Structural Phase Behaviour Via Monte Carlo Techniques

There are few reliable computational techniques applicable to the problem of structural phase behaviour. This is starkly emphasised by the fact that there are still a number of unanswered questions concerning the solid state of some of the simplest models of matter. To determine the phase behaviour of a given system we invoke the machinery of statistical physics, which identifies the equilibrium phase as that which minimises the free-energy. This type of problem can only be dealt with fully via numerical simulation, as any less direct approach will involve making some uncontrolled approximation. In particular, a numerical simulation can be used to evaluate the free-energy difference between two phases if the simulation is free to visit them both. However, it has proven very difficult to find an algorithm which is capable of efficiently exploring two different phases, particularly when one or both of them is a crystalline solid. This thesis builds on previous work (Physical Review Letters 79 p.3002), exploring a new Monte Carlo approach to this class of problem. This new simulation technique uses a global coordinate transformation to switch between two different crystalline structures. Generally, this `lattice switch' is found to be extremely unlikely to succeed in a normal Monte Carlo simulation. To overcome this, extended-sampling techniques are used to encourage the simulation to visit `gateway' microstates where the switch will be successful. After compensating for this bias in the sampling, the free-energy difference between the two structures can be evaluated directly from their relative probabilities. As concrete examples on which to base the research, the lattice-switch Monte Carlo method is used to determine the free-energy difference between the face-centred cubic (fcc) and hexagonal close-packed (hcp) phases of two generic model systems --- the hard-sphere and Lennard-Jones potentials. The structural phase behaviour of the hard-sphere solid is determined at densities near melting and in the close-packed limit. The factors controlling the efficiency of the lattice-switch approach are explored, as is the character of the `gateway' microstates. The face-centred cubic structure is identified as the thermodynamically stable phase, and the free-energy difference between the two structures is determined with high precision. These results are shown to be in complete agreement with the results of other authors in the field (published during the course of this work), some of whom adopted the lattice-switch method for their calculations. Also, the results are favourably compared against the experimentally observed structural phase behaviour of sterically-stabilised colloidal dispersions, which are believed to behave like systems of hard spheres. The logical extension of the hard sphere work is to generalise the lattice-switch technique to deal with `softer' systems, such as the Lennard-Jones solid. The results in the literature for the structural phase behaviour of this relatively simple system are found to be completely inconsistent. A number of different approaches to this problem are explored, leading to the conclusion that these inconsistencies arise from the way in which the potential is truncated. Using results for the ground-state energies and from the harmonic approximation, we develop a new truncation scheme which allows this system to be simulated accurately and efficiently. Lattice-switch Monte Carlo is then used to determine the fcc-hcp phase boundary of the Lennard-Jones solid in its entirety. These results are compared against the experimental results for the Lennard-Jones potential's closest physical analogue, the rare-gas solids. While some of the published rare-gas observations are in approximate agreement with the lattice-switch results, these findings contradict the widely held belief that fcc is the equilibrium structure of the heavier rare-gas solids for all pressures and temperatures. The possible reasons for this disagreement are discussed. Finally, we examine the pros and cons of the lattice-switch technique, and explore ways in which it can be extended to cover an even wider range of structures and interactions

Unconstrained Global Optimization of Molecules on Surfaces: From globally optimized structures to scanning-probe data

The adsorption of molecules on a surface plays a vital role in heterogeneous catalysis. For a proper unterstanding of the reaction mechanisms involved, the adsorption ge ometry of the molecules on the surface needs to be known. So far, experimental data from tunneling microscopes and spectroscopy, such as STM and IRAS are the main ways to obtain such knowledge. Due to the vast search space of adsorption geometries, especially for oligomers, optimizations using ab initio methods can be used to confirm the experimental data only if good initial guesses are available. Global optimization can serve two purposes in these situations. On the one hand it allows for a thorough investigation of the given search space, which can provide good initial guesses for subsequent high-level structural refinements. On the other hand, given a known reaction mechanism, it could also be used to find catalysts that influence e.g. the relevant bonds. With respect to this idea the topic of this thesis is to find a local optimization method cheap enough such that the total computational cost of global optimization does not exceed availability and yet good enough that the results are meaningful to the problem at hand. With this in mind multiple force field and semiempirical methods have been tested and evaluated mainly on benzene, acetophenone and ethyl pyruvate on Pt(111) surfaces. Some other adsorbates have also been tested shortly. In addition to these global optimization results, DFT geometry optimizations of ethyl pyruvate on Pt(111) have been performed and the structures of the best adsorption geometry from global optimization and from DFT are compared. Furthermore, from the DFT data STM images have been calculated that are compared to experimental results. The theoretical and experimental STM images agree well

