# Publications

## Modelling defects in Ni–Al with EAM and DFT calculations

F. Bianchini, J.R. Kermode, and A. De Vita, Modelling defects in Ni–Al with EAM and DFT calculations, Modell. Simul. Mater. Sci. Eng. **24**, 045012 (2016).

We present detailed comparisons between the results of embedded atom model (EAM) and density functional theory (DFT) calculations on defected Ni alloy systems. We find that the EAM interatomic potentials reproduce low-temperature structural properties in both the γ and ${{\gamma}^{\prime}}$ phases, and yield accurate atomic forces in bulk-like configurations even at temperatures as high as ~1200 K. However, they fail to describe more complex chemical bonding, in configurations including defects such as vacancies or dislocations, for which we observe significant deviations between the EAM and DFT forces, suggesting that derived properties such as (free) energy barriers to vacancy migration and dislocation glide may also be inaccurate. Testing against full DFT calculations further reveals that these deviations have a local character, and are typically severe only up to the first or second neighbours of the defect. This suggests that a QM/MM approach can be used to accurately reproduce QM observables, fully exploiting the EAM potential efficiency in the MM zone. This approach could be easily extended to ternary systems for which developing a reliable and fully transferable EAM parameterisation would be extremely challenging e.g. Ni alloy model systems with a W or Re-containing QM zone.

## A universal preconditioner for simulating condensed phase materials

D. Packwood, J. Kermode, L. Mones, N. Bernstein, J. Woolley, N. Gould, C. Ortner, and G. Csányi, A universal preconditioner for simulating condensed phase materials, J. Chem. Phys. **144**, 164109 (2016)

We introduce a universal sparse preconditioner that accelerates geometry optimisation and saddle point search tasks that are common in the atomic scale simulation of materials. Our preconditioner is based on the neighbourhood structure and we demonstrate the gain in computational efficiency in a wide range of materials that include metals, insulators, and molecular solids. The simple structure of the preconditioner means that the gains can be realised in practice not only when using expensive electronic structuremodels but also for fast empirical potentials. Even for relatively small systems of a few hundred atoms, we observe speedups of a factor of two or more, and the gain grows with system size. An open source Python implementation within the Atomic Simulation Environment is available, offering interfaces to a wide range of atomistic codes.

## Development of an exchange–correlation functional with uncertainty quantification capabilities for density functional theory

Manuel Aldegunde, James R. Kermode, and Nicholas Zabaras, *J. Comput. Phys.* **311**, 173-195, doi:10.1016/j.jcp.2016.01.034

This paper presents the development of a new exchange–correlation functional from the point of view of machine learning. Using atomization energies of solids and small molecules, we train a linear model for the exchange enhancement factor using a Bayesian approach which allows for the quantification of uncertainties in the predictions. A relevance vector machine is used to automatically select the most relevant terms of the model. We then test this model on atomization energies and also on bulk properties. The average model provides a mean absolute error of only 0.116 eV for the test points of the G2/97 set but a larger 0.314 eV for the test solids. In terms of bulk properties, the prediction for transition metals and monovalent semiconductors has a very low test error. However, as expected, predictions for types of materials not represented in the training set such as ionic solids show much larger errors.

## Low Speed Crack Propagation via Kink Formation and Advance on the Silicon (110) Cleavage Plane

James R. Kermode, Anna Gleizer, Guy Kovel, Lars Pastewka, Gábor Csányi, Dov Sherman, and Alessandro De Vita, *Phys. Rev. Lett.* **115**, 135501, doi:10.1103/PhysRevLett.115.135501

We present density functional theory based atomistic calculations predicting that slow fracturing of silicon is possible at any chosen crack propagation speed under suitable temperature and load conditions. We also present experiments demonstrating fracture propagation on the Si(110) cleavage plane in the

## Classical interaction potentials for diverse materials from ab initio data: a review of potfit

Peter Brommer, Alexander Kiselev, Daniel Schopf, Philipp Beck, Johannes Roth and Hans-Rainer Trebin, *Modelling Simul. Mater. Sci. Eng.* **23 **074002 (2015). doi:10.1088/0965-0393/23/7/074002

Force matching is an established technique to generate effective potentials for molecular dynamics simulations from first-principles data. This method has been implemented in the open source code potfit . Here, we present a review of the method and describe the main features of the code. Particular emphasis is placed on the features added since the initial release: interactions represented by analytical functions, differential evolution as optimization method, and a greatly extended set of interaction models. Beyond the initially present pair and embedded-atom method potentials, potfit can now also optimize angular dependent potentials, charge and dipolar interactions, and electron-temperature-dependent potentials. We demonstrate the functionality of these interaction models using three example systems: phonons in type I clathrates, fracture of α-alumina, and laser-irradiated silicon

## Effect of oxygen and nitrogen functionalization on the physical and electronic structure of graphene

Alexander J. Marsden, Peter Brommer, James J. Mudd, M. Adam Dyson, Robert Cook, María Asensio, Jose Avila, Ana Levy, Jeremy Sloan, David Quigley, Gavin R. Bell, and Neil R. Wilson, *Nano Research* (2015). doi: 10.1007/s12274-015-0768-0

