as a function of z to capture its gradually changing behavior and the total value is shown

by a horizontal dotted line. For the equilibrium distance, the calculated Ap is -0.21

Debye leading to a change of -0.09 eV in WF, AO which is in excellent agreement

with both direct estimation and experiments. When the C60 iS moved up from its

equilibrium position, by 0.8 A+ in the z direction, the calculated charge transfer, change in










dipole moment, and work function are 0.2e-, -0.73 Debye and 4.91 eV (a 0.33 eV

decrease), respectively. The WF further decreases by -0.33 eV. The gradual change of

work function and charge transfer with respect to the binding distance are shown in

Figure 2-9. The results from the two direct estimation methods and the surface dipole

method match very well, especially over short distance ranges.

0.0 .. 0.8
S ~ ~ L Dipole Correction Dipole Correction
e -0.1. -- Double layer -- -- Double Layer

E 0.6



r -0,4 .


-0.5 0.0
2.0 2,4 2.8 3.2 2.0 2.4 2.8 3.2
Distance (A) Distance (A()
(a) (b)

Figure 2-9. Work function change and electronic charge transfer as functions of the
distance between a C60 ML and a Cu(111) surface. The work function change
and electronic charge transfer are shown in (a) and (b), respectively. The solid
and dashed line shows the results from the dipole correction and the
calculation using a double monolayer, respectively.

The change of surface dipole moment induced by molecule-surface interaction at

the interface is complicated in general; it cannot be estimated simply as a product of the

charge transferred and the distance between molecule and the surface. The electron

depletion region inside the C60 cage has great impact on the work function decrease as

seen in both Figure 2-7 and Figure 2-8. Its effect can only be taken into account with an

explicit integration in Eq.2-14. The change of work function is the result of a compromise

between the two systems: A strong bond formed between the C60 and the metal surface

occurs at the cost of weakening the interaction within both C60 and the metal surface,

since electrons must be shared in the interface region.









2.3.2 Adsorption of a C6o ML on Ag (111) and Au(111) Surfaces

2.3.2.1 Energetics and Adsorption Geometries

The ( 2J x 22/ )R3 0o structure of a C60 mOnolayer adsorbed on Ag( 111) and

Au(111) surfaces is shown in Figure 2-10(a). The calculated lattice constants of bulk Ag

and Au are 4.02 and 4.07 A+, respectively. The corresponding values of 9.85 and 9.97 A

for the vector length of the (2J x 2J )R3 0o surface unit cell match closely with the

nearest neighbor distance in solid C60, which is 10.01 A+. Four possible adsorption sites

are considered, as shown in Figure 2-10(b), the on-top, bridge, fcc and hcp sites. To find

the lowest energy configuration on each adsorption site, we consider both a hexagon and

a pentagon of C60 in a plane parallel to the surface. Two parameters determine the lowest

energy configuration on each adsorption site with a certain face of C60 parallel to the

surface. One is the binding distance between the bottom of C60 and the top surface layer,

the other is the rotational angle of the C60 alOng the direction perpendicular to the surface.

The adsorption energies after ionic relaxation of the lowest energy configuration on each

site with a pentagon or a hexagon parallel to the surface are listed in Table 2-4. The

configuration of a hexagon of C60 parallel to the surface is more favorable energetically

than is a pentagon on all adsorption sites by an average of 0.3 eV for Ag( 111) and 0.2 eV

for Au( 111). With a hexagon of C60 parallel to both Ag( 111) and Au( 111) surfaces, the

most favorable site is the hcp, then the fcc and bridge sites. The on-top site is the least

favorable. The preference of the hcp over the fcc site is less than 0. 1 eV. With a pentagon

of C60 parallel to both surfaces, the fcc site is slightly more favorable than the hcp site by

less than 0.01 eV. The rest of the ordering is the same as in the case of hexagon.



















(a) (b)

Figure 2-10. Surface geometry and adsorption sites for a C60 ML on Ag(1 11) and
Au( 111) surfaces. (a) top view of C60 ML adsorbed on the Ag( 111) and
Au(111) surfaces (four unit cells are shownn; (b) the (22~ x 25) R30o
surface unit cell and the adsorption sites on the Ag(1 11) and Au(1 11)
surfaces, 1, on-top; 2, fcc; 3, bridge; and 4, hcp site. Sites 2 and 4 are not
equivalent due to differences in the lower surface layers (not shown).

Table 2-4. Adsorption energies of a C60 ML on Ag( 111) and Au( 111) surfaces on various
sites. The energies listed are the lowest ones obtained after ionic relaxation.
The energy is in unit of eV/lmolecule.
Configuaton Hp Fcc Bridge On-to
Hexagon on Ag(111) -1.54 -1.50 -1.40 -1.27
Pentagon on Ag( 111 -1.20 -1.20 -1.18 -0.89
Hexagon on Au(111) -1.27 -1.19 -1.13 -0.86
Pentagon on Au(111) -1.03 -1.04 -0.99 -0.60


The average binding distance between the bottom hexagon of C60 and the top

surface layer for different adsorption configurations is 2.4 A+ for the Ag(1 11) surface and

2.5 A+ for the Au( 111) surface. For the same configurations, the adsorption energy of C60

on the Ag(1 11) surface is larger than that on the Au(111) surface by 0.3 eV. Thus the

binding of C60 mOnolayer with the Ag(1 11) surface is stronger than the binding with the

Au(111) surface as seen in both adsorption energies and binding distances. This finding is

in agreement with the experimental observation that the interaction between C60 and Au

is the weakest among the noble metals [10]. As seen in Table 2-4, a hexagon of C60 On an

hcp site is the most favored configuration on both surfaces, while a pentagon on an on-










top site is the least favored configuration. The difference in adsorption energy is about

0.7 eV for both surfaces. In STM experiments, Altman and Colton [13-15] proposed that

the adsorption configuration was a pentagon of C60 On an on-top site for both the Ag( 111)

and Au(1 11) surfaces. However, Sakurai, et al. [16] proposed also from the results of

STM experiments, that the favored adsorption site should be the three-fold on-hollow site

on the Ag( 111) surface, but they did not specify the orientation of the C60 mOlecule. Our

calculations support the model proposed by Sakurai, et al. For the Cu(111) surface, we

have shown earlier in this chapter that the adsorption configuration is a hexagon of C60 On

the three-fold on-hollow site. Based on the similarity of the electronic properties of the

noble metals, it is not unreasonable that C60 Occupies the same adsorption site on Ag(1 11)

and Au(1 11) surfaces as on the Cu(111) surface.

-0.2 -0.2 .
-bridge --o--fc ~-*-bridge ... -foc
-0.4t +...- hop -+-- on-top .( ~-- hop ~- on-top
-0.4 + 0


-0.8
-1.2
I o I a a I

0 20 40 60 80 100 1.10 0 20 40 60 80 100 1.10
Rotational Angle (degree) Rotational Angle (degree)
(a) (b)

Figure 2-1 1. Adsorption energies as functions of rotational angle of C60 ML on Ag( 111)
and Au(111) surfaces. (a) on the Ag(1 11) surface, and (b) on the Au(1 11)
surface. The zero angle orientation is defined in Figure 2-10(a) with a
hexagon of C60 parallel to the surface on all sites.

To obtain the rotational barriers, we plot the adsorption energies as functions of the

rotational angle along the direction perpendicular to the surface on all sites with a

hexagon of C60 parallel to the surfaces in Figure 2-11. Since the binding distance on

various adsorption sites differs very little, less than 0.1 A+, with respect to rotational angle,









we keep the binding distance Eixed during the rotation of C60 mOlecule. For each

rotational angle, the atomic positions are also Eixed. The calculated rotational energy

barriers.

Table 2-5. The relaxed structure of a C60 ML adsorbed on Ag(1 11) and Au(111) surfaces
with its lowest energy configuration. On both surfaces, the lowest energy
configuration is a hexagon of C60 On the hcp site, as shown in Figure 2-10(a).
The parameters. Ab ;0 and Ab ;~C are the relative change in the shorter and

longer bond of C60 with respect to a free molecule. The parameters Ab^f-
and Ab^' ^' are the maximum increase and decrease, respectively, in bond
length between two neighboring metal atoms in the top surface layer with
respect to the bulk,,,.. value. +, Th praeerd describes the buckling,
defined as the maximum vertical distance among the metal atoms in the top
surface layer, and dMzC is the average distance between the bottom hexagon
of C60 and the top surface layer.
Ab ,c (%) Ab"'' BbM (% Ab^(%) Ab^' 'l(%) ddd '(A) dar-C(
Ag(111) 1.8 1.0 4.3 -1.2 0.02 2.29
Au(111) 1.8 1.4 7.3 -2.5 0.08 2.29


On both Ag(1 11) and Au(1 11) surfaces, the rotational barrier for the on-top site is

the highest, 0.5 eV for the Ag(1 11) surface and 0.3 eV for the Au(111) surface. The next

highest rotational barriers are on the fcc and hcp sites, which are 0.3 eV for the Ag(1 11)

surface and 0.2 eV for the Au(111) surface. Note that 30o and 900 rotations are not

equivalent due to the three-fold symmetry. The lowest rotational barriers are on the

bridge site, which are 0.2 eV for the Ag(1 11) surface and 0.1 eV for the Au(111) surface.

The rotational barriers on both surfaces are small enough that the C60 Can TOtate freely at

room temperature, which agrees with the experimental observations [13-15]. In general,

the rotational barriers on the Au(111) surface are lower than on the Ag(1 11) surface,

which is consistent with the weaker binding between C60 and the Au(111) surface than

the Ag(1 11) surface. This result is also in agreement with STM experiments, which show









that the on-site rotation of C60 On the Au( 111) surface is faster than that on the Ag( 111)

surface [13-15].

Several parameters of the relaxed structure in the lowest energy configuration on

both the Ag(1 11) and Au(111) surfaces are listed in Table 2-5. The lowest energy

configuration on both surfaces is a hexagon of C60 adsorbed on an hcp site, as shown in

Figure 2-10(a). On the Ag( 111) surface, the bond lengths of the shorter and longer C-C

bonds in the bottom hexagon of the C60 inCreaSe by 1.8% and 1.0%, respectively, but the

bond length of the C-C bonds in the top hexagon of the C60 does not change. The

neighboring Ag-Ag bond lengths in the top surface layer increase by as much as 4.3% for

the atoms directly below the C60 and decrease by as much as 1.2% in other locations. The

relaxation of the Ag atoms in the top surface layer causes a very small buckling of 0.02

A+, which is defined as the maximum vertical distance among the Ag atoms. This value is

much less than the corresponding value of 0.08 A+ on Au( 111) surface. The average

vertical distance between the bottom of the C60 and the top surface layer is 2.29 A+. On the

Au( 111) surface, the values of these parameters are somewhat larger than those on the

Ag(1 11) surface, which means that the Au(111) surface tends to reconstruct. However,

the interaction of C60 with the Ag( 111) surface is still stronger than that on the Au(1 11)

surface as seen from the adsorption energies in Table 2-4.

2.3.2.2 Electronic Structure and Bonding Mechanism

The total density of states and partial density of states (PDOS) proj ected on C60 and

the substrate are shown in Figure 2-12 (a) and (c) for the Ag(1 11) and Au(111) surfaces,

respectively. The Ag 4d band is 3 eV below the Fermi level and the Au 5d band is 1.7 eV

below the Fermi level. The dominant features near the Fermi level are from the substrate.











e~ ~ toa 30- before

S80 ----C ----fe
Ag 25
a 60 20 '


10


-3 -2-1 0 12 -3 -2-1 01 2
Energy (eV) Energy (eV)
(a) (b)
100, ., 35 .
q~~ total F~--- before
80 so 30----- fe
a 1 Au a 25-
a 60 re 20 .



-3 -2 3 2 -
Eng (eV Enrg (V
v(c (d)v

Fiur 2-12 Denit of stte fo h dopino 6 Lo g11 n u11
sufaes Th toa O n atalDSpoetdo heC0 gadA r







