Theoretical Studies of Free and Supported Nanoalloy Clusters by Ramli Ismail A thesis submitted to The University of Birmingham for the examination of DOCTOR OF PHILOSOPHY School of Chemistry University of Birmingham July 2012 University of Birmingham Research Archive e-theses repository This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. Abstract Nanoclusters offer unique physical and chemical behaviour, with the possibility of fine-tuning size and structures. Clusters of transition metals of group 10 (Ni, Pd, Pt), group 11 (Cu, Ag and Au), and crossover combinations (nanoalloys) between the two groups are of importance for their excellent physical, catalytic, optical, electronic and magnetic properties. Upon alloying, activity, selectivity and stability enhancement is possible and another dimension arises – chemical ordering (i.e., mixed vs. segregated phases). Detailed theoretical studies can extend our understanding of these compli- cated systems, giving a better understanding of experimental observations and allowing prediction of chemical and physical properties. In this research, a good balance be- tween accuracy and computational cost in describing electronic structure was sought via a combined Empirical Potential (EP) - Density Functional Theory (DFT) method. At the EP level, global optimisation searches were performed using the Birmingham Cluster Genetic Algorithm and Basin-Hopping Monte Carlo algorithm coupled with potentials derived from the semi-empirical Gupta potential. The sensitivity of the potentials was further studied for various potential parameterisations. The DFT cal- culations were performed with the NWChem and Quantum ESPRESSO codes. At the EP level, exploration of Pd-Au, Pd-Pt and Ni-Al clusters evidence the transition from polyicosahedra – decahedra – face-centered cubic (fcc), for small (≤ 100 atoms) clus- ters, but interrupted at 38- and 98-atoms, due to the magic size of the fcc truncated octahedron (TO) and Leary tetrahedron, respectively. Below 50 atoms, these motifs are energetically very competitive, which led to a detailed structural study for the 34- and 38-atom clusters, as a function of composition. A qualitatively good agreement between EP and DFT was found, with a prevalence towards core-shell Dh34 and TO38 structure for Pd-Au and Pd-Pt clusters. The performance of empirical calculations varies with composition and these were investigated by calculations on a TO motif at fixed compositions – (32,6) and (6,32). The DFT calculations showed that the aver- age potential gave a good estimation of the heteronuclear interactions of Pd-Au and Pd-Pt systems. However, biased parameters exhibit better behaviour for Ni-Al, Pt-Au, Cu-Pd and Cu-Pt clusters. On an MgO support, Pd-Au clusters showed significant size and composition effects, based on 30- and 40-atom cluster models with variation in the bimetallic compositions (Pd-rich, Au-rich and medium composition). Consistent with the available experimental findings, Pd atoms preferentially bind to the oxygen sites at the interface and good cluster-substrate epitaxy was observed. The results gave fair confidence for application of the empirical potential for larger clusters, for which global exploration with the ab initio methods was not feasible. Abbreviations and Acronyms ANND average nearest-neighbour distance BCGA Birmingham Cluster Genetic Algorithm BHMC Basin-Hopping Monte Carlo DFT Density Functional Theory DZ basis sets of double-ζ EAM Embedded-Atom Model ECP effective core potentials EP-DF Empirical Potential - Density Functional Theory approach EP Empirical Potential method GA genetic algorithm GGA generalised gradient approximation GM global minimum LDA local density approximation LSDA local spin density approximation NP nanoparticle PBE Perdew-Burke-Ernzerhof exchange-correlation functional PDF pair distribution functions PES potential energy surface PEW parallel excitable walkers PW91 Perdew-Wang exchange-correlation functional PWscf plane-wave self-consistent field PZ81 Perdew-Zunger local-density approximations QE Quantum ESPRESSO – ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimisation TZVP basis sets of triple-ζ-plus-polarization XC exchange-correlation Structural Motifs Abbreviations detailed description in Chapter 4 Dh-Ih mixed decahedral - icosahedral motifs Dh-cp(DT) mixed decahedral-close-packed motifs with a double tetrahedral core Dh-cp(T) mixed decahedral-close-packed motifs with a single tetrahedron core Dh decahedral motifs Ih icosahedral motifs LT Leary tetrahedron Oh-Ih mixed octahedra-icosahedra TO truncated octahedron bcc body-centered cubic motifs cp(T) close-packed with a tetrahedral core cp close-packed motifs fcc-hcp mixed face-centred cubic-hexagonal close-packed