Knowledge Led Master Code Search for Atomic and Electronic Structures of LaF3 Nanoclusters on Hybrid Rigid Ion-Shell Model-DFT Landscapes

Stable and metastable atomic configurations of stoichiometric (LaF3)n nanoclusters are obtained for n = 1 to 6 using Monte Carlo global optimization techniques implemented in newly developed software. All configurations are refined using an all-electron DFT approach with the PBEsol exchange and correlation functional. To reduce the computational cost, approximate configurations were initially filtered out using a basin hopping algorithm that was biased toward finding either the global minimum or all metastable minima on the six energy landscapes defined by interatomic potentials within a polarizable shell model. In both algorithms, standard local optimization methods are employed to relax trial random atomic configurations whereby the polarization of the ions is initially constrained to improve convergence to local energy minima. The global optimization routines were implemented within the in-house Knowledge Led Master Code (KLMC). Electronic characterization of the refined structures included the calculation of vertical ionization potentials and electron affinities using the ΔSCF approach at the PBEsol DFT level and the many-body G0W0/PBEsol0 theory which employs the hybrid density functional initial guess of the quasi-particle orbitals. The atomic structure of the nanoclusters can be seen to evolve with size from a trigonal pyramid to ring structures and finally to compact symmetrical configurations, where the coordination of higher charged La gradually increases. Additional fluorine ions are accommodated between two La ions: single fluoride (−F−) bridges are replaced by bridge pairs or trios, although more than three fluoride bridges between two cations are heavily penalized in energy and cluster ranking. There is also a trend for the external surface of LaF3 nanoclusters to be decorated by singly coordinated fluorine anions, one per outer La ion for larger nanoclusters. For the global minimum (LaF3)n nanoclusters, although the changes are modest, the ionization potential decreases, and the electron affinity increases with n, effectively decreasing the precursor of the band gap of the bulk phase. The majority of the metastable nanoclusters follows this trend, with the exception of configurations with at least one exposed cation at the surface which is not terminated by an anion. These nanoclusters have a greater electron affinity that could be attributed to structural features analogous to defects in solids

Microscopic origin of the optical processes in blue sapphire

Al2O3 changes from transparent to a range of intense colours depending on the chemical impurities present. In blue sapphire, Fe and Ti are incorporated; however, the chemical process that gives rise to the colour has long been debated. Atomistic modelling identifies charge transfer from Ti(III) to Fe(III) as being responsible for the characteristic blue appearance

Structure prediction of crystals, surfaces and nanoparticles

We review the current techniques used in the prediction of crystal structures and their surfaces and of the structures of nanoparticles. The main classes of search algorithm and energy function are summarized, and we discuss the growing role of methods based on machine learning. We illustrate the current status of the field with examples taken from metallic, inorganic and organic systems. This article is part of a discussion meeting issue 'Dynamic in situ microscopy relating structure and function'

An efficient genetic algorithm for structure prediction at the nanoscale

We have developed and implemented a new global optimization technique based on a Lamarckian genetic algorithm with the focus on structure diversity. The key process in the efficient search on a given complex energy landscape proves to be the removal of duplicates that is achieved using a topological analysis of candidate structures. The careful geometrical prescreening of newly formed structures and the introduction of new mutation move classes improve the rate of success further. The power of the developed technique, implemented in the Knowledge Led Master Code, or KLMC, is demonstrated by its ability to locate and explore a challenging double funnel landscape of a Lennard-Jones 38 atom system (LJ38). We apply the redeveloped KLMC to investigate three chemically different systems: ionic semiconductor (ZnO)1–32, metallic Ni13 and covalently bonded C60. All four systems have been systematically explored on the energy landscape defined using interatomic potentials. The new developments allowed us to successfully locate the double funnels of LJ38, find new local and global minima for ZnO clusters, extensively explore the Ni13 and C60 (the buckminsterfullerene, or buckyball) potential energy surfaces

Synthesis target structures for alkaline earth oxide clusters

Knowing the possible structures of individual clusters in nanostructured materials is an important first step in their design. With previous structure prediction data for BaO nanoclusters as a basis, data mining techniques were used to investigate candidate structures for magnesium oxide, calcium oxide and strontium oxide clusters. The lowest-energy structures and analysis of some of their structural properties are presented here. Clusters that are predicted to be ideal targets for synthesis, based on being both the only thermally accessible minimum for their size, and a size that is thermally accessible with respect to neighbouring sizes, include global minima for: sizes n = 9, 15, 16, 18 and 24 for (MgO)n; sizes n = 8, 9, 12, 16, 18 and 24 for (CaO) n ; the greatest number of sizes of (SrO) n clusters (n = 8, 9, 10, 12, 13, 15, 16, 18 and 24); and for (BaO) n sizes of n = 8, 10 and 16

