The structure of atomic and molecular clusters, optimised using classical potentials

The problem of the determination of the minimum energy configuration of an arrangement of N point particles under the interaction of their interatomic forces is discussed. The interatomic forces are described by classical many body potentials. Different optimisation methods are considered, multi level single link, topographical differential evolution and a genetic algorithm but it is shown that genetic algorithms combined with an efficient local optimisation method is especially quick and reliable for this task. In addition to comparing some different optimisation methods, the structures of clusters of atoms described by interatomic potential functions containing up to a few hundred atoms are calculated including some with some special symmetries. A number of applications are given including covalent carbon and silicon clusters, close-packed structures such as argon and silver and the two-component carbon-hydrogen system

A classical reactive potential for molecular clusters of sulphuric acid and water

We present a two-state empirical valence bond (EVB) potential describing interactions between sulphuric acid and water molecules and designed to model proton transfer between them within a classical dynamical framework. The potential has been developed in order to study the properties of molecular clusters of these species, which are thought to be relevant to atmospheric aerosol nucleation. The particle swarm optimisation method has been used to fit the parameters of the EVB model to density functional theory (DFT) calculations. Features of the parametrised model and DFT data are compared and found to be in satisfactory agreement. In particular, it is found that a single sulphuric acid molecule will donate a proton when clustered with four water molecules at 300 K and that this threshold is temperature dependent

Data-driven models of water and methane

In the field of materials modelling, traditional atomistic models seldom achieve high accuracy and speed at the same time. Recent developments using high-dimensional fits to approximate the quantum chemical potential energy surface (PES) have overcome this problem. This thesis presents such models for methane–water mixtures, in particular for methane clathrates. Since the discovery of their existence on Earth about half a century ago, methane clathrates have been subject to numerous studies motivated by industrial and environmental perspectives. This project develops atomistic models that describe methane–water interactions with high accuracy. The model development in this work focuses on the dimer and the trimer PESs, which are fitted to quantum mechanical data. The fitting methods used are the Gaussian Approximation Potentials (GAP) [1, 2] and the permutationally invariant polynomials (PIP) [3] methods, the latter applied in collaboration. The long-range electrostatic interactions are calculated using a classical force field, the modified TTM4F [4]. The resulting models are validated against quantum mechanical and experimental data. A clathrate phase diagram is calculated in the quasi-harmonic approximation using the model based on PIPs. As the fitted level, CCSD(T)-F12, is not applicable to larger systems, we compare the calculations to DMC results for the larger clusters and periodic systems. However, small systematic differences are found between the developed models and DMC; comparing different CCSD(T)-F12 versions against DMC, this inconsistency is confirmed to arise from the differences between the two quantum chemical methods. In another collaboration [5], different potential fitting methods are also compared using the same datasets and found to achieve similar accuracies when applied to only the energy differences.Peterhouse Research Studentship, BP International Centre for Advanced Materials (BP-ICAM

Tight-binding molecular-dynamics studies of defects and disorder in covalently-bonded materials

Tight-binding (TB) molecular dynamics (MD) has emerged as a powerful method for investigating the atomic-scale structure of materials --- in particular the interplay between structural and electronic properties --- bridging the gap between empirical methods which, while fast and efficient, lack transferability, and ab initio approaches which, because of excessive computational workload, suffer from limitations in size and run times. In this short review article, we examine several recent applications of TBMD in the area of defects in covalently-bonded semiconductors and the amorphous phases of these materials.Comment: Invited review article for Comput. Mater. Sci. (38 pages incl. 18 fig.