Covalent functionalization of graphene offers opportunities for tailoring its properties and is an unavoidable consequence of some graphene synthesis techniques. However, the changes induced by the functionalization are not well understood. By using atomic sources to control the extent of the oxygen and nitrogen functionalization, we studied the evolution in the structure and properties at the atomic scale. Atomic oxygen reversibly introduces epoxide groups whilst, under similar conditions, atomic nitrogen irreversibly creates diverse functionalities including substitutional, pyridinic, and pyrrolic nitrogen. Atomic oxygen leaves the Fermi energy at the Dirac point (i.e., undoped), whilst atomic nitrogen results in a net n-doping; however, the experimental results are consistent with the dominant electronic effect for both being a transition from delocalized to localized states, and hence the loss of the signature electronic structure of graphene.

## Diffusion of point defects in crystalline silicon using the kinetic activation-relaxation technique method

Mickaël Trochet, Laurent Karim Béland, Jean-François Joly, Peter Brommer, and Normand Mousseau, *Phys. Rev. B* **91**, 224106 (2015). doi:10.1103/PhysRevB.91.224106

We study point-defect diffusion in crystalline silicon using the kinetic activation-relaxation technique (k-ART), an off-lattice kinetic Monte Carlo method with on-the-fly catalog building capabilities based on the activation-relaxation technique (ART nouveau), coupled to the standard Stillinger-Weber potential. We focus more particularly on the evolution of crystalline cells with one to four vacancies and one to four interstitials in order to provide a detailed picture of both the atomistic diffusion mechanisms and overall kinetics. We show formation energies, activation barriers for the ground state of all eight systems, and migration barriers for those systems that diffuse. Additionally, we characterize diffusion paths and special configurations such as dumbbell complex, di-interstitial (IV-pair+2I) superdiffuser, tetrahedral vacancy complex, and more. This study points to an unsuspected dynamical richness even for this apparently simple system that can only be uncovered by exhaustive and systematic approaches such as the kinetic activation-relaxation technique.

## A framework for machine-learning-augmented multiscale atomistic simulations on parallel supercomputers

Caccin, M., Li, Z., Kermode, J. R. & De Vita, A. A framework for machine-learning-augmented multiscale atomistic simulations on parallel supercomputers. *Int. J. Quantum Chem.* (2015). doi:10.1002/qua.24952

Recent advances in quantum mechanical (QM)-based molecular dynamics (MD) simulations have used machine-learning (ML) to predict, rather than recalculate, QM-accurate forces in atomic configurations sufficiently similar to previously encountered ones. Here, we discuss how ML approaches can be deployed within large-scale QM/MM materials simulations on massively parallel supercomputers, making QM zones of ≳1000 atoms routinely attainable. We argue that the ML approach allows computational effort to be concentrated on the most chemically active subregions of the QM zone, significantly improving the overall efficiency of the simulation. We thus propose a novel method to partition large QM regions into multiple subregions, which can be computed in parallel to achieve optimal scaling. Then we review a recently proposed QM/ML MD scheme (Z. Li, J.R. Kermode, A. De Vita Phys. Rev. Lett., 2015, 114, 096405), discussing how this could be efficiently combined with QM-zone partitioning.

## Molecular Dynamics with On-the-Fly Machine Learning of Quantum-Mechanical Forces

Zhenwei Li, James R. Kermode and Alessandro De Vita, Phys. Rev. Lett. **114**, 096405 (2015)

doi:10.1103/PhysRevLett.114.096405

We present a molecular dynamics scheme which combines first-principles and machine-learning (ML) techniques in a single information-efficient approach. Forces on atoms are either predicted by Bayesian inference or, if necessary, computed by on-the-fly quantum-mechanical (QM) calculations and added to a growing ML database, whose completeness is, thus, never required. As a result, the scheme is accurate and general, while progressively fewer QM calls are needed when a new chemical process is encountered for the second and subsequent times, as demonstrated by tests on crystalline and molten silicon.

## Following atomistic kinetics on experimental timescales with the kinetic Activation–Relaxation Technique

N. Mousseau, L.K. Béland, P. Brommer, F. El-Mellouhi, J.-F. Joly, G.K. N'Tsouaglo, O. Restrepo, M. Trochet, *Comp. Mater. Sci. ***100 B**, 111–123 (2015), doi:10.1016/j.commatsci.2014.11.047

The properties of materials, even at the atomic level, evolve on macroscopic time scales. Following this evolution through simulation has been a challenge for many years. For lattice-based activated diffusion, kinetic Monte Carlo has turned out to be an almost perfect solution. Various accelerated molecular dynamical schemes, for their part, have allowed the study on long time scale of relatively simple systems. There is still a need, however, for methods able to handle complex materials such as alloys and disordered systems. Here, we review the kinetic Activation–Relaxation Technique (k-ART), one of a handful of off-lattice kinetic Monte Carlo methods, with on-the-fly cataloging, that have been proposed in the last few years.