To see th1. echnget of sttsrthe bandsdrpived from C60 up on adsorptio n, the PDO ofa


~~~o isolated C60 m1Lnolayerine and h D o the adsorbed C60 m~oae r ltedtgte npnls b

and(d fr heAg(1 11) and Au(1 11) surfaces, respectively. Ith iash clear thcat asmlpotn






of the C60 LUMO (tlu)-derived band shifts below the Fermi level, indicating electron

transfer from the substrate to C60. The magnitude of the electron transfer can be estimated

from the area of the C60 LUMO-derived band below the Fermi level. The calculated

charge transfer is 0.5 and 0.2 electron per molecule from the Ag(1 11) and Au(111)








surfaces, respectively, to the C60 mOnolayer. These values are somewhat smaller than the

experimental estimate of 0.8 electrons per molecule on both surfaces [10, 22].






(a)3 (b)




.r 'T~- r *

(c) (d)
Fiue2-3 sosracso leto dniy ifrec o teasopin faC6 Lo






e/(1 xbh) i b ad()

Alhuh hr i oeevdne rmbthteryadexeiet o letoi
chagetrasfrT frmnbemtlsufcst 6,th aueo hbnigcnntb
assgne a ioic itoutexaintio ofth elctrn ensty iferece;reallSecio




2.3.e21.3. Teiso-surfaces of electron density difference are pltte dfor biniongo dsancesM


of 2.3 A and .1 Afrthe Ag(111)ac saurae in 1. Figure 2-13 (a nd (b) and 2.4 A and 30.2









A+ for the Au(111) surface in Figure 2-13 (c) and (d). In all panels, the three-fold

symmetry of electron density redistribution can be seen clearly. As shown in panels (a)

and (c), the electron density redistribution is very similar for the adsorbed C60 mOnolayer

at the equilibrium binding distances on both the Ag(1 11) and Au(111) surfaces.

Three observations can be made from the data shown in Figure 2-13. First, the

change in the electron density is confined mostly to the top surface layer, the bottom half

of the C60, and the interface region. Close examination shows that the electron density in

the top half of the C60 changes very little, which agrees with the finding that no change in

the C-C bond length occurs after ionic relaxation. Second, there is significant electron

depletion around both the top surface layer and the bottom hexagon of the C60.

Specifically, the dumbbell shape lying in the direction perpendicular to the surface with a

small ring of electron accumulation near the top surface layer indicates the character of

noble metal do and d, electrons. In addition to the electron density depletion region just

below the bottom hexagon of the C60, there are small regions inside the C60 cage and just

above the bottom hexagon, where the electron density also decreases. Third, although the

electron density increases in some regions just above the bottom hexagon of the C60, the

most significant electron accumulation occurs in the middle of the interface region, which

has a dumbbell shape parallel to the surface. When the C60 mOnolayer is pulled 0.8 A+

away from the equilibrium binding distances, the region with electron accumulation in

the middle of the interface can be seen more clearly in Figure 2-13 (b) and (d).

Evidently the electron density shared in the middle of the interface region derives

from both the Ag(1 11) and Au(1 11) surfaces and the C60 mOnolayer. As a result, the

bonding between them is best described as ionic-covalent with a small magnitude of









electronic charge transfer. The bond strength between the C60 mOnolayer and noble metal

surfaces decreases in the order Cu(111), Ag(1 11) and Au(111) according to both our

calculations and the experimental observations. The covalent bonding explains why a

hexagon is preferred to a pentagon when a C60 mOnolayer adsorbs on noble metal

surfaces. As is well known, for an isolated C60 mOlecule, the hexagon region has a higher

electron density than the pentagon region because the C60 HOMO is centered on the

bonds between two hexagons, and the C60 LUMO is centered on the bonds between a

hexagon and a pentagon. To form covalent bonds with noble metal surfaces, the hexagon

is more efficient than a pentagon because more electrons are available. If the bond were

ionic in nature, we would expect the most stable configuration to be a pentagon facing

toward the surface. Although similar, there are slight differences in the electron

redistribution in the C60-Ag(1 11) and C60-Au(111) systems. Specifically, the Au(111)

surface tends to spill out fewer electrons than the Ag(1 11) surface for sharing with the

C60. As a result, C60 On an Au(111) surface provides more electrons than it does on an

Ag(111) surface for covalent bonding. These different features have a large impact on the

different behavior of work function change on these two noble metal surfaces, which we

will discuss in detail in the following section.

To understand the energetic preferences of the various adsorption configurations,

the PDOS of a hexagon of C60 On an hcp site and two other configurations on the

Ag(1 11) and Au(111) surfaces are compared in Figure 2-14. The upper panels are the

PDOS proj ected on the bottom hexagon or pentagon of the C60 parallel to the surface.

The lower panels are the PDOS proj ected on the top surface layer.











-hex on hop
6 JY ......... pen on on-top

4-
nCII

20

40

30-

20-

10-


-7 -6 -5 -4 -3 -2 -1 0 1 2


-7 -6 -5 -4 -3 -2 -1 0 1 2


Energy (eV)
(a)


Energy (eV)
(b)


Ol0* *'* **** I Y
-7 -6 -5 -4 -3 -2 -*1 0 1 2


O l0'.. K I I I V
-7 -6 -5 -4 -3 -2 -1 0 1 2


Energy (eV)
(c)


Energy (eV)
(d)


Figure 2-14. Partial DOS of different adsorption configurations for a C60 ML On Ag( 111)
and Au( 111) surfaces. In (a)-(d), the upper panel is the PDOS of the bottom
hexagon or pentagon parallel to the surface and the lower panel is the PDOS
of the top surface layer. In panel (a), the solid line represents a hexagon of C60
on an hcp site and the dotted line a hexagon on an on-top site on the Ag(1 11)
surface. In panel (b), the solid line represents a hexagon of C60 On an hcp site









and the dotted line a pentagon on an on-top site on the Ag(1 11) surface. In
panel (c), the solid line represents a hexagon of C60 On an hcp site and the
dotted line a hexagon on an on-top site on the Au(111) surface. In panel (d),
the solid line represents a hexagon of C60 On an hcp site and the dotted line a
pentagon on an on-top site on the Au(111) surface.

In Figure 2-14 (a), the PDOS of a hexagon of C60 On an hcp site is compared to that

of a hexagon on an on-top site on the Ag( 111) surface. The figure shows that there are

more electrons from the on-top site than the hcp site populating the top of Ag d bands

around -3 eV, which are the anti-bonding states. This is the reason why the hcp site is

preferred to the on-top site. When comparing a pentagon of C60 On an on-top site with an

hcp site, this feature can also be seen in Figure 2-14 (b). In addition, the C60 LUMO-

derived bands of the hexagon shift further below the Fermi level than those of a

pentagon, which indicates more electronic charge transfer. The Bader-like analysis

confirms this interpretation by predicting 0.5 and 0.4 electrons transferred for these two

cases, respectively. The same argument can also be applied to the adsorption of C60 On

the Au(111) surface, as shown in Figure 2-14 (c) and (d). Comparing the PDOS in Figure

2-14 (b) and (d), we notice that the C60 HOMO-1 bands hybridize significantly with the

Au dbands, but stay unchanged on the Ag(1 11) surface. The reason for this behavior is

that the Au dbands are closer to the Fermi level than the Ag dbands. The Au dbands

align well with the C60 HOMO-1 bands.

2.3.2.3 Work Function Change

A puzzling phenomenon observed in C60-metal adsorption systems is the work

function change [10, 12]. Traditionally, work function change is associated closely with

the direction and the magnitude of electron transfer between the substrate and the

adsorbate. An increase in the work function indicates that electrons have been transferred

from the substrate to the adsorbate; a decrease in the work function indicates that









electrons have been transferred in the opposite direction. The argument can also be used

in an inverse sense. If electron transfer occurs from the substrate to the adsorbate, an

increase in the work function would be expected. For a C60 mOnolayer adsorbed on noble

metal surfaces, electron transfer from the surface to the C60 mOnolayer is observed in

both the experiments and our first-principles DFT calculations. As already discussed,

measurements of the work function in experiments have found that the work function

actually decreases for Cu(l111) [9] and Au( 111) [10] surfaces upon adsorption of a C60

monolayer.

Table 2-6. Work function change of a C60 ML adsorbed on Cu(111), Ag(1 11) and
Au( 111) surfaces. AW is calculated directly from the difference of the work
functions. AO is calculated from the change in the surface dipole moment,
Ap induced by adsorption of C60.
Exp (eV) AW (eV) AO (eV) Apu (Debye)
Cu(111) -0.08a -0.09 -0.09 -0.21
Ag(111) +0.14 +0.11 +0.24
Au(111) -0.6b -0.58 -0.60 -1.37
a. [9] and b. [10]

We study this issue as in Section 2.3.1.3. The results are given in Table 2-6. The

work function change calculated from the direct difference is listed as AW Once again,

the change in the surface dipole moment, Apu, induced by the adsorption of C60 iS

calculated by integrating the electron density difference times the distance with respect to

the top surface layer from the center of the slab to the center of the vacuum as in Eq. 2-

14. The work function change, AO is then calculated according to the Helmholtz

equation in Eq. 2-15. Both AO and Apu are listed in Table 2-6. For comparison, we also

list in Table 2-6 the results for a C60 mOnolayer adsorbed on a Cu(111) surface in the

(4x4) surface unit cell [73] from Table 2-3.








































;d3.2 A "
I r

r___
1, ,


IV
Q
ap
ar 0
ce
o
O -10
d
r,
~-20


z (A)


z (A)


30
20F I h d = 2.4 A I

10



-20
-30
10
0

-20
-30
-40 -... .... I.... .. ...... .. .
-50
-60 ** *
-4 -2 U 2 4 6 8 10 12

z (A)

(c)


'I *
-2 6 4 6 10 1
z (A)
(d


-50 L
-4


Figure 2-15. Planar averaged electron density differences (upper panel) and the change in
surface dipole moment (lower panel) for the adsorption of a C60 ML on
Ag(1 11) and Au(1 11) surfaces. They are the functions of z, the direction
perpendicular to the surface. The distance between the bottom hexagon of the
C60 and the first Ag(1 11) surface layer is 2.3 A+ in (a) and 3.1 A+ in (b). The
distance is 2.4 A+ in (c) and 3.2 A+ in (d) for C60 adsorbed on the Au(111)
surface. The solid vertical lines indicate the positions of the top two surface
layers and the dashed vertical lines indicate the positions of the two parallel
boundary hexagons in C60. The dotted horizontal line indicates the total
change in the surface dipole moment.









As seen in Table 2-6, the work function change for the Au(1 11) surface is -0.58 eV

via the direct calculation and -0.60 eV via the surface dipole calculation, which agrees

very well with the experimental value of -0.6 eV [10]. The corresponding change in the

surface dipole is -1.37 Debye. For the Ag(1 11) surface, we find the work function

change is +0. 14 eV and +0. 11 eV using the two methods, respectively. The change in the

surface dipole in this case is +0.24 Debye. There are no experimental data on the work

function change for the C60-Ag(1 11) system. However, experimentally the work function

increases by 0.4 eV for C60 adsorbed on an Ag(1 10) surface [l l], which supports our

results.

Despite the opposite change of the work function on the Ag( 111) and Au( 111)

surfaces upon C60 adsorption, calculations of the change in the surface dipole moment

reproduce the work function change very well. This result suggests that the origin of the

work function change is indeed the dipole formation around the interface. The simple

picture of electronic charge transfer of an ionic nature from the substrate to the adsorbate

fails to describe the entire picture of the complicated surface dipole formation.

A full understanding of the different behavior of the work function change on

Ag( 111) and Au( 111) surfaces requires close examination of the electron density

differences. To elucidate more clearly, the planar averaged electron density differences

along the z direction are shown in the upper panels of Figure 2-15 (a) and (c) at the

equilibrium binding distances. The top surface layer is at zero distance, as indicated by a

solid vertical line. The interface region is between the solid vertical line at zero and the

nearby dashed vertical line at 2.0 A+. As discussed in the previous section, the common

feature of both figures is the indication of covalent bonding rather than ionic bonding.









Electron density spills out from the top metal surface layer, which increases the surface

dipole. At the same time, electron density from C60 allSo spills out from the cage toward

the interface region, which decreases the surface dipole. For approximately the same

amount of electron accumulation in the middle of the interface region, the electron

depletion from the Ag(1 11) surface is larger than that from the Au(111) surface. At the

same time, electron depletion around the C60 iS Smaller on the Ag(1 11) surface than on

the Au(111) surface. These differences in the multiple dipole formations result in the

increase of the surface dipole for C60 adsorbed on the Ag( 111) surface and decrease of

the surface dipole for C60 adsorbed on the Au(111) surface, as shown in the lower panels

in Figure 2-15 (a) and (c). When the C60 mOnolayer is pulled 0.8 A+ away from the

equilibrium distance, there is still significant electron depletion from C60 On the Ag(1 11)

surface as seen in Figure 2-15 (b). On the Au(1 11) surface, at 0.8 A+ away from the

equilibrium distance, as seen in Figure 2-15 (d), the electron accumulation in the middle

of the interface region comes even more from the C60 than from the metal surface. These

features can also be seen in the three dimensional graphs in Figure 2-13 (b) and (d).

The distance dependence of the work function change on the Ag( 111) and Au( 111)

surfaces is shown in Figure 2-16 (a) and (c). On both surfaces, the work function

decreases as the distance increases. To explain this observation, we plot the electronic

charge transfer as a function of distance in Figure 2-16 (b) and (d). The charge transfer

decreases as the distance increases. Less charge transfer means less electron density spills

out from the surface and the bonding is less ionic in character, becoming more covalent

as the distance increases. These observations are consistent with the electron density

difference analysis in Figure 2-13 and 2-15. So relatively more electrons in the middle of











the interface region are derived from the C60 and fewer electrons are derived from the

metal surface at larger distance. As a result, the surface dipole moment decreases and the

work function decreases, too.



~0.14- -1 0.5





S0.108 1
oP 0.2


0.06 ** *
2.2 2.4 2.6 2.8 3.0 3.2 2.2 2.4 2.6 2.8 3.0 3.2
Distance (A) Distance (A)

0.16
S-0.58-
\ 1 0.12-
-0.608

0~p 0.08




-0.66 *
2.4 2.6 2.8 3.0 3.2 2.4 2.6 2.8 3.0 3.2
Distance (A) Distance (A)
(c) (d)

Figure 2-16. Work function change and electronic charge transfer as functions of the
distance between the C60 and the metal surfaces. (a) and (b) are for the
Ag(1 11) surface; (c) and (d) are for the Au(111) surface.

2.3.2.4 Simulated STM Images

Tersoff and Hamann [74] showed that the tunneling current in STM experiments

can be approximated at small voltages by


I 15 ac v, (7,k: ,,k) d = p (r, EF V) (2-16)
I 7,k


where EF is the Fermi energy of the system and V is the applied bias. The STM image


is simulated by the local density of states around the Fermi energy. The simulated STM









images of the most favorable adsorption configuration are shown in Figure 2-17 for a C60

monolayer adsorbed on the Ag(1 11) surface ((a) and (b)) and the Au(111) surface ((c)

and (d)). A bias of -2.0 V is used in panels (a) and (c), and +2.0 V is used in (b) and (d).

The STM image is simulated by the local density of states at the position of 1.5 A+ above

the top of C60 mOnolayer.













(a) b












(c) (d)

Figure 2-17. Simulated STM images for a C60 ML adsorbed on Ag(1 11) and Au(111)
surfaces. Panels (a) and (b) are for the Ag(1 11) surface with a bias of -2.0 and
+2.0 V, respectively. Panels (c) and (d) are for the Au(111) surface with a bias
of -2.0 and +2.0 V, respectively. On both surfaces, the tip is 1.5 A+ away from
the top of the C60.

The images on the different surfaces are almost the same. The negative bias

produces a ring-like shape and the positive bias produces a three-leaf shape. These

images are in good agreement with the STM images simulated by Maruyama, et al. [47]









The negative bias shows features of the C60 HOMO, which is centered on the C-C bonds

between two hexagons, while the positive bias shows features of the LUMO, centered on

the C-C bonds between a hexagon and a pentagon. These images correspond well to the

most preferred adsorption configuration of a hexagon of C60 On an hcp site, as shown in

Figure 2-10(a). Since C60 Can TOtate freely on both the Ag(1 11) and Au(111) surfaces at

room temperature, the STM images observed in experiments are dynamical averages.

2.3.2.5 Difference in Band Hybridization


60 -: .


40 -r ** $


~4 -3 -2 -1 0 1 2

Energy (eV)


-7 -6 -5 -


Figure 2-18. Difference in electronic structures for the adsorption of a C60 ML on noble
metal (111) surfaces. The upper and lower panel show the partial DOS
proj ected on the bottom hexagon of the C60 ML and the top metal surface
layer, respectively. The dotted lines stand for the adsorption of the C60 ML on
the Cu(111) surface, the dashed lines for the Ag(1 11) surface, and solid lines
for the Au(111) surfaces.









The difference in electronic structures for the adsorption of a C60 ML on a noble

metal (1 11) surface is shown in Figure 2-18 by the partial density of states proj ected on

the bottom hexagon of C60 and on the top metal surface layer. The Cu 3dband is 1 eV

below the Fermi level, while the Ag 4dband is 3 eV below the Fermi level. The

consequence is that the Cu 3dband hybridizes much more with the C60 HOMO-1

derived band because of the better alignment. As for the case of Au 5d band, because of

relativistic effects [75], it is broadened and pushed toward the Fermi level. The resulting

Au 5dband is only 1.7 eV below the Fermi level, which also has stronger hybridization

with the C60 HOMO-1 derived band than Ag 4dband. This explains why the C60 ML has

the smallest electron depletion on Ag(1 11) surface among the three noble metals. Thus,

unlike Cu(111) and Au(111) surfaces, the Ag(1 11) surface has a decrease in work

function upon the adsorption of the C60 M1.

2.3.3 Adsorption of C6o ML on Al(111) and Other Surfaces

The adsorption of C60 OH Various surfaces other than noble metal (1 11) surfaces has

also been studied [8, 12]. From experiments, it has been found that C60 iS weakly bonded

to graphite and silica surfaces. The interaction is mostly of van der Waals type. Very

strong covalent bonding has been found between C60 and Si, Ge and transition metal

surfaces. The strength of the bonding between C60 and noble metal surfaces is in the

middle of these two categories. From our first-principles DFT calculations, the bonding

between a C60 ML and noble metal (111) surface has features of both covalent and ionic

character. Another metal surface that binds C60 at similar strength as the noble metal

surfaces is Al. Al is also a fcc metal with the lattice constant of 3.76 A+, which is about

6% smaller than that of Ag and Au. It has been found from both experiments [12] and










first-principles calculation [49] that the (2J x 2 ) surface structure of a C60 MI

adsorbed on Al(111) surface is only a metastable phase. The underlying Al atoms tend to

reconstruct and form a more stable (6x6) surface structure with one out three C60 lifted.

The bonding between C60 and Al(111) surface has been claimed to be predominantly

covalent.

80 .. 35
total before

60 -- A 25



-3 -2 -1 1 2 3 -
Enrg (eV Enrg(V
4(a (b)8

Figur 2-9 Dest of sttsfrteasrtino 6 Lo l(1)srae n()
th oa Oth ata O 'prjce ion: th 6 Ladh l11
surac aesonThDOofniolatdC0M sldln)adtePO






Asur a-9 comparative study, wote invsortigtthbondn of a C60 ML withl111)srac.I Al11 ),

suraceinthe soame (2 x )h surfiaceO structued as the Ag(111) and t Au(1 11)sufc.

For th s metastbe structure, whe found f tat the ostfaoed ad sorpion site) is the hpDO

site~ o wihahexagsonof C60 parlle tothe surfae. The bionding dis.tane bsetw veenC60and


teAl(111 sumprface istuy 2.5 A, nd et the adort onenegy is -1.5 eV which arclose to the






results for the noble metal (111) surfaces. In Figure 2-19 (a) the total DOS and partial

DOS proj ected on C60 and Al are shown. The dominant feature around the Fermi level is

from the Al s and p electrons. As seen in Figure 2-19 (b), the HOMO-1 and LUMO




































d 2.5 A







"
"
"
~~-~-r~-~~-~--~-~~-~-r~-~~-:
r _r
I rl I
I I- I
III
II I
II I
Ilv I
II I
III

I I
I I


derived bands of an isolated C60 ML are broadened and slightly split as compared to


those in Figure 2-12 (b) and (d). This change is caused by the stress induced by the


smaller lattice constant of Al compared to Ag and Au. After its adsorption on Al(1 11)


surface, the C60 derived bands shift toward lower energy and part of the LUMO (tlu)-


derived band shifts below the Fermi level in a similar pattern to those for a C60 M1


adsorbed on noble metal (111) surfaces. This shows there is also a significant electronic


charge transfer from the Al(111) surface to the adsorbed C60 M1.


20

oo
(P 0
8
~ -20


8 -40


60

00 40
(p

d 20

6! 0

-sn


-4 -2


~


0 2 4 6 8 10 '12

z(IA)

(b)


Figure 2-20. Electron density difference and change in surface dipole moment for a C60
ML on a Al(111)surface. The binding distance is 2.5 A+. In (a), the Iso-
surfaces of electron density difference are shown at the value of +1.0
e/(10 xbohr)3. Electron density decreases in darker (red) regions and increases
in lighter (yellow) regions. The planar averaged electron density difference
and the change in surface dipole moment are shown in the upper and lower
panel of (b), respectively. The solid vertical lines indicate the positions of the
top two surface layers and the dashed vertical lines indicate the positions of
the two parallel boundary hexagons in C60. The dotted horizontal line
indicates the total change in the surface dipole moment









In Figure 2-20(a), the electron density difference is shown for the equilibrium

binding distance of 2.5 A+ on the hcp site. The planar averaged electron density difference

and the integration of the change in surface dipole are also shown in Figure 2-20(b).

Compared with those for the noble metal (111) surfaces, the electron depletion from the

bottom hexagon of C60 iS Very small, much less than that from the Al (1 11) surface, and

the electron accumulation region is even closer to the bottom hexagon of C60 than for any

noble metal surface. This combination indicates a large electronic charge transfer. The

magnitude of the charge transfer is evaluated to be 1.0 electrons per molecule, which is

larger than the value of 0.8 for Cu(l111) surface. The corresponding surface dipole change

is 2. 10 Debye, which corresponds to an increase of 0.90 eV in work function.

Consequently, we think the interaction between C60 and Al(111) surface has more ionic

feature than noble metal (111) surfaces.

The surface reconstruction has also been found for a C60 ML adsorbing on open

surfaces of noble and transition metals, such as (1 10) and (100) surfaces. Generally, a

much larger surface unit cell is needed to include surface reconstruction. The study of

such adsorption systems poses a great challenge for large scale first-principles DFT

calculation. With more efficient algorithms, faster computer hardware, and new

developments in multiscale modeling, such as the embedding atom-j ellium model

presented in Chapter 4, these issues of C60 induced surface reconstructionn will be

addressed in the near future.

2.3.4 Adsorption of SWCNT on Au(111) Surface

Another fullerene that also attracts intensive research is the single wall carbon

nanotube (SWCNT). In experiments [76], it has been used to constructt a single electron

transistor and thus is regarded as a promising candidate for future nano-electronics. In









these experiments, a SWCNT is always used with Au electrodes. The study of the

adsorption of SWCNTs on an Au surface therefore is of basic interest. It has been found

from first-principles calculations that the outer wall of a SWCNT interacts weakly with

Au surface [77, 78]. In this section, we carry out first-principles DFT calculation to study

the adsorption of a metallic (5,5) and a semiconductor (8,0) SWCNT on Au(111) surface.

SWCNTs come in two flavors, metallic and semiconducting, depending on the

chirality (n,m) of the underlying graphite sheet. When the Brillouin zone boundary of a

SWCNT unit cell crosses with the apex of the underlying Brillouin zone of graphite, the

SWCNT is metallic, otherwise, semiconducting. This is summarized in the following

formula for an arbitrary (n,m) SWCNT,

mod = (2-17)r
3 nonlzero, semiconducting (-7

There are exceptions for SWCNT with very small diameters. For example, large

curvature makes the (5,0) SWCNT metallic [79]. There are two groups of SWCNT with

the shortest repeating unit cells: the armchair (n,n) with the lattice constant of ag, and the


zig-zag (n,0) with the lattice constant of ag s, where a, is the lattice constant of the

underlying graphite.

Once again, we use LDA with ultrasoft pseudopotentials as implemented in VASP

to do the calculation. The lattice constant of fcc Au is 4.07 A+. The structure of free-

standing SWCNT is first calculated. The starting C-C bond length is 1.42 A+ for both

armchair and zig-zag SWCNT. After relaxation, the bond length in the axial direction is

increased to 1.44 A+ and the bond length is decreased to 1.40 A+ in other directions. To

accommodate several unit cells of SWCNT on an Au(111) lattice, the in-plane lattice









constant of Au must be shrunk a little. For a (5,5) SWCNT, we construct the (4 x J5)

surface unit cell to include three SWCNT cells by shrinking the in-plane Au lattice

constant by 2%. For a (8,0) SWCNT, we construct the (2 J x3) surface unit cell to

include three SWCNT cells by shrinking the in-plane Au lattice constant by 3%. The

dimensions of the surface unit cells are large enough that the interaction between two

neighboring SWCNTs is negligible.

To find the lowest energy configuration for a SWCNT adsorbed on a Au(111)

surface, we first rotate the tube along its axis to search for the optimal orientation. Then

we search for the adsorption site which gives the lowest energy with this orientation. A

metallic (5,5) SWCNT prefers to adsorb with a hexagon, rather than a zig-zag C-C bond

along the axial direction, facing down to the surface. The most favorable adsorption site

for the hexagon is the site halfway between a hcp and bridge site. The binding distance is

2.9 A+ and adsorption energy is -0.13 eV/A. A semiconducting (8,0) SWCNT prefers to

adsorb with both a hexagon and an axial C-C bond facing down to the surface. The

lowest energy configuration corresponds to one of the axial C-C bonds centered on a

bridge site. The binding distance is 2.9 A+ and the adsorption energy is -0.13 eV/A, which

are the same as for the (5,5) SWNT. For both tubes, the energy preference over any other

adsorption configuration is very small. So a SWCNT can easily roll and translate on a

Au( 111) surface. The strength of the interaction between a SWCNT and a Au( 111)

surface is much weaker than that of a C60 ML, as indicated in both the binding distance

and adsorption energies.

The density of states for the adsorption of a (5,5) SWCNT on a Au( 111) surface is

shown in Figure 2-21. The partial DOS proj ected on the tube remains almost the same,










before and after its adsorption on the Au surface. In contrast to the large shift of the C60

derived bands toward lower energy when a C60 ML adsorbs on a Au(1 11) surface, the

(5,5) SWCNT derived bands shift slightly toward higher energy. This indicates that the

electronic charge transfer is from the tube to the Au surface. This is reasonable since the

(5,5) SWCNT has the work function of 4.61 eV, which is much lower than 5.4 eV of the

Au(111) surface as indicated from our DFT-LDA calculations.

60.s. 35
Total 3 before
50 ---- SWGNT(5,) 0 --- fe


Au 25





-3 -2 -1 0 1 2 -3 -2 -1 0 1 2
Energy (eV) Enerygy~e)

(a) (b)

Figure 2-21. Density of states for the adsorption of a (5,5) SWCNT on a Au( 111) surface.
In (a), the total DOS, the partial DOS proj ected on the SWCNT and the
Au( 111) surface are shown. The DOS of an isolated SWCNT (solid line) and
the PDOS of the adsorbed SWCNT (dashed line) are shown in (b). The dashed
vertical lines represent the Fermi level.

The charge transfer from a (5,5) SWCNT to a Au(111) surface is clearly shown by

the electron density difference in Figure 2-22. Substantially more electrons are depleted

from the tube than from the Au surface to form an electron accumulation region inside

the interface. The amount of charge transfer is 0.09 electrons per surface unit cell. The

induced change in the surface dipole is -1.30 Debye, as see in Figure 2-22 (b), which

corresponds to a decrease in the work function of the combined system with respect to

the Au(111) surface by 0.90 eV.






















































derived bands shift toward lower energy with considerable broadening.


oF 10 \ d= 2.9 A .



-1 -5

-15 -5
-20 I




-4;3T9 -2: 0 68101
az (A)
(a) (b
Figure~~~~~ 2-2 lcrndniydferneadcag nsrae ioemmn o 55
SWCT o a u(11)srfae. he indngdisanc is2.9A. n (), he so

e/(10 xbor)3 Elcto dest derese in dake (rd rein and increases -- --



Figur 2and Eetho eni dfenc d change in surface dipole moment ar hwni heup r an lower
panel of (b) resecivlylsufc. The soind vriaines idisacaete pos. 8. itins of the I
topae tof srae laersn aendthe dashrened vreria liones idte talhebounare of.
te SWCNThr. Theco dotedhoizotal linrea indiatkes thed t gotal cange in theae
a t cag surface dipole moment.aesoni h pe n oe



The density of states for the adsorption of a (8,0) SWCNT on a Au( 111) surface is

shown in Figure 2-23. Unlike a (5,5) SWCNT, the bands derived from the (8,0) SWCNT

do not shift in a uniform way when it adsorbs on the Au(111) surface. The HOMO-1

derived band shifts toward higher energy, while the HOMO, LUMO and LUMO+1










35
2 30
"a


-3 -2 -1 0
Energy (eV)


-3 -2 -1 0 1 2
Energy (eV)


1 2


Figure 2-23. Density of states for the adsorption of a (8,0) SWCNT on a Au( 111) surface.
In (a), the total DOS, the partial DOS proj ected on the SWCNT and the
Au( 111) surface are shown. The DOS of an isolated SWCNT (solid line) and
the PDOS of the adsorbed SWCNT (dashed line) are shown in (b). The dashed
vertical lines represent the Fermi level.


30 --
20 -
10-


-10-
-20

40-
20


-20
-40


-4 -2


n


d=-2.9 A


0 2 4 6 8 10 12

z (A)


r


1


1 I


Figure 2-24. Electron density difference and change in surface dipole moment for a (8,0)
SWCNT on a Au( 111)surface. The binding distance is 2.9 A+. In (a), the Iso-
surfaces of electron density difference are shown at the value of +1.0
e/(10 xbohr)3. Electron density decreases in darker (red) regions and increases
in lighter (yellow) regions. The planar averaged electron density difference


- before
------ after









and the change in surface dipole moment are shown in the upper and lower
panel of (b), respectively. The solid vertical lines indicate the positions of the
top two surface layers and the dashed vertical lines indicate the boundaries of
the SWCNT. The dotted horizontal line indicates the total change in the
surface dipole moment

The electron density difference shown in Figure 2-24 indicates an electronic charge

transfer from the tube to the surface. Similar to the case of a (5,5) SWCNT, there are

many more electrons depleted from the tube than the Au surface. The amount of charge

transfer is 0.14 electrons per surface unit cell. The induced surface dipole is -2. 14 Debye,

which corresponds to 0.90 eV decrease in the work function after division by the surface

area of the unit cell. The planar averaged electron density difference for the (8,0)

SWCNT adsorbed on the Au(111) surface has almost the same features as that for a C60

ML adsorbed on the Au(111) surface shown in Figure 2-15 (d) at the binding distance of

3.2 A+.

2.4 Conclusion

In summary, we have presented a detailed microscopic picture of the interaction

between a C60 ML and noble metal (111) surfaces. Large-scale first-principles DFT

calculations have provided complete microscopic picture of the interaction between a C60

ML and noble metal (111) surfaces. We find that the most energetically preferred

adsorption configuration on all noble metal (111) surfaces corresponds to a hexagon of

C60 aligned parallel to the surface and centered on an hcp site. The strength of the

interaction between the C60 ML and noble metal (111) surfaces decreases in the order of

Cu, Ag and Au. Analysis of the electron density difference and density of states indicates

that the interaction between C60 and the noble metal surfaces has a strong covalent

character besides the ionic character (a small amount of electronic charge transfer from

the surfaces to C60). This picture is in contrast with the common notion, developed from









experiments, that the interaction between C60 and noble metal surfaces is mostly ionic.

The puzzling observation of the work function change on noble metal surfaces can only

be explained by including this covalent feature and close examination of the surface

dipole formation in the interface region.

For comparison, we have studied the adsorption of a C60 ML on a Al(1 11) surface

in the (2J x 2 5) structure. The interaction between a C60 ML and the Al(111) surface

shows more ionic character than noble metal (111) surfaces with larger electronic charge

transfer from the surface to the C60

In addition, we have also studied the adsorption of SWCNTs on a Au(111) surface.

The strength of the interaction between the Au(1 11) surface and SWCNTs is much

weaker than that of a C60 ML. We find a very small electronic charge transfer from the

SWCNTs to the Au( 111) surface and the SWCNTs become p-doped.















CHAPTER 3
MOLECULAR DYNAMICS SIMULATION OF POTENTIAL SPUTTERING ON LIF
SURFACE BY SLOW HIGHLY CHARGED IONS

3.1 Introduction

In recent years, with developments in ion-source technology such as the electron

beam ion trap [80-85] and electron cyclotron resonance [86], highly charged ion (HCI)

beams with charge states q greater than 44 have become available. In these experiments,

electron beams with a given energy and density collide with the target ions and strip off

their electrons. The resulting HCIs are then magnetically mass-to-charge separated into

an ultrahigh vacuum chamber. The HCI beam is then decelerated before it bombards the

target surface. The kinetic energy of the HCI can be as low as 5 x q eV [87]. Because of

the potential application of these energetic particles in nanoscale science, the interaction

of HCIs with solid surfaces has become one of the most active areas in the field of

particle-solid interactions. A HCI possesses a large amount of potential energy, which in

slow (hyperthermal) collision with a solid surface can greatly exceed its kinetic energy

and therefore dominate the ion-surface interaction. The subj ect includes a rich variety of

physical phenomena of both fundamental and applicational importance.

Investigations that focus on the neutralization dynamics of HCI proj ectiles have

revealed the following features [88-93]: When a HCI proj ectile approaches a surface, the

potential energy barrier between the surface and the available empty Rydberg states of

the HCI proj ectile decreases. Below a certain approach distance, electrons can be

captured via resonant neutralization (RN) and a so-called hollow atom can form rapidly.









The emission of secondary electrons and the formation of dynamical screening charges

give rise to strong image interactions between the HCI proj ectile and the surface. When

the HCI proj ectile enters the surface, further RN and Auger neutralization can take place

and fill the inner shell vacancies of the HCI proj ectile and finally neutralize it. Fast Auger

electrons and X-rays can be emitted in this process. Despite the complex nature of the

problem, a classical over-barrier model (COB) [88, 89] has successfully explained the

image energy gain in the reflected HCI beam. In the experiments with a HCI beam at

grazing incidence on a metal or insulator surface, the q3/2 dependence of the image

energy gain can be derived by the simple COB model [89, 92, 93]. Detailed simulations

based on the stair-wise COB model [94] and the dynamical COB model [95] have also

been performed to reproduce the experimental results.

The high potential energy of a HCI projectile at a surface can be released either via

emission of electrons and photons (X-rays), or via structure distortion and sputtering of

the target surface ions, atoms, or molecules. The surface modification caused by the

incident ions varies according to the material characteristics of the target surfaces.

Bombardment of metallic surfaces such as Au [96-99], Cu [100] is exclusively dominated

by kinetic energy transfer from the HCI proj ectile to target surface particles. In this case,

part of the potential energy of the HCI is transformed to kinetic energy due to the

interaction between the HCI and the surface. For semiconductor and insulator surfaces

such as Si [99, 101-104], GaAs [101, 102, 105], LiF [87, 101, 102, 106-115], SiO2 [99,

101, 102, 108, 116], and metal oxides [101, 102, 114, 117, 118], the sputtering patterns of

target surface particles are found to be highly sensitive to the charge states of the

proj ectile ions. This process is known as potential sputtering or electronic sputtering as










opposed to the conventional sputtering caused by kinetic energy transfer [87, 108]. In

contrast to metals, the valence electrons in insulators are localized. An insulator surface

has a considerably larger effective work function than a metal because of its large band

gap. Consequently, a smaller secondary electron yield is observed in the experiments [87,

101, 102]. The localized electronic excitation and electron-hole pairs in the valence bands

can survive long enough to convert potential energy into kinetic energy of sputtered

target surface particles.

Among the above-mentioned systems, LiF surfaces display unique features when

interacting with a HCI. Solid LiF is well known for its strong electron-phonon coupling,

which is the cause of electron and photon stimulated desorption [1 19-122]. Experimental

studies of collisions between slow HCIs such as Ar4' (q = 4, 8, 9, 1 1, and 14) or Xe4

(q = 14, 19, and 27) and LiF surfaces have been reported in recent years [87, 101, 106-

115]. The measured sputtering yields increase drastically with increasing incident HCI

charge states (i.e., higher electrostatic potential energy). To capture the characteristic

feature of strong electron-phonon coupling as mentioned above, a defect-mediated

sputtering model (DMS) [87, 101, 102, 108, 111, 123, 124] has been proposed as the

mechanism accounting for the observed potential sputtering of LiF surfaces by slow

HCIs. According to this model, the electronic excitation in the F(2p) valence band is

trapped into a highly excited electronic defect, namely, self-trapped excitons (STE).

Above room temperature the STE can decay immediately into a pair of H and F-color

centers. A H-center is a F2- molecular ion at an anion lattice site. A F-center is an electron

at the next or the second next anion lattice site relative to the Li+ cation. These H-and F-

color centers are highly mobile at room temperature and decay by emitting Fo atoms and









neutralizing Li+ cations, respectively, when reaching the surface. The desorption or

sputtering of the atoms is the result of a series of bond-breaking processes.

In order to understand the underlying physical mechanisms for various surface

modification, other models have also been proposed. For Si, the Coulomb explosion

model [125] as well as the bond-breaking model [126-128] have been used to explain the

dynamical process. Molecular dynamics (MD) simulations have been reported to

demonstrate the dynamical consequences of the proposed mechanisms [129-132]. While

Coulomb explosion and bond-breaking model are successful in many systems, they are

unable to describe the specific electronic excitations in LiF.

Inspired by the experimental findings, we formulate a model for MD simulations to

study HCI-LiF systems. The model involves high-level quantum chemistry calculations

as well as MD simulations under a variety of initial conditions. We aim to understand

surface modification processes, the dynamics of surface particles (both atoms and ions),

and the correlation of initial conditions with final sputtering outcome. The chapter is

organized in the following manner: Section 3.2 discusses the modeling and simulation,

section 3.3 presents results and discussion, and section 3.4 contains the conclusions.

3.2 Modeling and Simulation