The ReaxFF reactive force-field : development, applications and future directions

The reactive force-field (ReaxFF) interatomic potential is a powerful computational tool for exploring, developing and optimizing material properties. Methods based on the principles of quantum mechanics (QM), while offering valuable theoretical guidance at the electronic level, are often too computationally intense for simulations that consider the full dynamic evolution of a system. Alternatively, empirical interatomic potentials that are based on classical principles require significantly fewer computational resources, which enables simulations to better describe dynamic processes over longer timeframes and on larger scales. Such methods, however, typically require a predefined connectivity between atoms, precluding simulations that involve reactive events. The ReaxFF method was developed to help bridge this gap. Approaching the gap from the classical side, ReaxFF casts the empirical interatomic potential within a bond-order formalism, thus implicitly describing chemical bonding without expensive QM calculations. This article provides an overview of the development, application, and future directions of the ReaxFF method

Improving the efficiency of computation of free energy differences

There has been a recent focus on investigating the properties of semi-conductors at the nanoscale as it is well known that the band-gap of semi-conducting materials is altered due to quantum confinement effects. The potential to fine-tune a material's properties based solely on particle size has raised significant interest both in experimental and computational studies. Zinc sulfide is one of the most studied metal sulfide semi-conductor minerals, due to its potential technological applications.Computational studies of the structural and thermodynamic properties of zinc sulfide nanoparticles and bulk structures have been performed throughout this work. A variety of computational methods have been employed, including molecular dynamics, lattice dynamics, first principles calculations, and free energy techniques, such as metadynamics and free energy perturbation. The thermodynamic stability of zinc sulfide nanoparticles as a function of size and shape has been studied. Investigation of the phase space of these systems required the use of enhanced sampling methods. The metadynamics method was specifically utilised to explore as many structures as possible in combination with extensive simulations. The use of first principles methods for these exploratory simulations was found to be prohibitively expensive, and so force field methods were primarily utilised. Throughout this investigation several force fields were used to compare and contrast their accuracy, while first principles calculations were performed, where possible, to assist in the interpretation and validation of the results.In the present study, two different collective variables, the trace of the inertia tensor and the Steinhardt bond order parameters, have been implemented and their performance in metadynamics compared. The trace of the inertia tensor was found to be useful for exploring clusters of small sizes, while the Q4 Steinhardt parameter, which describes the crystalline order of a solid, is more applicable to larger clusters. Both of these metadynamics studies resulted in clusters displaying zeolite structural motifs, including the zeolite framework `BCT'. This led us to investigate more thoroughly the stability of different zinc sulfide zeolite analogues, thereby highlighting the strengths and weaknesses of all the force fields employed. Many force fields are found to be unable to accurately represent the order of stability for bulk polymorphs.First principles calculations also highlighted that the BCT phase is less stable than either of the bulk polymorphs of zinc sulfide, in contrast to the order of stability obtained by force fields lacking a torsional term, both from literature and the rigid ion model developed during the current study. The larger nanoparticles cleaved from wurtzite exhibited internal strain upon relaxation. A new hypothetical zeolite framework was constructed from the distorted core of these clusters, and was found to possess structural similarities with the `APC' framework. The APC framework is composed of double crankshaft-chains with ”ABCABC…” stacking, while the hypothetical framework identified is formed by the same composite building unit with `ABAB: : : ' type stacking. For all the force fields used the new hypothetical framework was lower in energy than the APC framework, but higher in energy than sphalerite, wurtzite or the BCT phase.Free energy differences between small ZnS clusters in vacuum were calculated using the path variable technique, and also using static methods within the quasi-harmonic approximation. Similar values were obtained using both of these methods, validating the path collective variables used with metadynamics as an effective means of obtaining free energy differences for clusters in vacuum.In addition to clusters in vacuum, a number of studies of ZnS clusters in water were also performed. Both force field and first principles studies were employed to validate the ZnS-water interactions used for the binding energies of water to small clusters. As a further validation, the free energies of solvation of Zn2+ and S2?? in aqueous solution were calculated. The free energy of solvation for the sulfide anion was found to be close to the experimental value, while the parameters for Zn2+-water were found to require substantial modification as the solvation free energy was in error by 500 kJ/mol. While newly derived ZnS-water parameters may prove to be superior for describing ZnS clusters in bulk water, a repetition of the binding energy calculations for individual water molecules bound to ZnS clusters gave energies 2-3 times greater than those obtained via first principles methods and using the five other force fields investigated. These results highlight the issues present when attempting to transfer a model fitted in a certain way to a different application. In particular, the many-body and polarisation effects present when modelling water need to be considered when parameterising ZnS-water interactions