motifs fcc face-centred cubic motifs hcp hexagonal close-packed motifs inc-Ih-Mackay incomplete Mackay-polyicosahedral motifs inc-Ih-anti-Mackay incomplete anti-Mackay-polyicosahedral motifs pIh polyicosahedral motifs 6 pIh polyicosahedra with 6 interpenetrating Ih13 units 7 pIh polyicosahedra with 7 interpenetrating Ih13 units 8 pIh polyicosahedra with 8 interpenetrating Ih13 units 12 pIh polyicosahedra with a 12 interpenetrating Ih13 units pIh(LS) low-symmetry polyicosahedra motifs pIh(T) polyicosahedra with a 10 atom tetrahedron core pIh-M(DT) incomplete Mackay-icosahedron with a double tetrahedral component pIh-M-pc5 five-fold pancake Mackay-icosahedron pIh-M Mackay-polyicosahedral motifs pIh-aM anti-Mackay-polyicosahedral motifs pIh-db polyicosahedra with a double Ih13 core Teristimewa untuk Rose dan anak-anak yang tersayang..... Siti Aisyah Farzana Muhammad Afif Fahmi bayi MMXIII Acknowledgements I would like to acknowledge my supervisor, Professor Roy Johnston, for the guidance and support throughout my Ph.D. program. I would like to thank my collaborators: Prof. Riccardo Ferrando (Universitá di Genova, Italy), Dr. Ziyou Li and Dr. Yisong Han (Nanoscale Physics Research Laboratory, Birmingham). I would also like to thank my second supervisor, Dr. Graham Worth. Special thanks for funding /cpu-time from different sources: Universiti Pen- didikan Sultan Idris (study leave /sponsorship), Ministry of Higher Education, Malaysia (sponsorship), University of Birmingham, BlueBEAR (Birmingham Environment for Academic Research), COST (European Cooperation in Science and Technology), CINECA supercomputing and HPC-Europa2 Transnational Access project. I would like to express my appreciation to past and present members of the Johnston research group for their help, encouragement and friendship: Oliver, Paul West, Andy Logsdail, Andy Bennett, Alina, Josafat, Lewis, Mark, Paul Jennings, Chris, Ivaylo, Louis, Samara, Haydar, Sven and Joe Watkins. I would also like to acknowledge friends in Molecular Processes and Theory (MPT) labs: Jan, Heather, Laura, Adam, Duncan, Raja, Emma and Tom. To my wife, Mrs. Rosmawati Razali, thanks for your love and support. And last, but not least, thanks to all of those who give support and help during the completion of the program. Contents 1 Introduction 1 1.1 Thesis Organisation . 1 1.2 Nanoparticle Research . 3 1.3 Cluster Chemistry . 4 1.4 Mono-metallic Clusters . 6 1.4.1 Gold . 6 1.4.2 Palladium . 7 1.4.3 Platinum . 7 1.4.4 Nickel . 9 1.4.5 Aluminium . 10 1.5 Nanoalloy Clusters . 10 1.6 Chemical Ordering in Nanoalloys . 14 1.7 Transition Metal Nanoalloys . 17 1.7.1 Group 10: Ni-Pd, Ni-Pt and Pd-Pt . 20 1.7.2 Group 11: Cu-Ag, Cu-Au and Ag-Au . 20 1.7.3 Group 10 – Group 11: (Ni, Pd, Pt)–(Ag, Au, Cu) . 22 1.7.4 Group 10/11 – Other Transition Metals . 23 1.8 Supported Clusters . 25 1.8.1 Alumina, Al2O3 ........................... 26 1.8.2 Carbon (Graphite, Graphene, Carbon Nanotubes) . 26 1.8.3 Silica, SiO2 ............................. 27 Contents i Contents 1.8.4 Magnesia, MgO . 27 2 Theoretical Background and Methods 29 2.1 Electronic Structure Theory . 29 2.1.1 First Principles Methods . 31 2.1.2 Empirical Methods . 32 2.2 Density Functional Approach . 32 2.2.1 The Schrödinger Equation . 32 2.2.2 Variational Principle . 34 2.2.3 Hohenberg-Kohn Theorem . 34 2.2.4 Levy-Constrained Search Proof . 35 2.2.5 Thomas-Fermi (TF) Model . 36 2.2.6 Kohn-Sham Equation . 36 2.3 Density Functional Theory (DFT) . 38 2.4 Genetic Algorithm (GA) . 41 2.4.1 Birmingham Cluster Genetic Algorithm (BCGA) . 42 2.5 Basin-Hopping Monte Carlo (BHMC) Algorithm . 46 2.6 Gupta Semi-empirical Potential . 48 2.6.1 Heteronuclear Interactions . 50 2.6.2 Parameterisations of the Gupta Potential . 52 2.7 Combined Empirical Potential – Density Functional Method . 54 2.7.1 Empirical Global Searches . 55 2.7.2 DFT Local Optimisations . 56 2.8 Energetic Analysis . 59 2.9 Bonding Profile Analyses . 60 2.10 Chemical Ordering . 62 2.11 Symmetry Analysis . 62 Contents ii Contents 3 Small Pd-Au and Pd-Pt Clusters 65 3.1 Introduction . 65 3.2 Computational Details . 68 3.3 Results and Discussion . 68 3.3.1 (Pd-Au)N , N ≤ 100 . 68 3.3.2 (Pd-Pt)N , N ≤ 100 . 77 3.3.3 98-atom Pd-Pt Clusters . 81 3.4 Chapter Conclusions . 83 4 Structure Database of Pd-Au, Pd-Pt and Ni-Al Clusters 86 4.1 Introduction . 86 4.2 Computational Details . 88 4.2.1 Compositional Mixing Degree, σN . 89 4.3 Structural Motifs of 34- and 38-atom Clusters . 90 4.3.1 Decahedral Packing . 90 4.3.2 Close-packing . 94 4.3.3 Anti-Mackay-icosahedral Packing . 95 4.3.4 Mackay-icosahedral Packing . 101 4.3.5 Mixed Packing . 101 4.4 Global Minima Variations . 104 4.4.1 (Pd-Au)34 .............................. 104 4.4.2 (Pd-Pt)34 .............................