The difficulties of applying MD to HCI-surface interactions come from the fact that

multiple electronic excitations and nuclear motion are entangled during the sputtering

process. Therefore, a careful analysis of the problem is necessary. The key issue is to

treat the different time scales properly and to separate the electronic degree of freedom

from the nuclear ionic ones. Typically, there are three time scales involved in the HCI-

surface interaction. The first is the time scale for a HCI to excite the surface electrons.

Second is the time scale for the rearrangement of the surface atoms and ions via defect-










mediated mechanism. Third is the time scale for the HCI to approach the surface. In order

to observe the effects of potential energy sputtering, the second time scale must be

shorter than the lifetime of the electronic excitation. In other words, the excited states

rather than the ground state should dominate the nuclear motion during the sputtering

process.

The first time scale is quite short compared to the lattice motion, which occurs at

the second time scale. Thus one can treat the electronic degree of freedom separately by

assuming the ions in a few outermost surface layers to be in excited states at the

beginning of the MD simulation [126, 129-134]. Such pre-existing electronic excitations

will last throughout the second time scale if the lifetime of the excitation is long enough.

The interaction between the proj ectile ion and the surface particles, as well as the

interactions among the surface particles, including both ground and excited states,

determines the nuclear dynamics. In a slow HCI-surface collision, the sputtering takes

place before the HCI proj ectile reaches the surface (the third time scale), which allows us

to neglect the kinetic energy effects of the incoming HCI. In many cases, we can omit the

proj ectile ion in the simulation provided that the electrostatic potential energy is

deposited in the form of electronic excitation in the surface at time zero [126, 129-134].

A test study has been performed to include the HCI explicitly. It shows that the kinetic

energy of a HCI affects the surface dynamics in similar ways in single ion-surface

collisions, which have been studied in previous work [129-132]. To simplify the

simulation, we decided not to include the dynamics of HCIs in the system.

A crucial step in constructing an adequate simulation model that describes the HCI-

surface interaction is to treat the multiple electronic excitations as well as the ground state










properly. To this end, we employ a high-level quantum chemistry methodology to

calculate the pair potential energy functions for all possible combinations of atoms and

ions. We use coupled cluster theory with single, double and perturbative triple excitations

(CCSD[T]) for the ground state and an equation of motion coupled cluster method

(EOM)-CCSD[T] for the excited state [13 5-140]. The coupled cluster theory is one of the

most accurate methods available, especially for excited states, which are the center of our

interest.



Ground State

-13.8-









-- -14.4 --



0 2 4 6 8 10 12 14 16 18 20
Bond Length (bohr)

Figure 3-1. Calculated ground state potential energy function for (Lili ) from CCSD[T].

3.2.1 Calculations of Potential Energy Functions

During the HCI-surface interaction, there are four types of particles in a LiF crystal

with partial electronic excitations, Li F Lio, and Fo, which give rise to ten different

types of pair interactions as follows, (Li Li ), (FF ), (Li F ), (Li Lio), (LioF ), (LioLio)

(Li Fo), (FoF ), (LioFo), and (FoFo). The LiF molecule in the gas phase has long been

regarded as a role model for first-principles calculations. The main interest has been in










the nonadiabatic crossing between the potential energy function of the covalent bond

from the excited state and the potential energy function of the ionic bond from the ground

state. A number of calculations have been done since the early 1970s and 1980s using

Hartree-Fock and configuration interaction methods [141-145]. But none of them

provides all the possible ten pair interactions required to model HCI-LiF surface

processes.



SGround State

-198.8-





-199.2-






0 2 4 6 8 10 12 14 16 18 20
Bond Length (bohr)


Figure 3-2. Calculated ground state potential energy function for (FF )from CCSD[T].

To obtain all the potential energy functions needed for simulations, we have

performed state-of-the-art first-principles calculations using the ACES II program [139,

140], which is an implementation of coupled cluster theory. We choose 6-31 1+G as the

basis set to get the desired accuracy. The calculations are performed on the dimers, which

is a good approximation to the effective potential for LiF crystalline structure (see the

discussion below). For the three pair interactions between two ions, i.e., (Li+i ), (FT ),

and (Li F ), which represent the ground state interactions in crystalline LiF, we have










calculated only the potential energy functions of the electronic ground states (see Figure

3-1-3-3). For the other seven pair interactions that involve neutral atoms, which come

from the excited states in crystalline LiF, potential energy functions of the ground state

and at least four low-lying excited states are calculated (see Figure 3-3 to 3-9). Note that

even the ground state of a dimer that consists of a neutral atom and an ion represents an

excited state in crystalline LiF.



SGround State

-106.6-


a -106.8-





1- -107.2 -


-107.4 *
0 2 4 6 8 10 12 14 16 18 20
Bond Length (bohr)


Figure 3-3. Calculated potential energy functions for (Li+ ) and (LioFo) from CCSD[T].
The ground state (crosses) and six low-lying excited states are calculated.
Among the excited states, the C' (hollow squares) is chosen in the MD
simulations.

The potentials for (Li F ) and (LioFo) are shown together in Figure 3-3 since they

have the same charge configuration. The accuracies of the binding energy and electronic

excitation energy are 1 meV and 0.1 eV, respectively. This accuracy is acceptable in a

MD simulation since the approximations made in the model lead to larger errors. In

general, the calculations for the closed-shell excited states are more accurate than those










for the open-shell; the calculations near the equilibrium distances are more accurate than

those at other distances.


-14.0


-14.2


-14.4


-14.6


-14.8


0 2 46 8
Bond


10 12 14 16

Length (bohr)


18 20


Figure 3-4. Calculated potential energy functions for (Li+io) from CCSD[T]. The ground
state (crosses) and five low-lying excited states are calculated.


-106.6


-106.8


-107.0


-107.2


-107.4


0 2 4 6 8 10 12 14 16 18 20

Bond Length (bohr)


Figure 3-5. Calculated potential energy functions for (LioF ) from CCSD[T]. The ground
state (crosses) and five low-lying excited states are calculated.










-1 4.2


-14.4



-1 4.6



-1 4.8


-15.0 ) s r
0 2 4 6 8 10 12 14 16


18 20


Bond Length (bohr)


Figure 3-6. Calculated potential energy functions for (LioLio) from CCSD[T]. The ground
state (crosses) and five low-lying excited states are calculated.


-105.6

-105.8


P' -106.0C Y




S-106.4-

9 -106.6

-106.8

-107.0 i i* I l .
0 2 4 6 8 10 12 14 16 18 20

Bond Length (bohr)


Figure 3-7. Calculated potential energy functions for (Li+Fo) from CCSD[T]. The ground
state (crosses) and five low-lying excited states are calculated.










-198.6

-198.7

-198.8

-198.9

-199.0

-199.1

-1 99.2

-199.3


-199.5 C = l i l l a i m i l I

0 2 4 6 8 10 12 14 16


18 20


Bond Length (bohr)


Figure 3-8. Calculated potential energy functions for (FoF )from CCSD[T]. The ground
state (crosses) and four low-lying excited states are calculated.


-1 98.5

-198.6

-198.7

-1 98.8

-198.9

-199.0

-199.1

-1 99.2


-199.3

0 2 4 6 8 10 12 14 16


18 20


Bond Length (bohr)


Figure 3-9. Calculated potential energy functions for (FoFo) from CCSD[T]. The ground
state (crosses) and five low-lying excited states are calculated.









Some features of each of the potential energy functions should be noted. For

interactions (Li Li ) and (FF ) (see Figure 3-1 and 3-2), the ground state potentials are

repulsive everywhere as expected, because of the dominant Coulombic repulsion between

two ions of like charge. For the interaction (LiY ) (see Figure 3-3), the ground state

potential has a region with strong attraction and a -1/ r tail from Coulombic interaction,

which gives rise to the ionic bonding. For the interaction (LioFo) (also see Figure 3-3),

which is considered as the excited state of the ionic pair (Li F ), all six low-lying excited

states are repulsive everywhere due to covalent anti-bonding. This set of excited states

plays crucial roles in surface processes. For the interaction (Li Lio) (see Figure 3-4),

potentials of the ground state and the first excited state have regions of attraction, but are

separated by 0.07-0.1 hartree in region r > 4ao (bohr). The next four potentials from

low-lying excited states are repulsive everywhere. For the interaction (LioF ) (see

Figure 3-5), the potential of the ground state and the five low-lying excited states all have

regions of strong attraction, which lead to one of the unique features in the HCI-LiF

surface dynamics presented below. For the interaction (LioLio) (see Figure 3-6), all

potentials have an attractive region, except for the second excited state, which is

repulsive everywhere. For the interaction (Li Fo) (see Figure 3-7), potentials of the

ground state and the first excited state are almost identical; both have regions of weak

attraction. The potential of the second excited state is just above the first excited state

with a region that is slightly repulsive. The next three potentials of low-lying excited

states are approximately 0.4 hartree above the ground state at r > 4ao For the interaction

(FoF ) (see Figure 3-8), all potentials are repulsive everywhere. For the interaction (FoFo)

(see Figure 3-9), the ground state potential has a very narrow attraction range between










2.5 a, and 4.0 a,. Outside of this region, the interaction is repulsive with a barrier at


4.0 a,. All the potentials from the low-lying excited states are repulsive everywhere.

3.2.2 Two-body Potentials for MD Simulation

Constructing interatomic potential energy functions from first-principles

calculations is an art of simulation. As already mentioned, all our calculations on the LiF

system are based on dimers. When many-body effects in a system are significant,

effective two-body, three-body, or N-body potentials should be constructed accordingly.

In the case of a simple ionic system such as LiF, the two-body interaction dominates.

0.10 ,,,,
Catlow
0.05 ---e--- present study

S 0.00-



m -0.15-



0 0 1 4 1 8 2
BodLnth(or

Fiur 3-1. Poteta nryfntosfrgon tt L .Tesldlnsfo
Caowealsppr[4]Th circe r acltd rmCS[]i h
prset tuy

For the2 grudsae euetecluae w-oyitrcin.Tecluae
par poeta f(iF)i eysmiatoteefcieprptnilusdnpevusM




studies [146. The bnding energy ducio ffers by 4%nd sthe bindingTh dstanclie 6% (see










Figure 3-10). Using the calculated pair potential to construct the LiF crystal, we get

7.88 ao for the lattice constant and 0.37 hartree per pair for the cohesive energy. The

experimental values are 7.58 ao and 0.39 hartree per pair, respectively [147]. Our results

differ from the experimental values only by 4%. Around the equilibrium position, the two

curves are shifted with respect to each other by nearly a constant, such that the difference

in force constant is almost zero. Since our focus is on the dynamical consequences of the

HCI interaction and the errors in the force constant are negligible, the difference will not

affect the main outcome of the simulation. Beyond the equilibrium position, the

calculated pair potential is more reliable than the effective pair potential, which is not

optimized for long distance interaction.

For the excited states, there is no effective two-body potential derived from first-

principles calculations for extended surface. To date, there is no method yet to treat an

extended system at CCSD[T] level. As an approximation, we use the true two-body (as

contrasted with effective two-body) potentials for a MD simulation. Furthermore, to

simplify the simulations and keep the results tractable, we choose a two-state model, i.e.,

the ground state and one excited state, for MD simulations. We have compared the

oscillator strengths between the ground state and various excited states, and find that low-

lying excited states, in general, have higher strengths than highly excited states. Since, in

the crystalline LiF, the excitation can be more complicated than in dimers, it is reasonable

to take the average of all low-lying states with relatively strong oscillator strengths

instead of using one specific state. On the other hand, the energies among the low-lying

states are close enough such that any one of them will give results similar to those given

by the averaged potential. Also note that for dimers consisting of neutral particles such as







73



Lio or Fo, the ground state of a dimer represents the lowest excited state in the solid as


there is no ground state neutral particle in the LiF crystal.

0.7 ., 0.7 .. .
0.6C -( Li' LI') 06 (iF
F 01.5 --L'F .5 -(F
(Li'LiD) i(L F')
01.4 (iF .4 -- FF
0.3 -0.3



S02 .. 2

0.3 : : I *' *0.3 1 i e --0

0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20
Bond Length (bohr) Bond Length (bohr)


(a) (b)


0.6C -(Lr' LIN) .6 (L
03 -" (iF 0.5 0-( F
(LPlle) (Lf1 e
z 0.4 --(If 0.4 FF



J 0.1 0.1

-0.2 -.2
-0.3 *L L '* -.3 i i i i .
u 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 101 12 14 16 18 20
Bond Length (bohr) Bond Length (bohr)


(c) (d)


Figure 3-1 1. Four sets of potential energy functions for each species in LiF surface used
in the MD simulations. Panel (a) represents FL panel (b) F, panel (c) Lio,
and panel (d) Fo.

For a system of four distinguishable particles, ten pair-wise potential energy


functions are needed. In our model, as mentioned before, the interactions between the


ions are in the electronic ground states such as for (Li Li ), (Li F ), and (FF ) (see


Figure 3-1-3-3). The interaction (i Fo) (see Figure 3-7) is chosen to be the average of


the ground state and the first two low-lying excited states since they are very close to

each other. For the interactions (iLiio), (LioLio), (ioF ), (FoF ), and (OFo~o, according to









the rules mentioned above we take the average values of potentials that are grouped

together and are relatively low-lying. The highest states in Figure 3-8 and 3-9 are

excluded from the selection because of their small oscillator strengths. For (LioFo), we

include the excited C' state, as it is known to have a strong transition probability from the

ground state. Consequently, most of the interactions involving excited states are repulsive

everywhere, except for the interaction (LioF ), which has a very strong attractive region,

and (Li Fo), which has a slightly attractive region.

The potential energy functions as described above are plotted in Figure 3-11. All

curves are shifted slightly such that the energies and forces are zero at large distance in

order to implement them in the MD simulations. In this figure, each panel depicts the

potential energy functions for each type of particle interacting with other three types of

particle and with its own type. A Li+ (see Figure 3-11(a)) is strongly attractive to F- and

strongly repulsive to another Li The interaction between a Li+ and a Lio is repulsive

everywhere, but less strong than an ionic pair of the same charge. The interaction

between a Li+ and a Fo has a very weak attractive region compared to (Li F ) interaction.

For a F (see Figure 3-11(b)), the Coulombic interaction with a Li+ is strongly attractive

in the binding region, and repulsive everywhere with another F The interaction between

F- and Fo is slightly repulsive at r > 4ao, while the interaction between F- and Lio has a

strong attractive feature comparable to the (Li F ) interaction. When a Lio (see Figure 3-

11(c)) interacts with a neutral species, Fo and another Lio, the potentials are slightly

repulsive at r > 4ao It should be noted that a Lio interacts with ions in ways similar to a

Li+ ion. In contrast, a Fo (see Figure 3-11(d)) interacts very differently from its ionic form

F All the interactions are quite short ranged and repulsive everywhere, except for a









slight attractive region when interacting with a Li These features of the potential energy

functions determine the dynamics of the systems as we will discuss in detail in the

following sections.





















Figure 3-12. Snapshot of the LiF surface at t = 0 for simulation 6. The ions in the
topmost two layers are 100% excited. The small darker ball is Li the small
lighter ball Lio, the large darker ball F and the large lighter ball Fo.

3.2.3 Simulation Details

The simulation box contains 12, 168 particles that are divided into four different

regions (from the bottom to the top of the surface): A static region, a temperature control

region, a dynamical region and a region consisting of excited particles. Both the static

and temperature control region contain two atomic layers (i.e., 1,352 particles). The

lattice constant in our study is 7.88 ao, as mentioned previously. Periodic boundary

conditions are applied in the x and y directions. Before electronic excitations, the LiF

surface is prepared at room temperature (300 K) with all the particles in their electronic

ground states, i.e., only Li+ and F- ions are present. Thermalization techniques are










applied as follows: At first, heat exchange between the system and an external heat bath

is allowed to give all the dynamical particles thermal speeds according to the Maxwell

distribution. Once equilibrium is reached, heat exchange is limited to the temperature

control region just above the static region. These steps are achieved using conventional

classical MD.

The simulation of HCI-surface bombardment begins when a collection of particles

is excited under the influence of the HCI proj ectile. Each dynamical particle in the

system follows Newton' s equation of motion. In this work, the total potential energy is

the summation of all pair interactions that consist of the ten types of interactions

described in the previous section. The Gear predictor and corrector algorithm [1] is used

to integrate Newton's equations. The time step is 0.3 fs throughout the simulations. This

time step is found to give very good energy conservation (better than 10-4 for a. 103 Steps

test run). The total simulation time for most of the runs is approximately 1.2 ps. During

this time period, most important dynamical processes are developed according to our

analysis. Beyond 1.2 ps, the energetic atoms are at distances far away from the surface

that lead to weak interactions. The change in sputtering yields is very small.

3.3 Results and Discussion

3.3.1 Initial Condition

Ten simulation runs were carried out with different excitation configurations; each

represents a possible initial condition. In simulations 1, 2, and 3, 20%, 60%, and 100% of

the ions in the topmost layer are excited, respectively. In simulations 4, 5, and 6, 20%,

60%, and 100% of the ions in the two topmost layers are excited, respectively. In

simulations 7 and 8, 100% of the ions in the three and four topmost layers, respectively,

are excited. In simulations 9 and 10, 100% of the ions in a hemispherical and a






77


cylindrical region, respectively, on the surface are excited. The amount of excitation is

thus controlled either by changing the size of the excited region or by modulating the

probability of particles to be excited.


















Fiue3-3 naso f h iFsrac tt= s o imlto 6 ntily tein
intetpms w ayr r 00 xie. h iuato o s rjce
on~ Y th ln.Thesaldre ali ith ml ihe alLo h

large*c~L darerbal F, ad helarelgtrbl o h pteigfotcnan
mostly Lio
3.3.2~ Surfac Modification
The ten sim j~:ulaios give iffrn ucmsadytshr oesmlrte.W

exaineoneof heminde~-,Vstai an opr oteohr.Siuain6i hsna
prootye. igue 312is nphto h ytma iezr.Tesaldre ali
for Li, th smll ighe,,cr ball for a Lo h agedre al o Fan h ag










78





lighter ball for a Fo. The initial condition of excitation in simulation 6 is that the ions in



the two topmost layers are fully excited (i.e., with a 100% probability), so an amount of




potential energy is deposited in the form of electronic excitation. After 1.2 ps, the



potential energy will be released via dynamical processes, which results in surface



modification.


Y
V
V
Y
V
Y



Y yyV
U Vy
I
ry

u u
r
u v
u
v
u
ur u

v y


cC.


u u
u
v
u
u u
u
u
u w
u
u
u
u



V,

) V
,,



~ str.


Figure 3-14. Snapshot of the the LiF surface at t = 1.2 ps for simulation 9. Initially, the

ions in a hemispherical region on the surface are 100% excited. The

simulation box is proj ected on the y-z plane. The small darker ball is Li the

small lighter ball Lio, the large darker ball F and the large lighter ball Fo.



The surface modification is depicted in Figure 3-13, which is a snapshot taken at



t = 1.2 ps. The shading and sizes of the balls are the same as in Figure 3-13. To get a



better view of the surface modification, the simulation box is proj ected on the y-z plane.







79


The distinct features of different regions are very clear from the bottom to the top. Right

above the static layers and the temperature control layer are several dynamical layers,

which are about half the thickness of the original simulation box. Atoms in these layers

move very little from their equilibrium, which means that our simulation box is thick

enough to include both the surface and bulk response of the impact of a HCI. Above this

region are the layers close to the surface, where the structure has been very much

perturbed. Most of the particles in this region are ions, depicted in darker shading.

Several Li+ ions in this region try to escape from the surface. Above the surface region,

there are particles sputtered from the surface. Almost all of them are neutral species,

which are depicted in lighter shading. However, the distributions of Lio and Fo are rather

different. Lio and Fo are well separated because of the differences in masses, as well as in

the potential energy functions. The topmost region is the sub-region that consists of only

Lio. Between this region and the surface is a spacious sub-region consisting mostly of Fo

and very few Li .


300C 1 ---- ---- F .0- -------- F'
2Mo~L 0 05- LF --- F



-10 -5 0 0 10 10 0 5 00 -0 0 0 0 10 10 0 5
z (behr 2 (bohr
(a b
Fiue3-5 isrbtinfncin of th nube ;of atcesadpteta neg ln
the dieto att=12p orsmlto Iiily tein n homs
tw laesae10 xctd ae a epeet h ubr fprils n
panel~~~~~~~~~ (b h oenileeg. nbt aeltesld ierpeensL h
dahe line-. F h dte ln io n tedshdtelieF









To compare different initial conditions, we also take a snapshot from simulation 9

at t = 1.2 ps (see Figure 3-14). The initial condition for simulation 9 is that the ions in a

hemispherical region on the surface are 100% excited. It can be seen that the distribution

of the atoms sputtered from the surface is quite different from that in simulation 6. There

is not front layer of Lio in the : direction.

3.3.3 Sputtering Yield

To analyze these data, a one-dimensional grid is set up along the : direction with

each grid point equally separated in distance. The profiles of physical quantities along the

: direction are calculated by averaging over the x-y plane on each grid point. Figure 3-15

depicts the profile of the number of particles and potential energy for each species at

t = 1.2 ps in simulation 6. As seen in Figure 3-15(a), most of the ions stay in the surface,

and the particles that escape from the surface are primarily neutral species. A close

examination indicates that Fo neutrals are evenly spread out in the : direction in the

region above the surface, in which very few Li+ are present. The distribution of Lio is

very different from Fo. It has two peaks: One is just above the surface and the other is

above the sputtered Fo layers, further away from the surface. These features can also be

seen in the snapshot taken for the same moment in Figure 3-13.

All these features can be understood by the distribution of the potential energy in

Figure 3-15(b). For ions far below the surface, there are strong ionic interactions to bind

them together. The averaged potential looks like a deep square well. This pattern

demonstrates a nearly undisturbed crystal structure. Near the top of the surface, the

potential energy of Li+ ions rises steeply from negative to zero, with small fluctuations

above the surface region. Therefore, a Li+ ion has to overcome a strong attraction to leave

the surface. The potential energy for F- anions oscillates in a deeper negative well near









the surface and rises very sharply to zero. This oscillation corresponds to a very perturbed

surface, but the strong attraction from the surface prohibits a F ion from escaping. The

neutral species only distribute around and above the surface region. The potential energy

for Fo is very small throughout the whole space. It is only slightly negative around the

surface region. These characteristics give rise to the even distribution of Fo. Finally, for

Lio, the potential energy has a quite deep dip in the surface region, and a very shallow

negative region in the sputtering front, which corresponds to the two peaks of the Lio

di stributi on.

To calculate the sputtering yield, we first define the criterion. As shown in

Figure 3-15(b), the potential energies of all the species inside the surface are negative

because the large number of ions acts as an attractive center. As particles move along the

z direction, they feel less and less interaction with other particles, especially with ions,

since ions tend to stay in the surface. The potential energies eventually become zero at

z = 40ao, which suggests that it is reasonable to set the escape distance to be 40ao in this

case.

According to this criterion, the numbers of particles that are sputtered out of the

surface in simulation 6 are seven Li O F 342 Lio and 465 Fo. The mass-sputtering yield

for neutral species is 99.6%. Table I shows the initial conditions and respective sputtering

yields for all ten simulations. It can be seen that with the same number of layers,

increasing the probability of initial excitation can dramatically increase the neutral mass-

sputtering yield. When only a monolayer is excited, the neutral mass-sputtering yields are

64.6%, 71.2%, and 99.1% for the initial conditions, in which 20%, 60%, and 100% of the

ions are excited, respectively. When two layers are involved, the neutral mass-sputtering









yields are 81.0%, 82.0%, and 99.6% for the initial conditions in which 20%, 60%, and

100% of the ions are excited, respectively. The reason is trivial: The higher the

probability of excitation in the initial condition, the more Fo particles are there to be

sputtered out of the surface. With the same probability of excitation, increasing the

number of layers in the initial state increases the total number of neutral sputtering

particles. But the ratio of sputtering yields among different species of particles remains

roughly the same. For simulations 7 and 8, three and four layers are 100% excited, and

the neutral mass sputtering yields are 99.7% and 99.8%, respectively. These results are in

agreement with experimental observation of more than 99% neutral sputtering yield [87].

To fully examine the effects of excitation configuration, we performed simulations

9 and 10, in which particles inside hemispherical and cylindrical regions are 100%

excited initially. These configurations are based on the assumption that the excitation is

local in nature. Note that the unit cell used in the MD simulation is sufficiently large that

the interaction of excited regions in neighboring unit cells can be neglected. The neutral

mass-sputtering yield is 95.6% for the hemisphere and 92.4% for the cylinder, lower than

the experimental data by 4-7%. All sputtering outcomes have some common features, for

example, most Li+ and F- ions remain on the surface. Only a very few ions can leave the

surface and go beyond 100 ao. For Lio and Fo atoms, substantial numbers of these neutral

atoms can leave the surface and go beyond 100 ao













Three
Configuration One layer Two layers Four Layers Hemi sphere Cylinder
layers
Probability (%) 20 60 100 20 60 100 100 100 100 100
Simulation 1 2 3 4 5 6 7 8 9 10

Li+ 0 10 5 2 21 7 3 7 2 4

F 1 14 1 1 13 0 1 0 2 6

Lio 5 35 34 1 8 342 433 470 19 33

Fo 0 31 288 7 91 465 616 865 53 78

Neutral mass yield (%) 64.6 71.2 99.1 81.0 82.0 99.6 99.7 99.8 95.6 92.4


Table3-1. Sputtering yields of ten MD simulations with different initial conditions.










This picture of dominant neutral sputtering yield is expected from the DMS

model [87, 101, 102, 108, 112, 123, 124]. At the surface, H-centers decay by emitting Fo

atoms and F-centers neutralize Li+ cations. The newly created neutral Lio atoms at the

surface form a metallic layer, which is stable at room temperature, but will evaporate at

increased temperature. Since these Lio atoms are weakly bound to the surface, when a

HCI approaches the surface, which is not included explicitly in our simulations, the

momentum transfer will be large enough to sputter these Lio atoms out the surface as a

retarded sputtering effect [87, 101, 102, 108, 112, 123, 124].



0.12 4---

0.10
-~i -...-





0.0 *
-100 -5 0 10 15 0 5 0
z bor

Figre -1. Dstiuinfntosothkieienryaogtedietoatt=12p
fo iuain6 ntal, h osi h oms wolyr r 0%ectd
Th soi iei orL+ h ahe ieFte otdln io n h ah
dotdlieF
Th pteigotoecnol eudrsodi et yeaiigtefaue

ofte oetileeryfucins h fraion of a ae fLoaom ntpoh

sufc istersl o h trciointe(oF)petalnrgfuconse









Figure 3-5). The everywhere-repulsive feature of the other potential energy functions that

involve neutral atoms determines the dominant sputtering of the neutral atoms.

So far, the simulations results have demonstrated two key characteristics of the

DMS model: First, the sputtering yield is dominantly neutral; and second, there is a layer

of Lio atoms bound to the surface. We believe that this layer of Lio atoms can be sputtered

out of the surface if a sufficient momentum transfer from the proj ectile ions to the atoms

can be realized.





o 0.08 F



-5 0.06-


2.0





0 20 40 60 80 100 1 20 140 160 1 80
Azimuth Angle (degree)

Figure 3-17. Normalized angular distribution functions of the neutral particles averaged
over simulations 3, 6, 7, and 8 at t -1.2 ps. The solid line represents Lio, the
dashed line Fo, and the dotted line the total neutral particles.

3.3.4 Profile of Dynamics

In order to obtain a full, quantitative description of the HCI-LiF surface dynamics,

we present the distribution functions of kinetic energy along the : direction. The same

one-dimensional grid is used as for the number of particles and potential energy in

Figure 3-15. Again, results from simulation 6 are used to illustrate the analysis. As shown







86


in Figure 3-16, most of the kinetic energy of the system is carried by the particles

sputtered out of the surface. The ions far below the surface region only have very little

kinetic energy. The kinetic energy of both Li+ and F increases at the surface. For the

very few Li+ ions that have successfully escaped from the surface, the kinetic energy is

higher than the Li+ in the surface. For Lio and Fo neutrals, the kinetic energy in the :

direction increases as a function of distance. The fastest particles are the sputtered

particles in the front. In addition, kinetic energies of Lio neutrals also have strong peaks

around the surface region, which are from the Li+ remaining on the surface, but with

smaller magnitudes compared to the sputtered atoms. The magnitudes are comparable to

that of F In the surface region, the fastest particles are Lio and F.

350 0.10 .
t= 0.005 ps t- 0.006ps
300 ----- ---- t= 0.042 ps- 0.5--t= .02p
at= 0.600 ps t = 0.600 ps:~~
B 250 .----- t=1.200 ps- ---- t=1.200ps6

$ ~-0.05-
S150C -




-100 -50 0 50 100 150 2001 250 300 -100 -50 0 50 100 150 2001 250 310
a (bohr) a (bohr)


Figure 3-18. Distribution functions of the number of particles and potential energy along
the z direction of Lio at different time instants for simulation 6. Panel (a)
represents the number of particles, and panel (b) the potential energy. In both
panels, the solid line is for t = 0.006 ps, the dashed line for t = 0.042 ps, the
dotted line for t = 0.600 ps, and the dash-dotted line for t = 1.200 ps.

The next question is the angular distribution of the sputtered atoms due to the

escaping velocity. A complete analysis of all ten simulations indicates that full-layer

excitation, i.e., 100% ions in the top surface layers, has the feature of nearly vertical back

scattering. The averaged angular distribution functions of the sputtered atoms from

simulations 3, 6, 7, and 8 are presented in Figure 3-17. The maxima of the angular







87


distribution are located closely at zero degree because of the repulsion among the excited

particles. For partial-layer excitation or localized excitation, the angular distribution does

not have a sharp peak near zero degree. These results suggest that angular distribution

functions can be used, in conjunction with sputtering yields, to determine the geometry

and nature of initial excitation when compared to experiments.

To obtain a picture of how these features have been developed through time, we

analyze the distributions of the number of particles and potential energy for Lio and Fo as

functions of time from simulation 6. In Figure 3-18 and 3-19, these physical quantities

are shown at four instants, t = 0.006, 0.042, 0.6, and 1.2 ps. At the beginning of the

simulation, all Lio neutrals are evenly distributed in the topmost two layers (see Figure 3-

18(a)). These Lio have very high positive potential energy (see Figure 3-18(b)). The

potential energy of the Lio neutrals in the surface region decreases dramatically in the

first 0.6 ps, from positive to negative.

350 .. 0.05 ...
t- t= .006 ps t = .006 ps
300 I -- -- -- t= 0.042 ps 0.04 --------- t= 0.042 ps-
a t = 0.000 ps t = 0.000 ps
B 250 .-- -- t=1.Z20ps- C 0.03 .----- t=1.200Dps.



0 i i * .0 * * *
-1200 -5 0 0 10 15 0 50 30 -00 5 0 10 15 0 5
a (bh)a(or







for0 t = 0.60 ps, and the1 dah-ote line for t = 1.20 ps. 502(120 0









As time evolves, the Lio neutrals gain kinetic energy and lose potential energy.

Very shortly, around 0.042 ps, the single peak for the distribution starts to split into two

peaks, as shown in Figure 3-18(a) by a dashed line. The main peak near the surface does

not move as much as the front peak in the z direction, which eventually separates entirely

from the main peak around 0.6 ps. Later, the front peak continues its motion in the z

direction with high velocity while maintaining a similar shape, which can be seen from

the profiles at 0.6 and 1.2 ps. During the simulation, there is always a substantial amount

of Lio neutrals on the surface. The Lio neutrals in the front peak are the fastest particles

due to the small mass of a Lio compared to a Fo.

In contrast to Lio, the profile of Fo does not change much at 0.042 ps when the

profile of Lio starts to split into two peaks (see Figure 3-19(a)). As time evolves, the

potential energy of Fo decreases to slightly negative (see Figure 3-19(b)). The distribution

of Fo spreads in time and becomes evenly distributed over z during the simulation, as can

be seen at 1.2 ps in Figure 3-19(a).

Similar analyses of the other nine simulations indicate that when the excitation

probability exceeds 60% of the excited region, there will always be a Lio enriched surface

layer as a consequence of HCI-LiF interaction. This characteristic vanishes at low

excitations, i.e., when only 20% of the ions in the surface layer are excited initially.

Therefore, the neutral Lio layer alone is not a sufficient condition to determine the nature

of excitation, i.e., local vs extended. However, the combination of this feature with

neutral/ion ratios in sputtering yields and angular distribution of the sputtered particles

can pinpoint the problem.




Full Text

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A COMPUTATIONAL STUDY OF SURFACE ADSORPTION AND DESORPTION By LIN-LIN WANG A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2004

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Copyright 2004 by Lin-Lin Wang

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To my parents.

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ACKNOWLEDGMENTS I have benefited from numerous people and many facilities during my graduate study at the University of Florida. First, I would like to acknowledge my advisor, Professor Hai-Ping Cheng, whose enthusiasm and expertise were greatly appreciated. I would also like to thank Professors James W. Dufty, Arthur F. Hebard, Jeffery L. Krause and Samuel B. Trickey for serving on my supervisory committee. I am very grateful for many current and former members of the Quantum Theory Project for their support. Of special note are Dr. Ajith Perera, Dr. Magnus Hedstrm, and Dr. Andrew Kolchin. I spent a wonderful student life in the University of Florida with numerous friends. They are Dr. Mao-Hua Du, Mr. Chun Zhang, Dr. Rong-Liang Liu, Dr. Lin-Lin Qiu, Dr. Zhi-Hong Chen, Mr. Xu Du, Mr. Ling-Yin Zhu, Mr. Wu-Ming Zhu, Mr. Chun-Lin Wang and many others. At last, I would like to thank my loving parents, Xue-Ping Li and Xiang-Jin Wang, and my beautiful wife, Dr. Yi Wu, for their endless support. This work has been supported by DOE/Basic Energy Science/Computational Material Science under contract number DE-FG02-97ER45660 iv

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TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES............................................................................................................vii LIST OF FIGURES.........................................................................................................viii ABSTRACT.......................................................................................................................xi CHAPTER 1 OVERVIEW.................................................................................................................1 2 DENSITY FUNCTIONAL STUDY OF THE ADSORPTION OF A C 60 MONOLAYER ON NOBLE METAL (111) SURFACES..........................................6 2.1 Introduction.............................................................................................................6 2.2 Theory, Method, and Computational Details.......................................................11 2.2.1 DFT Formulism with a Plane Wave Basis Set...........................................11 2.2.2 Computational Details................................................................................14 2.3 Results and Discussion.........................................................................................16 2.3.1 Adsorption of a C 60 ML on Cu(111) Surface.............................................16 2.3.1.1 Energetics and Adsorption Geometries............................................16 2.3.1.2 Electronic Structures........................................................................19 2.3.1.3 Electron Density Redistribution and Work Function Change..........24 2.3.2 Adsorption of a C 60 ML on Ag (111) and Au(111) Surfaces.....................30 2.3.2.1 Energetics and Adsorption Geometries............................................30 2.3.2.2 Electronic Structure and Bonding Mechanism.................................34 2.3.2.3 Work Function Change....................................................................40 2.3.2.4 Simulated STM Images....................................................................45 2.3.2.5 Difference in Band Hybridization....................................................47 2.3.3 Adsorption of C 60 ML on Al(111) and Other Surfaces..............................48 2.3.4 Adsorption of SWCNT on Au(111) Surface..............................................51 2.4 Conclusion............................................................................................................57 3 MOLECULAR DYNAMICS SIMULATION OF POTENTIAL SPUTTERING ON LiF SURFACE BY SLOW HIGHLY CHARGED IONS..........................................59 3.1 Introduction...........................................................................................................59 v

