A hybrid neural network potential for multilayer graphene systems developed by Wen and Tadmor (2019) v001

Mingjian Wen; Ellad B. Tadmor

doi:10.25950/a74cc44e

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hNN_WenTadmor_2019Grx_C__MO_421038499185_001

Interatomic potential for Carbon (C).
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Title A single sentence description.	A hybrid neural network potential for multilayer graphene systems developed by Wen and Tadmor (2019) v001
Description A short description of the Model describing its key features including for example: type of model (pair potential, 3-body potential, EAM, etc.), modeled species (Ac, Ag, ..., Zr), intended purpose, origin, and so on.	A hybrid neural network (NN) and Lennard-Jones (LJ) model driver for multilayer graphene systems. The NN term models short-range intralayer and orbital overlap interactions and the theoretically-motivated LJ term models long-range dispersion. The potential is trained against a large dataset of monolayer graphene, bilayer graphene, and graphite configurations obtained from ab initio total-energy calculations based on density functional theory (DFT). The potential provides accurate energy and forces for both intralayer and interlayer interactions, correctly reproducing DFT results for structural, energetic, and elastic properties such as the equilibrium layer spacing, interlayer binding energy, elastic moduli, and phonon dispersions to which it was not fit.
Species The supported atomic species.	C
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	This model is designed for multilayer graphene systems and graphite. It is not appropriate for bulk carbon structures.