From mathematical models to quantum chemistry in cluster science : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Chemistry at Massey University, Albany, New Zealand

Listed in 2019 Dean's List of Exceptional ThesesThe structures and stabilities of hollow gold clusters are investigated by means of density functional theory (DFT) as topological duals of carbon fullerenes. Fullerenes can be constructed by taking a graphene sheet and wrapping it around a sphere, which requires the introduction of exactly 12 pentagons. In the dual case, a (111) face-centred cubic (fcc) gold sheet can be deformed in the same way, introducing 12 vertices of degree five, to create hollow gold nano-cages. This one-to-one relationship follows trivially from Euler’s polyhedral formula and there are as many golden dual fullerene isomers as there are carbon fullerenes. Photoelectron spectra of the clusters are simulated and compared to experimental results to investigate the possibility of detecting other dual fullerene isomers. The stability of the hollow gold cages is compared to compact structures and a clear energy convergence towards the (111) fcc sheet of gold is observed. The relationship between the Lennard-Jones (LJ) and sticky-hard-sphere (SHS) potential is investigated by means of geometry optimisations starting from the SHS clusters. It is shown that the number of non-isomorphic structures resulting from this procedure depends strongly on the exponents of the LJ potential. Not all LJ minima, that have been discovered in previous work, can be retrieved this way and the mapping from the SHS to the LJ structures is therefore non-injective and non-surjective. The number of missing structures is small and they correspond to energetically unfavourable minima on the energy landscape. The optimisations are also carried out for an extended Lennard-Jones potential derived from coupled-cluster calculations for the xenon dimer, and, although the shape of the potential is not too different from a regular (6,12)-LJ potential, the number of minima increases substantially. Gregory-Newton clusters, which are clusters where 12 spheres surround and touch a central sphere, are obtained from the complete set of SHS clusters. All 737 structures result in an icosahedron, when optimised with a (6,12)-LJ potential. Furthermore, the contact graphs, consisting only of atoms from the outer shell of the clusters, are all edge-induced sub-graphs of the icosahedral graph. For higher LJ exponents the symmetry of the potential energy surface breaks away from the icosahedral motif towards the SHS landscape, which does not support a perfect icosahedron for energetic reasons. This symmetry breaking is mainly governed by the shape of the potential in the repulsive region, with the long-range attractive region having little influence

Ab Initio Molecular Dynamics (Aimd)- a New Approach for Development of Accurate Potentials

In this study a new approach is presented for the development of accurate potential-energy hypersurfaces based on ab initio calculations that can be utilized to conduct molecular dynamics and Monte Carlo simulations to study chemical and mechanical properties at the atomistic level. The method integrates ab initio electronic structure calculations with the interpolation capability of multilayer neural networks. A sampling technique based on novelty detection is also developed to ensure that the neural network fitting for the potential energy spans the entire configuration space involved during the simulation. The procedure can be initiated using an empirical potential or direct dynamics simulation. The procedure is applied for developing the potential energy hypersurface for five-atom clusters within a silicon workpiece. Ab initio calculations were performed using Gaussian 98 electronic structure program. Results for five-atom silicon clusters representing the bulk and the surface structure are presented.Mechanical & Aerospace Engineerin

Understanding the Structure of Materials at the Intersection of Rationalisation, Prediction and Big Data

