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Kamal
Choudhary
*^{ab},
Brian
DeCost
^{c},
Lily
Major
^{de},
Keith
Butler
^{e},
Jeyan
Thiyagalingam
^{e} and
Francesca
Tavazza
^{c}
^{a}Material Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, 20899, MD, USA. E-mail: kamal.choudhary@nist.gov
^{b}Theiss Research, La Jolla, 92037, CA, USA
^{c}Materials Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, 20899, MD, USA
^{d}Department of Computer Science, Aberystwyth University, SY23 3DB, UK
^{e}Scientific Computing Department, Rutherford Appleton Laboratory, Science and Technology Facilities Council, Harwell Campus, Didcot, OX11 0QX, UK

Received
12th September 2022
, Accepted 12th January 2023

First published on 23rd January 2023

Classical force fields (FFs) based on machine learning (ML) methods show great potential for large scale simulations of solids. MLFFs have hitherto largely been designed and fitted for specific systems and are not usually transferable to chemistries beyond the specific training set. We develop a unified atomisitic line graph neural network-based FF (ALIGNN-FF) that can model both structurally and chemically diverse solids with any combination of 89 elements from the periodic table. To train the ALIGNN-FF model, we use the JARVIS-DFT dataset which contains around 75000 materials and 4 million energy-force entries, out of which 307113 are used in the training. We demonstrate the applicability of this method for fast optimization of atomic structures in the crystallography open database and by predicting accurate crystal structures using a genetic algorithm for alloys.

Recently, machine learning based FFs^{14,15} have been used to systematically improve the accuracy of FFs and have successfully been used for multiple systems. One of the pioneer MLFFs were developed by Behler–Parinello in 2007 using a neural network.^{16} It was initially used for molecular systems and now has been extended to numerous other applications.^{17} Although a neural network is one of the most popular regressors, other methods such as Gaussian process-based Gaussian approximation potential (GAP),^{18} as well as linear regression and basis function-based spectral neighbor analysis potential (SNAP)^{19} have also been thoroughly used. Such FFs use two and three body descriptors to describe the local environment. Other popular MLFF formalisms include smooth overlap of atomic positions (SOAP),^{20} moment tensor potential (MTP),^{21,22} symbolic regression^{23} and polynomial-based approaches.^{24} One of the critical issues in developing and maintaining classical force-fields is that they are hard to update with software and hardware changes. Luckily, MLFFs are more transparently developed and maintained compared to other classical FFs. A review article on this topic can be found elsewhere.^{17} Nevertheless, early-generation MLFFs are also limited to a narrow chemical space and may require hand-crafted descriptors which may take time to be identified. Conventional MLFFs are usually trained on specific chemistry only as the number of parameters (cross-terms) exponentially increases with the number of elements in the system. This is where GNN based methods can be particularly useful for generalizability. We note that the number of model parameters do not scale explicitly with the number of elements, because there are no explicit cross-terms for interactions between different pairs of chemical species. Moreover, the model does not require retraining for new systems. So it could be shared and many researchers can make use of pre-trained models.

Graph neural network (GNN) based methods have shown remarkable improvements over descriptor based machine learning methods and can capture highly non-Euclidean chemical space.^{15,25–33} GNN FFs have been also recently proposed and are still in the development phase.^{34,35} We developed an atomistic line graph neural network (ALIGNN) in our previous work^{36} which can capture many body interactions in graph and successfully models more than 70 properties of materials, either scalar or vector quantities, such as formation energy, bandgap, elastic modulus, superconducting properties, adsorption isotherm, electron and density of states etc.^{36–41} The same automatic differentiation capability that allows training these complex models allows for physically consistent prediction of quantities such as forces and energies; this enables GNNs to be used in quickly identifying relaxed or equilibrium states of complex systems. However, there is a need for a large and diverse amount of data to train unified force-fields.