Contributor	Mingjian Wen
Maintainer	Mingjian Wen
Developer	Mingjian Wen Ellad B. Tadmor
Published on KIM	2019
How to Cite	This Model originally published in [1] is archived in OpenKIM [2-5]. [1] Wen M, Tadmor EB. Hybrid neural network potential for multilayer graphene. Physical Review B. 2019;100(19):195419. doi:10.1103/PhysRevB.100.195419 — (Primary Source) A primary source is a reference directly related to the item documenting its development, as opposed to other sources that are provided as background information. [2] Wen M, Tadmor EB. A hybrid neural network potential for multilayer graphene systems developed by Wen and Tadmor (2019) v001. OpenKIM; 2019. doi:10.25950/a74cc44e [3] Wen M, Tadmor EB. A hybrid neural network model driver for multilayer two-dimensional materials developed by Wen and Tadmor (2019) v001. OpenKIM; 2019. doi:10.25950/9fa4935a [4] Tadmor EB, Elliott RS, Sethna JP, Miller RE, Becker CA. The potential of atomistic simulations and the Knowledgebase of Interatomic Models. JOM. 2011;63(7):17. doi:10.1007/s11837-011-0102-6 [5] Elliott RS, Tadmor EB. Knowledgebase of Interatomic Models (KIM) Application Programming Interface (API). OpenKIM; 2011. doi:10.25950/ff8f563a Click here to download the above citation in BibTeX format.
Citations This panel presents information regarding the papers that have cited the interatomic potential (IP) whose page you are on. The OpenKIM machine learning based Deep Citation framework is used to determine whether the citing article actually used the IP in computations (denoted by "USED") or only provides it as a background citation (denoted by "NOT USED"). For more details on Deep Citation and how to work with this panel, click the documentation link at the top of the panel. The word cloud to the right is generated from the abstracts of IP principle source(s) (given below in "How to Cite") and the citing articles that were determined to have used the IP in order to provide users with a quick sense of the types of physical phenomena to which this IP is applied. The bar chart shows the number of articles that cited the IP per year. Each bar is divided into green (articles that USED the IP) and blue (articles that did NOT USE the IP). Users are encouraged to correct Deep Citation errors in determination by clicking the speech icon next to a citing article and providing updated information. This will be integrated into the next Deep Citation learning cycle, which occurs on a regular basis. OpenKIM acknowledges the support of the Allen Institute for AI through the Semantic Scholar project for providing citation information and full text of articles when available, which are used to train the Deep Citation ML algorithm.	This panel provides information on past usage of this interatomic potential (IP) powered by the OpenKIM Deep Citation framework. The word cloud indicates typical applications of the potential. The bar chart shows citations per year of this IP (bars are divided into articles that used the IP (green) and those that did not (blue)). The complete list of articles that cited this IP is provided below along with the Deep Citation determination on usage. See the Deep Citation documentation for more information. 37 Citations (4 used) Show Model Used Show All Help us to determine which of the papers that cite this potential actually used it to perform calculations. If you know, click the . J. G. Mchugh, P. Mouratidis, and K. Jolley, “Ripplocations in layered materials: Sublinear scaling and basal climb,” arXiv: Materials Science. 2020. link Times cited: 9 Abstract: The ripplocation is a crystallographic defect which is uniqu… read more Abstract: The ripplocation is a crystallographic defect which is unique to layered materials, combining nanocale delamination with the crystallographic slip of a basal dislocation. Here, we have studied basal dislocations and ripplocations using analytical and computational techniques. Expressions for the energetic and structural scaling factors of surface ripplocations are derived, which are in close correspondence to the physics of a classical carpet ruck. Our simulations demonstrate that the lowest-energy structure of dislocation pile-ups in layered materials is the ripplocation, while large dislocation pile-ups in bulk graphite demonstrate multilayer delamination, curvature and voids. This can provide a concise explanation for the large volumetric expansion seen in irradiated graphite. read less H. Tran and H. Chew, “Surface morphology and carbon structure effects on sputtering: Bridging scales between molecular dynamics simulations and experiments,” Carbon. 2023. link Times cited: 4 H. Zhai and J. Yeo, “Multiscale mechanics of thermal gradient coupled graphene fracture: A molecular dynamics study,” International Journal of Applied Mechanics. 2022. link Times cited: 2 Abstract: The thermo-mechanical coupling mechanism of graphene fractur… read more Abstract: The thermo-mechanical coupling mechanism of graphene fracture under thermal gradients possesses rich applications whereas is hard to study due to its coupled non-equilibrium nature. We employ non-equilibrium molecular dynamics to study the fracture of graphene by applying a fixed strain rate under different thermal gradients by employing different potential fields. It is found that for AIREBO and AIREBO-M, the fracture stresses do not strictly follow the positive correlations with the initial crack length. Strain-hardening effects are observed for"REBO-based"potential models of small initial defects, which is interpreted as blunting effect observed for porous graphene. The temperature gradients are observed to not show clear relations with the fracture stresses and crack propagation dynamics. Quantized fracture mechanics verifies our molecular dynamics calculations. We provide a unique perspective that the transverse bond forces share the loading to account for the nonlinear increase of fracture stress with shorter crack length. Anomalous kinetic energy transportation along crack tips is observed for"REBO-based"potential models, which we attribute to the high interatomic attractions in the potential models. The fractures are honored to be more"brittle-liked"carried out using machine learning interatomic potential (MLIP), yet incapable of simulating post-fracture dynamical behaviors. The mechanical responses using MLIP are observed to be not related to temperature gradients. The temperature configuration of equilibration simulation employing the dropout uncertainty neural network potential with a dropout rate of 0.1 is reported to be the most accurate compared with the rest. This work is expected to inspire further investigation of non-equilibrium dynamics in graphene with practical applications in various engineering fields. read less P. Ying, H. Dong, T. Liang, Z. Fan, Z. Zhong, and J. Zhang, “Atomistic insights into the mechanical anisotropy and fragility of monolayer fullerene networks using quantum mechanical calculations and machine-learning molecular dynamics simulations,” Extreme Mechanics Letters. 2022. link Times cited: 15 C. Hong et al., “Applications and training sets of machine learning potentials,” Science and Technology of Advanced Materials: Methods. 2023. link Times cited: 0 Abstract: ABSTRACT Recently, machine learning potentials (MLPs) have b… read more Abstract: ABSTRACT Recently, machine learning potentials (MLPs) have been attracting interest as an alternative to the computationally expensive density-functional theory (DFT) calculations. The data-driven approach in MLPs requires carefully curated training datasets, which define the valid domain of simulations. Therefore, acquiring training datasets that comprehensively span the domain of the desired simulations is important. In this review, we attempt to set guidelines for the systematic construction of training datasets according to target simulations. To this end, we extensively analyze the training sets in previous literature according to four application types: thermal properties, diffusion properties, structure prediction, and chemical reactions. In each application, we summarize characteristic reference structures and discuss specific parameters for DFT calculations such as MD conditions. We hope this review serves as a comprehensive guide for researchers and practitioners aiming to harness the capabilities of MLPs in material simulations. IMPACT STATEMENT This review reports on the selection of training sets for machine learning potentials tailored to their specific applications, which is currently not standardized in the rapidly evolving field. read less P. Ying and Z. Fan, “Combining the D3 dispersion correction with the neuroevolution machine-learned potential,” Journal of Physics: Condensed Matter. 