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We present an accurate machine learning (ML) model for atomistic simulationsof carbon, constructed using the Gaussian approximation potential (GAP)methodology. The potential, named GAP-20, describes the properties of the bulkcrystalline and amorphous phases, crystal surfaces and defect structures withan accuracy approaching that of direct ab initio simulation, but at asignificantly reduced cost. We combine structural databases for amorphouscarbon and graphene, which we extend substantially by adding suitableconfigurations, for example, for defects in graphene and other nanostructures.The final potential is fitted to reference data computed using the optB88-vdWdensity functional theory (DFT) functional. Dispersion interactions, which arecrucial to describe multilayer carbonaceous materials, are therefore implicitlyincluded. We additionally account for long-range dispersion interactions usinga semianalytical two-body term and show that an improved model can be obtainedthrough an optimisation of the many-body smooth overlap of atomic positions(SOAP) descriptor. We rigorously test the potential on lattice parameters, bondlengths, formation energies and phonon dispersions of numerous carbonallotropes. We compare the formation energies of an extensive set of defectstructures, surfaces and surface reconstructions to DFT reference calculations.The present work demonstrates the ability to combine, in the same ML model, thepreviously attained flexibility required for amorphous carbon [Phys. Rev. B,95, 094203, (2017)] with the high numerical accuracy necessary for crystallinegraphene [Phys. Rev. B, 97, 054303, (2018)], thereby providing an interatomicpotential that will be applicable to a wide range of applications concerningdiverse forms of bulk and nanostructured carbon.

An Accurate and Transferable Machine Learning Potential for Carbon