Modelling the Properties of Gold Nanoparticles

Transcription

1 Modelling the Properties of Gold Nanoparticles A Thesis presented for the degree of Doctor of Philosophy by Benjamin Jean-Sebastien Soule de Bas B. Sc. (Eng.): Universite de Technologic de Compiegne M. Sc. (Mat. Sci. V Eng.): Virginia Tech Institute for Nanoscale Technology Faculty of Science University of Technology, Sydney September 2005

2 Certificate of Originality I certify that the work in this thesis has not previously been submitted for a degree nor has it been submitted as part of requirements for a degree except as fully acknowledged within the text. 1 also certify that the thesis has been written by me. Any help that I have received in my research work and the preparation of the thesis itself has been acknowledged. In addition, 1 certify that all information sources and literature used are indicated in this thesis. Benjamin J.-S. Soule de Bas 1

3 Acknowledgements First of all, I would like to thank my supervisor, Associate Professor Michael Ford, for his limitless availability, patience and guidance that made this work possible. I am also grateful to Mike for giving me the opportunity to present my thesis work at several international conferences, which in addition to being of great standard, took place at exciting locations. I would like to thank my cosupervisor. Professor Michael Cortie, for sharing his experience and expertise on gold as well as being a constant source of encouragement. I am also indebted to Dr Carl Masons who has been of great help in getting me started with SIESTA. I would like to acknowledge the friendship and assistance of my fellow research students in the Institute for Nanoscale Technology (INT): Burak Cankurtarn, Nadine Harris, Rainer Hoft. Donald McLurcan, Enid Mahomudally, Dakrong Pissuwan. Dean Wu and Xiaoda (David) Xu. Special thanks to Rainer for the many fruitful discussions about quantum chemistry and to David for always helping me with my Microsoft-related problems. I am grateful to the University of Technology, Sydney (UTS) for the receipt of an International Postgraduate Research Scholarship (IPRS) and stipend from the Faculty of Science. I would like to express my gratitude to my parents, Marie-Paule and Picrre- Jaeques Soule de Bas, and to my godfather, Jean Bulf, for having been very supportive throughout my entire education. Finally and most of all. I would like to thank Jacqueline for her outstanding support and understanding that have been essential at the most stressful times. n

4 Contents Certificate of Originality Acknowledgements Glossary of Acronyms Abstract i ii xix xxi 1 Introduction Motivation for the Current Work Background Structure of Gold Clusters Thermal Behaviour of Small Gold Clusters Adsorption of Gold Cluster on MgQ Present Study Theory Ab Initio Methods Schrodinger Equation Hartree Theory Hartree-Fock Theory Post Hartree-Fock Theories Density Functional Theory Thomas-Fermi Theory Hohenberg-Kohn Theorems Kohn-Sham equations iii

5 CONTENTS Exchange-Correlation Functionals Basis Set Expansion Pseudopotential Approximation Software and Hardware Molecular Dynamics Empirical Search of the Potential Energy Surface Simulated Anneal Interatomic Potentials Validation Pseudopotentials Au Pseudopotential Mg and 0 Pseudopotentials Input Parameters Mesh-Cutoff Orbital Confinement, k-point, Sampling Unit Cell Dimensions MgO Slab Dimensions Molecular Dynamics Timestep Thermal Inertia Parameter An and MgO Bulk Lattice Parameters Cohesive Energies Bulk Modulii Au Structure of Gold Clusters Method Potential Energy Surface Au Au Au IV

6 CONTENTS 4.3 DFT Structure Relaxation Structure of Small Clusters: Aug to Au Structure of Mid-Size Clusters: Au2o to A Trends in Binding Energy and Electronic Structure Conclusions...Ill 5 Thermal Behaviour of Gold Clusters Method Molecular Dynamics Simulations of Au Pentagonal Bipyramid Capped Triangle Analysis of Au7 Thermal Behaviour Molecular Dynamics Simulations of A Ground-State Structure Icosahedron Analysis of A1113 Thermal Behaviour Molecular Dynamics Simulations of A Tetrahedron Disordered Structure Analysis of Au2o Thermal Behaviour Conclusions Adsorption of Gold Cluster on MgO Method Molecular Dynamics Simulations of Au2o on MgO Search for the Au20/MgO Adsorption Geometry Detailed Analysis of the Au20 - MgO Interaction Fs-Centre Modelling Search for the Au20/MgO(Fs) Adsorption Geometry Detailed Analysis of the Au20 - MgO(Fs) Interaction Conclusions Conclusions 180 v