2023. link Times cited: 0 Abstract: Machine-learned potentials (MLPs) have become a popular appr… read more Abstract: Machine-learned potentials (MLPs) have become a popular approach of modeling interatomic interactions in atomistic simulations, but to keep the computational cost under control, a relatively short cutoff must be imposed, which put serious restrictions on the capability of the MLPs for modeling relatively long-ranged dispersion interactions. In this paper, we propose to combine the neuroevolution potential (NEP) with the popular D3 correction to achieve a unified NEP-D3 model that can simultaneously model relatively short-ranged bonded interactions and relatively long-ranged dispersion interactions. We show that improved descriptions of the binding and sliding energies in bilayer graphene can be obtained by the NEP-D3 approach compared to the pure NEP approach. We implement the D3 part into the gpumd package such that it can be used out of the box for many exchange-correlation functionals. As a realistic application, we show that dispersion interactions result in approximately a 10% reduction in thermal conductivity for three typical metal-organic frameworks. read less J. A. Vita et al., “ColabFit exchange: Open-access datasets for data-driven interatomic potentials.,” The Journal of chemical physics. 2023. link Times cited: 2 Abstract: Data-driven interatomic potentials (IPs) trained on large co… read more Abstract: Data-driven interatomic potentials (IPs) trained on large collections of first principles calculations are rapidly becoming essential tools in the fields of computational materials science and chemistry for performing atomic-scale simulations. Despite this, apart from a few notable exceptions, there is a distinct lack of well-organized, public datasets in common formats available for use with IP development. This deficiency precludes the research community from implementing widespread benchmarking, which is essential for gaining insight into model performance and transferability, and also limits the development of more general, or even universal, IPs. To address this issue, we introduce the ColabFit Exchange, the first database providing open access to a large collection of systematically organized datasets from multiple domains that is especially designed for IP development. The ColabFit Exchange is publicly available at https://colabfit.org, providing a web-based interface for exploring, downloading, and contributing datasets. Composed of data collected from the literature or provided by community researchers, the ColabFit Exchange currently (September 2023) consists of 139 datasets spanning nearly 70 000 unique chemistries, and is intended to continuously grow. In addition to outlining the software framework used for constructing and accessing the ColabFit Exchange, we also provide analyses of the data, quantifying the diversity of the database and proposing metrics for assessing the relative diversity of multiple datasets. Finally, we demonstrate an end-to-end IP development pipeline, utilizing datasets from the ColabFit Exchange, fitting tools from the KLIFF software package, and validation tests provided by the OpenKIM framework. read less M. C. Venetos, M. Wen, and K. Persson, “Machine Learning Full NMR Chemical Shift Tensors of Silicon Oxides with Equivariant Graph Neural Networks,” The Journal of Physical Chemistry. a. 2023. link Times cited: 1 Abstract: The nuclear magnetic resonance (NMR) chemical shift tensor i… read more Abstract: The nuclear magnetic resonance (NMR) chemical shift tensor is a highly sensitive probe of the electronic structure of an atom and furthermore its local structure. Recently, machine learning has been applied to NMR in the prediction of isotropic chemical shifts from a structure. Current machine learning models, however, often ignore the full chemical shift tensor for the easier-to-predict isotropic chemical shift, effectively ignoring a multitude of structural information available in the NMR chemical shift tensor. Here we use an equivariant graph neural network (GNN) to predict full 29Si chemical shift tensors in silicate materials. The equivariant GNN model predicts full tensors to a mean absolute error of 1.05 ppm and is able to accurately determine the magnitude, anisotropy, and tensor orientation in a diverse set of silicon oxide local structures. When compared with other models, the equivariant GNN model outperforms the state-of-the-art machine learning models by 53%. The equivariant GNN model also outperforms historic analytical models by 57% for isotropic chemical shift and 91% for anisotropy. The software is available as a simple-to-use open-source repository, allowing similar models to be created and trained with ease. read less L. O. AGBOLADE et al., “Recent advances in density functional theory approach for optoelectronics properties of graphene,” Heliyon. 2023. link Times cited: 1 D. M. Anstine and O. Isayev, “Machine Learning Interatomic Potentials and Long-Range Physics,” The Journal of Physical Chemistry. a. 2023. link Times cited: 12 Abstract: Advances in machine learned interatomic potentials (MLIPs), … read more Abstract: Advances in machine learned interatomic potentials (MLIPs), such as those using neural networks, have resulted in short-range models that can infer interaction energies with near ab initio accuracy and orders of magnitude reduced computational cost. For many atom systems, including macromolecules, biomolecules, and condensed matter, model accuracy can become reliant on the description of short- and long-range physical interactions. The latter terms can be difficult to incorporate into an MLIP framework. Recent research has produced numerous models with considerations for nonlocal electrostatic and dispersion interactions, leading to a large range of applications that can be addressed using MLIPs. In light of this, we present a Perspective focused on key methodologies and models being used where the presence of nonlocal physics and chemistry are crucial for describing system properties. The strategies covered include MLIPs augmented with dispersion corrections, electrostatics calculated with charges predicted from atomic environment descriptors, the use of self-consistency and message passing iterations to propagated nonlocal system information, and charges obtained via equilibration schemes. We aim to provide a pointed discussion to support the development of machine learning-based interatomic potentials for systems where contributions from only nearsighted terms are deficient. read less M. Wen, E. Spotte-Smith, S. M. Blau, M. J. McDermott, A. Krishnapriyan, and K. Persson, “Chemical reaction networks and opportunities for machine learning,” Nature Computational Science. 2023. link Times cited: 11 A. M. Barboza, L. C. R. Aliaga, D. Faria, and I. Bastos, “Bilayer Graphene Kirigami,” SSRN Electronic Journal. 2022. link Times cited: 1 Y. Kurniawan et al., “Bayesian, frequentist, and information geometric approaches to parametric uncertainty quantification of classical empirical interatomic potentials.,” The Journal of chemical physics. 2021. link Times cited: 6 Abstract: In this paper, we consider the problem of quantifying parame… read more Abstract: In this paper, we consider the problem of quantifying parametric uncertainty in classical empirical interatomic potentials (IPs) using both Bayesian (Markov Chain Monte Carlo) and frequentist (profile likelihood) methods. We interface these tools with the Open Knowledgebase of Interatomic Models and study three models based on the Lennard-Jones, Morse, and Stillinger-Weber potentials. We confirm that IPs are typically sloppy, i.e., insensitive to coordinated changes in some parameter combinations. Because the inverse problem in such models is ill-conditioned, parameters are unidentifiable. This presents challenges for traditional statistical methods, as we demonstrate and interpret within both Bayesian and frequentist frameworks. We use information geometry to illuminate the underlying cause of this phenomenon and show that IPs have global properties similar to those of sloppy models from fields, such as systems biology, power systems, and critical phenomena. IPs correspond to bounded manifolds with a hierarchy of widths, leading to low effective dimensionality in the model. We show how information geometry can motivate new, natural parameterizations that improve the stability and interpretation of uncertainty quantification analysis and further suggest simplified, less-sloppy models. read less T. Leadbetter, A. Seiphoori, C. Reina, and P. Purohit, “Emergence of viscosity and dissipation via stochastic bonds,” Journal of the Mechanics and Physics of Solids. 