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3.2 Modeling and Simulation....................................................................................62 3.2.1 Calculations of Potential Energy Functions...............................................64 3.2.2 Two-body Potentials for MD Simulation...................................................71 3.2.3 Simulation Details......................................................................................75 3.3 Results and Discussion........................................................................................76 3.3.1 Initial Condition..........................................................................................76 3.3.2 Surface Modification..................................................................................77 3.3.3 Sputtering Yield..........................................................................................80 3.3.4 Profile of Dynamics....................................................................................85 3.4 Conclusion...........................................................................................................89 4 AN EMBEDDING ATOM-JELLIUM MODEL........................................................90 4.1 Introduction...........................................................................................................90 4.2 DFT Formulism for Embedding Atom-jellium Model.........................................92 4.3 Results and Discussion.........................................................................................95 5 FRACTURE AND AMORPHIZATION IN SiO 2 NANOWIRE STUDIED BY A COMBINED MD/FE METHOD................................................................................98 5.1 Introduction...........................................................................................................98 5.2 Methodology.......................................................................................................100 5.2.1 Summary of Finite Element Method........................................................100 5.2.2 Hybrid MD/FE: New Gradual Coupling..................................................104 5.3 Results.................................................................................................................106 5.3.1 Interface Test............................................................................................107 5.3.2 Stretch Simulation....................................................................................110 6 SUMMARY AND CONCLUSIONS.......................................................................113 APPENDIX A TOTAL ENERGY CALCULATION OF SYSTEM WITH PERIODIC BOUNDARY CONDITIONS..................................................................................115 B REVIEW OF DEVELOPMENT IN FIRST-PRINCIPLES PSEUDOPOTENTIAL125 B.1 Norm-Conserving Pseudopotential....................................................................125 B.2 Ultrasoft Pseudopotential and PAW..................................................................131 LIST OF REFERENCES.................................................................................................143 BIOGRAPHICAL SKETCH...........................................................................................156 vi

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LIST OF TABLES Table page 2-1. Structural and energetic data of an isolated C 60 molecule..........................................15 2-2. Structural and energetic data for bulk Cu, Ag, Au, clean Cu(111), Ag(111) and Au(111) surfaces......................................................................................................15 2-3. Work function change of a C 60 ML adsorbed on a Cu(111) surface..........................28 2-4. Adsorption energies of a C 60 ML on Ag(111) and Au(111) surfaces........................31 2-5. The relaxed structure of a C 60 ML adsorbed on Ag(111) and Au(111) surfaces with its lowest energy configuration................................................................................33 2-6. Work function change of a C 60 ML adsorbed on Cu(111), Ag(111) and Au(111) surfaces.....................................................................................................................41 3-1. Sputtering yields of ten MD simulations with different initial conditions.................83 vii

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LIST OF FIGURES Figure page 2-1. Surface geometry and adsorption sites for a C 60 ML on a Cu(111) surface...............17 2-2. Adsorption energies as functions of rotational angle for a C 60 ML on a Cu(111) surface......................................................................................................................18 2-3. Total density of states and partial DOS projected on the C 60 ML and the Cu(111) surface......................................................................................................................19 2-4. Band structure for the adsorption of a C 60 ML on a Cu(111) surface........................20 2-5. DOS of an C 60 ML before and after its adsorption on a Cu(111) surface..................21 2-6. Partial DOS of different adsorption configurations for a C 60 ML on a Cu(111) surface......................................................................................................................23 2-7. Iso-surfaces of electron density difference for a C 60 ML on a Cu(111) surface........25 2-8. Planar averaged electron density differences and the change in surface dipole moment for the adsorption of a C 60 ML on a Cu(111) surface................................26 2-9. Work function change and electronic charge transfer as functions of the distance between a C 60 ML and a Cu(111) surface................................................................29 2-10. Surface geometry and adsorption sites for a C 60 ML on Ag(111) and Au(111) surfaces.....................................................................................................................31 2-11. Adsorption energies as functions of rotational angle of C 60 ML on Ag(111) and Au(111) surfaces......................................................................................................32 2-12. Density of states of a C 60 ML on Ag(111) and Au(111) surfaces............................35 2-13. Iso-surfaces of electron density difference for the adsorption of a C 60 ML on Ag(111) and Au(111) surfaces.................................................................................36 2-14. Partial DOS of different adsorption configurations for a C 60 ML on Ag(111) and Au(111) surfaces......................................................................................................39 2-15. Planar averaged electron density differences and the change in surface dipole moment of a C 60 ML on Ag(111) and Au(111) surfaces.........................................42 viii

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2-16. Work function change and electronic charge transfer as functions of the distance between the C 60 and the metal surfaces....................................................................45 2-17. Simulated STM images of a C 60 ML on Ag(111) and Au(111) surfaces.................46 2-18. Difference in electronic structures for the adsorption of a C 60 ML on noble metal (111) surfaces...........................................................................................................47 2-19. Density of states for the adsorption of a C 60 ML on a Al(111) surface....................49 2-20. Electron density difference and change in surface dipole moment for a C 60 ML on a Al(111)surface..........................................................................................................50 2-21. Density of states for the adsorption of a (5,5) SWCNT on a Au(111) surface........54 2-22. Electron density difference and change in surface dipole moment for a (5,5) SWCNT on a Au(111)surface..................................................................................55 2-23. Density of states for the adsorption of a (8,0) SWCNT on a Au(111) surface........56 2-24. Electron density difference and change in surface dipole moment for a (8,0) SWCNT on a Au(111)surface..................................................................................56 3-1. Calculated ground state potential energy function for (Li + Li + ) from CCSD[T]........64 3-2. Calculated ground state potential energy function for (F F ) from CCSD[T]...........65 3-3. Calculated potential energy functions for (Li + F ) and (Li 0 F 0 ) from CCSD[T]..........66 3-4. Calculated potential energy functions for (Li + Li 0 ) from CCSD[T]............................67 3-5. Calculated potential energy functions for (Li 0 F ) from CCSD[T].............................67 3-6. Calculated potential energy functions for (Li 0 Li 0 ) from CCSD[T]............................68 3-7. Calculated potential energy functions for (Li + F 0 ) from CCSD[T].............................68 3-8. Calculated potential energy functions for (F 0 F ) from CCSD[T]..............................69 3-9. Calculated potential energy functions for (F 0 F 0 ) from CCSD[T]...............................69 3-10. Potential energy functions for ground state (Li + F ).................................................71 3-11. Four sets of potential energy functions for each species in LiF surface used in the MD simulations........................................................................................................73 3-12. Snapshot of the LiF surface at t 0 for simulation 6..............................................75 3-13. Snapshot of the LiF surface at t 1.2 ps for simulation 6.......................................77 ix

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3-14. Snapshot of the the LiF surface at t 1.2 ps for simulation 9.................................78 3-15. Distribution functions of the number of particles and potential energy along the z direction at t ps for simulation 6.....................................................................79 1.2 3-16. Distribution functions of the kinetic energy along the z direction at ps for simulation 6..............................................................................................................84 1.2t 3-17. Normalized angular distribution functions of the neutral particles averaged over simulations 3, 6, 7, and 8 at t 1.2 ps.....................................................................85 3-18. Distribution functions of the number of particles and potential energy along the z direction of Li 0 at different time instants for simulation 6.......................................86 3-19. Distribution functions of the number of particles and potential energy along the z direction of F 0 at different times for simulation 6....................................................87 4-1. A jellium surface modeled by a seven-layer Al slab with 21 electrons.....................95 4-2. The quantum size effect of jellium surfaces, (a) Al and (b) Cu.................................96 4-3. Partial density of states projected on atomic orbitals................................................97 5-1. Geometry of the -cristobalite (SiO 2 ) nanowire.......................................................107 5-2. Energy conservation test with respect to time for (a) FE only, (b) MD only, and (c) both FE and MD.....................................................................................................108 5-3. Distributions of force and velocity in the y direction during a pulse propagation test for the MD/FE interface.........................................................................................109 5-4. The stress-strain relation for a uniaxial stretch applied in the y direction of the nanowire at speed of 0.035 1ps ............................................................................110 5-5. Five snapshots from the tensile stretch applied in the y direction of the nanowire at speed of 0.035 ps................................................................................................111 1 5-6. Pair correlation functions of the nanowire during the uniaxial stretch simulation...112 x

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy A COMPUTATIONAL STUDY OF SURFACE ADSORPTION AND DESORPTION By Lin-Lin Wang May 2004 Chair: Hai-Ping Cheng Major Department: Physics In this work, the phenomena of surface adsorption and desorption have been studied by various computational methods. Large-scale density functional calculations with the local density approximation have been applied to investigate the energetics and electronic structure of a C 60 monolayer adsorbed on noble metal (111) surfaces. In all cases, the most energetically preferred adsorption configuration corresponds to a hexagon of C 60 adsorbing on an hcp site. A small amount of electronic charge transfer of 0.8, 0.5 and 0.2 electrons per molecule from the Cu(111), Ag(111) and Au(111) surfaces to C 60 has been found. We also find that the work function decreases by 0.1 eV on Cu(111) surface, increases by 0.1 eV on Ag(111) surface and decreases by 0.6 eV on Au(111) surface upon the adsorption of a C 60 monolayer. The puzzling work function change is well explained by a close examination of the surface dipole formation due to electron density redistribution in the interface region. Potential sputtering on the lithium fluoride (LiF) (100) surface by slow highly charged ions has been studied via molecular dynamics (MD) simulations. A model that is xi

PAGE 12

different from the conventional MD is formulated to allow electrons to be in the ground state as well as the low-lying excited states. The interatomic potential energy functions are obtained by a high-level quantum chemistry method. The results from MD simulations demonstrate that the so-called defect-mediated sputtering model provides a qualitatively correct picture. The simulations provide quantitative descriptions in which neutral particles dominate the sputtering yield by 99%, in agreement with experiments. An embedding atom-jellium model has been formulated into a multiscale simulation scheme to treat only the top metal surface layers in atomistic pseudopotential and the rest of the surface in a jellium model. The calculated work functions of Al and Cu clean surfaces agree well with the all-atomistic calculations. The multiscale scheme of combining finite element (FE) and MD methods is also studied. A gradual coupling of the FE and MD in the interface region is proposed and implemented, which shows promising results in the simulation of the breaking of a SiO 2 nanowire by tensile stretch. xii

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CHAPTER 1 OVERVIEW The importance of understanding surface phenomena stems from the fact that for many physical and chemical phenomena, a surface plays a key role. A better understanding and, ultimately, a predictive description of surface and interface properties is vital for the progress of modern technology, such as catalysis, miniaturization of electronic circuits, and emerging nanotechnology. The richness of physical and chemical properties of surfaces finds its fundamental explanation in the arrangement of atoms, the distribution of electrons, and their response to external perturbations. For examples, the processes of surface adsorption and desorption are the results of the interplay between geometric structure and electronic structure of the adsorbate and substrate. The ground state electronic structure fully determines the equilibrium geometry of the adsorption system. The ground state electronic structure also largely determines the chemical reaction and dynamics on the surface, such as transition states and reaction barriers. Nevertheless, more severe processes of surface dynamics, such as surface desorption stimulated by external laser fields, electron and charged ion bombardments, always involve electronic excited states and energy exchange between electronic and ionic degree of freedom. To study these processes, the electronic structure of excited states must be included. Computer simulation has been proved to be a powerful tool, besides experiment and theory, to study surface science in recent decades. There are two categories of simulation, which are characterized by the degrees of freedom they consider and the 1

PAGE 14

2 implemented scales. One is molecular dynamics (MD) [1], which treats atoms and molecules as classical particles and omits the degrees of freedom from the electrons. The other is quantum mechanical methods, which treats electrons explicitly. Although the two kinds of simulation are different, they are strongly connected and compose a hierarchy of knowledge of the system studied. In MD, classical particles move according to the coupled Newtons equations in force fields. Although no electron is included in such simulations, the force fields have input in principle from electronic information. In quantum mechanical methods, the Schrdinger equation is solved to include the many-body interaction among electrons explicitly. Once the electronic structure is known, the total energy of the system can be calculated. Molecule dynamics can be done with the force calculated from first-principles. To solve a many-body Schrdinger equation, two categories of methods are available. Traditionally, in quantum chemistry [2], wave-function-based methods are pursued, such as the Hartree-Fock method, which only treats the exchange effect of electrons explicitly. The omitted correlation effect of electrons is included by many post Hartree-Fock methods, such as configuration interaction (CI) and various orders of many-body perturbation theory (MBPT). The coupled-cluster method is closely related, in that the correlation effect of electrons can be improved systematically by considering the single, double, triple, etc, excitations. Recently, the electron-density based method, i.e., density functional theory (DFT) [3, 4], has become popular because it can reach intermediate accuracy, comparable to single CI, at relatively low computational cost. According to the Hohenberg-Kohn theorem [5, 6], the ground state total energy of an electronic system is a unique functional

PAGE 15

3 of the electron density. The exchange-correlation (XC) energy from the many-body effects can be treated as a functional of electron density. Thus, DFT in the Kohn-Sham approach maps the many-body problem for interacting electrons into a set of one-body equations for non-interacting electrons subjected to an effective potential. The proof of the Hohenberg-Kohn-Sham theorems and related development of XC functional of electrons are not the focus of this work. The remaining one-particle Kohn-Sham (KS) equation still poses a substantial numerical challenge. Among the various strategies, plane wave basis sets with pseudopotentials stands out as a popular choice because of its efficiency. In the past decade, new developments in pseudopotential formalism, more efficient algorithm in iterative minimization, and faster computer hardware have made large-scale, first-principles DFT simulation treating hundreds of atoms a reality. In this dissertation, we use all of these methods to study the phenomenon of surface adsorption and desorption. In Chapter 2, the ground state properties of a C 60 monolayer (ML) adsorbed on noble metal (Cu, Ag and Au) (111) surfaces are studied by large-scale DFT calculations. The adsorption energetics, such as the lowest energy configuration, translational and rotational barriers are obtained. Electronic structure information, such as density of states, charge transfer, and electron density redistribution, are also studied. With the detailed information on electronic structure, we explain very well the opposite change of work function on Cu and Au surfaces vs. Ag surface, which has been a puzzling phenomenon observed in experiments. In Chapter 3, we study a surface dynamical process, the response of a LiF(100) surface to the impact of highly charged ions (HCI) via MD simulation. We extend the conventional MD formalism to include the forces from electronic excited states

PAGE 16

4 calculated by a high-level quantum chemistry method. Within this new model, the so-called potential sputtering mechanism is examined by MD simulations. Our results agree well with the experimental results on the sputtering pattern and the observation of dominant sputtering yield in neutral particles. We found that the potential sputtering mechanism can be well-explained by the two-body potential energy functions from the electronic excited states. We will also address the issues of multiscale simulation in Chapter 4 and 5. There are two major reasons for multiscale simulations. One is the compromise between accuracy and efficiency. Only a crucial central region needs to be treated in high accurate method; the surrounding region can be treated in less accurate, but more computationally tractable approximation. In Chapter 4, we consider using jellium model as a simplified pseudopotential together with the atomistic pseudopotential to study the properties of metal surfaces in DFT calculation. The other reason to do multiscale simulation, which is more important, is that some phenomena in nature are intrinsically scale-coupled in different time, length and energy scales. For less scale-coupled phenomena, a sequential multiscale scheme usually works fine. One such example is the potential sputtering on LiF surface by HCI studied in Chapter 2. In that study, first, a highly accurate quantum chemistry method is used to calculate the potential energy functions. Then this information is fed to the MD simulation to study the dynamical processes. For strongly scale-coupled phenomena, only an intrinsic multiscale model can capture all the relevant physical processes, for example, material failure and crack propagation. The stress field, plastic deformation around the crack tip, and bond breaking inside the crack tip all depend on each other. These three different length scales are coupled strongly. In Chapter

PAGE 17

5 5, we construct a combined finite element and molecule dynamics method to investigate the breaking of a SiO 2 nanowire.

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CHAPTER 2 DENSITY FUNCTIONAL STUDY OF THE ADSORPTION OF A C 60 MONOLAYER ON NOBLE METAL (111) SURFACES 2.1 Introduction Ever since its discovery [7], C 60 has attracted much research attention because of its extraordinary physical properties and potential application in nanotechnology. The adsorption of the C 60 molecule on noble metal surfaces has been studied intensively in experiments over the last decade [8]. Due to the high electron affinity of the C 60 molecule as well as the metallic nature of the surfaces, the interaction has been understood in terms of electronic charge transfer from noble metal surfaces to the adsorbed C 60 monolayer (ML). According to the conventional surface dipole theory, all noble metal surfaces should have an increase in work function upon the adsorption of a C 60 ML. However, a small decrease in work function on Cu surfaces [9] and Au surfaces [10], and a small increase in work function on Ag surfaces [11] have been observed in experiments with the adsorption of a C 60 ML. Electronic charge transfer alone can not explain this phenomenon [9, 10, 12]. Furthermore, the most preferred adsorption site and orientation of the C 60 ML on Ag(111) and Au(111) surfaces are still unclear [13-16]. All these basic issues require additional insight to understand the fundamental nature of the interaction. Evidence for electronic charge transfer from noble metal (111) surfaces to C 60 has been observed in various experiments. The C 60 -Cu film is a system in which fascinating phenomena have been observed in studies of conductance as a function of the thickness of Cu film [17]. Experiments indicate that when a C 60 monolayer is placed on top of a 6

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7 very thin Cu film, the resistance of the monolayer is measured about 8000 which leads to resistivity corresponding to half of the three-dimensional alkali-metal-doped compounds A 3 C 60 (A=K, Rb). When the C 60 is beneath the Cu film, the ML also enhances the conductance. It is suggested from experimental analysis that the enhancement of conductance in the C 60 -Cu systems is due to charge transfer from Cu to C 60 at the interface. Further experimental measurements indicate that when the thickness of the Cu film increases, the resistance curves cross. As the thickness of the Cu film increases, the conductance of the film increases to approach the bulk Cu limit, which is much higher than the conductance of the electron-doped C 60 When the thick Cu film is covered with a C 60 -ML, the resistance of the system is increased. This effect is understood as a result of the diffusive surface scattering process. More direct evidence for electronic charge transfer from noble metal (111) surfaces to an adsorbed C 60 monolayer come from photon emission spectroscopy (PES). In valence band PES [9, 10, 18-25], a small peak appears just below the Fermi level due to the lowest unoccupied molecule orbital (LUMO) derived bands of the C 60 which cross the Fermi level and are partially filled upon adsorption. In carbon 1s core level PES [9, 10, 18, 19, 21, 24, 26], the binding energy shifts toward lower energy and the line shape becomes highly asymmetric due to the charge transfer. Modification in the electronic structure of the molecules is also found to be responsible for the enhancement in Raman spectroscopy [19, 27-31]. A substantial shift of the Ag(2) pentagonal pinch mode to lower frequency for C 60 molecule adsorbed on noble metal surfaces has a pattern similar to that from the alkali metal doped C 60 compound.

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8 In regard to the magnitude of electronic charge transfer from noble metal surfaces to an adsorbed C 60 monolayer, different techniques give different results. By comparing the size of the shift of the Ag(2) mode in Raman spectroscopy between C 60 adsorbed on polycrystalline noble metal surfaces and that for K 3 C 60 a charge transfer of less than three electrons per molecule can be derived [19]. In valence PES studies, the intensity of the C 60 LUMO-derived bands is compared to the intensity of the C 60 HOMO-derived bands or the intensity of the C 60 LUMO-derived bands co-adsorbed with alkali metals. These studies indicate that 1.6, 0.75 and 0.8 electrons per molecule are transferred from Cu(111) [10], Ag(111) [22] and Au(111) [10] surfaces to the C 60 monolayer. Another study shows that 1.8, 1.7 and 1.0 electrons per molecule are transferred from polycrystalline Cu, Ag and Au surfaces, respectively, to the C 60 monolayer [20]. Based on the observed electronic charge transfer, the interaction between the C 60 and the noble metal surfaces is assigned as ionic in nature. The geometry of an adsorbed C 60 monolayer on noble metal (111) surfaces has been studied in numerous STM experiments [13-16, 32-42] as well as by x-ray diffraction experiments [43-46]. At the beginning of the adsorption on these surfaces, C 60 is mobile on the terrace and occupies initially the step sites to form a closely packed pattern. After the first monolayer is complete, C 60 forms a commensurate hexagonal (4) structure on the Cu(111) surface. On the Ag(111) surface, C 60 forms a commensurate hexagonal ( 2323 )R30 o structure, and some additional structures rotated by 14 o or 46 o from the foregoing structure [16]. Then after annealing, only the ( 2323 )R30 o structure remains, which indicates that this is the most energetically favored structure. On the Au(111) surface, the adsorption configuration is more complicated, due to reconstruction

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9 of the free Au(111) surface. In addition to the commensurate hexagonal ( 2323 )R30 o structure and the rotated structures, C 60 can also form a (38) in-plane structure [13-15, 36, 37]. After annealing, only the well-ordered ( 2323 )R30 o structure remains. The reconstruction of the free Au(111) surface is lifted. Recently, another commensurate close-packed (7) structure was proposed [39]. Considering the adsorption site and the orientation of the C 60 monolayer in the (4) structure on the Cu(111) surface, the Sakurai group [33] found that C 60 adsorbs on a threefold hollow site with a hexagon parallel to the surface. They observed clearly a threefold symmetric STM image of C 60 with a ring shape and a three-leaf shape for negative and positive bias respectively. So it must be a hexagon of C 60 parallel to the Cu(111) surface. With this orientation, because of the nonequivalent 60 o rotation, there should be only two domains in the well-ordered (4) structure if C 60 occupies the on-top site. Their observation shows four domains, which indicates that C 60 occupies the threefold hollow sites, both hcp and fcc sites. For the ( 2323 )R30 o structure of C 60 on the Ag(111) and Au(111) surfaces, Altman and Colton [13-15] proposed, on the basis of experimental STM images, that the adsorption configuration is a pentagon of C 60 on an on-top site for both surfaces. However, Sakurai et al. [16], again based on interpretations of experimental STM images, proposed that the adsorption site is the threefold hollow site for the Ag(111) surface, in analogy to the (4) structure of C 60 monolayer adsorbed on the Cu(111) surface [33]. But they did not specify the orientation of the C 60 molecules on the Ag(111) surface. Despite the large amount of experimental data on electronic, transport, and optical properties, many basic issues remain unanswered. Although electronic charge transfer

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10 from the noble metal substrates to the C 60 over-layer is evident, the work function actually decreases on the Cu(111) surface by 0.08 eV [9], decreases on the Au(111) surface by 0.6 eV [10], and increases on the Ag(110) surface by 0.4 eV [11], which cannot be understood at all within the simple description of surface dipole layer formation due to charge transfer that is ionic in nature. Furthermore, the adsorption site and orientation of the C 60 monolayer on Ag(111) and Au(111) surfaces are still in debate [13-16]. All these basic issues require additional insight to understand the fundamental nature of the interaction between the noble metal (111) surfaces and the adsorbed C 60 monolayer. On the theoretical side, very few first-principles calculations of C 60 -metal adsorption systems have been performed. Such calculations involve hundreds of atoms, and so the calculations are computationally demanding. There were density functional calculations treating a C 60 molecule immersed in a jellium lattice to mimic the presence of the metal surface [47]. Only recently, a system consisting of an alkali-doped C 60 monolayer and an Ag(111) surface has been calculated fully in first-principles to study the dispersion of the C 60 LUMO-derived bands [48]. In addition, the (6) reconstruction phase of a C 60 monolayer adsorbed on an Al(111) surface has been studied by first-principles density functional calculations [49]. In this work, we study the adsorption of a C 60 monolayer on noble metal (111) surfaces using large-scale first-principles DFT calculations. We address a collection of issues raised in a decade of experimental work, such as C 60 adsorption sites and orientation, barriers to translation and rotation on the surface, surface deformation, electronic structure, charge transfer and work function change. The chapter is organized

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11 as follows. In Section 2.2, the basics of DFT total energy calculations using a plane wave basis set and pseudopotential are outlined, and the computational details described. In Section 2.3, we present calculated results and discussion. The adsorption of C 60 on the Cu(111) surface is presented in Section 2.3.1. In Section 2.3.2, we show results for C 60 adsorbed on Ag(111) and Au(111) surfaces. As a comparative study, we also show results for a C 60 ML adsorbed on Al(111) surface in Section 2.3.3 and a single wall carbon nanotube (SWCNT) adsorbed on Au(111) surface in Section 2.3.4. 2.2 Theory, Method, and Computational Details 2.2.1 DFT Formalism with a Plane Wave Basis Set In this work, DFT [5, 6] total energy calculations have been used to determine all structural, energetic and electronic results. The Kohn-Sham (KS) equations are solved in a plane wave basis set, using the Vanderbilt ultrasoft pseudopotential [50, 51] to describe the electron-ion interaction, as implemented in the Vienna ab initio simulation program (VASP) [52-54]. Exchange and correlation are described by the local density approximation (LDA). We use the exchange-correlation functional determined by Ceperly and Alder [55] and parameterized by Perdew and Zunger [56]. According to the Hohenberg-Kohn theorem [3-6], the ground state total energy of an electronic system is a unique functional of the electron density 0,extxcesEFnVnTnEnEn rrrr r (2-1) where T is the kinetic energy of non-interacting electrons, is the exchange-correlation energy, which includes all the many-body effects, and is the electrostatic 0 xcE esE

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12 energy due to the Coulombic interaction among electrons and ions. They are all functionals of the electron density 2,,,iiinwfkkkkr r (2-2) which has been expressed in Bloch wave functions ,i krk,i for electrons in a system with period boundary condition (PBC). The index of i and are for the state and k-point, respectively. The integral in the first Brillouin zone has been changed to a summation over the weight of each k-point The symbol of wk f k is the occupation number. The total energy can be written as 23,,,,2,iiixciHionionionIEwfdrEnEnEnE kkkkkrrrrR r (2-3) where H E is the Hartree energy, is the energy due to Coulombic interaction between electrons and ions, and is the Coulomb energy among ions. The evaluation of these energies for a system with PBC is nontrivial and is discussed in detail in Appendix A. ionE ionionE Applying the variational principle to the total energy with respect to electron density, the Kohn-Sham equation is obtained, 2,,,1,,2xcHioniiiVnVnVkkkrrrr r, (2-4) or ,, K SiiiH kk k (2-5) where ,i k is the eigenvalue of the Kohn-Sham Hamiltonian K SH The Kohn-Sham Hamiltonian is

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13 221,21,,2KSeffxcHionHVnVnVnVrrr ,r (2-6) where the effective potential V consists of three parts, eff ,xcxcEnVnn rrr (2-7) ,HHEnVnn rrr (2-8) ionionEnVrn rr (2-9) They are the exchange-correlation potential, Hartree potential and potential due to ions. The KS equation is a self-consistent equation because the effective potential depends on the electron density. To solve the KS equation, it is natural to expand the Bloch wave function in a plane wave basis set as 2,,1,2cutiiiiEce kGrkkkGr G (2-10) where G is a reciprocal lattice vector and is the kinetic energy cutoff, which controls the size of the basis set. The advantages of using a plane wave basis set is its wellbehaved convergence and the use of efficient Fast Fourier Transform (FFT) techniques. However, a huge basis set is needed to include the rapid oscillation of radial wave function near the nuclei. Since the chemical properties of atoms are mostly determined by the valence states, a frozen core approximation is usually used to avoid the rather inert core states. In addition, the valence states can be treated in a pseudopotential, which cutE

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14 smooths the rapid oscillation of valence wave function in the core region and reproduces the valence wave function outside a certain cutoff radius. Thus the size of the basis set can be reduced dramatically. With the developments of first-principles pseudopotentials in recent years, the plane wave basis set plus pseudopotential has become a very powerful tool in DFT total energy calculations. The details of the developments of first-principles pseudopotentials are reviewed in Appendix B. 2.2.2 Computational Details The kinetic energy cutoff for the plane wave basis set is 286 eV. For the calculation of a single C 60 molecule, a 20 simple cubic box is used with sampling only of the k-point. A Gaussian smearing of 0.02 eV is used for the Fermi surface broadening. For all other calculations, we use the first-order Methfessel-Paxton [57] smearing of 0.4 eV. In the calculation of the bulk properties of Cu, Ag and Au, a (14) Monkhorst-Pack [58] k-point mesh is used, which corresponds to 104 irreducible k points in the first Brillouin zone. All metal surfaces are modeled by a seven-layer slab with the bottom three layers held fixed. For a C 60 ML adsorbed on Cu(111) surface, we use the (4) surface unit cell, which consists of 60 carbon atoms, 112 copper atoms, and 1472 electrons in total. For a C 60 ML adsorbed on Ag(111) and Au(111) surfaces, the ( 2323 )R30 o surface unit cell is used, which includes 60 carbon atoms, 84 metal atoms, and 1164 electrons. The thickness of the vacuum between the adsorbate and the neighbor metal surface is larger than 15 The first Brillouin zone is sampled on a (3) Monkhorst-Pack k-point mesh corresponding to 5 irreducible k points. Convergence tests have been performed with respect to the k-point mesh, slab thickness and vacuum spacing. The total energy converges to 1 meV/atom. The ionic structure

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15 relaxation is performed with a quasi-Newton minimization using Hellmann-Feynman forces. For ionic structure relaxation, the top four layers of the slab are allowed to relax until the absolute value of the force on each atom is less than 0.02 eV/. Table 2-1. Structural and energetic data of an isolated C 60 molecule. The parameters CC s hortb and b are the shorter and longer bonds between two neighboring carbon atoms, respectively. E CClong coh is the cohesive energy per carbon atom. CC s hortb () CClongb () E coh (eV/atom) Present study 1.39 1.44 9.74 Experiment 1.40 a 1.45 a a. [59] Table 2-2. Structural and energetic data for bulk Cu, Ag, Au, clean Cu(111), Ag(111) and Au(111) surfaces. The parameters a 0, E coh and B 0 are the lattice constant, cohesive energy per atom and bulk modulus for the FCC lattice, respectively. The parameters E surf and d ij are the work function, surface energy, and interlayer distance relaxation for the clean FCC(111) surfaces, respectively. a 0 () E coh (eV/atom) B 0 (GPa) (eV) E surf (eV/ 2 ) d 12 d 23 d 34 (%) Cu(111) 3.53 4.75 188 5.24 0.11 -0.92 -0.11 0.17 Expt 3.61 a 3.49 b 137 b 4.94 c 0.11 d -0.7 e Ag(111) 4.02 3.74 133 4.85 0.072 -0.45 -0.22 0.21 Expt 4.09 a 2.95 b 101 b 4.74 c 0.078 d -0.5 f Au(111) 4.07 4.39 185 5.54 0.071 0.37 -0.36 0.05 Expt 4.08 a 3.81 b 173 b 5.31 c 0.094 d 0.0 g a. [60], b. [61], c. [62], d. [63], e. [64], f. [65], and g. [66] The calculated properties of an isolated C 60 molecule and the relevant experimental data are listed in Table I. The bond lengths are in very good agreement with experiments. The calculated properties of bulk Cu, Ag and Au, and the clean Cu(111), Ag(111) and Au(111) surfaces are compared with experimental data in Table II. The calculated fcc bulk lattice constants of 3.53, 4.02 and 4.07 for Cu, Ag and Au, respectively, are in very good agreement with experiment. The cohesive energies and bulk modulus are within the typical error of LDA with pseudopotential. As we derive adsorption energy as the energy difference or compare adsorption energies among different adsorption sites,

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16 error cancellations further increase the accuracy of LDA. The work function of the (111) surfaces are overestimated compared to the experimental data. Our values are in very good agreement with other DFT calculations using the Vanderbilt ultrasoft pseudopotential and LDA [67]. The values for work function are 0.2 eV higher than the experimental data, a difference due to the ultrasoft pseudopotential. A test has been performed using a norm-conserving pseudopotential, with which the calculated work function for a clean Cu(111) surface is 5.0 eV, which agrees very well with the experimental data. Note that the difference among the work functions calculated using ultrasoft pseudopotentials for the Cu(111), Ag(111) and Au(111) surfaces is in error by only 0.1 eV as compared to experiment. Thus, the calculations reproduce the characteristic differences among the Cu(111), Ag(111) and Au(111) surfaces very well. For the interlayer relaxation of the Cu(111) and Ag(111) surface, our data reproduce the experimental data well. For the interlayer relaxation of the Au(111) surface, our data are in good agreement with previous DFT-LDA calculations [68]. Band structure and the density of states (DOS) are not sensitive to the level of exchange-correlation approximations made in this study at all. Major conclusions from this study are not influenced by LDA. 2.3 Results and Discussion 2.3.1 Adsorption of a C 60 ML on Cu(111) Surface 2.3.1.1 Energetics and Adsorption Geometries STM experiments [33] have been interpreted to show that C 60 adsorbs on a threefold on-hollow site of the Cu(111) surface with a hexagon parallel to the surface, as seen in Figure 2-1(a). Our calculations first confirm that this orientation of C 60 is more energetically preferred than the one with a pentagon parallel to the surface. However,

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17 there are two different on-hollow sites, hcp and fcc, which cannot be distinguished experimentally. Our calculations indicate that the hcp site is slightly favored to the fcc site, by only 0.02 eV. We further investigated two other potential adsorption sites, bridge and on-top sites as shown in Figure 2-1(b) for the same orientation. We found that the hcp site is indeed the most stable one. The calculated adsorption energy on a hcp site is 2.24 eV, followed by bridge at 2.22 eV, fcc 2.22 eV and on-top 2.00 eV. (a) (b) Figure 2-1. Surface geometry and adsorption sites for a C 60 ML on a Cu(111) surface. (a) depicts a C 60 monolayer on hcp sites in the (4) unit cells with the lowest energy configuration (4 cells are shown); and (b) adsorption sites on a Cu(111) surface: 1, on-top; 2, fcc; 3 bridge; and 4, hcp. Sites 2 and 4 are not equivalent because of the differences in lower layers (not shown). The adsorption energy as a function of various rotational angles of the hexagon on all four adsorption sites is plotted in Figure 2-2 (the configuration of zero degree rotation corresponds to Figure 2-1(a)). It can be seen in Figure 2-2 that, at certain orientations, a C 60 molecule can easily move via translational motion from one hcp site to another with a nearly zero barrier (translation from hcp to bridge, to fcc and then to hcp). The 360 o on-site rotational energy barrier on all the adsorption sites is about 0.3 eV. Note that a 60 o on-site rotation on hcp and fcc sites is subject to a barrier of only 0.1 eV. These energetic features determine the diffusion of C 60 molecules on the Cu(111) surface. Experiments have found that C 60 is extremely mobile on a Cu surface, which is a result of the low