7 CONTENTS A Ordered Structures 183 B Semi-Empirical Minima 185 B.l Lennard-Jones Clusters B. 2 Gupta Clusters C DFT Energy Tables 189 C. l Total Energies C. 2 HOMO-LUMO Energies D Bond-Length Fluctuation Curves 192 D. l Au7 Pentagonal Bipyramid D.2 Au7 Capped Triangle D.3 Aui3 Ground-State Structure D.4 Aiii3 Icosahedron D.5 A mo Tetrahedron D.6 Au2o Disordered Structure E MD Simulation of Au2o on MgO 209 F Publication Report 212 F.l Journal Articles F.2 Poster Presentation F.3 Oral Presentation vi

8 List of Figures 2.1 Schematic illustration of all-electron wavefunction and potential (red lines) and their pseudo counterparts (blue lines) I)FT total energy of Au2 as a function of interatomic distance. The total energy of Ain was shifted by ev for the fitting procedure Au Pseudopotential for 1 = Au Pseudopotential for l = Au Pseudopotential for 1 = Au Pseudopotential for / = Mg Pseudopotential for l = 0... GO 3.G Mg Pseudopotential for / = 1... G1 3.7 Mg Pseudopotential for 1 = Mg Pseudopotential for l = Pseudopotential for l = O Pseudopotential for / = Pseudopotential for 1 = O Pseudopotential for / = Au7 total energy (a) and computation time (b) as a function of mesh-cutoff A1113 total energy (a) and computation time (b) as a function of mesh-cutoff Au2o total energy (a) and computation time (b) as a function of mesh-cutoff vii

9 LIST OF FIGURES 3.1G Au3o total energy (a) and computation time (b) as a function of mesh-cutoff Au,38 total energy (a) and computation time (b) as a function of mesh-cutoff layer (100) MgO slab total energy as a function of mesh-cutoff Au2o interaction energy (a), computation time (b) and memory use (c) as a function PAO.EnergyShift layer (100) MgO slab total energy (a) and computation time (b) as a function of k-point sampling Aun total energy as a function of multiplication factor fa Au2o total energy as a function of multiplication factor fa Au;3q total energy as a function of multiplication factor fa AU38 total energy as a function of multiplication factor fa Au2o total energy as a function of unit cell side /d Au20 interaction energy (a) and computation time (b) as a function of (100) MgO slab number of layers Extended system total energy as a function of time Temperature of the system as a function of MD step Total energy as a function of lattice parameter of Au (a) and MgO (b) Illustration of the Au atom surrounded by 42 Au-ghost atoms Illustration of the Mg/O atom surrounded by 38 O/Mg-ghost and 18 Mg/O-ghost atoms Cohesive energy as a function of unit cell volume of Au (a) and MgO (b) Au,3 potential energy surface. The colour scale ranges from blue, which represents low-energy regions, through cyan, green, yellow, orange and finally red, which represents high-energy regions. The upward (A) and downward (y) facing triangles indicate the location of a saddle point and two local minima, respectively viii