Structure prediction of (BaO)n nanoclusters for n⩽24 using an evolutionary algorithm

Knowing the structure of nanoclusters is relevant to gaining insight into their properties for materials design. Computational studies predicting their structure should aim to reproduce experimental results. Here, barium oxide was chosen for its suitability for both computational structure prediction and experimental structure determination. An evolutionary algorithm implemented within the KLMC structure prediction package was employed to find the thermodynamically most stable structures of barium oxide nanoclusters (BaO)n with n=4-18and24. Evolutionary algorithm runs were performed to locate local minima on the potential energy landscape defined using interatomic potentials, the structures of which were then refined using density functional theory. BaO clusters show greater preference than MgO for adopting cuts from its bulk phase, thus more closely resemble clusters of KF. (BaO)4, (BaO)6, (BaO)8, (BaO)10 and (BaO)16 should be magic number clusters and each are at least 0.03 eV/BaO more stable than all other PBEsol local minima clusters found for the same size

Approaching Bulk from the Nanoscale: Extrapolation of Binding Energy from Rock-Salt Cuts of Alkaline Earth Metal Oxides

A systematic DFT study is performed on (MgO)_{B}, (CaO)_{n}, (SrO)_{n}, and (BaO)_{n} clusters with 6 < n < 50, and which display a cuboid 2X2X2 atomic motif seen in the bulk, rock-salt, configuration. The stability and energy progression of these clusters are used to predict the energies of infinitely long nanorods, or nanowires, slabs, and the bulk global minimum energy

Applying a new interatomic potential for the modelling of hexagonal and orthorhombic YMnO3

We develop and apply an interatomic potential for YMnO3, based on the shell model together with the angular overlap model, which can model ligand field effects. The potential parameters accurately reproduce the complex structure of both hexagonal and orthorhombic phases of YMnO3. The rotation of the MnO6 octahedra in o-YMnO3 suggests the E-type AFM order. The potential is further employed to investigate the energies of intrinsic defects in the material. Lower defect energies were found in o-YMnO3. Oxygen Frenkel and Y2O3 partial Schottky are the most favourable defects in h-YMnO3 and o-YMnO3, respectively. The defect models proposed have implications for the properties of the related non-stoichiometric phases

Quantum computing and materials science: A practical guide to applying quantum annealing to the configurational analysis of materials

Using quantum computers for computational chemistry and materials science will enable us to tackle problems that are intractable on classical computers. In this paper, we show how the relative energy of defective graphene structures can be calculated by using a quantum annealer. This simple system is used to guide the reader through the steps needed to translate a chemical structure (a set of atoms) and energy model to a representation that can be implemented on quantum annealers (a set of qubits). We discuss in detail how different energy contributions can be included in the model and what their effect is on the final result. The code used to run the simulation on D-Wave quantum annealers is made available as a Jupyter Notebook. This Tutorial was designed to be a quick-start guide for the computational chemists interested in running their first quantum annealing simulations. The methodology outlined in this paper represents the foundation for simulating more complex systems, such as solid solutions and disordered systems

Morphology of Cu clusters supported on reconstructed polar ZnO (0001) and (0001̄) surfaces

Unbiased Monte Carlo procedures are applied to investigate the structure of Cu clusters of various sizes deposited over reconstructed polar ZnO surfaces. Four distinct reconstructed polar ZnO surfaces (two Zn terminated (0001) reconstructions and two O terminated (000[1 with combining macron]) reconstructions) were investigated, having previously been determined to be the most stable under typical conditions, as revealed by the grand canonical ensemble studies. Random sampling was performed considering ∼400 000 random initial structural configurations of Cu atoms over the ZnO surfaces, with each structure being optimised using interatomic potential techniques, and the most stable resultant structures being refined using a plane-wave DFT approach. The investigation reveals the key role of surface adatoms and vacancies arising from the reconstruction of the polar ZnO surface in determining the morphology of deposited Cu clusters. Strong Cu–Zn interactions play an essential role in Cu cluster growth, with reconstructed polar ZnO surfaces featuring sites with undercoordinated Zn surface atoms promoting highly localised three dimensional Cu cluster morphologies, whist reconstructions featuring undercoordinated O atoms tend to result in more planar Cu clusters, in order to maximise the favourable Cu–Zn interaction. This is the first study that evaluates the thermodynamically most stable Cu/ZnO structures using realistic reconstructed ZnO polar surfaces, and thus provides valuable insights into the factors affecting Cu cluster growth over ZnO surfaces, as well as model catalyst surfaces that can be utilised in future computational studies to explore catalytic activity for key processes such as CO2 and CO hydrogenation to methanol