Computational Techniques

This chapter introduces fundamental computational approaches and ideas to energy materials. These can be divided into two main streams: one dealing with the motion of atoms or ions described at a simplified level of theory and another focusing on electrons. The modeling framework, which covers both streams, is outlined. The atomistic simulation techniques discussed in the chapter are concerned with describing the energy landscape of individual atoms or ions, where classical mechanics can be usefully employed as the first successful approximation. Multiscale approaches could be the method of choice if one is interested in large molecules, inhomogeneous solids, complex environments or geometrical arrangements, systems that are far away from equilibrium or have particularly long evolution times. One of the principal objectives of atomistic simulations is to derive an accurate and coherent approach to the prediction of defect structure, energetics and properties. Two of the most widely employed methods are outlined. This edition first published 2013 © 2013 John Wiley & Sons, Ltd

Magnetic coupling constants for MnO as calculated using hybrid density functional theory

The properties of MnO have been calculated using generalised gradient approximation (GGA-) and hybrid (h-) density functional theory (DFT), specifically variants of the popular PBE and PBESol exchange–correlation functionals. The GGA approaches are shown to be poor at reproducing experimental magnetic coupling constants and rhombohedral structural distortions, with the PBESol functional performing worse than PBE. In contrast, h-DFT results are in reasonable agreement with experiment. Calculation of the Néel temperatures using the mean-field approximation gives overestimates relative to experiment, but the discrepancies are as low as 15 K for the PBE0 approach and, generally, the h-DFT results are significant improvements over previous theoretical studies. For the Curie–Weiss temperature, larger disparities are observed between the theoretical results and previous experimental results

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)n, (CaO)n, (SrO)n, and (BaO)n clusters with 6 < n < 50, and which display a cuboid 2×2×2 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

Modelling the chemistry of Mn-doped MgO for bulk and (100) surfaces

We have investigated the energetic properties of Mn-doped MgO bulk and (100) surfaces using a QM/MM embedding computational method, calculating the formation energy for doped systems, as well as for surface defects, and the subsequent effect on chemical reactivity. Low-concentration Mn doping is endothermic for isovalent species in the bulk but exothermic for higher oxidation states under p-type conditions, and compensated by electrons going to the Fermi level rather than cation vacancies. The highest occupied dopant Mn 3d states are positioned in the MgO band gap, about 4.2 eV below the vacuum level. Surface Mn-doping is more favourable than subsurface doping, and marginally exothermic on a (100) surface at high O2 pressures. For both types of isovalent Mn-doped (100) surfaces, the formation energy for catalytically important oxygen defects is less than for pristine MgO, with F0 and F2+-centres favoured in n- and p-type conditions, respectively. In addition, F+-centres are stabilised by favourable exchange coupling between the Mn 3d states and the vacancy-localised electrons, as verified through calculation of the vertical ionisation potential. The adsorption of CO2 on to the pristine and defective (100) surface is used as a probe of chemical reactivity, with isovalent subsurface Mn dopants mildly affecting reactivity, whereas isovalent surface-positioned Mn strongly alters the chemical interactions between the substrate and adsorbate. The differing chemical reactivity, when compared to pristine MgO, justifies further detailed investigations for more varied oxidation states and dopant species

Computational study of native defects and defect migration in wurtzite AlN: an atomistic approach

We derive an empirical, lattice energy consistent interatomic force field model for wurtzite AlN to predict consistently a wide range of physical and defect properties. Using Mott–Littleton techniques, we calculate formation energies of vacancies and interstitials, which show good agreement with previous ab initio calculations at the edge of the band gap. A novel N3− interstitialcy configuration is proposed to be of lower energy than the octahedral-channel-centred counterpart. With the assistance of the QM/MM method, our potential can predict a VBM level (−7.35 eV) comparable to previous experimental measurements. We further investigate the migration mechanisms and energy barriers of the main intrinsic defects. For the vacancy migration, the axial migration barrier is found to be lower than the basal migration barrier, in contrast to previous calculations. Two interstitialcy migration mechanisms for the interstitial defects are proposed, the “knock-out” mechanism for Al interstitial and the “hand-over” mechanism for N interstitialcy defects. The new force field model proposed here demonstrates that the empirical two-body interatomic potential is still effective for the study of defect properties, electronic states, and other extended systems of III/V semiconductors and further can be employed with QM/MM embedded techniques