10 LIST OF FIGURES 4.2 Au3 partial potential energy surface. The colour scale ranges from blue, which represents low-energy regions, through cyan, green, yellow, orange and finally red. which represents high-energy regions. The upward (A) and downward (v) facing triangles indicate the location of a saddle point and two local minima, respectively Au4 partial potential energy surface between the square structure and the planar rhombus. The colour scale ranges from blue, which represents low-energy regions, through cyan, green, yellow, orange and finally red, which represents high-energy regions. The downward facing triangle (v) indicates the location of the minimum Au4 partial potential energy surface between the Y-sliaped structure and the planar rhombus. The colour scale ranges from blue, which represents low-energy regions, through cyan, green, yellow, orange and finally red, which represents high-energy regions. The upward (A) and downward (y) facing triangles indicate the location of a saddle point and two local minima, respectively A114 partial potential energy surface between the 3D tetrahedron and the planar rhombus. The colour scale ranges from blue, which represents low-energy regions, through cyan, green, yellow, orange and finally red, which represents high-energy regions. The upward (A) and downward (y) facing triangles indicate the location of a saddle point and two local minima, respectively A115 partial potential energy surface between the W-shaped structure and the trigonal bipyramid. The colour scale ranges from blue, which represents low-energy regions, through cyan, green, yellow, orange and finally red, which represents high-energy regions. The upward (A) and downward (y) facing triangles indicate the location of a saddle point and two local minima, respectively Au5 tetragonal pyramid A115 X-shaped structure IX

11 LIST OF FIGURES 4.9 Low energy structures of Au6 to Aui0. The clusters with letter indices correspond to isomers. AE is the difference in total energy (ev/atom) between the isomer and the ground-state structure Low energy structures of Aun to Au15. The clusters with letter indices correspond to isomers. AE is the difference in total energy (ev/atom) between the isomer and the ground-state structure Low energy structures of Aui6 to Aiiig. The clusters with letter indices correspond to isomers. AE is the difference in total energy (ev/atoin) between the isomer and the ground-state structure Low energy structures of Au2q to Au25. The clusters with letter indices correspond to isomers. AE is the difference in total energy (ev/atom) between the isomer and the ground-state structure Low energy structures of Au26 to Au32. The clusters with letter indices correspond to isomers. AE is the difference in total energy (ev/atom) between the isomer and the ground-state structure Low energy structures of Au33 to Au38. The clusters with letter indices correspond to isomers. AE is the difference in total energy (ev/atom) between the isomer and the ground-state structure Bulk relative total energy Er(ii) (ev/atom) as a function of cluster size Second differences in energy A2E(n) (ev/atom) as a function of cluster size HOMO-LUMO energy Eh-lM (ev) as a function of cluster size Au7 bipyramid bond-length fluctuation 6 (a), time averaged gradient of bond-length fluctuation (ds) (b) and total energy (c) as a function of temperature Structural isomers of Au7 lying close in energy to the bipyramid structure Au7 capped triangle bond-length fluctuation 5 (a), time averaged gradient of bond-length fluctuation (ds) (b) and total energy (e) as a function of temperature x

12 LIST OF FIGURES 5.4 Au7 capped triangle atomic rearrangement (a) and isomerisation process (b) Illustration of the Au7 bipyramid atomic vibrations at u = 50.6 (a) (b) and 52.6 (c) cm-1. The amplitudes of the largest displacement are 0.71 A at 50.6 cm-1 (a) A at 52.0 cm-1 (b) and 0.71 A at 52.6 cm-1 (c) A1113 ground-state structure bond-length fluctuation S (a), time averaged gradient of bond-length fluctuation (ds) (b) and total energy (c) as a function of temperature Structural isomers of Aui3 lying close in energy to the ground-state structure AU13 icosahedron bond-length fluctuation 6 (a), time averaged gradient of bond-length fluctuation (ds) (b) and total energy (c) as a function of temperature Illustration of the Aiii3 ground-state structure atomic vibrations at uj cm-1. The amplitude of the largest displacement is 0.43 A Au20 tetrahedron bond-length fluctuation S (a), time averaged gradient of bond-length fluctuation (ds) (b) and total energy (c) as a function of temperature Au2o disordered structure bond-length fluctuation 5 (a), time averaged gradient of bond-length fluctuation (ds) (b) and total energy (c) as a function of temperature Structural isomers of Au2o Illustration of the Au20 tetrahedron atomic vibrations at uj = 31.6 (a) (b) and 36.9 (c) cm-1. The amplitudes of the largest displacement are 0.51 A at 31.6 cm-1 (a) A at 34.6 cm-1 (b) and 0.43 A at 36.9 cm"1 (c) Bond-length fluctuation 6 of MgO-supported and unsupported Au20 tetrahedron as a function of MD steps xi

