# 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

## 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.

## Atomistic aspects of fracture

E. Bitzek, J. R. Kermode and P. Gumbsch, Atomistic aspects of fracture, Int. J. Fract. (2015), doi: 10.1007/s10704-015-9988-2

Any fracture process ultimately involves the rupture of atomic bonds. Processes at the atomic scale therefore critically influence the toughness and overall fracture behavior of materials. Atomistic simulation methods including large-scale molecular dynamics simulations with classical potentials, density functional theory calculations and advanced concurrent multiscale methods have led to new insights e.g. on the role of bond trapping, dynamic effects, crack- microstructure interactions and chemical aspects on the fracture toughness and crack propagation patterns in metals and ceramics. This review focuses on atomistic aspects of fracture in crystalline materials where significant advances have been achieved over the last ten years and provides an outlook on future perspectives for atomistic modelling of fracture.

## Accuracy of buffered-force QM/MM simulations of silica

Anke Peguiron, Lucio Colombi Ciacchi, Alessandro De Vita, James R. Kermode and Gianpietro Moras, Accuracy of buffered-force QM/MM simulations of silica**, **J. Chem. Phys., **142**, 064116 (2015), doi: 10.1063/1.4907786

We report comparisons between energy-based quantum mechanics/molecular mechanics (QM/MM) and buffered force-based QM/MM simulations in silica. Local quantities—such as density of states, charges, forces, and geometries—calculated with both QM/MM approaches are compared to the results of full QM simulations. We find the length scale over which forces computed using a finite QM region converge to reference values obtained in full quantum-mechanical calculations is ∼10 Å rather than the ∼5 Å previously reported for covalent materialssuch as silicon. Electrostatic embedding of the QM region in the surrounding classical point charges gives only a minor contribution to the force convergence. While the energy-based approach provides accurate results in geometry optimizations of point defects, we find that the removal of large force errors at the QM/MM boundary provided by the buffered force-based scheme is necessary for accurate constrained geometry optimizations where Si–O bonds are elongated and for finite-temperature molecular dynamics simulations of crack propagation. Moreover, the buffered approach allows for more flexibility, since special-purpose QM/MM coupling terms that link QM and MM atoms are not required and the region that is treated at the QM level can be adaptively redefined during the course of a dynamical simulation.