In this work, we present a dataset of energy and forces with 4 million entries for around 75000 materials in the JARVIS-DFT dataset which have been developed over the past 5 years.^{42} We extend the ALIGNN model to also predict derivatives that are necessary for FF formalism. There can be numerous applications of such a unified FF; however, in this work we limit ourselves to pre-optimization of structures, genetic algorithm based structure, and molecular dynamics applications. The developed model will be publicly available on the ALIGNN GitHub page (https://github.com/usnistgov/alignn) with several examples and a brief documentation.

We convert the atomic structures to a graph representation using an atomistic line graph neural network (ALIGNN). Details on the ALIGNN can be found in the related paper.^{36} In brief, each node in the atomistic graph is assigned 9 input node features based on its atomic species: electronegativity, group number, covalent radius, valence electrons, first ionization energy, electron affinity, block and atomic volume. The inter-atomic bond distances are used as edge features with a radial basis function up to an 8 Å cut-off. We use a periodic 12-nearest-neighbor graph construction. This atomistic graph is then used for constructing the corresponding line graph using interatomic bond-distances as nodes and bond-angles as edge features. The ALIGNN uses edge-gated graph convolution for updating nodes as well as edge features. One ALIGNN layer composes an edge-gated graph convolution on the bond graph with an edge-gated graph convolution on the line graph. The line graph convolution produces bond messages that are propagated to the atomistic graph, which further updates the bond features in combination with atom features.

In this work, we developed the functionality for atomwise and gradient predictions in the ALIGNN framework. Quantities related to gradients of the predicted energy, such as forces on each atom, are computed by applying the chain rule through the automatic differentiation system used to train the GNN. Usually, MLFF datasets are not transferable. We share a large dataset of energy and forces (available on the Figshare repository: https://doi.org/10.6084/m9.figshare.21667874), which can be used for other applications as well. Importantly, this dataset is continuously expanding, making it very systematic and transferable across multiple elements and their combinations. In a closed system, the forces on each atom i depend on its position with respect to every other particle j through a force-field as:

(1) |

(2) |

The 307113 data points are split into a 90:5:5 ratio for training, validation and testing. We train the model for 250 epochs using the same hyper-parameters as in the original ALIGNN model.^{36} The ALIGNN is based on deep graph library (DGL),^{48} PyTorch^{49} and JARVIS-Tools packages.^{42} We optimize a composite loss function (l) with weighted mean absolute error terms for both forces and energies:

(3) |

The ALIGNN-FF model has been integrated with an atomic simulation environment (ASE)^{50} as an energy, force and stress calculator for structure optimization and MD simulations. This calculator can be used for optimizing atomic structures using a genetic algorithm,^{51} and running molecular dynamics simulations, for example constant-temperature, constant-volume ensemble (NVT) simulations. The structural relaxations are carried out with the fast inertial relaxation engine (FIRE),^{52} available in ASE. In order to predict the equation of state/energy–volume–curve (EV) simulation, we apply volumetric strains in the range of −0.1 to 0.1 with an interval of 0.01. Although the current implementation is in ASE only, we plan to implement this FF in high-performance MD codes such as LAMMPS^{53} in the future which can provide significantly better performance.

While the above results are for a force tunable weighting factor of 10, we also train the models with other weighting factors as shown in Table 1. We find that as we increase the weighting factors, the MAEs increase for increase in energies but decrease for forces. As the MAD for forces is 0.1 eV Å^{−1}, we choose to work with the model obtained for the lowest MAE for forces and to analyze its applications in the rest of the paper. Nevertheless, we share model parameters for other weighting factors for those interested in analyzing its effect on property predictions.

Weight | MAE-Energies (eV per atom) | MAE-Forces (eV Å^{−1}) |
---|---|---|

0.1 | 0.034 | 0.092 |

0.5 | 0.044 | 0.089 |

1.0 | 0.051 | 0.088 |

5.0 | 0.082 | 0.054 |

10.0 | 0.086 | 0.047 |

We find that the EV curves from these methods coincide near the minimum for all systems but for Al_{2}CoNi and CrFeCoNi, the GPAW equilibrium volume is slightly smaller than that for the EAM and ALIGNN-FF, suggesting that the lattice constants for the ALIGNN-FF and EAM might be overestimated compared to those for GPAW. Nevertheless, EAM and ALIGNN-FF data agree well. Comparing the EAM and ALIGN-FF, it's important to remember that GNNs have no fundamental limitation to the number of species they can model (i.e. high chemical diversity), and can, in principle, even extrapolate to species not contained in the training set, which is extremely powerful compared to conventional FFs like the EAM.