13 LIST OF FIGURES 6.2 Initial geometry of Au2o on (100) MgO (simulation with initial temperature Tmi = 900 K). The green atoms correspond to Mg and the red atoms to O. The same convention will be used throughout the rest of the thesis Geometry of Au2o on (100) MgO after 1000 MD steps (simulation with Tmi = 900 K) Geometry of Au2o on (100) MgO after 2000 MD steps (simulation with 7jni = 900 K) Geometry of Au20 on (100) MgO after 3000 MD steps (simulation with TAi = 900 K) Geometry of Au2o on (100) MgO after 4000 MD steps (simulation with Tnil = 900 K) Graphic representation of the (100) MgO surface primitive cell. The green atoms correspond to Mg and the red atoms to O Most favourable adsorption geometry of An20 on the (100) MgO surface. Only three MgO atomic layers arc represented in the side view for clarity Illustration of Au2o absorbed on an edge perpendicularly to the (100) MgO Surface. Only three MgO atomic layers are represented for clarity Illustration of Au2o absorbed on a corner atom perpendicularly to the (100) MgO Surface. Only three MgO atomic layers are represented for clarity Optimum adsorption geometry of Au20 on the (100) MgO surface. Only three MgO atomic layers are represented in the side view for clarity Atomic distances from the centre of mass of the MgO-supported and unsupported Au2o tetrahedron Overlap population -PMgo(e) between the Mg and O atoms located in the top layer of the (100) MgO slab Overlap population Pau{^) between the Au atoms located in the basal plane of the Au20 tetrahedron xii

14 LIST OF FIGURES G.15 Overlap population between the Mg, O and Au atoms located at the Au2o/MgO interface Mulliken charge differences (10~2 e) of the Mg and O atoms located in the top layer of the MgO slab ( dqmuii < 0.01 e not reported) Mulliken charge differences (10~2 e) of the Au atoms located in the basal plane of the tetrahedron Mulliken charge differences (10-2 e) of the Au atoms located in the second layer of the tetrahedron Mulliken charge differences (10~2 e) of the Au atoms located in the third layer of the tetrahedron Mulliken charge differences (10-2 e) of the Au atom located at the top of the tetrahedron (Oil) schematic representation of the charge density difference cross sections Charge density difference cross section Charge density difference cross section Charge density difference cross section Charge density difference cross section Charge density difference cross section Representation of the initial (100) MgO(Fg) slab. The green and red atom correspond to unconstrained Mg and O atoms, respectively. The grey atoms correspond to fixed atoms Representation of the optimised Mg25()i3 embedded cluster Cross section of the charge density difference pmg0 (fs) - P\rgo (0Vac) at the MgO(Fs) surface Graphic representation of the Au20 basal plane containing equivalent face-centre (Fc). corner (C) and edge (E) atoms xiii

15 LIST OF FIGURES G.31 Relative energies of the Au2o/MgO(Fg) system for Au2o centred on a basal face-centre (Fc), corner and edge atom as a function of rotation angle with z^n2q = 2.25 (a), 2.50 (b) and 2.75 (c) A. The total energy of the system with Au2o centred on an edge atom and rotated by 45 at zall20 = 2.50 A (i.e. the 0 ev value) is ev Most favourable adsorption geometry of Au20 on the (100) MgO(Fg) surface. Only three MgO atomic layers are represented in the side view for clarity Optimum geometry of Au20 on the (100) MgO(Fy) surface Atomic distances from the cent re of mass of the MgO(Fs)-supported and unsupported Au20 tetrahedron Overlap population between the Mg and O atoms located in the top layer of the (100) Mg()(Fy) slab Overlap population between the Au atoms located in the basal plane of the Au2o tetrahedron supported on the (100) MgO(Fs) slab Overlap population between the Mg. O and Au atoms located at the Au2o/MgO(Fs) interface Mulliken charge differences (10~2 e) of the Mg and O atoms located in the top layer of the MgO(Fg) slab ( g?qmu1i < 0.01 e not reported) Mulliken charge differences (10-2 e) of the Au atoms located in the basal plane of the tetrahedron ( dqmuii < 0.01 e not reported) Mulliken charge differences (10-2 e) of the Au atoms located in the second layer of the tetrahedron Mulliken charge differences (10-2 e) of the Au atoms located in the third layer of the tetrahedron Mulliken charge differences (10-2 e) of the Au atom located at the top of the tetrahedron (Oil) schematic representation of the charge density difference cross sections. The white atom corresponds to the Fg-centre Charge density difference cross section xiv