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18 energy barrier when the molecule rotates and translates simultaneously. So far, there are no experimental data reported for C 60 adsorption energy on Cu(111) surface, but the experimental adsorption energy of a C 60 ML on an Au(111) surface is 1.87 eV [10], which is estimated to be smaller than that from a Cu surface. We conclude that the adsorption energy of a C 60 ML on Cu(111) surface is between 1.9 and 2.2 eV. Figure 2-2. Adsorption energies as functions of rotational angle for a C 60 ML on a Cu(111) surface. Zero-angle orientation is defined as in Figure 2-1(a). The system has a three-fold symmetry because of the Cu lattice. When the angle is 0 o 60 o 120 o ,, the hcp (filled circle), bridge (filled square) and fcc (open square) sites but not the on-top (open circle) have similar energy. A C 60 molecule can translate from one site to another, among hcp, fcc and bridge, freely with the exception of the on-top site. The equilibrium binding distance between the bottom hexagon of C 60 and the top Cu surface layer is 2.0 on a hcp site, 2.1 on a fcc site, 2.2 on a bridge site, and 2.3 on a on-top site. This sequence parallels the adsorption energy, as expected. The C 60 -Cu(111) interaction modifies the underlying Cu lattice as follows: At the C 60 -Cu(111) contact, the Cu-Cu bond length in the triangle right underneath the molecule expands by 5-6% (very significant), and the short and long C-C bonds in the C 60 hexagon right above

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19 the Cu surface increase by 3% and 2% (not negligible); the Cu atoms beneath the molecule lower their positions by 0.14 and the Cu atoms surrounding the molecule rise by 0.10 with respect to the average atomic position in the surface layer. The deformation and the perturbation from the molecule cause electrons in the surface to undergo diffusive reflection when they encounter the interface, thus reducing the conductance of a relatively thick metal film [17]. (a) (b) Figure 2-3. Total density of states and partial DOS projected on the C 60 ML and the Cu(111) surface. They are plotted in the full energy range and near the Fermi level in (a) and (b), respectively. The dashed vertical line represents the Fermi level. 2.3.1.2 Electronic Structures To analyze electronic structure, the density of states and energy bands are projected onto the C 60 molecule and the Cu surface via the relationships 2,,iiigwkkkkrr (2-11) and 2,,iipwkkkrr (2-12) respectively. Here, and ,i k are the atomic and Bloch wave functions, respectively; w k is the weight of each k point, and the indices and (i,k) are labels for atomic orbitals

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20 and Bloch states, respectively. The projection provides a useful tool for analyzing the electronic band structure and the density of states. (a) (b) (c) (d) Figure 2-4. Band structure for the adsorption of a C 60 ML on a Cu(111) surface. (a) is the first Brillouin zone of the two-dimensional space group of p3m1. The irreducible region is indicated by shadowing. (b) is the band structure of an isolated C 60 ML near the Fermi level. (c) are the projection coefficients of the bands on the C 60 (solid line) and the Cu surface (dotted line) near the Fermi level. (d) depicts two bands across the Fermi level that are likely to originate from the C 60 LUMO(t 1u )-derived bands. Their projections on the C 60 ML are 3% and 13%, respectively. The total density of states (DOS) and partial DOS projected on Cu and C 60 of a C 60 ML adsorbed on an hcp site with a hexagon parallel to the surface are shown in Figure 2-3. The Fermi level is located above the range of the strong Cu d band as seen in Figure 2-3(a). The sharp peaks below 8 eV indicate that the states in that low energy range are

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21 modulated strongly by the features of the C 60 ML. It can be seen in Figure 2-3(b) that the DOS near the Fermi level is dominated by states from the Cu(111) surface. Figure 2-5. DOS of an C 60 ML before and after its adsorption on a Cu(111) surface. The solid and dashed line stand for before and after the adsorption, respectively. The band structure of an isolated C 60 ML is shown along the -M-Kdirections in Figure 2-4(b) together with the first surface Brillouin zone in Figure 2-4(a). It shows that an isolated C 60 ML is a narrow gap semiconductor, with a gap of 1.0 eV. The threefold degeneracy in the LUMO (t1u) of a C 60 molecule is lowered by the two-dimensional symmetry. The LUMO turns into three bands closely grouped from 0.5 to 1.0 eV. Projections of all bands near the Fermi level on C 60 and Cu of the C 60 -Cu(111) system are given in Figure 2-4(b). We found that projections on C 60 are small fractions compared to the metal surface. The band structure of the C 60 -Cu(111) system suggests a strong band mixing, thus making it difficult to trace the origin of any given band. We identify two energy bands that cross the Fermi energy in Figure 2-4(d), which are likely to be bands from the t 1u orbital of the isolated C 60 -ML. These bands have projections of only 3% and

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22 13% on C 60 It can be seen from these curves that the hybridization between molecular and surface states is significant, indicating strong molecule-surface interactions. The partial DOS projected on a C 60 ML adsorbed on the Cu(111) surface (dashed line) is compared to an isolated C 60 ML (solid line) in Figure 2-5. Relative to the isolated C 60 ML, states near the Fermi energy of the adsorbed C 60 ML have shifted to lower energy as a result of molecule-surface interaction. The LUMO (t 1u )-derived band is now broadened and partially filled below the Fermi energy because of the surface-to-molecule electronic charge transfer. The calculated DOS compares nicely with experimental results from photoemission spectroscopy. This energy shiftcharge transfer phenomenon is very characteristic in molecule-surface interactions. It is a compromise between the two systems: A strong bond between the molecule and the surface has formed at the cost of weakening the interaction within both the C 60 ML and within the metal surface. Integration of the partially filled C 60 LUMO(t 1u )-derived band leads to a charge transfer of 0.9 electrons per molecule from the copper surface to the adsorbed C 60 ML. To confirm the magnitude of charge transfer, we also implemented a modified Bader-like approach [69] to analyze the electron density in real space. The bond critical plane is first located by searching for the minimum electron density surface inside the C 60 -metal interface region using 0z r (2-13) where is the electron density and z is the direction normal to the Cu surface. Then the electron density between the bond critical plane and the middle of the vacuum is integrated and the result is assigned as the electrons associated with C r 60 A charge

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23 transfer of 0.8 electrons per molecule is observed using this analysis from the surface to the C 60 molecule, which is in agreement with the analysis of the DOS. (a) (b) (c) (d) Figure 2-6. Partial DOS of different adsorption configurations for a C 60 ML on a Cu(111) surface. Partial DOS is projected on the bottom hexagon of C 60 (upper panel in a-d) and on the first surface layer of Cu(111) surface (lower panel in a-d)

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24 for different adsorption sites and orientations. Panel (a) is hcp (solid line) vs. fcc (dotted line); (b) hcp (solid line) vs. on-top (dotted line); (c) hcp (solid line) vs. hcp with a 90 o rotation (dotted line); and (d) on-top (solid line) vs. on-top with a 30 o rotation (dotted line). Furthermore, to understand the energetic preference of different adsorption sites, we analyze their DOS in Figure 2-6. The DOS is projected on the bottom hexagon of C 60 and the top Cu surface layer in the upper and lower panel of Figure 2-6, respectively. It can be seen in Figure 2-6(a) that the DOS of a fcc site differs very little from that of a hcp site, which explains why they have very close adsorption energy. In Figure 2-6(b), the DOS of an on-top site has a quite visible population shift, with respect to that of a hcp site, from the bottom of the Cu d band around 3.5 eV to the top of the Cu d band around 1.5 eV. It is well known [70] that the Cu bonding states, d, located at the bottom of the d band and the anti-bonding states, located at the top of the d band. Consequently, an increased population in higher energy states means less bonding, while an increased population in lower energy states indicate more bonding. This explains why the on-top site has less binding energy than the hcp site, as reflected in the difference of DOS. Similar features are also depicted for rotations of a C xy dx2y2 60 molecule on the hcp and the on-top sites in Figure 2-6(c) and (d), respectively. 2.3.1.3 Electron Density Redistribution and Work Function Change The electron density difference, r is obtained by subtracting the densities of the clean substrate and the isolated C 60 ML from the density of the adsorbate-substrate system. This quantity gives insight into the redistribution of electrons upon the adsorption of a C 60 ML. In Figure 2-7 (a) and (b), the iso-surfaces of electron density difference are plotted for binding distances of 2.0 and 2.8 for a C 60 ML adsorbed on a hcp site with a hexagon parallel to the surface. In both panels, the three-fold symmetry of the electron

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25 density redistribution can be seen clearly. When C 60 is at the equilibrium distance, 2.0 from the surface, the redistribution of electrons is quite complicated especially in the interface region between the surface and the molecule as seen in Figure 2-7(a). To get a better view, we plot the planar averaged electron density difference along the z direction, in the upper panels of Figure 2-8(a). z (a) (b) Figure 2-7. Iso-surfaces of electron density difference for a C 60 ML on a Cu(111) surface. Electron density decreases in darker (red) regions and increases in lighter regions (yellow): (a) depicts the equilibrium position and (b) corresponds to the C 60 being lifted by 0.8 The iso-surface values are .0 and .4 e/(10bohr) 3 in (a) and (b) respectively. The complexity of the distribution shown leads to a net charge transfer from the surface to the C 60 ML and a dipole moment that is opposite to the direction of charge transfer. Considering the charge transfer of 0.8 electrons per molecule from the surface to C 60 the simple picture of electrons depleting from the surface and accumulating on C 60 can not be found in these figures. Instead, it is a surprise to see such complexity in the electron density redistribution. The major electron accumulation is in the middle of the interface region, which is closer to the bottom of C 60 than the first Cu layer. This feature of polarized covalent bonding results in a charge-transfer from the surface to the C 60 Some electron accumulation also happens around the top two Cu layers and inside the C 60 cage. On the other hand, the major electron depletion is inside the interface region from

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26 places near either the first Cu layer or the bottom hexagon of C 60 There are also significant contributions of electron depletion from regions below the first Cu layer and inside the C 60 cage. When the C 60 is 0.8 away from the equilibrium distance, this feature of electron depletion inside the C 60 cage becomes relatively more pronounced as seen in Figure 2-7(a) and the upper panel of Figure 2-8(b). This feature has important effects on the surface dipole moment and the change of work function. (a) (b) Figure 2-8. Planar averaged electron density differences (upper panel) and the change in surface dipole moment (lower panel) for the adsorption of a C 60 ML on a Cu(111) surface. Both are the functions of z, the direction perpendicular to the surface. The distance between the bottom hexagon of C 60 and the first copper layer is 2.0 in (a) and 2.8 in (b). The solid vertical lines indicate the positions of the top two copper layers and the dashed vertical lines indicate the locations, in z direction, of the two parallel boundary hexagons in C 60 The dotted horizontal line indicates the total change in the surface dipole moment. The measured work functions (WF) of a clean Cu(111) surface and a C 60 ML covered Cu(111) surface from experiments are 4.94 and 4.86 eV [9], respectively. The WF actually decreases by a tiny amount of 0.08 eV, although a significant charge transfer

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27 from the substrate to C 60 is observed in both experiments and our calculation. This result is very puzzling with respect to the conventional interpretation of the relationship between WF change and charge transfer. According to a commonly used analysis based on simple estimation of a surface dipole moment, when electrons are transferred from absorbed molecule to the surface the WF will decrease, while transfer the other way will result in a WF increase. To resolve this puzzling phenomenon and to investigate the issue thoroughly, we employ two methods to calculate the work function change. One is to compute the difference directly between the work function of the adsorption system and that of the clean surface. The work function is obtained by subtracting the Fermi energy of the system from the electrostatic potential in the middle of the vacuum. To calculate the work function accurately, a symmetric slab with a layer of C 60 adsorbed on both sides of the slab or the surface dipole correction suggested by Neugebauer, et al. [71] have been used. The results are given in Table V as 1W and 2W respectively. To gain insight on the origin of the change in the work function, we apply a method suggested by Michaelides, et al. [72] to calculate the change in the surface dipole moment, induced by the adsorption of C 60 The quantity is calculated by integrating the electron density difference times the distance with respect to the top surface layer from the center of the slab to the center of the vacuum, 20cczazzzzdz (2-14) In this equation, is the center of the slab, is the top surface layer and is the length of the unit cell in the direction. The quantity cz 0z a z z is the planar averaged electron

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28 density difference along the direction. The work function change, is then calculated according to the Helmholtz equation. z 0A (2-15) where 0 is the permittivity of vacuum and is the surface area of the unit cell. Both and A are listed in Table 2-3. Table 2-3. Work function change of a C 60 ML adsorbed on a Cu(111) surface. and are calculated directly from the difference of the work functions with the dipole correction and a double monolayer adsorption, respectively. is calculated from the change in the surface dipole moment, 1W 2W induced by adsorption of C 60 Exp (eV) W 1 (eV) W 2 (eV) (eV) (Debye) 2.0 0.08 a 0.10 0.09 0.09 0.21 2.8 0.37 0.33 0.32 0.73 a. [9] The calculated WF of a neutral C 60 -ML is 5.74 eV. The calculated WF of a pure Cu(111) surface and C 60 ML covered surface are 5.24 and 5.15 eV, respectively, which are in good agreement with experiments (4.94 and 4.86 eV, respectively). The calculated work function change is 0.09 eV, which agrees very well with the change of 0.08 eV from experiments. The planar averaged charge density difference is depicted as a function of in the upper panels of Figure 2-8 for the equilibrium distance, 2.0 and the distance of 2.8 In the lower panels, the integration of the surface dipole is shown as a function of to capture its gradually changing behavior and the total value is shown by a horizontal dotted line. For the equilibrium distance, the calculated z z is 0.21 Debye leading to a change of 0.09 eV in WF, which is in excellent agreement with both direct estimation and experiments. When the C 60 is moved up from its equilibrium position, by 0.8 in the z direction, the calculated charge transfer, change in

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29 dipole moment, and work function are 0.2e 0.73 Debye and 4.91 eV (a 0.33 eV decrease), respectively. The WF further decreases by 0.33 eV. The gradual change of work function and charge transfer with respect to the binding distance are shown in Figure 2-9. The results from the two direct estimation methods and the surface dipole method match very well, especially over short distance ranges. (a) (b) Figure 2-9. Work function change and electronic charge transfer as functions of the distance between a C 60 ML and a Cu(111) surface. The work function change and electronic charge transfer are shown in (a) and (b), respectively. The solid and dashed line shows the results from the dipole correction and the calculation using a double monolayer, respectively. The change of surface dipole moment induced by molecule-surface interaction at the interface is complicated in general; it cannot be estimated simply as a product of the charge transferred and the distance between molecule and the surface. The electron depletion region inside the C 60 cage has great impact on the work function decrease as seen in both Figure 2-7 and Figure 2-8. Its effect can only be taken into account with an explicit integration in Eq.2-14. The change of work function is the result of a compromise between the two systems: A strong bond formed between the C 60 and the metal surface occurs at the cost of weakening the interaction within both C 60 and the metal surface, since electrons must be shared in the interface region.

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30 2.3.2 Adsorption of a C 60 ML on Ag (111) and Au(111) Surfaces 2.3.2.1 Energetics and Adsorption Geometries The ( 2323 )R30 o structure of a C 60 monolayer adsorbed on Ag(111) and Au(111) surfaces is shown in Figure 2-10(a). The calculated lattice constants of bulk Ag and Au are 4.02 and 4.07 respectively. The corresponding values of 9.85 and 9.97 for the vector length of the ( 2323 )R30 o surface unit cell match closely with the nearest neighbor distance in solid C 60 which is 10.01 Four possible adsorption sites are considered, as shown in Figure 2-10(b), the on-top, bridge, fcc and hcp sites. To find the lowest energy configuration on each adsorption site, we consider both a hexagon and a pentagon of C 60 in a plane parallel to the surface. Two parameters determine the lowest energy configuration on each adsorption site with a certain face of C 60 parallel to the surface. One is the binding distance between the bottom of C 60 and the top surface layer, the other is the rotational angle of the C 60 along the direction perpendicular to the surface. The adsorption energies after ionic relaxation of the lowest energy configuration on each site with a pentagon or a hexagon parallel to the surface are listed in Table 2-4. The configuration of a hexagon of C 60 parallel to the surface is more favorable energetically than is a pentagon on all adsorption sites by an average of 0.3 eV for Ag(111) and 0.2 eV for Au(111). With a hexagon of C 60 parallel to both Ag(111) and Au(111) surfaces, the most favorable site is the hcp, then the fcc and bridge sites. The on-top site is the least favorable. The preference of the hcp over the fcc site is less than 0.1 eV. With a pentagon of C 60 parallel to both surfaces, the fcc site is slightly more favorable than the hcp site by less than 0.01 eV. The rest of the ordering is the same as in the case of hexagon.

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31 (a) (b) Figure 2-10. Surface geometry and adsorption sites for a C 60 ML on Ag(111) and Au(111) surfaces. (a) top view of C 60 ML adsorbed on the Ag(111) and Au(111) surfaces (four unit cells are shown); (b) the ( 2323 ) R30 o surface unit cell and the adsorption sites on the Ag(111) and Au(111) surfaces, 1, on-top; 2, fcc; 3, bridge; and 4, hcp site. Sites 2 and 4 are not equivalent due to differences in the lower surface layers (not shown). Table 2-4. Adsorption energies of a C 60 ML on Ag(111) and Au(111) surfaces on various sites. The energies listed are the lowest ones obtained after ionic relaxation. The energy is in unit of eV/molecule. Configuration Hcp Fcc Bridge On-top Hexagon on Ag(111) -1.54 -1.50 -1.40 -1.27 Pentagon on Ag(111) -1.20 -1.20 -1.18 -0.89 Hexagon on Au(111) -1.27 -1.19 -1.13 -0.86 Pentagon on Au(111) -1.03 -1.04 -0.99 -0.60 The average binding distance between the bottom hexagon of C 60 and the top surface layer for different adsorption configurations is 2.4 for the Ag(111) surface and 2.5 for the Au(111) surface. For the same configurations, the adsorption energy of C 60 on the Ag(111) surface is larger than that on the Au(111) surface by 0.3 eV. Thus the binding of C 60 monolayer with the Ag(111) surface is stronger than the binding with the Au(111) surface as seen in both adsorption energies and binding distances. This finding is in agreement with the experimental observation that the interaction between C 60 and Au is the weakest among the noble metals [10]. As seen in Table 2-4, a hexagon of C 60 on an hcp site is the most favored configuration on both surfaces, while a pentagon on an on

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32 top site is the least favored configuration. The difference in adsorption energy is about 0.7 eV for both surfaces. In STM experiments, Altman and Colton [13-15] proposed that the adsorption configuration was a pentagon of C 60 on an on-top site for both the Ag(111) and Au(111) surfaces. However, Sakurai, et al. [16] proposed also from the results of STM experiments, that the favored adsorption site should be the three-fold on-hollow site on the Ag(111) surface, but they did not specify the orientation of the C 60 molecule. Our calculations support the model proposed by Sakurai, et al. For the Cu(111) surface, we have shown earlier in this chapter that the adsorption configuration is a hexagon of C 60 on the three-fold on-hollow site. Based on the similarity of the electronic properties of the noble metals, it is not unreasonable that C 60 occupies the same adsorption site on Ag(111) and Au(111) surfaces as on the Cu(111) surface. (a) (b) Figure 2-11. Adsorption energies as functions of rotational angle of C 60 ML on Ag(111) and Au(111) surfaces. (a) on the Ag(111) surface, and (b) on the Au(111) surface. The zero angle orientation is defined in Figure 2-10(a) with a hexagon of C 60 parallel to the surface on all sites. To obtain the rotational barriers, we plot the adsorption energies as functions of the rotational angle along the direction perpendicular to the surface on all sites with a hexagon of C 60 parallel to the surfaces in Figure 2-11. Since the binding distance on various adsorption sites differs very little, less than 0.1 with respect to rotational angle,

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33 we keep the binding distance fixed during the rotation of C 60 molecule. For each rotational angle, the atomic positions are also fixed. The calculated rotational energy barriers. Table 2-5. The relaxed structure of a C 60 ML adsorbed on Ag(111) and Au(111) surfaces with its lowest energy configuration. On both surfaces, the lowest energy configuration is a hexagon of C 60 on the hcp site, as shown in Figure 2-10(a). The parameters CC s hortb and CClongb are the relative change in the shorter and longer bond of C 60 with respect to a free molecule. The parameters M Mincb and M Mdecb are the maximum increase and decrease, respectively, in bond length between two neighboring metal atoms in the top surface layer with respect to the bulk value. The parameter 11 M M d describes the buckling, defined as the maximum vertical distance among the metal atoms in the top surface layer, and M Cd is the average distance between the bottom hexagon of C 60 and the top surface layer. CC s hortb (%) CClongb (%) M Mincb (%) M Mdecb (%) 11 M Md () M Cd () Ag(111) 1.8 1.0 4.3 -1.2 0.02 2.29 Au(111) 1.8 1.4 7.3 -2.5 0.08 2.29 On both Ag(111) and Au(111) surfaces, the rotational barrier for the on-top site is the highest, 0.5 eV for the Ag(111) surface and 0.3 eV for the Au(111) surface. The next highest rotational barriers are on the fcc and hcp sites, which are 0.3 eV for the Ag(111) surface and 0.2 eV for the Au(111) surface. Note that 30 o and 90 o rotations are not equivalent due to the three-fold symmetry. The lowest rotational barriers are on the bridge site, which are 0.2 eV for the Ag(111) surface and 0.1 eV for the Au(111) surface. The rotational barriers on both surfaces are small enough that the C 60 can rotate freely at room temperature, which agrees with the experimental observations [13-15]. In general, the rotational barriers on the Au(111) surface are lower than on the Ag(111) surface, which is consistent with the weaker binding between C 60 and the Au(111) surface than the Ag(111) surface. This result is also in agreement with STM experiments, which show

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34 that the on-site rotation of C 60 on the Au(111) surface is faster than that on the Ag(111) surface [13-15]. Several parameters of the relaxed structure in the lowest energy configuration on both the Ag(111) and Au(111) surfaces are listed in Table 2-5. The lowest energy configuration on both surfaces is a hexagon of C 60 adsorbed on an hcp site, as shown in Figure 2-10(a). On the Ag(111) surface, the bond lengths of the shorter and longer C-C bonds in the bottom hexagon of the C 60 increase by 1.8% and 1.0%, respectively, but the bond length of the C-C bonds in the top hexagon of the C 60 does not change. The neighboring Ag-Ag bond lengths in the top surface layer increase by as much as 4.3% for the atoms directly below the C 60 and decrease by as much as 1.2% in other locations. The relaxation of the Ag atoms in the top surface layer causes a very small buckling of 0.02 which is defined as the maximum vertical distance among the Ag atoms. This value is much less than the corresponding value of 0.08 on Au(111) surface. The average vertical distance between the bottom of the C 60 and the top surface layer is 2.29 On the Au(111) surface, the values of these parameters are somewhat larger than those on the Ag(111) surface, which means that the Au(111) surface tends to reconstruct. However, the interaction of C 60 with the Ag(111) surface is still stronger than that on the Au(111) surface as seen from the adsorption energies in Table 2-4. 2.3.2.2 Electronic Structure and Bonding Mechanism The total density of states and partial density of states (PDOS) projected on C 60 and the substrate are shown in Figure 2-12 (a) and (c) for the Ag(111) and Au(111) surfaces, respectively. The Ag 4d band is 3 eV below the Fermi level and the Au 5d band is 1.7 eV below the Fermi level. The dominant features near the Fermi level are from the substrate.

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35 (a) (b) (c) (d) Figure 2-12. Density of states for the adsorption of a C 60 ML on Ag(111) and Au(111) surfaces. The total DOS and partial DOS projected on the C 60 Ag and Au are shown in (a) on the Ag(111) surface and (c) on the Au(111) surface. The DOS of an isolated C 60 ML (solid line) and the PDOS of the adsorbed C 60 ML (dashed line) are shown in (b) and (d) for the adsorption system on the Ag(111) and Au(111) surfaces, respectively. The dashed vertical lines represent the Fermi level. To see the change of the bands derived from C 60 upon adsorption, the PDOS of an isolated C 60 monolayer and the adsorbed C 60 monolayer are plotted together in panels (b) and (d) for the Ag(111) and Au(111) surfaces, respectively. It is clear that a small portion of the C 60 LUMO (t1u)-derived band shifts below the Fermi level, indicating electron transfer from the substrate to C 60 The magnitude of the electron transfer can be estimated from the area of the C 60 LUMO-derived band below the Fermi level. The calculated charge transfer is 0.5 and 0.2 electron per molecule from the Ag(111) and Au(111)

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36 surfaces, respectively, to the C 60 monolayer. These values are somewhat smaller than the experimental estimate of 0.8 electrons per molecule on both surfaces [10, 22]. (a) (b) (c) (d) Figure 2-13. Iso-surfaces of electron density difference for the adsorption of a C 60 ML on Ag(111) and Au(111) surfaces. Electron density decreases in darker (red) regions and increases in lighter (yellow) regions. The distance between the bottom hexagon of C 60 and the first surface layer is 2.3 in (a) and 3.1 in (b) on the Ag(111) surface; and 2.4 in (c) and 3.2 in (d) on the Au(111) surface. The iso-surface value is .0 e/(10bohr) 3 in (a) and (c), and .4 e/(10bohr) 3 in (b) and (d). Although there is some evidence from both theory and experiment for electronic charge transfer from noble metal surfaces to C 60 the nature of the bonding can not be assigned as ionic without examination of the electron density difference; recall Section 2.3.1.3. The iso-surfaces of electron density difference are plotted for binding distances of 2.3 and 3.1 for the Ag(111) surface in Figure 2-13 (a) and (b), and 2.4 and 3.2

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37 for the Au(111) surface in Figure 2-13 (c) and (d). In all panels, the three-fold symmetry of electron density redistribution can be seen clearly. As shown in panels (a) and (c), the electron density redistribution is very similar for the adsorbed C 60 monolayer at the equilibrium binding distances on both the Ag(111) and Au(111) surfaces. Three observations can be made from the data shown in Figure 2-13. First, the change in the electron density is confined mostly to the top surface layer, the bottom half of the C 60 and the interface region. Close examination shows that the electron density in the top half of the C 60 changes very little, which agrees with the finding that no change in the C-C bond length occurs after ionic relaxation. Second, there is significant electron depletion around both the top surface layer and the bottom hexagon of the C 60 Specifically, the dumbbell shape lying in the direction perpendicular to the surface with a small ring of electron accumulation near the top surface layer indicates the character of noble metal d xz and d yz electrons. In addition to the electron density depletion region just below the bottom hexagon of the C 60 there are small regions inside the C 60 cage and just above the bottom hexagon, where the electron density also decreases. Third, although the electron density increases in some regions just above the bottom hexagon of the C 60 the most significant electron accumulation occurs in the middle of the interface region, which has a dumbbell shape parallel to the surface. When the C 60 monolayer is pulled 0.8 away from the equilibrium binding distances, the region with electron accumulation in the middle of the interface can be seen more clearly in Figure 2-13 (b) and (d). Evidently the electron density shared in the middle of the interface region derives from both the Ag(111) and Au(111) surfaces and the C 60 monolayer. As a result, the bonding between them is best described as ionic-covalent with a small magnitude of

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38 electronic charge transfer. The bond strength between the C 60 monolayer and noble metal surfaces decreases in the order Cu(111), Ag(111) and Au(111) according to both our calculations and the experimental observations. The covalent bonding explains why a hexagon is preferred to a pentagon when a C 60 monolayer adsorbs on noble metal surfaces. As is well known, for an isolated C 60 molecule, the hexagon region has a higher electron density than the pentagon region because the C 60 HOMO is centered on the bonds between two hexagons, and the C 60 LUMO is centered on the bonds between a hexagon and a pentagon. To form covalent bonds with noble metal surfaces, the hexagon is more efficient than a pentagon because more electrons are available. If the bond were ionic in nature, we would expect the most stable configuration to be a pentagon facing toward the surface. Although similar, there are slight differences in the electron redistribution in the C 60 -Ag(111) and C 60 -Au(111) systems. Specifically, the Au(111) surface tends to spill out fewer electrons than the Ag(111) surface for sharing with the C 60 As a result, C 60 on an Au(111) surface provides more electrons than it does on an Ag(111) surface for covalent bonding. These different features have a large impact on the different behavior of work function change on these two noble metal surfaces, which we will discuss in detail in the following section. To understand the energetic preferences of the various adsorption configurations, the PDOS of a hexagon of C 60 on an hcp site and two other configurations on the Ag(111) and Au(111) surfaces are compared in Figure 2-14. The upper panels are the PDOS projected on the bottom hexagon or pentagon of the C 60 parallel to the surface. The lower panels are the PDOS projected on the top surface layer.

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39 (a) (b) (c) (d) Figure 2-14. Partial DOS of different adsorption configurations for a C 60 ML on Ag(111) and Au(111) surfaces. In (a)-(d), the upper panel is the PDOS of the bottom hexagon or pentagon parallel to the surface and the lower panel is the PDOS of the top surface layer. In panel (a), the solid line represents a hexagon of C 60 on an hcp site and the dotted line a hexagon on an on-top site on the Ag(111) surface. In panel (b), the solid line represents a hexagon of C 60 on an hcp site

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40 and the dotted line a pentagon on an on-top site on the Ag(111) surface. In panel (c), the solid line represents a hexagon of C 60 on an hcp site and the dotted line a hexagon on an on-top site on the Au(111) surface. In panel (d), the solid line represents a hexagon of C 60 on an hcp site and the dotted line a pentagon on an on-top site on the Au(111) surface. In Figure 2-14 (a), the PDOS of a hexagon of C 60 on an hcp site is compared to that of a hexagon on an on-top site on the Ag(111) surface. The figure shows that there are more electrons from the on-top site than the hcp site populating the top of Ag d bands around 3 eV, which are the anti-bonding states. This is the reason why the hcp site is preferred to the on-top site. When comparing a pentagon of C 60 on an on-top site with an hcp site, this feature can also be seen in Figure 2-14 (b). In addition, the C 60 LUMO-derived bands of the hexagon shift further below the Fermi level than those of a pentagon, which indicates more electronic charge transfer. The Bader-like analysis confirms this interpretation by predicting 0.5 and 0.4 electrons transferred for these two cases, respectively. The same argument can also be applied to the adsorption of C 60 on the Au(111) surface, as shown in Figure 2-14 (c) and (d). Comparing the PDOS in Figure 2-14 (b) and (d), we notice that the C 60 HOMO1 bands hybridize significantly with the Au d bands, but stay unchanged on the Ag(111) surface. The reason for this behavior is that the Au d bands are closer to the Fermi level than the Ag d bands. The Au d bands align well with the C 60 HOMO1 bands. 2.3.2.3 Work Function Change A puzzling phenomenon observed in C 60 -metal adsorption systems is the work function change [10, 12]. Traditionally, work function change is associated closely with the direction and the magnitude of electron transfer between the substrate and the adsorbate. An increase in the work function indicates that electrons have been transferred from the substrate to the adsorbate; a decrease in the work function indicates that

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41 electrons have been transferred in the opposite direction. The argument can also be used in an inverse sense. If electron transfer occurs from the substrate to the adsorbate, an increase in the work function would be expected. For a C 60 monolayer adsorbed on noble metal surfaces, electron transfer from the surface to the C 60 monolayer is observed in both the experiments and our first-principles DFT calculations. As already discussed, measurements of the work function in experiments have found that the work function actually decreases for Cu(111) [9] and Au(111) [10] surfaces upon adsorption of a C 60 monolayer. Table 2-6. Work function change of a C 60 ML adsorbed on Cu(111), Ag(111) and Au(111) surfaces. W is calculated directly from the difference of the work functions. is calculated from the change in the surface dipole moment, induced by adsorption of C 60 Exp (eV) W (eV) (eV) (Debye) Cu(111) -0.08 a -0.09 -0.09 -0.21 Ag(111) +0.14 +0.11 +0.24 Au(111) -0.6 b -0.58 -0.60 -1.37 a. [9] and b. [10] We study this issue as in Section 2.3.1.3. The results are given in Table 2-6. The work function change calculated from the direct difference is listed as Once again, the change in the surface dipole moment, W induced by the adsorption of C 60 is calculated by integrating the electron density difference times the distance with respect to the top surface layer from the center of the slab to the center of the vacuum as in Eq. 2-14. The work function change, is then calculated according to the Helmholtz equation in Eq. 2-15. Both and are listed in Table 2-6. For comparison, we also list in Table 2-6 the results for a C 60 monolayer adsorbed on a Cu(111) surface in the (4) surface unit cell [73] from Table 2-3.

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42 (a) (b) (c) (d) Figure 2-15. Planar averaged electron density differences (upper panel) and the change in surface dipole moment (lower panel) for the adsorption of a C 60 ML on Ag(111) and Au(111) surfaces. They are the functions of z, the direction perpendicular to the surface. The distance between the bottom hexagon of the C 60 and the first Ag(111) surface layer is 2.3 in (a) and 3.1 in (b). The distance is 2.4 in (c) and 3.2 in (d) for C 60 adsorbed on the Au(111) surface. The solid vertical lines indicate the positions of the top two surface layers and the dashed vertical lines indicate the positions of the two parallel boundary hexagons in C 60 The dotted horizontal line indicates the total change in the surface dipole moment.

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43 As seen in Table 2-6, the work function change for the Au(111) surface is 0.58 eV via the direct calculation and 0.60 eV via the surface dipole calculation, which agrees very well with the experimental value of 0.6 eV [10]. The corresponding change in the surface dipole is 1.37 Debye. For the Ag(111) surface, we find the work function change is +0.14 eV and +0.11 eV using the two methods, respectively. The change in the surface dipole in this case is +0.24 Debye. There are no experimental data on the work function change for the C 60 -Ag(111) system. However, experimentally the work function increases by 0.4 eV for C 60 adsorbed on an Ag(110) surface [11], which supports our results. Despite the opposite change of the work function on the Ag(111) and Au(111) surfaces upon C 60 adsorption, calculations of the change in the surface dipole moment reproduce the work function change very well. This result suggests that the origin of the work function change is indeed the dipole formation around the interface. The simple picture of electronic charge transfer of an ionic nature from the substrate to the adsorbate fails to describe the entire picture of the complicated surface dipole formation. A full understanding of the different behavior of the work function change on Ag(111) and Au(111) surfaces requires close examination of the electron density differences. To elucidate more clearly, the planar averaged electron density differences along the z direction are shown in the upper panels of Figure 2-15 (a) and (c) at the equilibrium binding distances. The top surface layer is at zero distance, as indicated by a solid vertical line. The interface region is between the solid vertical line at zero and the nearby dashed vertical line at 2.0 As discussed in the previous section, the common feature of both figures is the indication of covalent bonding rather than ionic bonding.