2021. link Times cited: 0 A. Thompson et al., “LAMMPS - A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales,” Computer Physics Communications. 2021. link Times cited: 2377 Y. Zeng, Y.-X. Feng, L.-M. Tang, and K. Chen, “Effect of out-of-plane strain on the phonon structures and anharmonicity of twisted multilayer graphene,” Applied Physics Letters. 2021. link Times cited: 34 Abstract: Twisted bilayer and multilayer two-dimensional materials lin… read more Abstract: Twisted bilayer and multilayer two-dimensional materials linked by van der Waals interactions exhibit various unique physical properties. The phonon properties of such systems are of great importance, but have not been explored in detail. In this work, we use a hybrid neural-network potential to systematically investigate the evolution of the phonon structure of twisted multilayer graphene under out-of-plane strain. With increasing out-of-plane strain, the evolution of the phonon structure of the moire superlattice exhibits different behavior from that of AA and AB stacked multilayer graphene. Meanwhile, with twisting of the interlayer, a higher Gruneisen parameter and a lower phonon group velocity can be obtained. A possible method is revealed by which phonon anharmonic scattering in stacked multilayer graphene could be enhanced by varying the twist angle in combination with out-of-plane strain. Our work shows that the application of out-of-plane strain can serve as an effective way to amplify the effect of twist angle on phonon structures of twisted multilayer two-dimensional systems, with potential application to thermoelectric and thermal logical devices. read less D. Hedman, T. Rothe, G. Johansson, F. Sandin, J. Larsson, and Y. Miyamoto, “Impact of training and validation data on the performance of neural network potentials: A case study on carbon using the CA-9 dataset.” 2021. link Times cited: 3 S. Watanabe et al., “High-dimensional neural network atomic potentials for examining energy materials: some recent simulations,” Journal of Physics: Energy. 2020. link Times cited: 16 Abstract: Owing to their simultaneous accuracy and computational effic… read more Abstract: Owing to their simultaneous accuracy and computational efficiency, interatomic potentials machine-learned using first-principles calculation data are promising for investigating phenomena closely related to atomic motion in various energy materials. We have been working with one type of these potentials, high-dimensional (HD) neural network potentials (NNPs), and their applications, but we realized that our current understanding of HD NNPs, e.g. the meaning of the atomic energy mapping, remained insufficient, and that tuning their prediction performance for different target properties/phenomena often requires much trial and error. In this article, we illustrate the usefulness of NNPs through our studies on ion migration and thermal transport in energy and related materials. We also share our experiences with data sampling and training strategies and discuss the meaning of atomic energy mapping in HD NNPs. read less M. Babar, H. L. Parks, G. Houchins, and V. Viswanathan, “An accurate machine learning calculator for the lithium-graphite system,” Journal of Physics: Energy. 2020. link Times cited: 10 Abstract: Machine-learning potentials are accelerating the development… read more Abstract: Machine-learning potentials are accelerating the development of energy materials, especially in identifying phase diagrams and other thermodynamic properties. In this work, we present a neural network potential based on atom-centered symmetry function descriptors to model the energetics of lithium intercalation into graphite. The potential was trained on a dataset of over 9000 diverse lithium–graphite configurations that varied in applied stress and strain, lithium concentration, lithium–carbon and lithium–lithium bond distances, and stacking order to ensure wide sampling of the potential atomic configurations during intercalation. We calculated the energies of these structures using density functional theory (DFT) through the Bayesian error estimation functional with van der Waals correlation exchange-correlation functional, which can accurately describe the van der Waals interactions that are crucial to determining the thermodynamics of this phase space. Bayesian optimization, as implemented in Dragonfly, was used to select optimal set of symmetry function parameters, ultimately resulting in a potential with a prediction error of 8.24 meV atom−1 on unseen test data. The potential can predict energies, structural properties, and elastic constants at an accuracy comparable to other DFT exchange-correlation functionals at a fraction of the computational cost. The accuracy of the potential is also comparable to similar machine-learned potentials describing other systems. We calculate the open circuit voltage with the calculator and find good agreement with experiment, especially in the regime x ≥ 0.3, for x in Li x C6. This study further illustrates the power of machine learning potentials, which promises to revolutionize design and optimization of battery materials. read less Y. Shaidu, E. Kucukbenli, R. Lot, F. Pellegrini, E. Kaxiras, and S. de Gironcoli, “A systematic approach to generating accurate neural network potentials: the case of carbon,” npj Computational Materials. 2020. link Times cited: 18 X. Liu, Q. Wang, and J. Zhang, “Machine Learning Interatomic Force Fields for Carbon Allotropic Materials.” 2021. link Times cited: 0 A. Singh and Y. Li, “Reliable machine learning potentials based on artificial neural network for graphene,” ArXiv. 2023. link Times cited: 0 M. Qamar, M. Mrovec, Y. Lysogorskiy, A. Bochkarev, and R. Drautz, “Atomic Cluster Expansion for Quantum-Accurate Large-Scale Simulations of Carbon.,” Journal of chemical theory and computation. 2022. link Times cited: 17 Abstract: We present an atomic cluster expansion (ACE) for carbon that… read more Abstract: We present an atomic cluster expansion (ACE) for carbon that improves over available classical and machine learning potentials. The ACE is parametrized from an exhaustive set of important carbon structures over extended volume and energy ranges, computed using density functional theory (DFT). Rigorous validation reveals that ACE accurately predicts a broad range of properties of both crystalline and amorphous carbon phases while being several orders of magnitude more computationally efficient than available machine learning models. We demonstrate the predictive power of ACE on three distinct applications: brittle crack propagation in diamond, the evolution of amorphous carbon structures at different densities and quench rates, and the nucleation and growth of fullerene clusters under high-pressure and high-temperature conditions. read less H. Dong, C. Cao, P. Ying, Z. Fan, P. Qian, and Y. Su, “Anisotropic and high thermal conductivity in monolayer quasi-hexagonal fullerene: A comparative study against bulk phase fullerene,” International Journal of Heat and Mass Transfer. 2022. link Times cited: 14 J. G. Mchugh, P. Mouratidis, A. Impellizzeri, K. Jolley, D. Erbahar, and C. Ewels, “Prismatic Edge Dislocations in Graphite,” MatSciRN EM Feeds. 2021. link Times cited: 9 Abstract: Dislocations are a central concept in materials science, whi… read more Abstract: Dislocations are a central concept in materials science, which dictate the plastic deformation and damage evolution in materials. Layered materials such as graphite admit two general types of interlayer dislocations: basal and prismatic dislocations, of which prismatic dislocations have been relatively less studied. Using density functional theory (DFT) calculations, we have examined different prismatic core structures in graphite and evaluated their structure, energetics and mobility. We find close energetic interplay between bonded and “free-standing” core structures in both zigzag and armchair directions, with a reconstructed stable zigzag core identified. We explore grain boundaries and prismatic dislocation pile-up, identifying metastable structures which may be important in energy storage. The role of interlayer stacking in core structure, dislocation glide and climb is also considered in-depth. Our calculations suggest that the prismatic dislocation core is stable up to high temperatures of approximately 1500K in bulk graphite. Above this temperature, the breaking of bonds in the dislocation core can facilitate climb, grain-boundary motion, and the annealing of damage through prismatic dislocation glide. read less M. Wen, Y. Afshar, R. Elliott, and E. Tadmor, “KLIFF: A framework to develop physics-based and machine learning interatomic potentials,” Comput. Phys. Commun. 