Note that there are many other conventional FF repositories available (such as the Inter-atomic Potential Repository^{55} and JARVIS-FF^{56}) which contain data for a variety of systems. It is beyond the scope of the current work to compare all of them with the ALIGNN-FF; however, it would be an interesting effort for future work.

While the above examples are for individual crystals, it is important to distinguish different polymorphs of a composition system for materials simulation (i.e. structural diversity). As shown in Fig. 3, we analyze the energy–volume (EV) curve of four systems and their polymorphs using the ALIGNN-FF. We choose four such example systems because they are representative of different stable structures. In general, however, the EV-curve can be computed for any arbitrary system and structure. In Fig. 3a, we show the EV-curve for 4 silicon materials (JARVIS-IDs: JVASP-1002, JVASP-91933, JVASP-25369, and JVASP-25368) with diamond cubic correctly being the lowest in energy. Similarly, the EV-curve for naturally prevalent SiO_{2} systems (JARVIS-IDs: JVASP-58349, JVASP-34674, JVASP-34656, and JVASP-58394), binary alloy Ni_{3}Al (JARVIS-IDs: JVASP-14971, JVASP-99749, and JVASP-11979) and vdW bonded material MoS_{2} (JARVIS-IDs: JVASP-28733, JVASP-28413, and JVASP-58505) all have the correct structure corresponding to the minimum energy. Therefore, while the MAE for our overall energy model is high, such a model is able to distinguish polymorphs of compounds with meV level accuracy which is critical for atomistic applications.

After this example GA search for structures, we plot the convex hull diagram of these systems, as shown in Fig. 5. We find that the GA predicts AB and A_{3}B compounds which are in fact observed experimentally in such binary alloys.^{51,58} Additionally, Ni_{3}Al (spacegroup: Pmm) is known to be one of the best performing super-alloys^{51} which is reproduced in the above example. We also found that the formation energy of this structure (−0.47 eV per atom) is similar to Johannesson's^{51} findings of −0.49 eV per atom. Although the above example is carried out for binary systems, in principle, the same methodology can be applied for any other system as well.

Although the above examples are based on a few test cases, the ALIGNN-FF can, in principle, be used for several applications such as investigating defective systems, high-entropy alloys, metal–organic frameworks, catalysts, battery designs, etc. and its validity needs to be tested for other applications which is beyond the scope of the present work. Also, as the methods for including larger datasets improve (such as training on millions of data points), and integration of active learning and transfer learning strategies is achieved, we believe we can train more accurate models. Moreover, such a universal FF model can be integrated with a universal tight-binding model^{60} so that classical and quantum properties can be predicted for large systems. In the current state, such FFs can be very useful for structure optimization; however, there is lot of room for improvement in terms of other physical characteristics such as defects, magnetism, charges, electronic levels, etc. Under-parameterized potentials get drastically better energy and force accuracy, but are much narrower in scope and have much higher training data density in their regions of applicability, based on highly tailored (and expensive) fit-for-purpose dataset generation. Over-parameterized GNNs are currently trained on extremely sparse datasets that are repurposed from high throughput material discovery efforts (e.g. JARVIS-DFT). Their potential to generalize a much greater chemical diversity is good, but a lot of research is needed to close the gap in accuracy with more narrow MLFF methods. A happy path forward for future research is probably intermediate in terms of the breadth of chemical and structural space and dataset density. Additionally, availability of standard benchmark datasets of multi-component systems with important properties such as diffusion coefficients for a diverse set of solute species, stacking fault energies, defect formation energies (solute substitution, vacancy, Schottky/Frenkel, etc), thermal conductivity, mechanical properties, and interface properties would play a pivotal role in the development of universal force-fields.