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44 Electron density spills out from the top metal surface layer, which increases the surface dipole. At the same time, electron density from C 60 also spills out from the cage toward the interface region, which decreases the surface dipole. For approximately the same amount of electron accumulation in the middle of the interface region, the electron depletion from the Ag(111) surface is larger than that from the Au(111) surface. At the same time, electron depletion around the C 60 is smaller on the Ag(111) surface than on the Au(111) surface. These differences in the multiple dipole formations result in the increase of the surface dipole for C 60 adsorbed on the Ag(111) surface and decrease of the surface dipole for C 60 adsorbed on the Au(111) surface, as shown in the lower panels in Figure 2-15 (a) and (c). When the C 60 monolayer is pulled 0.8 away from the equilibrium distance, there is still significant electron depletion from C 60 on the Ag(111) surface as seen in Figure 2-15 (b). On the Au(111) surface, at 0.8 away from the equilibrium distance, as seen in Figure 2-15 (d), the electron accumulation in the middle of the interface region comes even more from the C 60 than from the metal surface. These features can also be seen in the three dimensional graphs in Figure 2-13 (b) and (d). The distance dependence of the work function change on the Ag(111) and Au(111) surfaces is shown in Figure 2-16 (a) and (c). On both surfaces, the work function decreases as the distance increases. To explain this observation, we plot the electronic charge transfer as a function of distance in Figure 2-16 (b) and (d). The charge transfer decreases as the distance increases. Less charge transfer means less electron density spills out from the surface and the bonding is less ionic in character, becoming more covalent as the distance increases. These observations are consistent with the electron density difference analysis in Figure 2-13 and 2-15. So relatively more electrons in the middle of

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45 the interface region are derived from the C 60 and fewer electrons are derived from the metal surface at larger distance. As a result, the surface dipole moment decreases and the work function decreases, too. (a) (b) (c) (d) Figure 2-16. Work function change and electronic charge transfer as functions of the distance between the C 60 and the metal surfaces. (a) and (b) are for the Ag(111) surface; (c) and (d) are for the Au(111) surface. 2.3.2.4 Simulated STM Images Tersoff and Hamann [74] showed that the tunneling current in STM experiments can be approximated at small voltages by 2,,,,FFEViiFEi I dEkkkrr V (2-16) where is the Fermi energy of the system and V is the applied bias. The STM image is simulated by the local density of states around the Fermi energy. The simulated STM FE

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46 images of the most favorable adsorption configuration are shown in Figure 2-17 for a C 60 monolayer adsorbed on the Ag(111) surface ((a) and (b)) and the Au(111) surface ((c) and (d)). A bias of 2.0 V is used in panels (a) and (c), and +2.0 V is used in (b) and (d). The STM image is simulated by the local density of states at the position of 1.5 above the top of C 60 monolayer. (a) (b) (c) (d) Figure 2-17. Simulated STM images for a C 60 ML adsorbed on Ag(111) and Au(111) surfaces. Panels (a) and (b) are for the Ag(111) surface with a bias of -2.0 and +2.0 V, respectively. Panels (c) and (d) are for the Au(111) surface with a bias of -2.0 and +2.0 V, respectively. On both surfaces, the tip is 1.5 away from the top of the C 60 The images on the different surfaces are almost the same. The negative bias produces a ring-like shape and the positive bias produces a three-leaf shape. These images are in good agreement with the STM images simulated by Maruyama, et al. [47]

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47 The negative bias shows features of the C 60 HOMO, which is centered on the C-C bonds between two hexagons, while the positive bias shows features of the LUMO, centered on the C-C bonds between a hexagon and a pentagon. These images correspond well to the most preferred adsorption configuration of a hexagon of C 60 on an hcp site, as shown in Figure 2-10(a). Since C 60 can rotate freely on both the Ag(111) and Au(111) surfaces at room temperature, the STM images observed in experiments are dynamical averages. 2.3.2.5 Difference in Band Hybridization Figure 2-18. Difference in electronic structures for the adsorption of a C 60 ML on noble metal (111) surfaces. The upper and lower panel show the partial DOS projected on the bottom hexagon of the C 60 ML and the top metal surface layer, respectively. The dotted lines stand for the adsorption of the C 60 ML on the Cu(111) surface, the dashed lines for the Ag(111) surface, and solid lines for the Au(111) surfaces.

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48 The difference in electronic structures for the adsorption of a C 60 ML on a noble metal (111) surface is shown in Figure 2-18 by the partial density of states projected on the bottom hexagon of C 60 and on the top metal surface layer. The Cu 3d band is 1 eV below the Fermi level, while the Ag 4d band is 3 eV below the Fermi level. The consequence is that the Cu 3d band hybridizes much more with the C 60 HOMO1 derived band because of the better alignment. As for the case of Au 5d band, because of relativistic effects [75], it is broadened and pushed toward the Fermi level. The resulting Au 5d band is only 1.7 eV below the Fermi level, which also has stronger hybridization with the C 60 HOMO1 derived band than Ag 4d band. This explains why the C 60 ML has the smallest electron depletion on Ag(111) surface among the three noble metals. Thus, unlike Cu(111) and Au(111) surfaces, the Ag(111) surface has a decrease in work function upon the adsorption of the C 60 ML. 2.3.3 Adsorption of C 60 ML on Al(111) and Other Surfaces The adsorption of C 60 on various surfaces other than noble metal (111) surfaces has also been studied [8, 12]. From experiments, it has been found that C 60 is weakly bonded to graphite and silica surfaces. The interaction is mostly of van der Waals type. Very strong covalent bonding has been found between C 60 and Si, Ge and transition metal surfaces. The strength of the bonding between C 60 and noble metal surfaces is in the middle of these two categories. From our first-principles DFT calculations, the bonding between a C 60 ML and noble metal (111) surface has features of both covalent and ionic character. Another metal surface that binds C 60 at similar strength as the noble metal surfaces is Al. Al is also a fcc metal with the lattice constant of 3.76 which is about 6% smaller than that of Ag and Au. It has been found from both experiments [12] and

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49 first-principles calculation [49] that the ( 23) surface structure of a C 23 60 ML adsorbed on Al(111) surface is only a metastable phase. The underlying Al atoms tend to reconstruct and form a more stable (6) surface structure with one out three C 60 lifted. The bonding between C 60 and Al(111) surface has been claimed to be predominantly covalent. (a) (b) Figure 2-19. Density of states for the adsorption of a C 60 ML on a Al(111) surface. In (a), the total DOS, the partial DOS projected on the C 60 ML and the Al(111) surface are shown. The DOS of an isolated C 60 ML (solid line) and the PDOS of the adsorbed C 60 ML (dashed line) are shown in (b). The dashed vertical lines represent the Fermi level. As a comparative study, we investigate the bonding of a C 60 ML with Al(111) surface in the same ( 2323 ) surface structure as the Ag(111) and Au(111) surfaces. For this metastable structure, we found that the most favored adsorption site is the hcp site with a hexagon of C 60 parallel to the surface. The binding distance between C 60 and the Al(111) surface is 2.5 and the adsorption energy is 1.5 eV, which are close to the results for the noble metal (111) surfaces. In Figure 2-19 (a) the total DOS and partial DOS projected on C 60 and Al are shown. The dominant feature around the Fermi level is from the Al s and p electrons. As seen in Figure 2-19 (b), the HOMO-1 and LUMO

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50 derived bands of an isolated C 60 ML are broadened and slightly split as compared to those in Figure 2-12 (b) and (d). This change is caused by the stress induced by the smaller lattice constant of Al compared to Ag and Au. After its adsorption on Al(111) surface, the C 60 derived bands shift toward lower energy and part of the LUMO (t1u)-derived band shifts below the Fermi level in a similar pattern to those for a C 60 ML adsorbed on noble metal (111) surfaces. This shows there is also a significant electronic charge transfer from the Al(111) surface to the adsorbed C 60 ML. (a) (b) Figure 2-20. Electron density difference and change in surface dipole moment for a C 60 ML on a Al(111)surface. The binding distance is 2.5 In (a), the Iso-surfaces of electron density difference are shown at the value of .0 e/(10bohr) 3 Electron density decreases in darker (red) regions and increases in lighter (yellow) regions. The planar averaged electron density difference and the change in surface dipole moment are shown in the upper and lower panel of (b), respectively. The solid vertical lines indicate the positions of the top two surface layers and the dashed vertical lines indicate the positions of the two parallel boundary hexagons in C 60 The dotted horizontal line indicates the total change in the surface dipole moment

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51 In Figure 2-20(a), the electron density difference is shown for the equilibrium binding distance of 2.5 on the hcp site. The planar averaged electron density difference and the integration of the change in surface dipole are also shown in Figure 2-20(b). Compared with those for the noble metal (111) surfaces, the electron depletion from the bottom hexagon of C 60 is very small, much less than that from the Al (111) surface, and the electron accumulation region is even closer to the bottom hexagon of C 60 than for any noble metal surface. This combination indicates a large electronic charge transfer. The magnitude of the charge transfer is evaluated to be 1.0 electrons per molecule, which is larger than the value of 0.8 for Cu(111) surface. The corresponding surface dipole change is 2.10 Debye, which corresponds to an increase of 0.90 eV in work function. Consequently, we think the interaction between C 60 and Al(111) surface has more ionic feature than noble metal (111) surfaces. The surface reconstruction has also been found for a C 60 ML adsorbing on open surfaces of noble and transition metals, such as (110) and (100) surfaces. Generally, a much larger surface unit cell is needed to include surface reconstruction. The study of such adsorption systems poses a great challenge for large scale first-principles DFT calculation. With more efficient algorithms, faster computer hardware, and new developments in multiscale modeling, such as the embedding atom-jellium model presented in Chapter 4, these issues of C 60 induced surface reconstruction will be addressed in the near future. 2.3.4 Adsorption of SWCNT on Au(111) Surface Another fullerene that also attracts intensive research is the single wall carbon nanotube (SWCNT). In experiments [76], it has been used to construct a single electron transistor and thus is regarded as a promising candidate for future nano-electronics. In

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52 these experiments, a SWCNT is always used with Au electrodes. The study of the adsorption of SWCNTs on an Au surface therefore is of basic interest. It has been found from first-principles calculations that the outer wall of a SWCNT interacts weakly with Au surface [77, 78]. In this section, we carry out first-principles DFT calculation to study the adsorption of a metallic (5,5) and a semiconductor (8,0) SWCNT on Au(111) surface. SWCNTs come in two flavors, metallic and semiconducting, depending on the chirality (n,m) of the underlying graphite sheet. When the Brillouin zone boundary of a SWCNT unit cell crosses with the apex of the underlying Brillouin zone of graphite, the SWCNT is metallic, otherwise, semiconducting. This is summarized in the following formula for an arbitrary (n,m) SWCNT, 0,mod,3metallicnmnonzerosemiconducting (2-17) There are exceptions for SWCNT with very small diameters. For example, large curvature makes the (5,0) SWCNT metallic [79]. There are two groups of SWCNT with the shortest repeating unit cells: the armchair (n,n) with the lattice constant of g a, and the zig-zag (n,0) with the lattice constant of 3 g a where g a is the lattice constant of the underlying graphite. Once again, we use LDA with ultrasoft pseudopotentials as implemented in VASP to do the calculation. The lattice constant of fcc Au is 4.07 The structure of free-standing SWCNT is first calculated. The starting C-C bond length is 1.42 for both armchair and zig-zag SWCNT. After relaxation, the bond length in the axial direction is increased to 1.44 and the bond length is decreased to 1.40 in other directions. To accommodate several unit cells of SWCNT on an Au(111) lattice, the in-plane lattice

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53 constant of Au must be shrunk a little. For a (5,5) SWCNT, we construct the (4 3 ) surface unit cell to include three SWCNT cells by shrinking the in-plane Au lattice constant by 2%. For a (8,0) SWCNT, we construct the (2 3 3) surface unit cell to include three SWCNT cells by shrinking the in-plane Au lattice constant by 3%. The dimensions of the surface unit cells are large enough that the interaction between two neighboring SWCNTs is negligible. To find the lowest energy configuration for a SWCNT adsorbed on a Au(111) surface, we first rotate the tube along its axis to search for the optimal orientation. Then we search for the adsorption site which gives the lowest energy with this orientation. A metallic (5,5) SWCNT prefers to adsorb with a hexagon, rather than a zig-zag C-C bond along the axial direction, facing down to the surface. The most favorable adsorption site for the hexagon is the site halfway between a hcp and bridge site. The binding distance is 2.9 and adsorption energy is 0.13 eV/. A semiconducting (8,0) SWCNT prefers to adsorb with both a hexagon and an axial C-C bond facing down to the surface. The lowest energy configuration corresponds to one of the axial C-C bonds centered on a bridge site. The binding distance is 2.9 and the adsorption energy is 0.13 eV/, which are the same as for the (5,5) SWNT. For both tubes, the energy preference over any other adsorption configuration is very small. So a SWCNT can easily roll and translate on a Au(111) surface. The strength of the interaction between a SWCNT and a Au(111) surface is much weaker than that of a C 60 ML, as indicated in both the binding distance and adsorption energies. The density of states for the adsorption of a (5,5) SWCNT on a Au(111) surface is shown in Figure 2-21. The partial DOS projected on the tube remains almost the same,

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54 before and after its adsorption on the Au surface. In contrast to the large shift of the C 60 derived bands toward lower energy when a C 60 ML adsorbs on a Au(111) surface, the (5,5) SWCNT derived bands shift slightly toward higher energy. This indicates that the electronic charge transfer is from the tube to the Au surface. This is reasonable since the (5,5) SWCNT has the work function of 4.61 eV, which is much lower than 5.4 eV of the Au(111) surface as indicated from our DFT-LDA calculations. (a) (b) Figure 2-21. Density of states for the adsorption of a (5,5) SWCNT on a Au(111) surface. In (a), the total DOS, the partial DOS projected on the SWCNT and the Au(111) surface are shown. The DOS of an isolated SWCNT (solid line) and the PDOS of the adsorbed SWCNT (dashed line) are shown in (b). The dashed vertical lines represent the Fermi level. The charge transfer from a (5,5) SWCNT to a Au(111) surface is clearly shown by the electron density difference in Figure 2-22. Substantially more electrons are depleted from the tube than from the Au surface to form an electron accumulation region inside the interface. The amount of charge transfer is 0.09 electrons per surface unit cell. The induced change in the surface dipole is 1.30 Debye, as see in Figure 2-22 (b), which corresponds to a decrease in the work function of the combined system with respect to the Au(111) surface by 0.90 eV.

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55 (a) (b) Figure 2-22. Electron density difference and change in surface dipole moment for a (5,5) SWCNT on a Au(111)surface. The binding distance is 2.9 In (a), the Iso-surfaces of electron density difference are shown at the value of .0 e/(10bohr) 3 Electron density decreases in darker (red) regions and increases in lighter (yellow) regions. The planar averaged electron density difference and the change in surface dipole moment are shown in the upper and lower panel of (b), respectively. The solid vertical lines indicate the positions of the top two surface layers and the dashed vertical lines indicate the boundaries of the SWCNT. The dotted horizontal line indicates the total change in the surface dipole moment. The density of states for the adsorption of a (8,0) SWCNT on a Au(111) surface is shown in Figure 2-23. Unlike a (5,5) SWCNT, the bands derived from the (8,0) SWCNT do not shift in a uniform way when it adsorbs on the Au(111) surface. The HOMO1 derived band shifts toward higher energy, while the HOMO, LUMO and LUMO+1 derived bands shift toward lower energy with considerable broadening.

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56 (a) (b) Figure 2-23. Density of states for the adsorption of a (8,0) SWCNT on a Au(111) surface. In (a), the total DOS, the partial DOS projected on the SWCNT and the Au(111) surface are shown. The DOS of an isolated SWCNT (solid line) and the PDOS of the adsorbed SWCNT (dashed line) are shown in (b). The dashed vertical lines represent the Fermi level. (a) (b) Figure 2-24. Electron density difference and change in surface dipole moment for a (8,0) SWCNT on a Au(111)surface. The binding distance is 2.9 In (a), the Iso-surfaces of electron density difference are shown at the value of .0 e/(10bohr) 3 Electron density decreases in darker (red) regions and increases in lighter (yellow) regions. The planar averaged electron density difference

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57 and the change in surface dipole moment are shown in the upper and lower panel of (b), respectively. The solid vertical lines indicate the positions of the top two surface layers and the dashed vertical lines indicate the boundaries of the SWCNT. The dotted horizontal line indicates the total change in the surface dipole moment The electron density difference shown in Figure 2-24 indicates an electronic charge transfer from the tube to the surface. Similar to the case of a (5,5) SWCNT, there are many more electrons depleted from the tube than the Au surface. The amount of charge transfer is 0.14 electrons per surface unit cell. The induced surface dipole is 2.14 Debye, which corresponds to 0.90 eV decrease in the work function after division by the surface area of the unit cell. The planar averaged electron density difference for the (8,0) SWCNT adsorbed on the Au(111) surface has almost the same features as that for a C 60 ML adsorbed on the Au(111) surface shown in Figure 2-15 (d) at the binding distance of 3.2 2.4 Conclusion In summary, we have presented a detailed microscopic picture of the interaction between a C 60 ML and noble metal (111) surfaces. Large-scale first-principles DFT calculations have provided complete microscopic picture of the interaction between a C 60 ML and noble metal (111) surfaces. We find that the most energetically preferred adsorption configuration on all noble metal (111) surfaces corresponds to a hexagon of C 60 aligned parallel to the surface and centered on an hcp site. The strength of the interaction between the C 60 ML and noble metal (111) surfaces decreases in the order of Cu, Ag and Au. Analysis of the electron density difference and density of states indicates that the interaction between C 60 and the noble metal surfaces has a strong covalent character besides the ionic character (a small amount of electronic charge transfer from the surfaces to C 60 ). This picture is in contrast with the common notion, developed from

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58 experiments, that the interaction between C 60 and noble metal surfaces is mostly ionic. The puzzling observation of the work function change on noble metal surfaces can only be explained by including this covalent feature and close examination of the surface dipole formation in the interface region. For comparison, we have studied the adsorption of a C 60 ML on a Al(111) surface in the ( 23) structure. The interaction between a C 23 60 ML and the Al(111) surface shows more ionic character than noble metal (111) surfaces with larger electronic charge transfer from the surface to the C 60 In addition, we have also studied the adsorption of SWCNTs on a Au(111) surface. The strength of the interaction between the Au(111) surface and SWCNTs is much weaker than that of a C 60 ML. We find a very small electronic charge transfer from the SWCNTs to the Au(111) surface and the SWCNTs become p-doped.

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CHAPTER 3 MOLECULAR DYNAMICS SIMULATION OF POTENTIAL SPUTTERING ON LIF SURFACE BY SLOW HIGHLY CHARGED IONS 3.1 Introduction In recent years, with developments in ion-source technology such as the electron beam ion trap [80-85] and electron cyclotron resonance [86], highly charged ion (HCI) beams with charge states q greater than 44 have become available. In these experiments, electron beams with a given energy and density collide with the target ions and strip off their electrons. The resulting HCIs are then magnetically mass-to-charge separated into an ultrahigh vacuum chamber. The HCI beam is then decelerated before it bombards the target surface. The kinetic energy of the HCI can be as low as 5 q eV [87]. Because of the potential application of these energetic particles in nanoscale science, the interaction of HCIs with solid surfaces has become one of the most active areas in the field of particle-solid interactions. A HCI possesses a large amount of potential energy, which in slow (hyperthermal) collision with a solid surface can greatly exceed its kinetic energy and therefore dominate the ion-surface interaction. The subject includes a rich variety of physical phenomena of both fundamental and applicational importance. Investigations that focus on the neutralization dynamics of HCI projectiles have revealed the following features [88-93]: When a HCI projectile approaches a surface, the potential energy barrier between the surface and the available empty Rydberg states of the HCI projectile decreases. Below a certain approach distance, electrons can be captured via resonant neutralization (RN) and a so-called hollow atom can form rapidly. 59

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60 The emission of secondary electrons and the formation of dynamical screening charges give rise to strong image interactions between the HCI projectile and the surface. When the HCI projectile enters the surface, further RN and Auger neutralization can take place and fill the inner shell vacancies of the HCI projectile and finally neutralize it. Fast Auger electrons and X-rays can be emitted in this process. Despite the complex nature of the problem, a classical over-barrier model (COB) [88, 89] has successfully explained the image energy gain in the reflected HCI beam. In the experiments with a HCI beam at grazing incidence on a metal or insulator surface, the 32q dependence of the image energy gain can be derived by the simple COB model [89, 92, 93]. Detailed simulations based on the stair-wise COB model [94] and the dynamical COB model [95] have also been performed to reproduce the experimental results. The high potential energy of a HCI projectile at a surface can be released either via emission of electrons and photons (X-rays), or via structure distortion and sputtering of the target surface ions, atoms, or molecules. The surface modification caused by the incident ions varies according to the material characteristics of the target surfaces. Bombardment of metallic surfaces such as Au [96-99], Cu [100] is exclusively dominated by kinetic energy transfer from the HCI projectile to target surface particles. In this case, part of the potential energy of the HCI is transformed to kinetic energy due to the interaction between the HCI and the surface. For semiconductor and insulator surfaces such as Si [99, 101-104], GaAs [101, 102, 105], LiF [87, 101, 102, 106-115], SiO 2 [99, 101, 102, 108, 116], and metal oxides [101, 102, 114, 117, 118], the sputtering patterns of target surface particles are found to be highly sensitive to the charge states of the projectile ions. This process is known as potential sputtering or electronic sputtering as

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61 opposed to the conventional sputtering caused by kinetic energy transfer [87, 108]. In contrast to metals, the valence electrons in insulators are localized. An insulator surface has a considerably larger effective work function than a metal because of its large band gap. Consequently, a smaller secondary electron yield is observed in the experiments [87, 101, 102]. The localized electronic excitation and electron-hole pairs in the valence bands can survive long enough to convert potential energy into kinetic energy of sputtered target surface particles. Among the above-mentioned systems, LiF surfaces display unique features when interacting with a HCI. Solid LiF is well known for its strong electron-phonon coupling, which is the cause of electron and photon stimulated desorption [119-122]. Experimental studies of collisions between slow HCIs such as Ar q+ ( q 4, 8, 9, 11, and 14) or Xe q+ (q14, 19, and 27) and LiF surfaces have been reported in recent years [87, 101, 106-115]. The measured sputtering yields increase drastically with increasing incident HCI charge states (i.e., higher electrostatic potential energy). To capture the characteristic feature of strong electron-phonon coupling as mentioned above, a defect-mediated sputtering model (DMS) [87, 101, 102, 108, 111, 123, 124] has been proposed as the mechanism accounting for the observed potential sputtering of LiF surfaces by slow HCIs. According to this model, the electronic excitation in the F(2p) valence band is trapped into a highly excited electronic defect, namely, self-trapped excitons (STE). Above room temperature the STE can decay immediately into a pair of H and F-color centers. A H-center is a Fmolecular ion at an anion lattice site. A F-center is an electron at the next or the second next anion lattice site relative to the Li 2 + cation. These H-and F-color centers are highly mobile at room temperature and decay by emitting F 0 atoms and

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62 neutralizing Li + cations, respectively, when reaching the surface. The desorption or sputtering of the atoms is the result of a series of bond-breaking processes. In order to understand the underlying physical mechanisms for various surface modification, other models have also been proposed. For Si, the Coulomb explosion model [125] as well as the bond-breaking model [126-128] have been used to explain the dynamical process. Molecular dynamics (MD) simulations have been reported to demonstrate the dynamical consequences of the proposed mechanisms [129-132]. While Coulomb explosion and bond-breaking model are successful in many systems, they are unable to describe the specific electronic excitations in LiF. Inspired by the experimental findings, we formulate a model for MD simulations to study HCI-LiF systems. The model involves high-level quantum chemistry calculations as well as MD simulations under a variety of initial conditions. We aim to understand surface modification processes, the dynamics of surface particles (both atoms and ions), and the correlation of initial conditions with final sputtering outcome. The chapter is organized in the following manner: Section 3.2 discusses the modeling and simulation, section 3.3 presents results and discussion, and section 3.4 contains the conclusions. 3.2 Modeling and Simulation The difficulties of applying MD to HCI-surface interactions come from the fact that multiple electronic excitations and nuclear motion are entangled during the sputtering process. Therefore, a careful analysis of the problem is necessary. The key issue is to treat the different time scales properly and to separate the electronic degree of freedom from the nuclear ionic ones. Typically, there are three time scales involved in the HCI-surface interaction. The first is the time scale for a HCI to excite the surface electrons. Second is the time scale for the rearrangement of the surface atoms and ions via defect

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63 mediated mechanism. Third is the time scale for the HCI to approach the surface. In order to observe the effects of potential energy sputtering, the second time scale must be shorter than the lifetime of the electronic excitation. In other words, the excited states rather than the ground state should dominate the nuclear motion during the sputtering process. The first time scale is quite short compared to the lattice motion, which occurs at the second time scale. Thus one can treat the electronic degree of freedom separately by assuming the ions in a few outermost surface layers to be in excited states at the beginning of the MD simulation [126, 129-134]. Such pre-existing electronic excitations will last throughout the second time scale if the lifetime of the excitation is long enough. The interaction between the projectile ion and the surface particles, as well as the interactions among the surface particles, including both ground and excited states, determines the nuclear dynamics. In a slow HCI-surface collision, the sputtering takes place before the HCI projectile reaches the surface (the third time scale), which allows us to neglect the kinetic energy effects of the incoming HCI. In many cases, we can omit the projectile ion in the simulation provided that the electrostatic potential energy is deposited in the form of electronic excitation in the surface at time zero [126, 129-134]. A test study has been performed to include the HCI explicitly. It shows that the kinetic energy of a HCI affects the surface dynamics in similar ways in single ion-surface collisions, which have been studied in previous work [129-132]. To simplify the simulation, we decided not to include the dynamics of HCIs in the system. A crucial step in constructing an adequate simulation model that describes the HCI-surface interaction is to treat the multiple electronic excitations as well as the ground state

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64 properly. To this end, we employ a high-level quantum chemistry methodology to calculate the pair potential energy functions for all possible combinations of atoms and ions. We use coupled cluster theory with single, double and perturbative triple excitations (CCSD[T]) for the ground state and an equation of motion coupled cluster method (EOM)-CCSD[T] for the excited state [135-140]. The coupled cluster theory is one of the most accurate methods available, especially for excited states, which are the center of our interest. Figure 3-1. Calculated ground state potential energy function for (Li + Li + ) from CCSD[T]. 3.2.1 Calculations of Potential Energy Functions During the HCI-surface interaction, there are four types of particles in a LiF crystal with partial electronic excitations, Li + F Li 0 and F 0 which give rise to ten different types of pair interactions as follows, (Li + Li + ), (F F ), (Li + F ), (Li + Li 0 ), (Li 0 F ), (Li 0 Li 0 ), (Li + F 0 ), (F 0 F ), (Li 0 F 0 ), and (F 0 F 0 ). The LiF molecule in the gas phase has long been regarded as a role model for first-principles calculations. The main interest has been in

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65 the nonadiabatic crossing between the potential energy function of the covalent bond from the excited state and the potential energy function of the ionic bond from the ground state. A number of calculations have been done since the early 1970s and 1980s using Hartree-Fock and configuration interaction methods [141-145]. But none of them provides all the possible ten pair interactions required to model HCI-LiF surface processes. Figure 3-2. Calculated ground state potential energy function for (F F ) from CCSD[T]. To obtain all the potential energy functions needed for simulations, we have performed state-of-the-art first-principles calculations using the ACES II program [139, 140], which is an implementation of coupled cluster theory. We choose 6-311+G as the basis set to get the desired accuracy. The calculations are performed on the dimers, which is a good approximation to the effective potential for LiF crystalline structure (see the discussion below). For the three pair interactions between two ions, i.e., (Li + Li + ), (F F ), and (Li + F ), which represent the ground state interactions in crystalline LiF, we have

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66 calculated only the potential energy functions of the electronic ground states (see Figure 3-1-3). For the other seven pair interactions that involve neutral atoms, which come from the excited states in crystalline LiF, potential energy functions of the ground state and at least four low-lying excited states are calculated (see Figure 3-3 to 3-9). Note that even the ground state of a dimer that consists of a neutral atom and an ion represents an excited state in crystalline LiF. Figure 3-3. Calculated potential energy functions for (Li + F ) and (Li 0 F 0 ) from CCSD[T]. The ground state (crosses) and six low-lying excited states are calculated. Among the excited states, the (hollow squares) is chosen in the MD simulations. The potentials for (Li + F ) and (Li 0 F 0 ) are shown together in Figure 3-3 since they have the same charge configuration. The accuracies of the binding energy and electronic excitation energy are 1 meV and 0.1 eV, respectively. This accuracy is acceptable in a MD simulation since the approximations made in the model lead to larger errors. In general, the calculations for the closed-shell excited states are more accurate than those

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67 for the open-shell; the calculations near the equilibrium distances are more accurate than those at other distances. Figure 3-4. Calculated potential energy functions for (Li + Li 0 ) from CCSD[T]. The ground state (crosses) and five low-lying excited states are calculated. Figure 3-5. Calculated potential energy functions for (Li 0 F ) from CCSD[T]. The ground state (crosses) and five low-lying excited states are calculated.

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68 Figure 3-6. Calculated potential energy functions for (Li 0 Li 0 ) from CCSD[T]. The ground state (crosses) and five low-lying excited states are calculated. Figure 3-7. Calculated potential energy functions for (Li + F 0 ) from CCSD[T]. The ground state (crosses) and five low-lying excited states are calculated.

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69 Figure 3-8. Calculated potential energy functions for (F 0 F ) from CCSD[T]. The ground state (crosses) and four low-lying excited states are calculated. Figure 3-9. Calculated potential energy functions for (F 0 F 0 ) from CCSD[T]. The ground state (crosses) and five low-lying excited states are calculated.

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70 Some features of each of the potential energy functions should be noted. For interactions (Li + Li + ) and (F F ) (see Figure 3-1 and 3-2), the ground state potentials are repulsive everywhere as expected, because of the dominant Coulombic repulsion between two ions of like charge. For the interaction (Li + F ) (see Figure 3-3), the ground state potential has a region with strong attraction and a 1/r tail from Coulombic interaction, which gives rise to the ionic bonding. For the interaction (Li 0 F 0 ) (also see Figure 3-3), which is considered as the excited state of the ionic pair (Li + F ), all six low-lying excited states are repulsive everywhere due to covalent anti-bonding. This set of excited states plays crucial roles in surface processes. For the interaction (Li + Li 0 ) (see Figure 3-4), potentials of the ground state and the first excited state have regions of attraction, but are separated by 0.070.1 hartree in region (bohr). The next four potentials from low-lying excited states are repulsive everywhere. For the interaction (Li 04ra 0 F ) (see Figure 3-5), the potential of the ground state and the five low-lying excited states all have regions of strong attraction, which lead to one of the unique features in the HCI-LiF surface dynamics presented below. For the interaction (Li 0 Li 0 ) (see Figure 3-6), all potentials have an attractive region, except for the second excited state, which is repulsive everywhere. For the interaction (Li + F 0 ) (see Figure 3-7), potentials of the ground state and the first excited state are almost identical; both have regions of weak attraction. The potential of the second excited state is just above the first excited state with a region that is slightly repulsive. The next three potentials of low-lying excited states are approximately 0.4 hartree above the ground state at For the interaction (F 04ra 0 F ) (see Figure 3-8), all potentials are repulsive everywhere. For the interaction (F 0 F 0 ) (see Figure 3-9), the ground state potential has a very narrow attraction range between

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71 2.5a and 4.0. Outside of this region, the interaction is repulsive with a barrier at 4.0a. All the potentials from the low-lying excited states are repulsive everywhere. 00 0a 3.2.2 Two-body Potentials for MD Simulation Constructing interatomic potential energy functions from first-principles calculations is an art of simulation. As already mentioned, all our calculations on the LiF system are based on dimers. When many-body effects in a system are significant, effective two-body, three-body, or N-body potentials should be constructed accordingly. In the case of a simple ionic system such as LiF, the two-body interaction dominates. Figure 3-10. Potential energy functions for ground state (Li + F ). The solid line is from Catlow et als paper [146]. The circles are calculated from CCSD[T] in the present study. For the ground state, we use the calculated two-body interactions. The calculated pair potential of (Li + F ) is very similar to the effective pair potential used in previous MD studies [146]. The binding energy differs by 4% and the binding distance 6% (see

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72 Figure 3-10). Using the calculated pair potential to construct the LiF crystal, we get 7.88 for the lattice constant and 0.37 hartree per pair for the cohesive energy. The experimental values are 7.58 and 0.39 hartree per pair, respectively [147]. Our results differ from the experimental values only by 4%. Around the equilibrium position, the two curves are shifted with respect to each other by nearly a constant, such that the difference in force constant is almost zero. Since our focus is on the dynamical consequences of the HCI interaction and the errors in the force constant are negligible, the difference will not affect the main outcome of the simulation. Beyond the equilibrium position, the calculated pair potential is more reliable than the effective pair potential, which is not optimized for long distance interaction. 0a 0a For the excited states, there is no effective two-body potential derived from first-principles calculations for extended surface. To date, there is no method yet to treat an extended system at CCSD[T] level. As an approximation, we use the true two-body (as contrasted with effective two-body) potentials for a MD simulation. Furthermore, to simplify the simulations and keep the results tractable, we choose a two-state model, i.e., the ground state and one excited state, for MD simulations. We have compared the oscillator strengths between the ground state and various excited states, and find that low-lying excited states, in general, have higher strengths than highly excited states. Since, in the crystalline LiF, the excitation can be more complicated than in dimers, it is reasonable to take the average of all low-lying states with relatively strong oscillator strengths instead of using one specific state. On the other hand, the energies among the low-lying states are close enough such that any one of them will give results similar to those given by the averaged potential. Also note that for dimers consisting of neutral particles such as

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73 Li 0 or F 0 the ground state of a dimer represents the lowest excited state in the solid as there is no ground state neutral particle in the LiF crystal. (a) (b) (c) (d) Figure 3-11. Four sets of potential energy functions for each species in LiF surface used in the MD simulations. Panel (a) represents Li + panel (b) F panel (c) Li 0 and panel (d) F 0 For a system of four distinguishable particles, ten pair-wise potential energy functions are needed. In our model, as mentioned before, the interactions between the ions are in the electronic ground states such as for (Li + Li + ), (Li + F ), and (F F ) (see Figure 3-1-3). The interaction (Li + F 0 ) (see Figure 3-7) is chosen to be the average of the ground state and the first two low-lying excited states since they are very close to each other. For the interactions (Li + Li 0 ), (Li 0 Li 0 ), (Li 0 F ), (F 0 F ), and (F 0 F 0 ), according to