2021. link Times cited: 12 Z. Fan et al., “Neuroevolution machine learning potentials: Combining high accuracy and low cost in atomistic simulations and application to heat transport,” Physical Review B. 2021. link Times cited: 42 Abstract: We develop a neuroevolution-potential (NEP) framework for ge… read more Abstract: We develop a neuroevolution-potential (NEP) framework for generating neural network based machine-learning potentials. They are trained using an evolutionary strategy for performing large-scale molecular dynamics (MD) simulations. A descriptor of the atomic environment is constructed based on Chebyshev and Legendre polynomials. The method is implemented in graphic processing units within the open-source GPUMD package, which can attain a computational speed over $10^7$ atom-step per second using one Nvidia Tesla V100. Furthermore, per-atom heat current is available in NEP, which paves the way for efficient and accurate MD simulations of heat transport in materials with strong phonon anharmonicity or spatial disorder, which usually cannot be accurately treated either with traditional empirical potentials or with perturbative methods. read less I. Demiroglu, Y. Karaaslan, T. Kocabaş, M. Keçeli, Á. Vázquez-Mayagoitia, and C. Sevik, “Computation of the Thermal Expansion Coefficient of Graphene with Gaussian Approximation Potentials,” The Journal of Physical Chemistry C. 2021. link Times cited: 5 C.-gen Qian, B. Mclean, D. Hedman, and F. Ding, “A comprehensive assessment of empirical potentials for carbon materials,” APL Materials. 2021. link Times cited: 22 Abstract: Carbon materials and their unique properties have been exten… read more Abstract: Carbon materials and their unique properties have been extensively studied by molecular dynamics, thanks to the wide range of available carbon bond order potentials (CBOPs). Recently, with the increase in popularity of machine learning (ML), potentials such as Gaussian approximation potential (GAP), trained using ML, can accurately predict results for carbon. However, selecting the right potential is crucial as each performs differently for different carbon allotropes, and these differences can lead to inaccurate results. This work compares the widely used CBOPs and the GAP-20 ML potential with density functional theory results, including lattice constants, cohesive energies, defect formation energies, van der Waals interactions, thermal stabilities, and mechanical properties for different carbon allotropes. We find that GAP-20 can more accurately predict the structure, defect properties, and formation energies for a variety of crystalline phase carbon compared to CBOPs. Importantly, GAP-20 can simulate the thermal stability of C60 and the fracture of carbon nanotubes and graphene accurately, where CBOPs struggle. However, similar to CBOPs, GAP-20 is unable to accurately account for van der Waals interactions. Despite this, we find that GAP-20 outperforms all CBOPs assessed here and is at present the most suitable potential for studying thermal and mechanical properties for pristine and defective carbon. read less N. B. Kovachki et al., “Multiscale modeling of materials: Computing, data science, uncertainty and goal-oriented optimization,” Mechanics of Materials. 2021. link Times cited: 24 B. Liu et al., “A learning-based multiscale method and its application to inelastic impact problems,” Journal of The Mechanics and Physics of Solids. 2021. link Times cited: 41 P. Yoo, M. Sakano, S. Desai, M. M. Islam, P. Liao, and A. Strachan, “Neural network reactive force field for C, H, N, and O systems,” npj Computational Materials. 2021. link Times cited: 30 M. Hu and Z. Yang, “Perspective on multi-scale simulation of thermal transport in solids and interfaces.,” Physical chemistry chemical physics : PCCP. 2020. link Times cited: 5 Abstract: Phonon-mediated thermal transport is inherently multi-scale.… read more Abstract: Phonon-mediated thermal transport is inherently multi-scale. The wave-length of phonons (considering phonons as waves) is typically at the nanometer scale; the typical size of a phonon wave energy packet is tens of nanometers, while the phonon mean free path (MFP) can be as long as microns. At different length scales, the phonons will interact with structures of different feature sizes, which can be as small as 0D defects (point defects), short to medium range linear defects (dislocations), medium to large range 2D planar defects (stacking faults and twin boundaries), and large scale 3D defects (voids, inclusions, and various microstructures). The nature of multi-scale thermal transport is that there are different heat transfer physics across different length scales and in the meantime the physics crossing the different scales is interdependent and coupled. Since phonon behavior is usually mode dependent, thermal transport in materials with a combined micro-/nano-structure complexity becomes complicated, making modeling this kind of transport process very challenging. In this perspective, we first summarize the advantages and disadvantages of computational methods for mono-scale heat transfer and the state-of-the-art multi-scale thermal transport modeling. We then discuss a few important aspects of the future development of multi-scale modeling, in particular with the aid of modern machine learning and uncertainty quantification techniques. As more sophisticated theoretical and computational methods continue to advance thermal transport predictions, novel heat transfer physics and thermally functional materials will be discovered for the pertaining energy systems and technologies. read less S. Wille, H. Jiang, O. Bünermann, A. Wodtke, J. Behler, and A. Kandratsenka, “An experimentally validated neural-network potential energy surface for H-atom on free-standing graphene in full dimensionality.,” Physical chemistry chemical physics : PCCP. 2020. link Times cited: 8 Abstract: We present a first principles-quality potential energy surfa… read more Abstract: We present a first principles-quality potential energy surface (PES) describing the inter-atomic forces for hydrogen atoms interacting with free-standing graphene. The PES is a high-dimensional neural network potential that has been parameterized to 75 945 data points computed with density-functional theory employing the PBE-D2 functional. Improving over a previously published PES [Jiang et al., Science, 2019, 364, 379], this neural network exhibits a realistic physisorption well and achieves a 10-fold reduction in the RMS fitting error, which is 0.6 meV per atom. The chemisorption barrier is 172 meV, which is lower than that of the REBO-EMFT PES (260 meV). We used this PES to calculate about 1.5 million classical trajectories with carefully selected initial conditions to allow for direct comparison to results of H- and D-atom scattering experiments performed at incidence translational energy of 1.9 eV and a surface temperature of 300 K. The theoretically predicted scattering angular and energy loss distributions are in good agreement with experiment, despite the fact that the experiments employed graphene grown on Pt(111). Compared to previous calculations, the agreement with experiments is improved. The remaining discrepancies between experiment and theory are likely due to the influence of the Pt substrate only present in the experiment. read less M. Wen and E. Tadmor, “Uncertainty quantification in molecular simulations with dropout neural network potentials,” npj Computational Materials. 2020. link Times cited: 46 S. Desai, S. Reeve, and J. Belak, “Implementing a neural network interatomic model with performance portability for emerging exascale architectures,” Comput. Phys. Commun. 2020. link Times cited: 9 B. Mortazavi et al., “Exploring phononic properties of two-dimensional materials using machine learning interatomic potentials,” arXiv: Materials Science. 2020. link Times cited: 111
Funding	Not available