16 LIST OF FIGURES 6.45 Charge density difference cross section G G.46 Charge density difference cross section Charge density difference cross section Charge density difference cross section A.l Cube A.2 Cuboctahedron A.3 Decahedron A.4 Pentagonal Dodecahedron A.5 Rhombic Dodecahedron A.6 Icosahedron A.7 Octahedron A.8 Pentagonal Bipyramid A. 9 Tetrahedron B. l Au.3 to Auio Lennard-Jones ground structures B.2 Aiin to A1130 Lennard-Jones ground structures B.3 Au2o to A1130 n-body Gupta ground structures B.4 A1131 to A1138 n-body Gupta ground structures D.l Long simulation bond-length fluctuation S as a function of MD step at various temperatures (K) D.2 Series 1 bond-length fluctuation 6 as a function of MD step at various temperatures (K) D.3 Series 2 bond-length fluctuation 5 as a function of MD step at various temperatures (K) D.4 Series 3 bond-length fluctuation 5 as a function of MD step at various temperatures (K) D.5 Long simulation bond-length fluctuation S as a function of MD step at various temperatures (K) D.6 Series 1 bond-length fluctuation 5 as a function of MD step at various temperatures (K) D.7 Series 2 bond-length fluctuation S as a function of MD step at various temperatures (K) xv

17 LIST OF FIGURES I).8 Series 3 bond-length fluctuation 8 as a function of MD step at various temperatures (K) D.9 Long simulation bond-length fluctuation S as a function of MD step at various temperatures (K) D. 10 Series 1 bond-length fluctuation 8 as a function of MD step at various temperatures (I\) D.ll Series 2 bond-length fluctuation 8 as a function of MD step at various temperatures (K) D. 12 Series 3 bond-length fluctuation 8 as a function of MD step at various temperatures (K) D.13 Long simulation bond-length fluctuation 8 as a function of MD step at various temperatures (K) D. 14 Series 1 bond-length fluctuation 8 as a function of MD step at various temperatures (K) D. 15 Series 2 bond-length fluctuation 8 as a function of MD step at various temperatures (K) D. 16 Series 3 bond-length fluctuation 8 as a function of MD step at various temperatures (K) D.17 Long simulation bond-length fluctuation 8 as a function of MD step at various temperatures (K) D. 18 Series 1 bond-length fluctuation 8 as a function of MD step at various temperatures (K) D. 19 Series 2 bond-length fluctuation 8 as a function of MD step at various temperatures (K) D.20 Series 3 bond-length fluctuation 8 as a function of MD step at various temperatures (K) D.21 Series 1 bond-length fluctuation 8 as a function of MD step at various temperatures (K) D.22 Series 2 bond-length fluctuation 8 as a function of MD step at various temperatures (K) D.23 Series 3 bond-length fluctuation 8 as a function of MD step at various temperatures (K) xvi

18 LIST OF FIGURES E.l Initial geometry of Au2o on (100) MgO (simulation with initial temperature Tjui 905 Iv) E.2 Geometry of A1120 on (100) MgO after 1000 MD steps (simulation with Tjni = 905 K) E.3 Geometry of Au2o on (100) MgO after 2000 MD steps (simulation with Tmi = 905 I\) E.4 Geometry of Au2o on (100) MgO after 3000 MD steps (simulation with Tini = 905 K) E.5 Geometry of Au20 on (100) MgO after 4000 MD steps (simulation with Tini = 905 K) xvii

