ReaxFF-nn: a reactive machine-learning potential in GULP/LAMMPS and its applications in the thermal conductivity calculations of carbon nanostructures

The term "ReaxFF-nn" refers to the reactive force field (ReaxFF) with neural networks. In the current work, we have incorporated it into the general utility lattice program (GULP) and the large-scale atomic/molecular massively parallel simulator (LAMMPS), which are programmed with modern FORTRAN and C++, respectively. The parameters of ReaxFF-nn can be trained using our I-ReaxFF package. By combining GULP, LAMMPS and ReaxFF-nn, various tasks, such as determination of thermal properties and crystal properties, and energy minimization, can be performed with precision at the quasi-density functional theory (DFT) level. Compared to other machine-learning potentials (MLPs), our approach does not involve the development of an entirely new machine-learning potential; instead, a small neural network was implemented to compute the bond order and bond energy. To validate the model in GULP and LAMMPS, the forces of graphene and carbon nanotube (CNT) structures were compared among the auto-differentiation, GULP, and LAMMPS packages with our codes. The differences between these calculations are within 10^-5. After the potential was trained against DFT calculations with losses of forces up to 10^-2 eV Å^-1 per atom, an example study of the thermal conductivity (<i>κ</i>) of graphene and carbon nanotubes (CNTs) using the Boltzmann transport equation (BTE) and non-equilibrium molecular dynamics (NEMD) methods was conducted. The value of <i>κ</i> for graphene obtained using ReaxFF-nn closely matches the results obtained from DFT calculations. The size dependence and the relations with the CNT diameter are discussed through NEMD calculations.