Short KIM ID The unique KIM identifier code.	MO_421038499185_001
Extended KIM ID The long form of the KIM ID including a human readable prefix (100 characters max), two underscores, and the Short KIM ID. Extended KIM IDs can only contain alpha-numeric characters (letters and digits) and underscores and must begin with a letter.	hNN_WenTadmor_2019Grx_C__MO_421038499185_001
DOI	10.25950/a74cc44e https://doi.org/10.25950/a74cc44e https://commons.datacite.org/doi.org/10.25950/a74cc44e
KIM Item Type Specifies whether this is a Portable Model (software implementation of an interatomic model); Portable Model with parameter file (parameter file to be read in by a Model Driver); Model Driver (software implementation of an interatomic model that reads in parameters).	Portable Model using Model Driver hNN__MD_435082866799_001
Driver	hNN__MD_435082866799_001
KIM API Version	2.0
Potential Type	hnn

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Grade	Name	Category	Brief Description	Full Results	Aux File(s)
P All elements claimed by model are supported in at least one of the tested configurations.	vc-species-supported-as-stated	mandatory	The model supports all species it claims to support; see full description.	Results	Files
P Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.	vc-periodicity-support	mandatory	Periodic boundary conditions are handled correctly; see full description.	Results	Files
P Model energy has permutation symmetry for all configurations the model was able to compute.	vc-permutation-symmetry	mandatory	Total energy and forces are unchanged when swapping atoms of the same species; see full description.	Results	Files
A The letter grade A was assigned because the normalized error in the computation was 4.60130e-10 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.	vc-forces-numerical-derivative	consistency	Forces computed by the model agree with numerical derivatives of the energy; see full description.	Results	Files
P The model is C^2 continuous. This means that the model has continuous energy and continuous derivatives up to order 2.	vc-dimer-continuity-c1	informational	The energy versus separation relation of a pair of atoms is C1 continuous (i.e. the function and its first derivative are continuous); see full description.	Results	Files
P Model energy and forces are invariant with respect to rigid-body motion (translation and rotation) for all configurations the model was able to compute.	vc-objectivity	informational	Total energy is unchanged and forces transform correctly under rigid-body translation and rotation; see full description.	Results	Files
P Model energy has inversion symmetry for all configurations the model was able to compute.	vc-inversion-symmetry	informational	Total energy is unchanged and forces change sign when inverting a configuration through the origin; see full description.	Results	Files
P No memory leak detected.	vc-memory-leak	informational	The model code does not have memory leaks (i.e. it releases all allocated memory at the end); see full description.	Results	Files
P All threads give identical results for tested case. Model appears to be thread-safe.	vc-thread-safe	mandatory	The model returns the same energy and forces when computed in serial and when using parallel threads for a set of configurations. Note that this is not a guarantee of thread safety; see full description.	Results	Files
P Unit conversion successful	vc-unit-conversion	mandatory	The model is able to correctly convert its energy and/or forces to different unit sets; see full description.	Results	Files