O(N) methods in electronic structure calculations

Linear scaling methods, or O(N) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. The theory behind the locality of electronic structure is described and related to physical properties of systems to be modelled, along with a survey of recent developments in real-space methods which are important for efficient use of high performance computers. The linear scaling methods proposed to date can be divided into seven different areas, and the applicability, efficiency and advantages of the methods proposed in these areas is then discussed. The applications of linear scaling methods, as well as the implementations available as computer programs, are considered. Finally, the prospects for and the challenges facing linear scaling methods are discussed.Comment: 85 pages, 15 figures, 488 references. Resubmitted to Rep. Prog. Phys (small changes

A theoretical investigation in heterogeneous gold catalysis

Includes bibliographical references.Despite the nobleness of bulk gold metal in air, small supported gold particles have been shown experimentally to be active in a wide range of chemical reactions. The objective of this work was to study, theoretically, some of the fundamental aspects of the reactivity of gold catalysts. Using activation of CO, CO2 and H2 as a test case, periodic and cluster density functional theory (DFT) calculations, within the generalized-gradient approximation (GGA), were performed to investigate the change in nobility of gold from the extended surface to small clusters. Potential methanol synthesis intermediates were optimized on the Au(111) surface. It was found that the molecules that are stable as gasphase species generally adsorbed weakly on the surface. Surface hydrogenation of CO-derived species appeared to be easier than surface hydrogenation of CO2- derived species. On an AU13 cluster, the energetics of CO2 adsorption and hydrogenation remain unfavourable. The cluster-size dependency of hydrogen and carbon monoxide adsorption was investigated. It was found that small gold clusters (1 to 13 atoms in size) can bind both H and CO strongly. Due to the changes in the orbital spatial symmetries and the energies of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) with cluster size in this small size range, the adsorption energies depend very strongly on the number of gold atoms present, i.e. each atom makes a difference. For H adsorption, there is a very marked oscillation in adsorption energies, with the clusters with an odd number of gold atoms (with lower LUMO energies) being generally more reactive than the even clusters, up to about 10 atoms when the HOMO-LUMO gap ceases to fluctuate strongly. The role of the support material in activating gold atoms was studied. A hybrid quantum mechanics/molecular mechanics (QMlMM) electronic embedding technique was employed to model the ZnO(000l) surface of zincite. The QM region of the surface, treated by density functional theory, consisted of a total of 13 zinc and oxygen atoms for the zinc-vacant site, and 14 atoms for the bulk-terminated island site. It was found that Au0 and Au+ could be stabilized at the zinc vacant site of this surface. The higher oxidation states are unstable with respect to auto-reduction by the ZnO surface (i.e. their LUMO energies were below the HOMO of a bare ZnO surface. However, gold hydroxyls, where gold has + 1 to +3 oxidation states, can be stabilized at the vacancy. As zinc-substitutional impurities on the bulk-terminated island site, Au+, Au2+ and Au3+ oxidation states can be stabilized. CO was used as a test molecule to probe the chemical reactivity of the gold atoms in different adsorption sites and oxidation states. It was found that supported Au+ was more reactive than Au0, Au2+, or Au3+. Furthermore, CO binds more strongly to supported Au0 than the free Au0 atom. This implies that the support does not simply disperse gold particles, but it also modifies their electronic properties. It was also found that the nucleation of gold atoms to clusters can be affected by the support. Supported charges Au clusters have shorter Au-Au distances than their gas-phase counterparts