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74 the rules mentioned above we take the average values of potentials that are grouped together and are relatively low-lying. The highest states in Figure 3-8 and 3-9 are excluded from the selection because of their small oscillator strengths. For (Li 0 F 0 ), we include the excited state, as it is known to have a strong transition probability from the ground state. Consequently, most of the interactions involving excited states are repulsive everywhere, except for the interaction (Li 0 F ), which has a very strong attractive region, and (Li + F 0 ), which has a slightly attractive region. The potential energy functions as described above are plotted in Figure 3-11. All curves are shifted slightly such that the energies and forces are zero at large distance in order to implement them in the MD simulations. In this figure, each panel depicts the potential energy functions for each type of particle interacting with other three types of particle and with its own type. A Li + (see Figure 3-11(a)) is strongly attractive to F and strongly repulsive to another Li + The interaction between a Li + and a Li 0 is repulsive everywhere, but less strong than an ionic pair of the same charge. The interaction between a Li + and a F 0 has a very weak attractive region compared to (Li + F ) interaction. For a F (see Figure 3-11(b)), the Coulombic interaction with a Li + is strongly attractive in the binding region, and repulsive everywhere with another F The interaction between F and F 0 is slightly repulsive at while the interaction between F 04ra and Li 0 has a strong attractive feature comparable to the (Li + F ) interaction. When a Li 0 (see Figure 3-11(c)) interacts with a neutral species, F 0 and another Li 0 the potentials are slightly repulsive at It should be noted that a Li 04ra 0 interacts with ions in ways similar to a Li + ion. In contrast, a F 0 (see Figure 3-11(d)) interacts very differently from its ionic form F All the interactions are quite short ranged and repulsive everywhere, except for a

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75 slight attractive region when interacting with a Li + These features of the potential energy functions determine the dynamics of the systems as we will discuss in detail in the following sections. Figure 3-12. Snapshot of the LiF surface at 0t for simulation 6. The ions in the topmost two layers are 100% excited. The small darker ball is Li + the small lighter ball Li 0 the large darker ball F and the large lighter ball F 0 3.2.3 Simulation Details The simulation box contains 12,168 particles that are divided into four different regions (from the bottom to the top of the surface): A static region, a temperature control region, a dynamical region and a region consisting of excited particles. Both the static and temperature control region contain two atomic layers (i.e., 1,352 particles). The lattice constant in our study is 7.88, as mentioned previously. Periodic boundary conditions are applied in the 0a x anddirections. Before electronic excitations, the LiF surface is prepared at room temperature (300 K) with all the particles in their electronic ground states, i.e., only Li y + and F ions are present. Thermalization techniques are

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76 applied as follows: At first, heat exchange between the system and an external heat bath is allowed to give all the dynamical particles thermal speeds according to the Maxwell distribution. Once equilibrium is reached, heat exchange is limited to the temperature control region just above the static region. These steps are achieved using conventional classical MD. The simulation of HCI-surface bombardment begins when a collection of particles is excited under the influence of the HCI projectile. Each dynamical particle in the system follows Newtons equation of motion. In this work, the total potential energy is the summation of all pair interactions that consist of the ten types of interactions described in the previous section. The Gear predictor and corrector algorithm [1] is used to integrate Newtons equations. The time step is 0.3 fs throughout the simulations. This time step is found to give very good energy conservation (better than 10 4 for a 10 3 steps test run). The total simulation time for most of the runs is approximately 1.2 ps. During this time period, most important dynamical processes are developed according to our analysis. Beyond 1.2 ps, the energetic atoms are at distances far away from the surface that lead to weak interactions. The change in sputtering yields is very small. 3.3 Results and Discussion 3.3.1 Initial Condition Ten simulation runs were carried out with different excitation configurations; each represents a possible initial condition. In simulations 1, 2, and 3, 20%, 60%, and 100% of the ions in the topmost layer are excited, respectively. In simulations 4, 5, and 6, 20%, 60%, and 100% of the ions in the two topmost layers are excited, respectively. In simulations 7 and 8, 100% of the ions in the three and four topmost layers, respectively, are excited. In simulations 9 and 10, 100% of the ions in a hemispherical and a

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77 cylindrical region, respectively, on the surface are excited. The amount of excitation is thus controlled either by changing the size of the excited region or by modulating the probability of particles to be excited. Figure 3-13. Snapshot of the LiF surface at 1.2t ps for simulation 6. Initially, the ions in the topmost two layers are 100% excited. The simulation box is projected on the y-z plane. The small darker ball is Li + the small lighter ball Li 0 the large darker ball F and the large lighter ball F 0 The sputtering front contains mostly Li 0 3.3.2 Surface Modification The ten simulations give different outcomes and yet share some similarities. We examine one of them in detail and compare to the others. Simulation 6 is chosen as a prototype. Figure 3-12 is a snapshot of the system at time zero. The small darker ball is for a Li + the small lighter ball for a Li 0 the large darker ball for a F and the large

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78 lighter ball for a F 0 The initial condition of excitation in simulation 6 is that the ions in the two topmost layers are fully excited (i.e., with a 100% probability), so an amount of potential energy is deposited in the form of electronic excitation. After 1.2 ps, the potential energy will be released via dynamical processes, which results in surface modification. Figure 3-14. Snapshot of the the LiF surface at t 1.2 ps for simulation 9. Initially, the ions in a hemispherical region on the surface are 100% excited. The simulation box is projected on the y-z plane. The small darker ball is Li + the small lighter ball Li 0 the large darker ball F and the large lighter ball F 0 The surface modification is depicted in Figure 3-13, which is a snapshot taken at ps. The shading and sizes of the balls are the same as in Figure 3-13. To get a better view of the surface modification, the simulation box is projected on the y-z plane. 1.2t

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79 The distinct features of different regions are very clear from the bottom to the top. Right above the static layers and the temperature control layer are several dynamical layers, which are about half the thickness of the original simulation box. Atoms in these layers move very little from their equilibrium, which means that our simulation box is thick enough to include both the surface and bulk response of the impact of a HCI. Above this region are the layers close to the surface, where the structure has been very much perturbed. Most of the particles in this region are ions, depicted in darker shading. Several Li + ions in this region try to escape from the surface. Above the surface region, there are particles sputtered from the surface. Almost all of them are neutral species, which are depicted in lighter shading. However, the distributions of Li 0 and F 0 are rather different. Li 0 and F 0 are well separated because of the differences in masses, as well as in the potential energy functions. The topmost region is the sub-region that consists of only Li 0 Between this region and the surface is a spacious sub-region consisting mostly of F 0 and very few Li + (a) (b) Figure 3-15. Distribution functions of the number of particles and potential energy along the z direction at 1.2t ps for simulation 6. Initially, the ions in the topmost two layers are 100% excited. Panel (a) represents the number of particles, and panel (b) the potential energy. In both panels, the solid line represents Li + the dashed line F the dotted line Li 0 and the dash-dotted line F 0

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80 To compare different initial conditions, we also take a snapshot from simulation 9 at ps (see Figure 3-14). The initial condition for simulation 9 is that the ions in a hemispherical region on the surface are 100% excited. It can be seen that the distribution of the atoms sputtered from the surface is quite different from that in simulation 6. There is not front layer of Li 1.2t 0 in the z direction. 3.3.3 Sputtering Yield To analyze these data, a one-dimensional grid is set up along the z direction with each grid point equally separated in distance. The profiles of physical quantities along the z direction are calculated by averaging over the x-y plane on each grid point. Figure 3-15 depicts the profile of the number of particles and potential energy for each species at ps in simulation 6. As seen in Figure 3-15(a), most of the ions stay in the surface, and the particles that escape from the surface are primarily neutral species. A close examination indicates that F 1.2t 0 neutrals are evenly spread out in the z direction in the region above the surface, in which very few Li + are present. The distribution of Li 0 is very different from F 0 It has two peaks: One is just above the surface and the other is above the sputtered F 0 layers, further away from the surface. These features can also be seen in the snapshot taken for the same moment in Figure 3-13. All these features can be understood by the distribution of the potential energy in Figure 3-15(b). For ions far below the surface, there are strong ionic interactions to bind them together. The averaged potential looks like a deep square well. This pattern demonstrates a nearly undisturbed crystal structure. Near the top of the surface, the potential energy of Li + ions rises steeply from negative to zero, with small fluctuations above the surface region. Therefore, a Li + ion has to overcome a strong attraction to leave the surface. The potential energy for F anions oscillates in a deeper negative well near

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81 the surface and rises very sharply to zero. This oscillation corresponds to a very perturbed surface, but the strong attraction from the surface prohibits a F ion from escaping. The neutral species only distribute around and above the surface region. The potential energy for F 0 is very small throughout the whole space. It is only slightly negative around the surface region. These characteristics give rise to the even distribution of F 0 Finally, for Li 0 the potential energy has a quite deep dip in the surface region, and a very shallow negative region in the sputtering front, which corresponds to the two peaks of the Li 0 distribution. To calculate the sputtering yield, we first define the criterion. As shown in Figure 3-15(b), the potential energies of all the species inside the surface are negative because the large number of ions acts as an attractive center. As particles move along the z direction, they feel less and less interaction with other particles, especially with ions, since ions tend to stay in the surface. The potential energies eventually become zero at which suggests that it is reasonable to set the escape distance to be in this case. 040z a 040a According to this criterion, the numbers of particles that are sputtered out of the surface in simulation 6 are seven Li + 0 F 342 Li 0 and 465 F 0 The mass-sputtering yield for neutral species is 99.6%. Table I shows the initial conditions and respective sputtering yields for all ten simulations. It can be seen that with the same number of layers, increasing the probability of initial excitation can dramatically increase the neutral mass-sputtering yield. When only a monolayer is excited, the neutral mass-sputtering yields are 64.6%, 71.2%, and 99.1% for the initial conditions, in which 20%, 60%, and 100% of the ions are excited, respectively. When two layers are involved, the neutral mass-sputtering

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82 yields are 81.0%, 82.0%, and 99.6% for the initial conditions in which 20%, 60%, and 100% of the ions are excited, respectively. The reason is trivial: The higher the probability of excitation in the initial condition, the more F 0 particles are there to be sputtered out of the surface. With the same probability of excitation, increasing the number of layers in the initial state increases the total number of neutral sputtering particles. But the ratio of sputtering yields among different species of particles remains roughly the same. For simulations 7 and 8, three and four layers are 100% excited, and the neutral mass sputtering yields are 99.7% and 99.8%, respectively. These results are in agreement with experimental observation of more than 99% neutral sputtering yield [87]. To fully examine the effects of excitation configuration, we performed simulations 9 and 10, in which particles inside hemispherical and cylindrical regions are 100% excited initially. These configurations are based on the assumption that the excitation is local in nature. Note that the unit cell used in the MD simulation is sufficiently large that the interaction of excited regions in neighboring unit cells can be neglected. The neutral mass-sputtering yield is 95.6% for the hemisphere and 92.4% for the cylinder, lower than the experimental data by 47%. All sputtering outcomes have some common features, for example, most Li + and F ions remain on the surface. Only a very few ions can leave the surface and go beyond 100. For Li 0a 0 and F 0 atoms, substantial numbers of these neutral atoms can leave the surface and go beyond 100. 0a

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83 Table3-1. Sputtering yields of ten MD simulations with different initial conditions. Configuration One layer Two layers Three layers Four Layers Hemisphere Cylinder Probability (%) 20 60 100 20 60 100 100 100 100 100 Simulation 1 2 3 4 5 6 7 8 9 10 Li + 0 10 5 2 21 7 3 7 2 4 F 1 14 1 1 13 0 1 0 2 6 Li 0 5 35 34 1 8 342 433 470 19 33 F 0 0 31 288 7 91 465 616 865 53 78 Neutral mass yield (%) 64.6 71.2 99.1 81.0 82.0 99.6 99.7 99.8 95.6 92.4

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84 This picture of dominant neutral sputtering yield is expected from the DMS model [87, 101, 102, 108, 112, 123, 124]. At the surface, H-centers decay by emitting F 0 atoms and F-centers neutralize Li + cations. The newly created neutral Li 0 atoms at the surface form a metallic layer, which is stable at room temperature, but will evaporate at increased temperature. Since these Li 0 atoms are weakly bound to the surface, when a HCI approaches the surface, which is not included explicitly in our simulations, the momentum transfer will be large enough to sputter these Li 0 atoms out the surface as a retarded sputtering effect [87, 101, 102, 108, 112, 123, 124]. Figure 3-16. Distribution functions of the kinetic energy along the z direction at t 1.2 ps for simulation 6. Initially, the ions in the topmost two layers are 100% excited. The solid line is for Li+, the dashed line F, the dotted line Li 0 and the dash-dotted line F 0 The sputtering outcome can only be understood in depth by examining the features of the potential energy functions. The formation of a layer of Li 0 atoms on top of the surface is the result of the attraction in the (Li 0 F ) potential energy function (see

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85 Figure 3-5). The everywhere-repulsive feature of the other potential energy functions that involve neutral atoms determines the dominant sputtering of the neutral atoms. So far, the simulations results have demonstrated two key characteristics of the DMS model: First, the sputtering yield is dominantly neutral; and second, there is a layer of Li 0 atoms bound to the surface. We believe that this layer of Li 0 atoms can be sputtered out of the surface if a sufficient momentum transfer from the projectile ions to the atoms can be realized. Figure 3-17. Normalized angular distribution functions of the neutral particles averaged over simulations 3, 6, 7, and 8 at 1.2t ps. The solid line represents Li 0 the dashed line F 0 and the dotted line the total neutral particles. 3.3.4 Profile of Dynamics In order to obtain a full, quantitative description of the HCI-LiF surface dynamics, we present the distribution functions of kinetic energy along the z direction. The same one-dimensional grid is used as for the number of particles and potential energy in Figure 3-15. Again, results from simulation 6 are used to illustrate the analysis. As shown

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86 in Figure 3-16, most of the kinetic energy of the system is carried by the particles sputtered out of the surface. The ions far below the surface region only have very little kinetic energy. The kinetic energy of both Li + and F increases at the surface. For the very few Li + ions that have successfully escaped from the surface, the kinetic energy is higher than the Li + in the surface. For Li 0 and F 0 neutrals, the kinetic energy in the z direction increases as a function of distance. The fastest particles are the sputtered particles in the front. In addition, kinetic energies of Li 0 neutrals also have strong peaks around the surface region, which are from the Li + remaining on the surface, but with smaller magnitudes compared to the sputtered atoms. The magnitudes are comparable to that of F In the surface region, the fastest particles are Li 0 and F Figure 3-18. Distribution functions of the number of particles and potential energy along the z direction of Li 0 at different time instants for simulation 6. Panel (a) represents the number of particles, and panel (b) the potential energy. In both panels, the solid line is for 0.006t ps, the dashed line for t ps, the dotted line for ps, and the dash-dotted line for ps. 0.0421.200 0.600t t The next question is the angular distribution of the sputtered atoms due to the escaping velocity. A complete analysis of all ten simulations indicates that full-layer excitation, i.e., 100% ions in the top surface layers, has the feature of nearly vertical back scattering. The averaged angular distribution functions of the sputtered atoms from simulations 3, 6, 7, and 8 are presented in Figure 3-17. The maxima of the angular

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87 distribution are located closely at zero degree because of the repulsion among the excited particles. For partial-layer excitation or localized excitation, the angular distribution does not have a sharp peak near zero degree. These results suggest that angular distribution functions can be used, in conjunction with sputtering yields, to determine the geometry and nature of initial excitation when compared to experiments. To obtain a picture of how these features have been developed through time, we analyze the distributions of the number of particles and potential energy for Li 0 and F 0 as functions of time from simulation 6. In Figure 3-18 and 3-19, these physical quantities are shown at four instants, t0.006, 0.042, 0.6, and 1.2 ps. At the beginning of the simulation, all Li 0 neutrals are evenly distributed in the topmost two layers (see Figure 3-18(a)). These Li 0 have very high positive potential energy (see Figure 3-18(b)). The potential energy of the Li 0 neutrals in the surface region decreases dramatically in the first 0.6 ps, from positive to negative. (a) (b) Figure 3-19. Distribution functions of the number of particles and potential energy along the z direction of F 0 at different times for simulation 6. Panel (a) represents the number of particles, and panel (b) the potential energy. In both panels, the solid line is for t ps, the dashed line for t 0.006 0.042 ps, the dotted line for ps, and the dash-dotted line for 0.600t 1.200 t ps.

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88 As time evolves, the Li 0 neutrals gain kinetic energy and lose potential energy. Very shortly, around 0.042 ps, the single peak for the distribution starts to split into two peaks, as shown in Figure 3-18(a) by a dashed line. The main peak near the surface does not move as much as the front peak in the z direction, which eventually separates entirely from the main peak around 0.6 ps. Later, the front peak continues its motion in the z direction with high velocity while maintaining a similar shape, which can be seen from the profiles at 0.6 and 1.2 ps. During the simulation, there is always a substantial amount of Li 0 neutrals on the surface. The Li 0 neutrals in the front peak are the fastest particles due to the small mass of a Li 0 compared to a F 0 In contrast to Li 0 the profile of F 0 does not change much at 0.042 ps when the profile of Li 0 starts to split into two peaks (see Figure 3-19(a)). As time evolves, the potential energy of F 0 decreases to slightly negative (see Figure 3-19(b)). The distribution of F 0 spreads in time and becomes evenly distributed over z during the simulation, as can be seen at 1.2 ps in Figure 3-19(a). Similar analyses of the other nine simulations indicate that when the excitation probability exceeds 60% of the excited region, there will always be a Li 0 enriched surface layer as a consequence of HCI-LiF interaction. This characteristic vanishes at low excitations, i.e., when only 20% of the ions in the surface layer are excited initially. Therefore, the neutral Li 0 layer alone is not a sufficient condition to determine the nature of excitation, i.e., local vs extended. However, the combination of this feature with neutral/ion ratios in sputtering yields and angular distribution of the sputtered particles can pinpoint the problem.

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89 3.4 Conclusion In this chapter, we have thoroughly investigated the possible outcomes during HCI-LiF surface interactions, which display unique characteristics among the HCI-surface bombardment. We have constructed potential energy functions from first-principles calculations, which govern the dynamics and energetics of particle-surface interactions. A one-to-one mapping between the initial condition and the sputtering outcome has been established to determine the nature of sputtering. Our results demonstrate that the higher the percentage of the excited ions in the surface layers, the higher the percentage of neutral sputtering particle yields in the final state. In most of the simulations, the surface after bombardment is Li 0 -enriched, which is in good agreement with the DMS model [87, 101, 102, 108, 112, 123, 124]. It is found that the 100%, extended surface excitation (simulations 3, 6, 7, and 8) generate results that are close to the published experimental observations of more than 99% neutral particle sputtering yields [87]. Our analysis indicates that the strong attraction of (Li 0 F ) is the dominating factor for forming a Li 0 neutral layer on the surface. The everywhere-repulsive feature of the other potential energy functions that involve neutral atoms determines the dominant neutral sputtering yield. Although some of important processes, such as Auger cascades, resonant states, and neutralization of ions are not included explicitly in our simulation model, crucial effects on lattice dynamics from these processes are included via different excitation configurations. Overall, we have made progress towards understanding the extremely complex dynamics of nuclei by including electronic excitation, and by correlating the initial state with the final state.

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CHAPTER 4 AN EMBEDDING ATOM-JELLIUM MODEL 4.1 Introduction In the jellium model, nuclei and core electrons together are replaced by a uniform positive background. Valence electrons move quantum mechanically in the field of this positive background. Using jellium to model a metal dates back to Drudes work on free electron conductance. The jellium model is also the simplest model to calculate the electronic structure of metal surfaces as demonstrated by Bardeen [148]. Lang and Kohn [149-151] were the first to do self-consistent calculations using the jellium model within DFT to study the properties of metal surfaces. They treated a metal surface as a semi-infinite jellium and explored the two-dimensional translation symmetry to set up a one-dimensional KS equation in the direction perpendicular to the jellium surface. In a sequence of papers [150-153], Lang and Kohn studied the surface energy and work function of different metal surfaces characterized only by the Wigner electron sphere parameter s r. They found that, within the jellium model, the work function can be reasonably well described for metal of all density range, while the surface energy is negative for a high density metal. With the introduction of ionic effects in a simple pseudopotential treated as a first order perturbation, the negative surface energy is corrected and the work function is improved. This idea is further pursued in Perdew et al.s stabilized jellium or structureless pseudopotential model [154-156], liquid drop model [157], and Shore and Roses ideal metal model [158-161]. 90

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91 It is not a surprise that the jellium model also was used in the pioneering work of atomic adsorption on metal surfaces studied by Grimley et al. [162], Lang and Williams [163, 164], and Gunnarsson et al. [165] In their atom-jellium model, Lang and Williams [163, 164] described the substrate as a semi-infinite jellium and solved self-consistently a Dyson equation, which couples the Greens function of the bare jellium surface with the electrostatic potential due to the adsorbate atom. The latter is treated as a perturbation to the bare jellium surface. Lang and Williams studied a group of atoms chemisorbed on a high density metal surface (r 2.07s ) like Al. Although the model is simple, it gives the correct picture of the qualitative difference among different types of chemisorption. They elaborated the difference in detailed analysis of density of states, charge transfer, and work function changes, which became a standard routine followed by a large number of subsequent first-principles DFT studies of surface adsorption. Later, the same atom-jellium model strategy was used by Price and Halley [166] in a three-dimensional repeated supercell approach and many others [167]. During the past decade, with the developments in first-principles pseudopotentials, iterative minimization algorithms and computer hardware, accurate and sophisticated DFT calculations of adsorption system with atomic surface became the choice, and the jellium model of metal surface seems outdated. However, the jellium model still has the advantage of numerical efficiency and can be taken as the simplest pseudopotential. Here we propose to extend Lang and Williamss atom-jellium model and combine the advantages of both atomic and jellium model in a multiscale sense to study molecular adsorption on metal surfaces. In our approach, the most important interface region, which includes the top metal layers and the adsorbate molecule, is described in the accurate

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92 atomic pseudopotential. This region is embedded in a jellium region, which is far enough from the interface region, that its rough description is acceptable. In doing so, the computational cost should be lowered without critical loss of accuracy. 4.2 DFT Formulism for Embedding Atom-jellium Model In our approach, part or all of the metal surface is modeled by a jellium slab as a uniform positive background, which occupies a certain volume jel in the surface unit cell. The charge density of the jellium slab is 0.jeljelnfornotherwise rr (4-1) The parameter corresponds to the average charge density of valence electrons in the metal. In Drudes theory of free electron systems, an electron is defined by the volume it occupies n 43 3 s r where s r is the classical radius of the electron. As for a fcc metal, assuming Z valence electrons for each metal atom, there is a simple relation 321434sarnZ (4-2) where is the lattice constant. a Again, we use pseudopotentials to describe the interaction between ions and electrons, and a plane wave basis set with a three-dimensional periodic boundary condition. With electrons, ions and a jellium slab, the total energy functional in DFT is 023,,,,2,.xcesiiixciHppionionIeljelionjelIjeljelETnEnEnwfdrEnEnEnEEnEnEn kkkkkrrrrrrrRrR r (4-3)

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93 The only difference from the conventional DFT expression in the pseudopotential approach is the electrostatic energy which now includes the contributions from the jellium slab. Among them, and are constant for a fixed geometry configuration because they are independent of electron density But these two terms need to be evaluated correctly in the total energy, which in turn will allow the correct Hellmann-Feynman force calculation. The self-consistent Kohn-Sham equation is esE ionjelE jeljelE ()nr 2,,,2xcHppjeliiiVVVVkkkrrrrr r (4-4) where the jellium potential 3jeljelnVdr rrrr (4-5) is the Coulomb interaction between the positive jellium slab and electrons. Following the formalism of total energy calculation with three-dimensional PBC in Appendix A, we can cast the energy between electrons and jellium into a reciprocal space expression 3333203320200,41414,eljeljelijelijeljeljelEdrndrndrndrnedrnedrnennVnGrrGGrGrGGGrrrrrrGrrGGGGGG i (4-6) where

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94 24jeljelVn GGG (4-7) is the Fourier transform of the jellium potential jelr V. Similarly, the energy between jellium and itself is 3301,2.2jeljeljeljeljeljelEdrndrnVn GrrrrGG (4-8) Because the interaction between the ions and the jellium is also straightforward Coulombic repulsion, the energy between them can be expressed as 33332020,414,ionjeljelIIIiijelIIIjelEdrndrZdrnedrZeSn GrGrGGrrRrrrrGGGG R (4-9) where I iIIZSeGRG (4-10) is the structure factor of the ions. Finally, the force exerted on the ions due to the jellium is 204,IionjelionjelIIiIjelEZien GRGFRRGGG (4-11) which will be added to all the other contributions from electrons and ions. The embedding atom-jellium method has been implemented in code of fhi98md [168], which uses Troullier-Martins type norm-conserving pseudopotential to describe the interaction between ions and electrons.

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95 4.3 Results and Discussion In Figure 4-1, the planar averaged electron density and potential are plotted in direction perpendicular to the (111) surface for a seven-layer Al jellium slab. The electron density fluctuates around the jellium edge and smears out into vacuum as seen in Figure 4-1(a). The fluctuation amplitude is reduced as the center of the positive jellium background is approached. This fluctuation in electron density has the characteristic of Friedel oscillation, which corresponds well with the electrostatic and total effective potentials shown in Figure 4-1(b). The electron exchange-correlation contributions lowers the potential effectively. z (a) (b) Figure 4-1. A jellium surface modeled by a seven-layer Al slab with 21 electrons.(a) Charge density along the direction perpendicular to the jellium surface, the solid line is the positive jellium charge density, the dashed line is the electronic charge density. (b) Potentials in the same direction, the solid line is the total effective potential, the dashed line is the part without the exchange correlation potential. The physical properties of metal thin film subjects to static quantum size effect (SQSE). As first shown by Schulte [169] and subsequently others [170-176], this is because the surface bands are shifted down to touch the Fermi level one by one as the thickness of the slab increases. When an empty band touches the Fermi level, the work

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96 function reaches a local minimum. The SQSE is more severe for a jellium slabs than for a real metal thin film. The work function SQSE for jellium Al and Cu slab is shown in Figure 4-2(a) and (b), respectively. The work function converges to 3.78 eV for jellium Al and 3.55 eV for jellium Cu, as indicated by the horizontal dashed lines in Figure 4-2. The work functions calculated from an unrelaxed seven-layer atomic slab are also shown as the horizontal solid lines at 4.21 eV and 5.19 eV for Al and Cu, respectively. (a) (b) Figure 4-2. The quantum size effect of jellium surfaces, (a) Al and (b) Cu. The dashed line corresponds to the converged work function for simple jellium model. The solid and dotted line are the work functions calculated from the atomic model and the embedding atom-jellium model, respectively. To improve the results from the pure jellium model, we introduce the embedding atom-jellium model by placing one atomic layer on a six-layer jellium slab. The distance between the atomic layer and the jellium surface is relaxed to give the lowest energy. The equilibrium distance is 1.7 and 1.5 for Al and Cu, respectively. In Figure 4-2, the dotted lines show that the work function for the embedding atom-jellium model is 4.22 and 4.93 eV for Al and Cu, respectively. The improvement of the embedding atom-jellium model over the pure jellium model is significant.

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97 The good agreement between the EAJ model and atomic model can be understood by examining the electronic structure. In Figure 4-3, the partial density of states projected on the first Al layer of atomic and EAJ model, and the second Al layer of the atomic model are shown. The PDOS of the first Al layer of EAJ model matches well with that from the atomic model. For the second Al layer, the PDOS of p x p y and p z are all the same. For first Al layer, p z orbital contributes more states around the Fermi level than p x and p y Figure 4-3. Partial density of states projected on atomic orbitals. (a) The first Al layer in the embedding atom-jellium model. (b) The upper and lower panel is for the first and second Al layer in the atomic model. The Fermi level is at the energy of zero.

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CHAPTER 5 FRACTURE AND AMORPHIZATION IN SIO 2 NANOWIRE STUDIED BY A COMBINED MD/FE METHOD 5.1 Introduction In the past decade, multiscale modeling has emerged in computational material science [177]. It combines models at different physical scales to build a comprehensive description of materials. The reason to do multiscale modeling is two-fold. First, there is a variety of phenomena that are strongly coupled in different physical scales. For example, in crack propagation, the bond breaking at the crack tip depends on the deformation of surrounding materials, which in turn depends on the long range strain field. On the other hand, the dissipation of strain energy is through dynamical processes at the crack tip including bond breaking, plastic deformation, and emission of elastic waves. All of these processes happen at the same time when crack propagates. So a successful description of crack propagation requires simultaneous resolution at both atomistic and continuum length scales. Secondly, it is not possible to compute all the relevant dynamical processes in the most accurate and intensive model with a reasonable computational cost. The idea of multiscale modeling is to find a balance between accuracy and efficiency, i.e., let the most dramatically changing region be dealt with via the most accurate method and broad surrounding regions dealt with by less accurate but more computationally efficient methods. The multiscale scheme of combining molecular dynamics (MD) and the finite element (FE) method has been studied by many researchers to investigate fracture and 98

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99 crack propagation in materials. One group of studies focuses on deriving the FE method not from the traditional continuum model, but from the underlying atomistic model. In the quasicontinuum technique proposed by Tadmor, Phillips and coworkers [178-181], the energy of each element is computed from an underlying atomistic Hamiltonian, such that nonlinear elastic effects can be included. In the coarse-grained molecular dynamics proposed by Rudd and Broughton [182], a similar idea is pursued. The interpolation functions in the FE mesh are assembled from the atomistic model. The other group of studies focuses on combining MD and FE through an interface. Kohlhoff et al. [183] introduced an interface plane between the MD and FE regions to pass the displacement as boundary conditions for the two regions. Abraham et al. [184-186] used a scheme based on coupling through force. In it, the FE elements sitting at the interface plane can have forces of MD nature. Smirnova et al. [187] extended the imaginary interface plane to a finite size. In this work, we propose an improved MD/FE interface with gradual coupling of force and use it to study the mechanical behavior of a SiO 2 nanowire. SiO 2 is one of the most extensively studied materials because of its importance in technology. Amorphous silica is the major constituent in optical fiber. Quartz is the material for timing in electronic circuits. Other crystalline silica, such as cristobalite, can be found in Si and SiO 2 interface in microchips [188, 189]. Since the discovery of carbon nanotubes, different types of nanotubes and nanowires have been studied both in theory and experiment. For example, a SiSe 2 nanowire has been proposed and studied with MD [190-192]. In experiments, both SiO 2 sheathed Si nanowires [193] and pure SiO 2 nanowires [194-196] have been found. SEM and TEM images show that the nanowires are several m long with diameter of 10-50 nm. Electron diffraction on SiO 2 sheathed Si

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100 nanowire shows that the core of the nanowire is crystalline Si and the outmost cover is amorphous SiO 2 In pure a SiO 2 nanowire, the structure is also amorphous. While the structures of crystalline silica are well understood as different arrangements of corner-sharing SiO 4 tetrahedral, the structure of the amorphous silica surface is still an open problem [197, 198]. Since we do not have a well-defined structure for the amorphous SiO 2 nanowire to start with, a closed crystalline structure should be used. Besides amorphous structure, silica can have as many as forty crystalline structures in nature [199]. Among these different silica polymorphs, only quartz ( ) and cristobalite ( ) are stable at atmospheric pressure. The density of -cristobalite is the closest to that of amorphous silica. So -cristobalite is often used as a preliminary model for amorphous silica. As the first step to understand the mechanical properties of an amorphous SiO 2 nanowire, we construct a -cristobalite nanowire and use the combined MD/FE method to study its amorphization and fracture under tensile stretch. As we will demonstrate, during the first period of tensile stretch, a phase transition occurs from -cristobalite to -cristobalite. With further tensile stretch, the nanowire become amorphous before it starts to fracture. 5.2 Methodology 5.2.1 Summary of Finite Element Method The finite element method is a general approach to solve a differential equation approximately [200]. A continuous system has infinite degree of freedom. The FE method uses finite degree of freedom to approximate the continuous solution. When a continuous system is divided into a finite element mesh, the displacement field

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101 cur within an element can be interpolated by the local displacement on the nodes of that element u as ei 1gNceiiiHurru (5-1) where is the interpolation function or shape function. The index runs from one to iHr i g N the number of nodes in each element. The continuous strain within an element can be symmetrically defined as [201], ,1112gNiiceiiHHuurr ,ei rrr (5-2) where all quantities are written out in their components and the indices and run from one to f N the degrees of freedom of each node. The equations above are usually expressed in matrix format ceurHru (5-3) and cerDru (5-4) where the local displacement is written as a vector of eu g fNN dimensions. The matrix is the strain-displacement matrix as defined from Eq.5-2. Dr In solid mechanics, the FE method is introduced as a minimization of the total potential functional [200] 12TTTSddupuq dS (5-5)