Integration with an external coding interface such as Alloy Theoretic Automated Toolkit (ATAT),^{61} calculation of phase diagrams (CALPHAD),^{62} Universal Structure Predictor (USPEX),^{63}ab initio random structure searching (AIRSS),^{64} genetic algorithm for structure and phase prediction (GASP),^{65,66} RASPA,^{67}etc. would further extend the applications for alloy design, structure predictions and designing nanoporous materials in the future. We note that the current force-field has been mainly evaluated for solids only, but in principle can be extended to polymers, and molecular and hybrid systems as well in the future. While there are several areas of improvements for such a unified force-field, we believe that this work would spark interest among materials scientists and engineers to enable a very wide range of atomistic applications.

- S. B. Ogale, Thin films and heterostructures for oxide electronics, Springer Science & Business Media, 2006 Search PubMed .
- M. P. Andersson, T. Bligaard, A. Kustov, K. E. Larsen, J. Greeley, T. Johannessen, C. H. Christensen and J. K. Nørskov, Toward computational screening in heterogeneous catalysis: Pareto-optimal methanation catalysts, J. Catal., 2006, 239, 501–506 CrossRef CAS .
- T. Liang, T.-R. Shan, Y.-T. Cheng, B. D. Devine, M. Noordhoek, Y. Li, Z. Lu, S. R. Phillpot and S. B. Sinnott, Classical atomistic simulations of surfaces and heterogeneous interfaces with the charge-optimized many body (COMB) potentials, Mater. Sci. Eng., R, 2013, 74, 255–279 CrossRef .
- X. Li, Y. Zhu, W. Cai, M. Borysiak, B. Han, D. Chen, R. D. Piner, L. Colombo and R. S. Ruoff, Transfer of large-area graphene films for high-performance transparent conductive electrodes, Nano Lett., 2009, 9, 4359–4363 CrossRef CAS PubMed .
- D. J. Srolovitz and V. Vitek, Atomistic Simulation of Materials: Beyond Pair Potentials, Springer Science & Business Media, 2012 Search PubMed .
- M. S. Daw and M. I. Baskes, Semiempirical, quantum mechanical calculation of hydrogen embrittlement in metals, Phys. Rev. Lett., 1983, 50, 1285 CrossRef CAS .
- G. P. Pun, V. Yamakov and Y. Mishin, Interatomic potential for the ternary Ni–Al–Co system and application to atomistic modeling of the B2–L10 martensitic transformation, Modell. Simul. Mater. Sci. Eng., 2015, 23, 065006 CrossRef .
- D. Farkas and A. Caro, Model interatomic potentials for Fe–Ni–Cr–Co–Al high-entropy alloys, J. Mater. Res., 2020, 35, 3031–3040 CrossRef CAS .
- M. S. Daw and M. I. Baskes, Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals, Phys. Rev. B: Condens. Matter Mater. Phys., 1984, 29, 6443 CrossRef CAS .
- T. Liang, B. Devine, S. R. Phillpot and S. B. Sinnott, Variable charge reactive potential for hydrocarbons to simulate organic-copper interactions, J. Phys. Chem. A, 2012, 116, 7976–7991 CrossRef CAS PubMed .
- D. W. Brenner, Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films, Phys. Rev. B: Condens. Matter Mater. Phys., 1990, 42, 9458 CrossRef CAS PubMed .
- A. C. Van Duin, S. Dasgupta, F. Lorant and W. A. Goddard, ReaxFF: a reactive force field for hydrocarbons, J. Phys. Chem. A, 2001, 105, 9396–9409 CrossRef CAS .
- D. W. Brenner, The art and science of an analytic potential, Phys. Status Solidi B, 2000, 217, 23–40 CrossRef CAS .
- I. Poltavsky and A. Tkatchenko, Machine learning force fields: Recent advances and remaining challenges, J. Phys. Chem. Lett., 2021, 12, 6551–6564 CrossRef CAS PubMed .