19 List of Tables 3.1 Au bulk parameters: cohesive energy Ec (ev), lattice parameter «o (A) and bulk modulus B (GPa) Au2 parameters: binding energy E\> (ev), bond length re (A) and vibration frequency uj (cm-1) Equivalence between the various positions of Au20 on (100) MgO surface. NE stands for Non-Equivalent Relative energy of Au2o on (100) MgO in distinct adsorption configurations with zau2o = 2.25 A Relative energy of Au2() on (100) MgO in distinct adsorption configurations with 2au A. The total energy of the system with Au'2o centred on site 12 and rotated by 15 is ev Relative energy of Au20 on (100) MgO in distinct adsorption configurations with 2au A B. l Gupta [1] energy (ev) of Aun with n = 20 to 38 atoms C. l DFT total energies (ev/atom) of Aun with n = 3 to 19 atoms C.2 DFT total energies (ev/atom) of Aun with n = 20 to 38 atoms. The bulk total energy Eym]k used in equation 4.1 is equal to ev/atom C.3 HOMO-LUMO energies (ev) of Aun with n = 3 to 38 atoms xviii

20 Glossary of Acronyms AE BSSE cc CCSD CG Cl CISD CM CP DFT DZP EAM FC Fs GCA HOMO LAPW LCAO EDA LJ LMTO LSDA All-Electron Basis Set Superposition Error Coupled Cluster Coupled Cluster with Singles and Doubles Conjugate Gradient Configuration Interaction with Singles and Doubles Configuration Interaction Centre of Mass Counterpoise Correction Density Functional Theory Double-^ plus Polarisation Embedded Atom Model Force Constant Surface F-centre Generalised Gradient Approximation Highest Occupied Molecular Orbital Linear Augmented Plane Wave Linear Combination of Atomic Orbitals Local Density Approximation Lennard-Jones Linear Muffin-Tin Orbitals Local Spin Density Approximation xix

21 GLOSSARY OF ACRONYMS LUMO MD MP2 PES PS PW SA TB-SMA TPR Lowest Unoccupied Molecular Orbital Molecular Dynamics Second-Order Mpller-Plesset Potential Energy Surface Pseudopotential Plane Wave Simulated Anneal Tight-Binding Second Moment Approximation Temperature Programmed Reaction xx

22 Abstract The physical and chemical properties of gold nanoparticles were investigated using first-principles density-functional theory in the local density approximation. The low-energv structures of gold nanoparticles containing from 3 to 38 atoms were determined using a combination of semi-empirical potential and DFT calculations. At the DFT-LSDA level, planar structures persist up to Au6 and lie close in energy to the 3D ground-state structures for 7 < n < 10 atoms. Ordered structures are predicted as being stable for n < 9. Beyond this size, disordered structures dominate with the notable exception of the tetrahedral Au20. The present DFT calculations predict numerous structural isomers being energetically equivalent or lying close in energy to the ground-state structures. The HOMO-LUMO energy gap is found to decrease as the cluster size increases, which indicates a transition towards a metallic behaviour at larger sizes. The thermal behaviour of gold clusters containing 7, 13 and 20 atoms was investigated using isothermal density-functional molecular-dynamics simulations. At each size, the global minimum energy structure and a low lying isomer are used as the starting structures. In most cases, the clusters exhibit high-temperature melting without showing any sharp transition from a solid-like to a liquid-like phase, but rather pass through a region of transformation between structural isomers. The starting structure used in the simulation is shown to have a considerable effect upon the subsequent thermal behaviour. The Au20 ground-state structure contrasts with the other clusters and remains tetrahedral up to its melting at about 1200 I\. The adsorption of Au2o on a regular and defective (100) MgO surface was investigated using a combination of DFT MI) simulations, single-point calculations and structure optimisations. Au20 is found to bind quite weakly to the regular (100) MgO surface, favouring Au-0 interactions. The Mulliken population analxxi

23 ABSTRACT ysis used in conjunction with charge density maps reveals that the resulting bond mainly arises from an electrostatic polarisation of the cluster by the substrate. When adsorbed on a surface F-centre defect. A1120 binds to the oxide surface with a significantly enhanced strength. The analysis of the resulting interaction indicates that, in addition to being polarised, Au2o is charged by the defective surface. Based upon the results of the present investigation, different reaction mechanisms for the oxidation of CO by Au2o supported on MgO are proposed. xx 11