Exploring the configuration space of elemental carbon with empirical and machine learned interatomic potentials

Abstract

In the present work we detail how the many-body potential energy landscape of elemental carbon, as described by interatomic potentials, can be explored by utilising the nested sampling algorithm, allowing the calculation of their pressure-temperature phase diagram up to high pressures. We present a comparison of four interatomic potential models: Tersoff, EDIP, GAP-20 and its recently updated version, GAP-20U. Our evaluation is focused on their macroscopic properties, particularly on their melting transition and on identifying thermodynamically stable solid structures up to at least 100 GPa. The studied models all form graphite structures upon freezing at lower pressure, then the diamond structure as the pressure increases. In the cases of the Tersoff, EDIP and GAP-20U potentials we were able to locate the transition between these phases. We placed particular focus on the state-of-the-art machine-learned models, the GAP-20 and GAP-20U, and calculated their phase diagrams up to 1 and 0.1 TPa, respectively, to evaluate their predictive capabilities well outside of the models’ fitting range. The phase diagrams of the GAP models showed remarkably good agreement with the experimental phase diagram up to 200 GPa. However, we found that the accuracy of the models’ descriptions of graphite was adversely affected by the relative stability of phases with incorrect layer spacing. By adding a suitable selection of graphite structures to the GAP training set and re-training the model, we have derived an improved model — referred to as the GAP-20U+gr — that suppresses erroneous local minima in the graphitic energy landscape. At extreme high pressure nested sampling identified two novel stable solid structures in the GAP-20 model, a strained diamond structure above 270 GPa and a strained hexagonal-close-packed structure above 890 GPa. However, the stability of these two phases were not confirmed by DFT calculations, highlighting potential routes to further improve the GAP model.

Transferable Machine Learning Interatomic Potential for Carbon Hydrogen Systems

“…Machine learning interatomic potentials (MLIPs), as computationally efficient alternatives to QM-based methods, have gained attention for their ability to capture complex atomic interactions and predict material properties with remarkable precision, enabling the exploration of extensive chemical spaces and previously inaccessible molecular dynamics (MD). There have been numerous efforts to develop MLIPs specifically for pure C. [23][24][25][26][27][28][29][30][31][32][33][34] These studies aim to improve the accuracy and transferability of the potential by training on dataset covering a broad spectrum of atomic environments and configurations, such as MD trajectories at different temperatures and pressures 23,24 or including 0D-3D systems to have diverse boundary conditions 25,26 to capture the bond diversity. Based on specific applications, ongoing efforts aim to improve MLIPs by presenting different versions.…”

“…Based on specific applications, ongoing efforts aim to improve MLIPs by presenting different versions. For instance, the Gaussian approximation potential (GAP) 30,31 was first developed to study the behavior of liquid and amorphous C, 32 later improved to encompass van der Waals corrections for C 60 fullerene and nanoporous C structures, 33,34 and later ordered graphite configurations with different stacking patterns were added to its training dataset for exploring the graphitic energy landscape of C. 29 The existence of MLIPs specifically tailored for pure C highlights the difficulty and challenges in modeling such systems. Pure C itself presents significant training challenges; incorporating H to develop accurate MLIPs for C-H systems adds further complexity.…”