This bar chart plot shows the mono-atomic body-centered cubic (bcc) lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: C

Cohesive Energy Graph

This graph shows the cohesive energy versus volume-per-atom for the current mode for four mono-atomic cubic phases (body-centered cubic (bcc), face-centered cubic (fcc), simple cubic (sc), and diamond). The curve with the lowest minimum is the ground state of the crystal if stable. (The crystal structure is enforced in these calculations, so the phase may not be stable.) Graphs are generated for each species supported by the model.

Species: C

Diamond Lattice Constant

This bar chart plot shows the mono-atomic face-centered diamond lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: C

Dislocation Core Energies

This graph shows the dislocation core energy of a cubic crystal at zero temperature and pressure for a specific set of dislocation core cutoff radii. After obtaining the total energy of the system from conjugate gradient minimizations, non-singular, isotropic and anisotropic elasticity are applied to obtain the dislocation core energy for each of these supercells with different dipole distances. Graphs are generated for each species supported by the model.

(No matching species)

FCC Elastic Constants

This bar chart plot shows the mono-atomic face-centered cubic (fcc) elastic constants predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: C

FCC Lattice Constant

This bar chart plot shows the mono-atomic face-centered cubic (fcc) lattice constant predicted by the current model (shown in red) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: C

FCC Stacking Fault Energies

This bar chart plot shows the intrinsic and extrinsic stacking fault energies as well as the unstable stacking and unstable twinning energies for face-centered cubic (fcc) predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

(No matching species)

FCC Surface Energies

This bar chart plot shows the mono-atomic face-centered cubic (fcc) relaxed surface energies predicted by the current model (shown in blue) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

(No matching species)

SC Lattice Constant

This bar chart plot shows the mono-atomic simple cubic (sc) lattice constant predicted by the current model (shown in the unique color) compared with the predictions for all other models in the OpenKIM Repository that support the species. The vertical bars show the average and standard deviation (one sigma) bounds for all model predictions. Graphs are generated for each species supported by the model.

Species: C

Cubic Crystal Basic Properties Table

Species: C

Tests

Disclaimer From Model Developer

This model is designed for multilayer graphene systems and graphite. It is not appropriate for bulk carbon structures.

CohesiveEnergyVsLatticeConstant__TD_554653289799_003

Cohesive energy versus lattice constant curve for monoatomic cubic lattices v003

Creators:
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/64cb38c5

This Test Driver uses LAMMPS to compute the cohesive energy of a given monoatomic cubic lattice (fcc, bcc, sc, or diamond) at a variety of lattice spacings. The lattice spacings range from a_min (=a_min_frac*a_0) to a_max (=a_max_frac*a_0) where a_0, a_min_frac, and a_max_frac are read from stdin (a_0 is typically approximately equal to the equilibrium lattice constant). The precise scaling and number of lattice spacings sampled between a_min and a_0 (a_0 and a_max) is specified by two additional parameters passed from stdin: N_lower and samplespacing_lower (N_upper and samplespacing_upper). Please see README.txt for further details.

Test	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Cohesive energy versus lattice constant curve for bcc C v004	view	7658
Cohesive energy versus lattice constant curve for diamond C v004	view	18111
Cohesive energy versus lattice constant curve for fcc C v004	view	12515
Cohesive energy versus lattice constant curve for sc C v004	view	4785

ElasticConstantsCubic__TD_011862047401_006

Elastic constants for cubic crystals at zero temperature and pressure v006

Creators: Junhao Li and Ellad Tadmor
Contributor: tadmor
Publication Year: 2019
DOI: https://doi.org/10.25950/5853fb8f

Computes the cubic elastic constants for some common crystal types (fcc, bcc, sc, diamond) by calculating the hessian of the energy density with respect to strain. An estimate of the error associated with the numerical differentiation performed is reported.

Test	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Elastic constants for bcc C at zero temperature v006	view	17902
Elastic constants for diamond C at zero temperature v001	view	141363
Elastic constants for fcc C at zero temperature v006	view	16614
Elastic constants for sc C at zero temperature v006	view	8072

ElasticConstantsHexagonal__TD_612503193866_004

Elastic constants for hexagonal crystals at zero temperature v004

Creators: Junhao Li
Contributor: jl2922
Publication Year: 2019
DOI: https://doi.org/10.25950/d794c746

Computes the elastic constants for hcp crystals by calculating the hessian of the energy density with respect to strain. An estimate of the error associated with the numerical differentiation performed is reported.