- K. Choudhary, B. DeCost, C. Chen, A. Jain, F. Tavazza, R. Cohn, C. W. Park, A. Choudhary, A. Agrawal and S. J. Billinge, et al., Recent advances and applications of deep learning methods in materials science, npj Comput. Mater., 2022, 8, 1–26 CrossRef .
- J. Behler and M. Parrinello, Generalized neural-network representation of high-dimensional potential-energy surfaces, Phys. Rev. Lett., 2007, 98, 146401 CrossRef PubMed .
- O. T. Unke, S. Chmiela, H. E. Sauceda, M. Gastegger, I. Poltavsky, K. T. Schütt, A. Tkatchenko and K.-R. Müllerr, Machine learning force fields, Chem. Rev., 2021, 121, 10142–10186 CrossRef CAS PubMed .
- A. P. Bartók, M. C. Payne, R. Kondor and G. Csányi, Gaussian approximation potentials: the accuracy of quantum mechanics, without the electrons, Phys. Rev. Lett., 2010, 104, 136403 CrossRef PubMed .
- M. A. Wood and A. P. Thompson, Extending the accuracy of the SNAP interatomic potential form, J. Chem. Phys., 2018, 148, 241721 CrossRef PubMed .
- A. P. Bartók, R. Kondor and G. Csányi, On representing chemical environments, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 87, 184115 CrossRef .
- A. V. Shapeev, Moment tensor potentials: A class of systematically improvable interatomic potentials, Multiscale Model. Simul., 2016, 14, 1153–1173 CrossRef .
- I. S. Novikov, K. Gubaev, E. V. Podryabinkin and A. V. Shapeev, The MLIP package: moment tensor potentials with MPI and active learning, Mach. learn.: sci. technol., 2020, 2, 025002 Search PubMed .
- A. Hernandez, A. Balasubramanian, F. Yuan, S. A. Mason and T. Mueller, Fast, accurate, and transferable many-body interatomic potentials by symbolic regression, npj Comput. Mater., 2019, 5, 1–11 CrossRef .
- R. Drautz, Atomic cluster expansion for accurate and transferable interatomic potentials, Phys. Rev. B, 2019, 99, 014104 CrossRef CAS .
- K. T. Schütt, H. E. Sauceda, P.-J. Kindermans, A. Tkatchenko and K.-R. Müller, Schnet–a deep learning architecture for molecules and materials, J. Chem. Phys., 2018, 148, 241722 CrossRef PubMed .
- T. Xie and J. C. Grossman, Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties, Phys. Rev. Lett., 2018, 120, 145301 CrossRef CAS PubMed .
- C. Chen, W. Ye, Y. Zuo, C. Zheng and S. P. Ong, Graph networks as a universal machine learning framework for molecules and crystals, Chem. Mater., 2019, 31, 3564–3572 CrossRef CAS .
- C. Chen and S. P. Ong, A universal graph deep learning interatomic potential for the periodic table, arXiv, 2022, preprint, arXiv:2202.02450.
- S. Kearnes, K. McCloskey, M. Berndl, V. Pande and P. Riley, Molecular graph convolutions: moving beyond fingerprints, J. Comput.-Aided Mol. Des., 2016, 30, 595–608 CrossRef CAS PubMed .
- J. Gilmer, S. S. Schoenholz, P. F. Riley, O. Vinyals and G. E. Dahl, Neural message passing for quantum chemistry, International conference on machine learning, 2017, pp. 1263–1272 Search PubMed .
- J. Klicpera, S. Giri, J. T. Margraf and S. Günnemann, Fast and uncertainty-aware directional message passing for non-equilibrium molecules, arXiv, 2020, preprint, arXiv:2011.14115.
- S. Batzner, A. Musaelian, L. Sun, M. Geiger, J. P. Mailoa, M. Kornbluth, N. Molinari, T. E. Smidt and B. E. Kozinsky, (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials, Nat. Commun., 2022, 13, 1–11 Search PubMed .
