An Accurate and Transferable Machine Learning Potential for Carbon (2006.13655v1)

Abstract: We present an accurate ML model for atomistic simulations of carbon, constructed using the Gaussian approximation potential (GAP) methodology. The potential, named GAP-20, describes the properties of the bulk crystalline and amorphous phases, crystal surfaces and defect structures with an accuracy approaching that of direct ab initio simulation, but at a significantly reduced cost. We combine structural databases for amorphous carbon and graphene, which we extend substantially by adding suitable configurations, for example, for defects in graphene and other nanostructures. The final potential is fitted to reference data computed using the optB88-vdW density functional theory (DFT) functional. Dispersion interactions, which are crucial to describe multilayer carbonaceous materials, are therefore implicitly included. We additionally account for long-range dispersion interactions using a semianalytical two-body term and show that an improved model can be obtained through an optimisation of the many-body smooth overlap of atomic positions (SOAP) descriptor. We rigorously test the potential on lattice parameters, bond lengths, formation energies and phonon dispersions of numerous carbon allotropes. We compare the formation energies of an extensive set of defect structures, surfaces and surface reconstructions to DFT reference calculations. The present work demonstrates the ability to combine, in the same ML model, the previously attained flexibility required for amorphous carbon [Phys. Rev. B, 95, 094203, (2017)] with the high numerical accuracy necessary for crystalline graphene [Phys. Rev. B, 97, 054303, (2018)], thereby providing an interatomic potential that will be applicable to a wide range of applications concerning diverse forms of bulk and nanostructured carbon.

Overview of "Supplemental Material: An Accurate and Transferable Machine Learning Potential for Carbon"

The paper is a supplemental material focusing on the Gaussian Approximation Potential (GAP) model for Carbon known as GAP-20. This model aims to provide a transferability and accurate description of carbon systems across different configurations, including crystalline and amorphous forms.

Summary of Key Findings

1. Crystalline Formation Energies: The work presents a detailed comparison of formation energies for carbon phases computed using GAP-20 against various empirical models and density functional theory (DFT). GAP-20 demonstrates improved accuracy with formation energy deviations from DFT values of less than 1%, which is a significant enhancement compared to other models such as Tersoff and REBO-II that show up to 22% deviation.

2. Phonon Dispersion Curves: The phonon dispersion curves for graphene, diamond, and carbon nanotubes were calculated using GAP-20. The model was able to predict phonon frequencies closely aligned with DFT reference data, showcasing its capability over traditional potentials like Tersoff and AIREBO, which suffer from inaccuracies in phonon band energy predictions.

3. Force and Energy Predictions: GAP-20 accurately reflects DFT forces and energy predictions across various carbon configurations, such as amorphous bulk and crystalline states, while maintaining computational efficiency compared to ab initio simulations.

4. Computational Efficiency: The practicality of employing GAP-20 over direct DFT simulations is evident in the significant cost reduction, maintaining accurate results even in simulations involving thousands of atoms.

Implications and Future Directions

The enhanced accuracy and computational efficiency of GAP-20 indicate its potential for widespread application in the modeling and simulation of carbon-based materials. Its transferability across diverse carbon configurations suggests utility in exploring new materials and optimizations in both industrial and academic settings.

This work provides a foundation for further exploring machine learning potentials in other elemental systems. Future research might encompass expanding this model's applicability to heteroatomic systems or optimizing light elements relevant to organic chemistry and biomaterials.

Additionally, the paper offers a perspective on the integration of machine learning models with quantum-based descriptors to further enhance predictive accuracy and explore new phenomena in material science.

In conclusion, GAP-20 represents a significant step forward in simulation practices, merging machine-learning approaches with material modeling to produce efficient and highly accurate descriptions of complex systems.