Computation of the Thermal Expansion Coefficient of Graphene with Gaussian Approximation Potentials

Abstract

Direct experimental measurement of thermal expansion coefficient without substrate effects is a challenging task for two-dimensional (2D) materials, and its accurate estimation with large-scale ab initio molecular dynamics is computationally very expensive. Machine learning-based interatomic potentials trained with ab initio data have been successfully used in molecular dynamics simulations to decrease the computational cost without compromising the accuracy. In this study, we investigated using Gaussian approximation potentials to reproduce the density functional theory-level accuracy for graphene within both lattice dynamical and molecular dynamical methods, and to extend their applicability to larger length and time scales. Two such potentials are considered, GAP17 and GAP20. GAP17, which was trained with pristine graphene structures, is found to give closer results to density functional theory calculations at different scales. Further vibrational and structural analyses verify that the same conclusions can be deduced with density functional theory level in terms of the reasoning of the thermal expansion behavior, and the negative thermal expansion behavior is associated with long-range out-of-plane phonon vibrations. Thus, it is argued that the enabled larger system sizes by machine learning potentials may even enhance the accuracy compared to small-size-limited ab initio molecular dynamics.

Recent Advances of Graphene and Related Materials in Artificial Intelligence

“…C. Sevik et al proved that the GAP model catches the lattice dynamics of graphene very well. The estimated TEC value is very close to the DFT‐calculated result [14a] …”

“…The machine‐learning interatomic potentials (MLIPs) are a powerful assistant to MD studies. [ 14 ] A. Michaelides et al developed an ML model to obtain a faithful representation of the DFT‐PES, constructing an accurate interatomic potential (GAP) for graphene. The GAP can quantitatively predict the lattice parameter, thermal expansion coefficient, and phonon properties of graphene with only a marginal compromise on accuracy.…”

Gaussian Approximation Potentials for Accurate Thermal Properties of Two-Dimensional Materials

“…In this study, we focus on GAP models, which typically require less data to be trained than neural network potentials, and have good scalability and computational efficiency for large-scale molecular dynamics simulations. In a previous study, 8 we demonstrated that GAP models trained with DFT calculations 9 provide accurate estimates of the thermal expansion properties of graphene. Other studies have also shown the success of GAP models for thermal properties of 2DMs, such as graphene, 10 carbon allotropes, 11 monolayer h-BN, 12 h-BN allotropes, 13 silicene, 6,14 and monolayer MoS 2 .…”

Gaussian approximation potentials for accurate thermal properties of two-dimensional materials

“…In this study, we focus on GAP models, which typically require less data to be trained than neural network potentials, and have good scalability and computational efficiency for large-scale molecular dynamics simulations. 12 In a previous study, 13 we demonstrated that GAP models trained with DFT calculations 14 provide accurate estimates of the thermal expansion properties of graphene, along with the dominant effect of the rippling/buckling on negative thermal expansion. 15 Other studies have also shown the success of GAP models for thermal properties of 2DMs, such as graphene, 16 carbon allotropes, 17 monolayer h -BN, 18 h -BN allotropes, 19 silicene, 11,20 and monolayer MoS 2 .…”