- A. Musaelian, S. Batzner, A. Johansson, L. Sun, C. J. Owen, M. Kornbluth and B. Kozinsky, Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics, arXiv, 2022, preprint, arXiv:2204.05249.
- C. W. Park, M. Kornbluth, J. Vandermause, C. Wolverton, B. Kozinsky and J. P. Mailoa, Accurate and scalable graph neural network force field and molecular dynamics with direct force architecture, npj Comput. Mater., 2021, 7, 1–9 CrossRef .
- S. Chmiela, H. E. Sauceda, K.-R. Müller and A. Tkatchenko, Towards exact molecular dynamics simulations with machine-learned force fields, Nat. Commun., 2018, 9, 1–10 CrossRef CAS PubMed .
- K. Choudhary and B. DeCost, Atomistic Line Graph Neural Network for improved materials property predictions, npj Comput. Mater., 2021, 7, 1–8 CrossRef .
- K. Choudhary, T. Yildirim, D. W. Siderius, A. G. Kusne, A. McDannald and D. L. Ortiz-Montalvo, Graph neural network predictions of metal organic framework CO2 adsorption properties, Comput. Mater. Sci., 2022, 210, 111388 CrossRef CAS .
- K. Choudhary and K. Garrity, Designing High-Tc Superconductors with BCS-inspired Screening, Density Functional Theory and Deep-learning, arXiv, 2022, preprint, arXiv:2205.00060.
- K. Choudhary and B. G. Sumpter, A Deep-learning Model for Fast Prediction of Vacancy Formation in Diverse Materials, arXiv, 2022, preprint, arXiv:2205.08366.
- P. R. Kaundinya, K. Choudhary and S. R. Kalidindi, Prediction of the electron density of states for crystalline compounds with Atomistic Line Graph Neural Networks (ALIGNN), JOM, 2022, 74, 1395–1405 CrossRef CAS .
- R. Gurunathan, K. Choudhary and F. Tavazza, Rapid Prediction of Phonon Structure and Properties using the Atomistic Line Graph Neural Network (ALIGNN), arXiv, 2022, preprint, arXiv:2207.12510.
- K. Choudhary, K. F. Garrity, A. C. Reid, B. DeCost, A. J. Biacchi, A. R. Hight Walker, Z. Trautt, J. Hattrick-Simpers, A. G. Kusne and A. Centrone, et al., The joint automated repository for various integrated simulations (JARVIS) for data-driven materials design, npj Comput. Mater., 2020, 6, 1–13 CrossRef .
- G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169 CrossRef CAS PubMed .
- G. Kresse and J. Furthmüller, Efficiency of ab initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci., 1996, 6, 15–50 CrossRef CAS .
- J. Klimeš, D. R. Bowler and A. Michaelides, Chemical accuracy for the van der Waals density functional, J. Phys.: Condens. Matter, 2009, 22, 022201 CrossRef PubMed .
- K. Choudhary, G. Cheon, E. Reed and F. Tavazza, Elastic properties of bulk and low-dimensional materials using van der Waals density functional, Phys. Rev. B, 2018, 98, 014107 CrossRef CAS PubMed .
- A. K. Subramaniyan and C. Sun, Continuum interpretation of virial stress in molecular simulations, Int. J. Solids Struct., 2008, 45, 4340–4346 CrossRef .
- M. Wang, D. Zheng, Z. Ye, Q. Gan, M. Li, X. Song, J. Zhou, C. Ma, L. Yu and Y. Gai, et al., Deep graph library: a graph-centric, highly-performant package for graph neural networks, arXiv, 2019, preprint, arXiv:1909.01315.
- A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga and A. Lerer, Automatic differentiation in pytorch, 2017 Search PubMed .
- A. H. Larsen, J. J. Mortensen, J. Blomqvist, I. E. Castelli, R. Christensen, M. Du lak, J. Friis, M. N. Groves, B. Hammer and C. Hargus, et al., The atomic simulation environment—a Python library for working with atoms, J. Phys.: Condens. Matter, 2017, 29, 273002 CrossRef PubMed .
