Hydrogen diffusion on Ni(100): A combined machine-learning, ring polymer molecular dynamics, and kinetic Monte Carlo study

We introduce a methodological framework coupling machine-learning potentials, ring polymer molecular dynamics (RPMD), and kinetic Monte Carlo (kMC) to draw a comprehensive physical picture of the collective diffusion of hydrogen atoms on metal surfaces. For the benchmark case of hydrogen diffusion on a Ni(100) surface, the hydrogen adsorption and diffusion energetics and its dependence on the local coverage is described via a neural-network potential, where the training data are computed via periodic density functional theory (DFT) and include all relevant optimized diffusion and desorption paths, sampled by nudged elastic band optimizations and molecular dynamics simulations. Nuclear quantum effects, being crucial for processes involving hydrogen at low temperatures, are treated by RPMD. The diffusion rate constants are calculated with a combination of umbrella samplings employed to map the free energy profile and separate samplings of recrossing trajectories to obtain the transmission coefficient. The calculated diffusion rates for different temperatures and local environments are then combined and fitted into a kMC model allowing access to larger time and length scales. Our results demonstrate an outstanding performance for the trained neural network potential in reproducing reference DFT energies and forces. We report the effective diffusion rates for different temperatures and hydrogen surface coverages obtained via this recipe in good agreement with the experimental results. The method combination proposed in this study can be instrumental for a wide range of applications in materials science.