Hydrogen Diffusion in the Confinement between Graphene and Ni(111): Full-Dimensional Simulation of Nuclear Quantum Effects

The temperature-dependent diffusion of hydrogen on a Ni(111) surface and in the confinement between Ni(111) and an adsorbed graphene sheet (Gr/Ni(111)) is studied by ring polymer molecular dynamics (RPMD) simulations on neural network potentials (NNPs). Static periodic density-functional theory (DFT) calculations reveal weakened bonding of hydrogen and higher diffusion barriers in the confinement. Further, the local density of hydrogen atoms has a significant influence on its shape and properties. For a hydrogen density of 0.25 ML, the graphene sheet switches to the weaker bound van der Waals configuration, resulting in a broad confinement with similar properties as the clean metal surface. For a hydrogen density of 0.04 ML, the graphene behaves like a carpet and bends up locally around the hydrogen atom. This presses the hydrogen atom to the surface, resulting in a lower intercalation energy and a higher diffusion barrier. The RPMD simulations were used to quantify the effect of temperature and nuclear quantum effects on the diffusion. For 0.25 ML hydrogen coverage, the diffusion coefficients are similar to the clean surface, with a crossover temperature to the deep-tunneling regime of approx. 100 K, whereas for 0.04 ML, diffusion at low temperatures is significantly decreased. At temperatures above 200 K, on the other hand, diffusion is more similar for both hydrogen coverages, due to a more flexible graphene sheet. This study reveals that two-dimensional confinements adapt to their content, and full-dimensional simulations with inclusion of nuclear quantum effects can greatly enhance our understanding of them, needed for their targeted usage as storage media or catalysts.