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102 where is the stress, is the body force per unit volume and q is the applied surface force per unit area. The FE method often deals with elastics, which means small strain, harmonic and no plasticity. The stress-strain relation is linear p CCDu (5-6) where C is the elastic matrix. As the system is divided into a finite element mesh, the elastic potential energy functional can be written as 1.2eeeeeeTTeeTTeTTSedduDCDuuHpuHq dS (5-7) To find the minimum of the total potential energy and the equilibrium of the system, the variational principle is used, 0()eeTeTTeSdd edS DCDuHpHqu (5-8) This gives 0eee KuF (5-9) where eeTd KDCD (5-10) is the local stiffness matrix and is the nodal force that results from the last two terms in Eq.5-8. There are as many as equations like the one in Eq.5-9, since is the total number of elements in the system. These equations are coupled through u. They can be assembled as one global matrix equation, eFeN eN e 0 KuF (5-11) where K is the global stiffness matrix and is the generalized displacement matrix. u

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103 Up to this point, we only get the equation for elastic statics, which is the most common application of the conventional FE method. To consider elastic dynamics, we have to introduce kinetic energy for an element, 212121,2eeeeTeeTeeTdd e rurHurHuuMu (5-12) where eeTd MrHH (5-13) is the local mass matrix. If we construct the Lagrangian and use the variational principle as before, a global dynamical equation can be obtained 0 MuKuF (5-14) With the condition of no external force and no boundary condition, the equation turns to the free response, 0 MuKu (5-15) The harmonic solution (0)ite uu gives an eigenvalue equation 20 MK (5-16) which is just the same as the dynamical matrix equation for a crystal lattice [202]. With the condition of no external force and strain applied on the boundary of the system, the dynamical equation is now KuuM (5-17)

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104 Generally, M is non-diagonal and is called the consistent-mass matrix. With a set of interpolation functions satisfying T HHI (5-18) M is diagonal and is called the lumped-mass matrix. The dynamical equation can be solved in the central difference method (Verlet) or Newmarks method [200]. The former is explicit and very computationally efficient when applied with lumped-matrix approximation. It acts just like Hookes law for each individual node. The later is numerically more stable. But it involves solving matrix equation implicitly and so more computationally demanding. 5.2.2 Hybrid MD/FE: New Gradual Coupling In our approach, the system is divided into three regions, i.e., core MD (CMD), dilute FE (DFE) and transition (TRN) region. FE nodes in the TRN region match the crystal lattice. The total Hamiltonian of the system is //,/,/,,.totCMDCMDTRNDFEDFETRNTRNHHCMDVCMDTRNHDFEVDFETRNHTRNrrrurururururr (5-19) In CMDH D FEH and we include the kinetic energy from each region and the contribution of the potential energy between any two particles or connecting nodes if they both are in the same region. In V and TRNH /CMDTRN / D FETRN V, we include the interaction between two particles or connecting nodes which are in nearby, different regions. Inside the TRN region, we have ,,1,MDTRNTRNFEHTRNTwwVururrurrrrur V (5-20)

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105 where the weight function, wr is determined by the distance of the nodes from the CMD and DFE regions. When the force is calculated between two FE nodes in the TRN region, we allow the MD force between them to contribute. The weight of such a contribution of MD nature is determined by the distance of the nodes from the CMD and DFE regions. So the hybrid force in the TRN region can change from the nonlocal MD force where the nodes are very close to the CMD region to the local FE force where the nodes are close to the DFE region. The interatomic potential we use for MD is due to van Beest et al [203]. It was generated by fitting the results of a H ab initio 4 SiO tetrahedron and the experimental crystalline data to the following formula, 4 6ssijijijijijbr s ssijssijijqqCrAerr s (5-21) where is the species of the ith particle. The potential has been intensively used in MD simulations of bulk silica and is commonly called the BKS potential. is We use a two-dimensional FE method by dividing the system into isoparametric triangular elements with linear interpolation functions. The number of nodes for each element and the degree of freedom of each node 3gN 2fN The total number of elements and nodes is and respectively. The potential energy is eN dN 6,112eNFEmmmppqqmpqVu Ku (5-22) and the stiffness matrix is 4TmmmLKDCA mD (5-23)

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106 where is the thickness in the reduced dimension and is the area of the element. In a two-dimensional system, the elastic constant matrix, [, is reduced to as L mA] C (33) 11121211140000CCCCCC (5-24) The strain-displacement matrix [ consists of coordinate differences of the nodes on each element. It is of the dimension ]D (36) The force on each element is mmppqFKu mq (5-25) where the index of p and runs from one to six. It is desirable to decompose the force on each node as q 31elNnminmlF mpF (5-26) where the index of runs from one to two. The kinetic energy is i 621112edNNFEmnmmpqpqmpqnTMuuu nM (5-27) and the mass matrix is 3113elNnmnmmlAML (5-28) where is the bulk density of the material and we have used the lumped-mass approximation. After the forces are calculated from different contributions, we use the Verlet algorithm to integrate the dynamical equations for both MD and FE. 5.3 Results The nanowire sample that we use is shown in Figure 5-1. The dimensions are 19.91 27.79 and 119.47 in the x and direction, respectively. The strain will be applied y z

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107 on the direction. The projection from MD particles to FE nodes in the TRN region is in the direction as shown in Figure 5-1(b). To construct the nanowire, we use the 12-basis unit cell for yz -cristobalite with the dimension of 4.978 4.9786.948 The CMD region has 4 unit cells with 1536 particles. Each of the TRN regions has 4 unit cells. It has the dimension larger than the cut off of the BKS potential. Each FE node in the TRN region corresponds to four MD particles in different layers. The TRN regions have 384 FE nodes, which correspond to 1536 MD particles. The two DFE regions have 32 FE nodes. In total, there are 408 FE nodes and 782 FE triangle elements in the sample. (a) (b) Figure 5-1. Geometry of the -cristobalite (SiO 2 ) nanowire projected on (a) xy and (b) yz planes. The CMD region is in the center. The two ends are the DFE regions. The region between the CMD and DFE regions are the TRN region. The two-dimensional FE mesh is projected on the xy plane from the three-dimensional crystal lattice. In the TRN region, FE nodes match with the positions of crystal lattice. 5.3.1 Interface Test After the code was developed, we did a few tests. First, the force generator from MD is turn off and only FE forces determine the dynamics. As seen in Figure 5-2(a), the

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108 kinetic energy and potential energy compensate each other and the total energy is conserved. If the FE force generator is turn off and only MD forces are used, the total energy is also conserved as shown in Figure 5-2(b). When both the MD and FE forces are used, the total energy calculated from the two parts is shown in Figure 5-2(c). To match the magnitude of the energy calculated from FE with that from MD, we have shifted the energy of the FE with an average potential energy density. The two curves are compensating. So the total energy is conserved very well. (a) (b) (c) Figure 5-2. Energy conservation test with respect to time for (a) FE only, (b) MD only, and (c) both FE and MD. In panel (a), the red (grey) line is the potential energy, the green (light grey) line is the kinetic energy, and the blue (dark grey) line is the total energy. In panel (b) the red (grey) line is the potential energy and the green (light grey) line is the kinetic energy. In panel (c) the red

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109 (grey) line is the total energy from MD part of the calculation and the green (light grey) line is the total energy from the FE part of the calculation, which has been shifted by an average potential energy to match with MD. (a) (b) (c) (d) Figure 5-3. Distributions of force and velocity in the y direction during a pulse propagation test for the MD/FE interface. Panel (a) shows the distribution of force in the y direction at time zero. Two atomic layers in the center on the xz plane have been squeezed. The distribution of velocity in the y direction is shown in panel (b), (c) and (d) at the time instants of 0.1, 0.6 and 1.2 ps, respectively.

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110 The main goal of the hybrid FE/MD interface is to let elastic waves propagate from the CMD region to DFE region. To test if our interface works well, we squeeze two central layers in the direction in the middle of the CMD region to make a pulse and let it propagate. As seen in Figure 5-3(a), at time zero, only the two central layers feel the stress. As the dynamics evolves, we plot the distribution of velocity in the direction in colors at different instants from Figure 5-3(b) to (d). At the beginning, the pulse is in the center of the wire. Later on, the pulse is propagated into the whole wire. At ps in Figure 5-3(b), the pulse reaches the TRN region. At y yt 0.1 0.24t ps in Figure 5-3(c), the pulse arrives at the DFE region. Finally, at t 0.6 ps in Figure 5-3(d), the pulse spreads all over the nanowire and causes some local distortions. Figure 5-4. The stress-strain relation for a uniaxial stretch applied in the y direction of the nanowire at speed of 0.035 1ps 5.3.2 Stretch Simulation Figure 5-4 shows the stress-strain relation for a uniaxial stretch applied in the y direction of the nanowire at the speed of 0.035 1ps The nanowire breaks at a strain of

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111 0.12. During the first period of stretch, the stress is actually going down from 10 GPa to 5 Gpa. That corresponds to the phase transition of -cristobalite to -cristobalite because the stretch in the y direction makes the unit cell change from tetragonal to cubic. (a) (b) (c) (d) (e) Figure 5-5. Five snapshots from the tensile stretch applied in the y direction of the nanowire at speed of 0.035 1ps The nanowire is viewed from the x direction at time instants of (a) 2.0, (b) 4.0, (c) 6.0, (d) 8.0, and (e) 10.0 ps.

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112 Under more strain at 2.0t ps, in Figure 5-5(a), the tetrahedral units around the surface of the nanowire start to rearrange themselves, to increase the Si-O-Si bond angles in the direction of the stretch, and to cause local amorphization on the surface. The neighboring tetrahedra along the x and direction get closer and closer with more applied strain. When the Si-O bond between neighboring tetrahedra becomes shorter than that inside the tetrahedron, the bond will break. A fracture tip will be formed if the bond breaking happens on the nanowire surface or a fracture void will be formed if it happens inside the nanowire as seen in Figure 5-5(b) at z 4.0t ps, when the applied strain is around 0.12. The fractures propagate and move under further applied strain, and cause more amorphization as seen in Figure 5-5(c) and (d) at the snapshots of and 8.0 ps. Eventually, the two ends of the nanowire detach around t 6.0t 10.0 ps in Figure 5-5(e). The pair correlation functions at t 0.0 and 4.0 ps are shown in Figure 5-6(a) and (b), respectively. The peaks corresponding to the Si-Si, Si-O and O-O distances at t 4.0 ps are broadened largely as the nanowire starts to break and becomes amorphous. (a) (b) Figure 5-6. Pair correlation functions of the nanowire during the uniaxial stretch simulation. Panel (a) is at 0.0 ps and panel (b) 4.0 ps. In all panels, the solid line is for Si-Si, the short dashed line Si-O, and the dotted line O-O.

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CHAPTER 6 SUMMARY AND CONCLUSIONS In this thesis, the phenomena of surface adsorption and desorption have been studied by various computational methods. I have presented a detailed microscopic picture of the interaction between a C 60 ML and noble metal (111) surfaces. Large-scale first-principles DFT calculations have provided complete information of the energetics and electronic properties, which govern the structure and dynamical processes observed in experiments. The results are important in understanding the fullerene-metal interfacial characteristics and properties. Especially, the analysis of changes in surface dipole moments clarifies the puzzling observation on the work function change of noble metal (111) surfaces upon the adsorption of a C 60 ML. For surface desorption, we have studied the potential sputtering of a LiF(100) surface stimulated by HCI. The MD formalism is extended to include the crucial information from electronic excited states, which are calculated by a high level quantum chemistry method. From the MD simulation, the experimentally observed sputtering pattern and yield are well reproduced. We find that the mechanism of potential sputtering has its root in the behaviors of potential energy functions from electronic excited states. An embedding atom-jellium model has been formulated into a multiscale simulation scheme to treat only the top metal surface layers in atomistic pseudopotential and the rest of surface in a jellium model. The calculated work functions of Al and Cu clean surfaces agree reasonably with the all-atomistic calculations. We have also studied a multiscale scheme for combining the FE and MD methods. A gradual coupling of the FE and MD in the interface region is proposed and 113

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114 implemented, which shows promising results in the simulation of the breaking of a SiO 2 nanowire by tensile stretch.

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APPENDIX A TOTAL ENERGY CALCULATION OF SYSTEM WITH PERIODIC BOUNDARY CONDITIONS The calculation of total energy per unit cell for a system with periodic boundary conditions (PBC) is non-trivial. In this appendix, first, a general form of electrostatic energy in three dimensional PBC is derived following Makov and Paynes paper (MP) [204]. Then the interaction among electrons, ions, and the interaction between them are calculated. We start with a charge density comprised of electrons and ions, iiinz rrr r (A-1) where electrons have a continuous distribution nr and ions are sitting at r. This charge density has a three dimensional periodicity, i rrl (A-2) where are the lattice vectors. The integration of the charge density over the volume of the unit cell, can be zero, l 330iidrdrnz rr (A-3) which corresponds to the charge neutrality. The electrostatic energy per unit cell can be written as 312Edrrr (A-4) where 115

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116 3dr rrrrll (A-5) is the electrostatic potential generated from the charge density. The lattice sum for the electrostatic potential in Eq.A-5 is only conditionally convergent. To make the sum absolutely convergent, we introduce a convergence factor in the form of Gaussian function, 2 s e. The parameter is a small positive quantity and approaches zero. In an absolutely convergent sum, we are allowed to exchange the sum and the integral; therefore, we consider the sum l s 21,sse xxlll (A-6) where Now we introduce the Gamma function identity xrr 22101atydtea yat (A-7) With the special case of 12a and 121 and the substitution of yxl the sum can be rewritten as 2212120,stsdttexxlll e (A-8) This integral is singular at the limit 0t when 0s To isolate this singularity, we split the integration range into two, 2 0, and 2, Thus ,sx is also split into two parts, 12,,,sssxxx (A-9) The second part is reduced to the complementary error function as

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117 222212122,.stssdtteerfcexxxxlllllll e (A-10) The first part can be rearranged into 2222222221212101212012120,.stttststststtstststssdtteedtteedtteexxxxxxlllllll (A-11) In the last line of Eq.A-11, the exchange of sum and integral is used. The goal is to convert the sum of Gaussian functions in 1,sx from real space to reciprocal space in Eq.A-11. To make notation concise, we introduce and ats utts The sum can be expressed in reciprocal space as 22,.auaieegae xxGxGGllll (A-12) In the first line of Eq.A-12 above, we made the substitution of u x x The coefficient is the Fourier transform of which is independent of as shown below, ,gaG 2aexll u

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118 2222233331324321,1111.kkkaiiaiaaxiGxkkagadxeedxeeedxedxeea i xGxGx-xGxGGllllll Gx (A-13) In the second line of Eq.A-13, the change of variable xxl is made. In the fourth line, is used and the integral is decomposed into each component. In the last line, the result of a one-dimensional Gaussian integral is used. ieGll N Putting Eq.A-12 and Eq.A-13 back into Eq.A-11, we get 2223241210,tstitststssdtttseeeGxGGx x (A-14) For the sum in Eq.A-14 is absolutely convergent when 0G 0s 22224210042,41.tiisdtteeeGGxGG0GGxG0xG e (A-15) However, the term is singular when 0G 0s Again we make the substitution of utts so that 2dtdutss to obtain 22212100,s s usduus e xG=x (A-16) Expand the exponential and carry out the integration of the first few terms to get

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119 22122210023322222222222,122322123223222.3ssduusussssssOsOssss 1Os G=xxxxxrrrr (A-17) In the third line of Eq.A-17 above, the expansion of denominators is used to keep terms other than Os. Now put all things together into Eq.A-5, take the limit of 0s and notice that when is multiplied by ,sx r and integrated over a charge neutral cell, the first three terms become zero. This means that the singularity of the potential at when simply cancels out for charge neutral cell. Thus we get 0G 0s 32,23dr 2 rrrrr rr (A-18) and 2242041,ierfceeGGrrGrrrrrrGlll (A-19) In calculating the energy, we again use the condition of charge neutrality. The first term of the following equation is zero, 233231222233drdrdrrrrrrr r (A-20) So we obtain the energy

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120 233312,23Edrdrdr rrrrr r (A-21) Put in the continuous electronic charge density and ionic point charges from Eq. A-1, and we get 333231,21,2,2.3ijijijiiiEdrndrnzzzdrndr rrRRrrRrr rr (A-22) The first term in Eq.A-22 is the electrostatic interaction among electrons, i.e., the Hartree energy. The second term is the interaction among ions, which is the Ewald term. The third term is the interaction between electrons and ions, which is usually evaluated from pseudopotential. The forth term is the dipole energy, which is determined by the choice of unit cell, and its value is arbitrary. The Hartree energy is evaluated entirely in reciprocal space by taking 33332033202001,21412141242,2HiiHEdrndrndrndrnedrnedrnennVnGrrGGrGrGGGrrrrrrGrrGGGGGG i (A-23) where

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121 24HVn GGG (A-24) is defined as the Hartre potential. The ion-ion interaction energy is 2220422200111,lim2214121211lim.22ionionijijiijiiijijijijijiijiiiiEzzzzzeeerfczzerfcerfczzGGrrG0RRGRRRRlllllllllll 1l (A-25) The last term in the first line is the unphysical interaction between a point charge with itself inside the central unit cell 0 l, which needs to be subtracted. After writing out all the terms explicitly in the second line, the first term is the summation in reciprocal space. The second term is the interaction between different ions in real space. The third term is the interaction between an ion with its image charge in the neighboring unit cells. The last term combines the term from the error function with 0 lfor and the unphysical term. Both of them diverge individually, but the combined term is finite because i j 2000112limlimyerfcdye 2 lllllll (A-26) So the ion-ion interaction energy is

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122 2242214121,2iionionijijijijiijiijEzzeeerfczzzGGrrG0GRRRRlll (A-27) where the star means for 0l ij The interaction between electrons and ions is 33332020,414,elioniiiiiiiiEdrndrzdrnedrzeSn GrGrGGrrRrrrrGGGG R (A-28) where iiiizSGRG e (A-29) defines the structure factor. Eq.A-28 has no practical use unless the ions reduce to nuclei in an all-electron calculation. The equation oversimplifies the interaction between extended ions and valence electrons. Usually, the interaction felt by valence electrons from ions is modeled by a pseudopotential V. We follow the notation from Ihm et al.s paper (IZC) [205] and write ,pslr 3,,,psipslliilEdrVP rrR r (A-30) where the projection operator is ,llmPlml m (A-31)

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123 The subscript i stands for both state and k-point, stands for ions, and and stands for angular and magnetic momentum number. With a plane wave expansion, l m ,,1iiiCe kGrkkGGr (A-32) and with a change of variable rRr Eq.A-30 can be cast into the reciprocal space 3,,,,,,,,,,,,,,.iiipsiipslliliipslilECCedreVPeCCSV kGrkGrGGRkGkGkGkGkGkGkGkGkGkGrGG (A-33) In Eq.A-33 above, the structure factor is 1iSe GGRGG (A-34) and the Fourier transform of the pseudopotential is 3,,,,2,421cosiipslpsllpsllllVdreVPeldrrVrjrjrP kGrkGrkGkGrkGkG (A-35) where cos kGkGkGkG (A-36) We have used the spherical Bessel functions and the Legendre polynomials We also have used lj lP 021coslillleiljrPrkGrkGrkGkG (A-37) For the local part of pseudopotential, it is straightforward to write

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124 3,33.psipsiipsipspsEdrVdrVndrVenSVn GrRGGrrRrRrGrGGG r (A-38) Notice that the diverging components of the electrostatic potential in Eq.A-23, Eq.A-25, and Eq.A-28 cancel out for a charge neutral cell is the result of purely Coulombic interaction. Since we replace the Coulombic interaction between ions and electrons by a smoother pseudopotential, an offset should be introduced. This is the 0G Z term in Ihm et al.s paper [205], which is just the difference between the Coulomb interaction and the pseudopotential at 0 G The band structure energies and Hellmann-Feyman theorem can be found in IZC paper. The treatment of aperiodic or charged system is in MP paper.

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APPENDIX B REVIEW OF DEVELOPMENT IN FIRST-PRINCIPLES PSEUDOPOTENTIAL B.1 Norm-Conserving Pseudopotential The idea of a pseudopotential is to eliminate the chemically inert core states within the frozen core approximation and concentrate on the chemically active valence states. The true potential of the valence states felt from the core states and nuclei is replaced by a much smoother effective potential. This pseudopotential results in pseudo wave functions that are the same as the true valence wave functions outside the small core region, but avoid the radial nodes that keep the true valence and core wave function orthogonal. There are two classes of pseudopotential seen in literature. Empirical pseudopotentials [206] are fitted with a few parameters to reproduce the experimental electronic structure. First-principles pseudopotentials date back to Herrings invention of the orthogonalized plane wave (OPW) method [207]. Later, Phillips et al. [208] and Antoncik [209] reformulated the OPW method, replaced the orthogonality condition by an effective potential, and established the first-principles pseudopotential method. Modern first-principles pseudopotential study starts from the works of Hamann, Schlter, and Chiang (HSC) [210] and Zunger and Cohen [211, 212]. There were improvements by Kerker [213], Troullier and Martins [214, 215], and Rappe et al. [216] Recently, major improvements were made by Vanderbilt [50] and Blch [217-219] to make the ultrasoft pseudopotential and the projector augmentation method (PAW), respectively. The construction of first-principles pseudopotentials starts with the solution of the all-electron Schrdinger equation for an isolated atom in a certain reference configuration 125

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126 with DFT formulism. After the angular part is separated, the scalar-relativistic radial Schrdinger equation is 2222111022lldVrllddrVruMrdrMrdrdrrr r (B-1) where 212l M rV r (B-2) ;HxcZVrVnrVnrr ; (B-3) and is the fine structure constant. The radial wave function nlur is defined as usual, ,,nlnlmnllmlmurrRrYYr (B-4) Since the angular wave function does not change in pseudoization, we mean pseudo wave function as for the pseudo radial wave function lr u. We use the convention that the symbols with tilde are for pseudo quantities. We also drop the quantum number n because it does not affect the process of pseudoization. There are several conditions that the pseudo wave function must meet with respect to the true wave function. (i) The pseudo wave function must have the same eigenvalue as the true wave function for the chosen electronic configuration (usually the atomic ground state), ll (B-5) (ii) The pseudo wave function must be nodeless and be identical to the true wave function beyond a chosen core radius,

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127 llururforrr cl (B-6) (iii) The charge enclosed within the core radius for the pseudo and true wave function must be equal, (B-7) 2200clclrrllurdrurdr (iv) Both the first and second derivatives of the pseudo wave function at the core radius must be matched to the values of the true wave functions. 2222.clclclcllrrlrrlrrlrrddururdrdrddururdrdr (B-8) From these conditions for pseudo wave function, requirements on the pseudopotential can be derived. From condition (ii) and (iii), the norm for the pseudo and true wave function are the same for any radius beyond the core radius as 2200rrllurdrurdrforrr cl (B-9) From Gauss theorem, this means that the electrostatic potential outside of the core radius is reproduced. With the identity [220, 221] 2201ln2rlllrudduuddrr dr (B-10) it can be derived that lnlnllddururforrrdrdr cl (B-11) This means the scattering property of the pseudopotential is the same as the true potential, which ensures the transferability of the pseudopotential. Practically, the

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128 conditions (i) through (iv) are used to determine the parameters for the pseudo wave function once its form is decided. The pseudopotential is then obtained by inversion of the non-relativistic radial Schrdinger equation with pseudo wave function, 22211022scrllllldVrurdrr (B-12) The resulting pseudopotential is 2221122scrlllllldVrurrurdr (B-13) It is labeled as a screened pseudopotential because it includes the screening effect from other valence states, in addition to the core states. There are a lot of recipes to generate pseudo wave functions and pseudopotentials in the literature. HSC used a scheme as following [210, 222]: After the all-electron scalar-relativistic radial Schrdinger equation is solved, the true potential is modified, which is then put into a non-relativistic radial Schrdinger equation to get an intermediate wave function. The intermediate wave function will then be modified to the pseudo wave function by meeting all the conditions. Finally the non-relativistic radial Schrdinger equation is inverted with the pseudo wave function to get the screened pseudopotential. Kerker [213] was the first to use the recipe that modifies the true wave function directly as the starting point to get the pseudo wave function. Then the pseudo wave function was used to invert the non-relativistic radial Schrdinger equation to get the screened pseudopotential. This scheme is more popular since the pseudopotential is derived in an analytically less complicated way and with no need to solve Schrdinger equation twice. The form of pseudo wave function is

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129 1,lclprlclurforrrurreforrr l (B-14) where 402iii p rccr (B-15) In the polynomial expansion, the coefficient of is omitted to avoid the singularity of the screened pseudopotential at the origin 1c 0r The screened pseudopotential is obtained as 2122AElclscrllcVrforrrVrprprprl l f orrrr (B-16) Troullier and Martins [214, 215] generalized Kerkers recipe by increasing the order of the polynomial to with only the even terms. The additional coefficients give the freedom to investigate the smoothness properties of the pseudopotential. 12n In stead of using polynomial and exponential functions, Rappe and Rabe et al. [216] used a linear combination of spherical Bessel functions as the pseudo wave function inside the core region. They also proposed a way to minimize the kinetic energy contained in the Fourier components of beyond a certain cutoff of wave vector. lu The pseudopotential that is directly used in solid state calculations is actually an ionic pseudopotential. The ionic pseudopotential is obtained by subtracting the contribution due to valence electrons from the screened pseudopotential, ;;ionscrllHxcVrVrVnrVnr (B-17)

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130 where n is the valence electron density. The total ionic pseudopotential can be written out as, ionionlmllmlmVYVrrrY rr r (B-18) It is in a semi-local form because the radial part is local, but the angular part is nonlocal. When the matrix element is evaluated for the ionic pseudopotential as, 33,ionionnnnlmllmnlmVdrdrYVrrrY rrrr (B-19) where stands for the state, k-point and spin index, the integral of n 2cosionlllldrrjrVrjrPkG.kG'kGkG (B-20) must be calculated by 12MNN times, where M is the number of k-points and is the number of plane wave vectors. Kleinmen and Bylander (KB) [223] proposed a fully separable form for the ionic pseudopotential as N ,ionionllllionionloclmlmionlmlllVuuVVVrYYuVurrr (B-21) where ionionionlllocVrVrVr (B-22) ionionllllVuVrur (B-23) and V is usually chosen to be V. Now the matrix element is evaluated as following, ionloc maxionl 3323,331.ionionnnnlocnionlmllionionnlmlllllmnVdrdrVrdrVrurdrYVrurdrVrurY rrrrrr (B-24)

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131 The number of operations is reduced to M N times. When using the KB fully separable form, spurious eigenstate or ghost states must be eliminated by close examination. B.2 Ultrasoft Pseudopotential and PAW The norm-conserving pseudopotential is very successful in describing the semiconductor elements and the elements nearby, such as, Si and Al. But it needs a very large kinetic energy cutoff to describe the first row elements, transition and noble metal elements, which have localized valence states. The difficulty comes from the fact that the cutoff core radius can not be increased too far away from where the maximal of the true radial wave function occurs. Otherwise, the norm-conserving condition can not be satisfied. This problem is solved in the ultrasoft pseudopotential formalism as proposed by Vanderbilt [50] and independently by Blchl [217]. Another improvement is made by including more reference energies to increase the transferability of the pseudopotential [50, 217, 224]. We follow the presentation of Vanderbilts paper [50]. Start with the all-electron Schrdinger equation for an isolated atom, 0AEiiTV (B-25) where i. Now a pseudo wave function ilm i is constructed satisfying the conditions. By choosing a local pseudopotential V, we can define, loc ilociTV i (B-26) where i is local and short ranged because beyond V cr locAEV and i i The nonlocal pseudopotential operator in the KB form is well-defined as,

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132 iiNLiiV (B-27) Now the eigenvalue problem is for the pseudo wave function and pseudo Hamiltonian, 0.iiilocNLiilociiiilociilociiTVVTVTVTV (B-28) Furthermore, we can introduce i as, 1ijijjB (B-29) where ijijB (B-30) It is shown below that i is the dual of i because 11 s isjjijijjBB sjsiB (B-31) Now the nonlocal part of the pseudopotential is simplified to be ,NLijijijVB (B-32) Notice that i is equivalent to the core orbital in the original Phillips-Kleinman pseudopotential [208] and the projection operator i p which we will show later in PAW method [218, 219]. The norm-conserving condition can be generalized to be 0 ijQ (B-33)

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133 where ccijijijrrQ (B-34) is a Hermitian operator. It can be shown that the matrix ij B and therefore V are Hermitian when We can write out NL 0ijQ ij B in terms of the radial wave function iurr associated with as ir 22201122crijijlocjlld B drurVrurdrr (B-35) After integration by parts, we get 12cijjijiijicjcicjcr B Burururur (B-36) Also from the all-electron Schrdinger equation, we have 102cjiijicjcicjcrurururur (B-37) Subtracting Eq.B-37 from Eq.B-36, we get ijjiijij B BQ (B-38) because the true and pseudo wave function and their derivatives match at So when cr 0ijQ ij B and V are both Hermitian. NL The constraint of is not necessary if one is willing to deal with a generalized eigenvalue problem in which an overlap operator 0ijQ ,1ijijijSQ (B-39) appears. It has the following property,

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134 ,.ccccijijstistrrstijijrijrSQQ j (B-40) Now the nonlocal pseudopotential operator can be defined as ,NLijijijVD (B-41) where ijijjijDBQ (B-42) The operators ij B and are given in Eq.B-30 and Eq.B-34 respectively. Although ijQ ij B is not Hermitian, and are Hermitian because ijQ ijD 0ijjiijjijijijiijijjiijDDBBQQQQ (B-43) The generalized eigenvalue problem follows as ,,,1,0.iilocNLiilociststtststiststiiststistlociisisslociisijjssjlociiiHSTVVSTVBQQTVBTVBBTV (B-44) The cost of solving the generalized eigenvalue problem does not increase comparing to the original eigenvalue problem, since the most time consuming procedure is the multiplication of H S with a trial vector

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135 The relaxation of the constraint of Q 0ij makes it possible to choose the cutoff radius to be well beyond the maximum of the true wave function, because the only constraint is the matching of ir and ir at the cutoff radius. Since a generalized eigenvalue problem must be solved in the target solid-state calculation, the deficit of the valence charge in the core region associated with a pseudo wave function needs to be restored. At first, the solution to the generalized eigenvalue problem in a solid-state calculation, n k should be normalized as nnS nn kk (B-45) where stands for a band index, a k-point and a spin index. The valence charge density is n ,,vnnijjinijn Q kkkrr r (B-46) where ,ijinnjn kkk (B-47) The variational electronic total energy is ,,ionionnlocijijnHvxcvnijETVDEnEnkkk cn (B-48) where V and are the unscreened parts of V and Applying a variation to the electronic total energy with the constraint in Eq.B-45, we get the secular equation as ionloc ionijD loc ijD 0locNLnnTVVS kk (B-49) where (B-50) ionloclocHxcVVV

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136 (B-51) ionHxcijijijDDD and vvcnnnHxcHxcVVVrr r (B-52) 3HxcijHxcijDdrVQ rr (B-53) The dependence of on ijD n through H xc V means that the pseudopotential must be updated as part of the self-consistent procedure. In the pseudopotential method, the key concept is the replacement of true atomic wave function with pseudo atomic wave function for chemically active valence states. The wave function we then get for the target system is also pseudo, in contrast to the true wave function of the system. But these pseudo wave functions totally determine the chemical properties that we are interested in. This concept of pseudization of wave functions is further generalized in the PAW method by Blchl [218, 219]. In general, there is a linear transformation between the true wave function and the pseudo wave function or the so called auxiliary wave function as nn (B-54) where, as usual, stands for a band index, a k-point and a spin index. The difference between the true and the auxiliary wave function is the nodal structure of the former and the smoothness of the later in the atomic core region. n The transformation operator must be able to modify the smooth auxiliary wave function to the true wave function in each atomic region. So it is straightforward to write it as an identity operator plus contributions from each atomic site as RS 1 RRS (B-55)

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137 where R denotes all the atomic sites. To find the local contribution, we start with the transformation between the true atomic wave function i and the pseudo atomic wave function i for the isolated atom on site They are also called the partial wave function and the auxiliary wave function, i 1iRiSfori R (B-56) Equivalently, RiiiS (B-57) which defines the local contribution to the transformation operator. As usual, we require that the partial wave RS i and its auxiliary counter part i are the same beyond a certain cutoff radius. To be able to apply the transformation to an arbitrary auxiliary wave function, we need to have the following expansion ,niinRiR cR p forr rrrR (B-58) where i p is defined as the projector function, which is a dual to i ,1,ijijiiRcRipand p forijRandrrR (B-59) Here i p is similar to i in ultrasoft pseudopotential method. The way to construct i p is discussed in detail in Blchls paper [218]. The local transformation operator can be expressed as

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138 RnRiiniiiniRiRSSpp (B-60) So the transformation operator is 11RiiRiSp i (B-61) where i goes over all the atomic sites and the partial waves within. Now applying the transformation operator to an arbitrary auxiliary wave function, we get 11,,nniiinnnRnRiRp (B-62) where 1,nRiiniRp (B-63) 1,nRiiniRp (B-64) The expectation value of an operator is A 1cNccnnniiniAfAA (B-65) It can be written out as 1111,,,,1111,,,,111111,,,,,,1111,,,,,nnnnRnRnnRnRRRnnnRnRnRnRRnRnRnnRnnRnRnRRnRnRnRnRRRAAAAAAAA (B-66)

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139 where the third line in Eq.B-66 is zero because the function 1,nRnR 1, is zero beyond a certain augmentation region and the function 1,nn R is zero inside that same augmentation region. So the product of them is zero. Similarly, the forth line in Eq.B-66 is zero because the functions 1,nRnR 1, from different atomic sites never overlap. So we have ,,1111,,,,11,,,cccRcRNccnnnnRnRnRnRiinRiNccnnniiniNNccccijjiiiijjiiiRijRiRRijRiRAfAAAAfAADAADAA (B-67) where ijnnjininnnjnn f pppfp (B-68) which is defined as the occupancies of each augmentation channel ,ij Here we introduce the auxiliary core wave functions ci which is identical to the tails of the true core wave functions ci outside the augmentation region. This allows us to include the tails of core wave functions in the plane wave expansion, which is better than the ultrasoft pseudopotential case. So every operators expectation value can be written as three parts. The first part is from the auxiliary wave functions of the whole system in the expansion of plane waves. What has been missed is the part from the core region, which is achieved by two parts. The second part from the true onsite partial wave expansion of each atom is added. Then the third part from the auxiliary onsite partial

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140 wave expansion, which is only nonzero outside the atomic region and must be subtracted. For example the electron density is 11RRRnnnn rrrr (B-69) where nnncnnf n rrr (B-70) 1,,RijjiijRn cRn rrr (B-71) 1,,RijjiijRn cRn rrr (B-72) and is the core density of the atom and is the auxiliary core density that is identical with outside the atomic region and a smooth continuation inside. Another example is the total energy ,cRn ,cRn ,cRn 11,niRRREREEE (B-73) and 233331122,nnnxcnZnZEdrdrdrn,ndrn rrrrr-rrrrr (B-74) ,122,113331111221,2cRNccRijjiiiijRiRxcEnZnZdrdrdrn,nrrrrrrr-r (B-75) 111233,311311122,RijjiijRxcnZnZEdrdrdrn,ndrn rrrrr-rrrrr (B-76)

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141 where is defined as the sum of the delta functions on the nuclear sites and Zr Zr is defined as a sum of angular-momentum-dependent Gaussian functions. It is constructed such that the augmentation charge density 11RRRRnZnZrrr r has zero electrostatic multipole moments outside the atomic region. This achieves the result that the electrostatic interaction of the one center parts between different sites vanishes. The matrix element of a general operator with the auxiliary wave functions may be slowly converging in the plane wave expansion. An example is the singular electrostatic potential of a nucleus. This problem can be can be solved as following: If an operator B is purely localized within an atomic region, we can use the identity between the auxiliary wave function and its own partial wave expansion 110nnnnBB (B-77) This is only exact for a complete set of projectors. This is why we introduce the potential r in the expressions of and to achieve their convergence individually. The potential E 1RE r must be localized within the atomic region as ,0nniijjnnijfpp 1 (B-78) Finally, the ultrasoft pseudopotential method can be derived as an approximation from the PAW method. The augmentation part of energy 1EEE ij is a functional of the one center occupancies of each augmentation channel In the expansion of E with respect to ij if we truncate the expansion after the linear term, the ultrasoft pseudopotential is recovered as follows,

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142 2,atatatijijijijijijijijEEEO (B-79) The linear term is the energy related to the nonlocal pseudopotential.

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BIOGRAPHICAL SKETCH Lin-Lin Wang was born on March 10, 1977, in Gangshang, a small town in Jiangsu Province, China. He graduated from Yunhe High school in 1993. He studied in Nanjing University and got a bachelors degree in physics in 1997. He came to the University of Florida in 1998. 156