Test	Test Results	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Elastic constants for hcp C at zero temperature v004		view	23744

EquilibriumCrystalStructure__TD_457028483760_002

Equilibrium structure and energy for a crystal structure at zero temperature and pressure v002

Creators:
Contributor: ilia
Publication Year: 2024
DOI: https://doi.org/10.25950/2f2c4ad3

Computes the equilibrium crystal structure and energy for an arbitrary crystal at zero temperature and applied stress by performing symmetry-constrained relaxation. The crystal structure is specified using the AFLOW prototype designation. Multiple sets of free parameters corresponding to the crystal prototype may be specified as initial guesses for structure optimization. No guarantee is made regarding the stability of computed equilibria, nor that any are the ground state.

Test	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_cF16_227_c v002	view	207556
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_cF240_202_h2i v002	view	3485415
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_cF8_227_a v002	view	126320
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_cI16_206_c v002	view	130235
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_cI16_229_f v002	view	81418
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_cI8_214_a v002	view	111167
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_cP1_221_a v002	view	64527
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_cP20_221_gj v002	view	100558
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_hP12_194_bc2f v002	view	90229
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_hP12_194_e2f v002	view	103879
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_hP16_194_e3f v002	view	140321
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_hP2_191_c v002	view	101007
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_hP4_194_bc v002	view	83486
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_hP4_194_f v002	view	78700
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_hP8_194_ef v002	view	47818
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_hR10_166_5c v002	view	100193
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_hR14_166_7c v002	view	125226
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_hR2_166_c v002	view	48973
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_hR4_166_2c v002	view	67322
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_hR60_166_2h4i v002	view	2213768
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_oC16_65_mn v002	view	261268
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_oC8_65_gh v002	view	102406
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_oI120_71_lmn6o v002	view	839156
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_tI8_139_h v002	view	58633

LatticeConstant2DHexagonalEnergy__TD_034540307932_002

Cohesive energy and equilibrium lattice constant of hexagonal 2D crystalline layers v002

Creators: Ilia Nikiforov
Contributor: ilia
Publication Year: 2019
DOI: https://doi.org/10.25950/dd36239b

Given atomic species and structure type (graphene-like, 2H, or 1T) of a 2D hexagonal monolayer crystal, as well as an initial guess at the lattice spacing, this Test Driver calculates the equilibrium lattice spacing and cohesive energy using Polak-Ribiere conjugate gradient minimization in LAMMPS

Test	Test Results	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Cohesive energy and equilibrium lattice constant of graphene v002		view	597

LatticeConstantCubicEnergy__TD_475411767977_007

Equilibrium lattice constant and cohesive energy of a cubic lattice at zero temperature and pressure v007

Creators: Daniel S. Karls and Junhao Li
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/2765e3bf

Equilibrium lattice constant and cohesive energy of a cubic lattice at zero temperature and pressure.

Test	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Equilibrium zero-temperature lattice constant for bcc C v007	view	4774
Equilibrium zero-temperature lattice constant for diamond C v007	view	11181
Equilibrium zero-temperature lattice constant for fcc C v007	view	5057
Equilibrium zero-temperature lattice constant for sc C v007	view	3046

LatticeConstantHexagonalEnergy__TD_942334626465_005

Equilibrium lattice constants for hexagonal bulk structures at zero temperature and pressure v005

Creators: Daniel S. Karls and Junhao Li
Contributor: karls
Publication Year: 2019
DOI: https://doi.org/10.25950/c339ca32

Calculates lattice constant of hexagonal bulk structures at zero temperature and pressure by using simplex minimization to minimize the potential energy.

Test	Test Results	Link to Test Results page	Benchmark time Usertime multiplied by the Whetstone Benchmark. This number can be used (approximately) to compare the performance of different models independently of the architecture on which the test was run. Measured in Millions of Whetstone Instructions (MWI)
Equilibrium lattice constants for hcp C v005		view	408951

Errors

EquilibriumCrystalStructure__TD_457028483760_002

Test	Error Categories	Link to Error page
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_mC16_12_4i v002	other	view
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_oC16_65_pq v002	other	view
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_oC8_67_m v002	other	view
Equilibrium crystal structure and energy for C in AFLOW crystal prototype A_oP16_62_4c v002	other	view

No Driver

Verification Check	Error Categories	Link to Error page
ThreadSafety__VC_881176209980_002	other	view

Files

ANN.params
CMakeLists.txt
LICENSE
LJ.params
kimprovenance.edn
kimspec.edn

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hNN_WenTadmor_2019Grx_C__MO_421038499185_001.txz	Tar+XZ	Linux and OS X archive
hNN_WenTadmor_2019Grx_C__MO_421038499185_001.zip	Zip	Windows archive

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This Model requires a Model Driver. Archives for the Model Driver hNN__MD_435082866799_001 appear below.

hNN__MD_435082866799_001.txz	Tar+XZ	Linux and OS X archive
hNN__MD_435082866799_001.zip	Zip	Windows archive

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hNN_WenTadmor_2019Grx_C__MO_421038499185_001

Verification Check Dashboard

Visualizers (in-page)

BCC Lattice Constant

Cohesive Energy Graph

Diamond Lattice Constant

Dislocation Core Energies

FCC Elastic Constants

FCC Lattice Constant

FCC Stacking Fault Energies

FCC Surface Energies

SC Lattice Constant

Cubic Crystal Basic Properties Table

Tests

Disclaimer From Model Developer

Errors

Files

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