- G. H. Johannesson, T. Bligaard, A. V. Ruban, H. L. Skriver, K. W. Jacobsen and J. K. Nørskov, Combined electronic structure and evolutionary search approach to materials design, Phys. Rev. Lett., 2002, 88, 255506 CrossRef CAS PubMed .
- E. Bitzek, P. Koskinen, F. Gähler, M. Moseler and P. Gumbsch, Structural relaxation made simple, Phys. Rev. Lett., 2006, 97, 170201 CrossRef PubMed .
- A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in’t Veld, A. Kohlmeyer, S. G. Moore and T. D. Nguyen, et al., LAMMPS-a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales, Comput. Phys. Commun., 2022, 271, 108171 CrossRef CAS .
- J. Enkovaara, C. Rostgaard, J. J. Mortensen, J. Chen, M. Du lak, L. Ferrighi, J. Gavnholt, C. Glinsvad, V. Haikola and H. Hansen, et al., Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method, J. Phys.: Condens. Matter, 2010, 22, 253202 CrossRef CAS PubMed .
- C. A. Becker, F. Tavazza, Z. T. Trautt and R. A. B. de Macedo, Considerations for choosing and using force fields and interatomic potentials in materials science and engineering, Curr. Opin. Solid State Mater. Sci., 2013, 17, 277–283 CrossRef CAS .
- K. Choudhary, F. Y. P. Congo, T. Liang, C. Becker, R. G. Hennig and F. Tavazza, Evaluation and comparison of classical interatomic potentials through a user-friendly interactive web-interface, Sci. Data, 2017, 4, 1–12 Search PubMed .
- M. Ji, C.-Z. Wang and K.-M. Ho, Comparing efficiencies of genetic and minima hopping algorithms for crystal structure prediction, Phys. Chem. Chem. Phys., 2010, 12, 11617–11623 RSC .
- A. van de Walle and G. Ceder, Automating first-principles phase diagram calculations, J. Phase Equilib., 2002, 23, 348–359 CrossRef CAS .
- J. P. Perdew, K. Burke and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett., 1996, 77, 3865 CrossRef CAS PubMed .
- K. F. Garrity and K. Choudhary, Fast and Accurate Prediction of Material Properties with Three-Body Tight-Binding Model for the Periodic Table, arXiv, 2021, preprint, arXiv:2112.11585.
- A. Van De Walle, M. Asta and G. Ceder, The alloy theoretic automated toolkit: A user guide, Calphad, 2002, 26, 539–553 CrossRef CAS .
- Z.-K. Liu, First-principles calculations and CALPHAD modeling of thermodynamics, J. Phase Equilib. Diffus., 2009, 30, 517–534 CrossRef CAS .
- C. W. Glass, A. R. Oganov and N. Hansen, USPEX—Evolutionary crystal structure prediction, Comput. Phys. Commun., 2006, 175, 713–720 CrossRef CAS .
- C. J. Pickard and R. Needs, High-pressure phases of silane, Phys. Rev. Lett., 2006, 97, 045504 CrossRef PubMed .
- B. C. Revard, W. W. Tipton and R. G. Hennig, Structure and stability prediction of compounds with evolutionary algorithms, Prediction and Calculation of Crystal Structures, 2014, pp. 181–222 Search PubMed .
- K. Choudhary, T. Liang, K. Mathew, B. Revard, A. Chernatynskiy, S. R. Phillpot, R. G. Hennig and S. B. Sinnott, Dynamical properties of AlN nanostructures and heterogeneous interfaces predicted using COMB potentials, Comput. Mater. Sci., 2016, 113, 80–87 CrossRef CAS .
- D. Dubbeldam, S. Calero, D. E. Ellis and R. Q. Snurr, RASPA: molecular simulation software for adsorption and diffusion in flexible nanoporous materials, Mol. Simul., 2016, 42, 81–101 CrossRef CAS .

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