Theoretical materials science has a large and growing role to play in modern society thanks to its ability to deliver materials with new and interesting properties. The properties of any material are, on some level, a function of its internal structure. In this work we combine three important tools spanning the last 100 years of materials research, rationalisation, prediction and big data in an attempt to understand the factors that underpin the stability of ordered structures and to build an understanding of structure that is agnostic of a particular element or building block. We apply rationalisation to data mining of the Inorganic Crystal Structure Database, using various proposed structure descriptors to probe the factors affecting structure stability. Extensive prediction is performed on the Fe-Ni-Si system at inner earth core pressures to determine the phases most likely to be present, yielding a new, stable, Ni-Si structure. A new prediction technique for 2D grain boundaries is presented that doubles the size of system that can reasonably be studied at the ab initio level of theory. The structurally rich phosphorus and arsenic systems are investigated using structure prediction, producing new metastable structures. Finally, we use a simple model for particles that attract at long range and repel at short to probe all the possible binary structures over a wide range of stoichiometries. By carrying out prediction over a wide range of potential parameters we build a database of almost 20M entries. Contained within are a number of unreported structures including many in parts of parameter space that go beyond the periodic table in terms of size and bond energy ratios. Our work provides hints that these hypothetical structures could be realised in self assembling systems made up from constituents with tunable interactions opening the door to the possibility of new properties

Particle Physics Reference Library

This second open access volume of the handbook series deals with detectors, large experimental facilities and data handling, both for accelerator and non-accelerator based experiments. It also covers applications in medicine and life sciences. A joint CERN-Springer initiative, the “Particle Physics Reference Library” provides revised and updated contributions based on previously published material in the well-known Landolt-Boernstein series on particle physics, accelerators and detectors (volumes 21A,B1,B2,C), which took stock of the field approximately one decade ago. Central to this new initiative is publication under full open access

2D organisation of complex organic molecules

The self-assembly of two-dimensional molecular systems is of significant interest, offering an insight into the fundamental interactions which drive the formation of complex supramolecular structures. A careful choice of the molecular 'building blocks' for such self-assembled systems potentially allows the design and production of nanoscale architectures with pre-determined geometries and specific chemical functionalities. Within this thesis the two-dimensional structures formed by the self-assembly of complex organic molecules, deposited on an Au(111) surface held in an ultrahigh vacuum (URV) environment, are studied using a combination of scanning tunnelling microscopy (STM), photoelectron spectroscopy (PES), molecular dynamics (MD), and density functional theory (DFT) techniques. A UHV electrospray deposition (URV-ESD) technique is employed to facilitate the introduction of thermally labile molecules into the URV environment. Bi-molecular networks, formed from perylene tetracarboxylic diimide (PTCDI) and melamine, have previously been observed to assemble on the Au(111) surface. Several more complex phases are reported here, as characterised by S'I'M, with the balance between isotropic and anisotropic interactions giving rise to a variety of structures. Chemical functionality may be added to these networks by incorporating functionalised derivatives of PTCDI. Alternative structures produced by altering the shape of the molecular 'building blocks' are also discussed. The URV-ESD technique is demonstrated here to be compatible with the deposition of the fullerene C60,the single molecule magnet Mn12012(02CCR3h6(H20)4 (Mn12(acetate)16), and porphyrin based oligomers (P4 and P6) and polymers (Pn). The URV-ESD of C60on the clean AU(ll1) surface, and on a surface prepatterned with a PTCDI/melamine network, results in similar structures to those previously observed to be produced by sublimation. Mn12(acetate)16 and the porphyrin oligomers and polymers represent complex molecules which are thermally labile and possess, respectively, novel magnetic and electronic properties. Mn12(acetate) 16is observed to form filamentary aggregates due to the anisotropic nature of the molecule-molecule and molecule-substrate interactions, while P4, P6 and Pn form highly ordered close-packed domains driven by the interdigitation of the alkyl chains attached to the porphyrin cores. The findings presented within this thesis demonstrate that self-assembled molecular structures can be understood in terms of intermolecular interactions, and that for systems containing complex molecules the molecule-molecule interaction potential can lead to the formation of novel structures

Bibliography of Lewis Research Center Technical Publications announced in 1991

This compilation of abstracts describes and indexes the technical reporting that resulted from the scientific engineering work performed and managed by the Lewis Research Center in 1991. All the publications were announced in the 1991 issues of STAR (Scientific and Technical Aerospace Reports) and/or IAA (International Aerospace Abstracts). Included are research reports, journal articles, conference presentations, patents and patent applications, and theses