Morphology of Cu clusters supported on reconstructed polar ZnO (0001) and (000[1]) 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

Embedded-Cluster Calculations in a Numeric Atomic Orbital Density-Functional Theory Framework

We integrate the all-electron electronic structure code FHI-aims into the general ChemShell package for solid-state embedding (QM/MM) calculations. A major undertaking in this integration is the implementation of pseudopotential functionality into FHI-aims to describe cations at the QM/MM boundary through effective core potentials and therewith prevent spurious overpolarization of the electronic density. Based on numeric atomic orbital basis sets, FHI-aims offers particularly efficient access to exact exchange and second order perturbation theory, rendering the established QM/MM setup an ideal tool for hybrid and double-hybrid level DFT calculations of solid systems. We illustrate this capability by calculating the reduction potential of Fe in the Fe-substituted ZSM-5 zeolitic framework and the reaction energy profile for (photo-)catalytic water oxidation at TiO2(110).Comment: 12 pages, 4 figure

The Thermal Agitated Phase Transitions on the Ti32 Nanocluster: a Molecular Dynamics Simulation Study

Molecular dynamics simulations were performed to investigate the stability with respect to increasing the simulated temperature from 300 to 2400 K of an isolated cluster composed of 32 titanium atoms. The interatomic interactions were modelled using Gupta potentials as implemented within the classical molecular dynamics simulation software DL_POLY. The radial distribution functions (RDF), diffusion coefficient, and density profiles were examined to study the structural changes as a function of temperature. It was found that the Ti32 nanocluster exhibits temperature structural transition. The icosahedron and pentagonal bi-pyramid structures were found to be the most dominant building block fragments. Deformation of the nanocluster was also measured by diffusion coefficient, and it was found that the Ti32 are mobile above the bulk melting point. The phase transitions from solid to liquid have been identified by a simple jump in the total energy curve, with the predicted melting temperature near the bulk melting point (1941.15 K). As expected, the RDF’s and density profile peaks decrease with increasing temperature

A computational investigation of the adsorption of small copper clusters on the CeO2(110) surface

We report a detailed density functional theory (DFT) study of the geometrical and electronic properties, and the growth mechanism of a Cun (n=1-4) cluster on a stoichiometric, and especially on a defective CeO2(110) surface with one surface oxygen vacancy, without using pre-assumed gas-phase Cun cluster shapes. This gives new and valuable theoretical insight into experimental work regarding debatable active sites of promising CuOx/CeO2-nanorod catalysts in many reactions. We demonstrate that CeO2(110) is highly reducible upon Cun adsorption, with electron transfer from Cun clusters, and that a Cun cluster grows along the long bridge sites until Cu3, so that each Cu atom can interact strongly with surface oxygen ions at these sites, forming stable structures on both stoichiometric and defective CeO2(110) surface. Cu-Cu interactions are, however, limited, since Cu atoms are distant from each other, inhibiting the formation of Cu-Cu bonds. This monolayer then begins to grow into a bilayer as seen in the Cu3 to Cu4 transition, with long-bridge site Cu as anchoring sites. Our calculations on Cu4 adsorption reveal a Cu bilayer rich in Cu+ species at the Cu-O interface

Heterostructures of GaN with SiC and ZnO enhance carrier stability and separation in framework semiconductors

A computational approach, using the density functional theory, is employed to describe the enhanced electron-hole stability and separation in a novel class of semiconducting composite materials, with the so-called double bubble structural motif, which can be used for photocatalytic applications. We examine the double bubble containing SiC mixed with either GaN or ZnO, as well as related motifs that prove to have low formation energies. We find that a 24-atom SiC sodalite cage inside a 96-atom ZnO cage possesses electronic properties that make this material suitable for solar radiation absorption applications. Surprisingly stable, the inverse structure, with ZnO inside SiC, was found to show a large deformation of the double bubble and a strong localisation of the photo-excited electron charge carriers, with the lowest band gap of ca. 2.15 eV of the composite materials considered. The nanoporous nature of these materials could indicate their suitability for thermoelectric applications