Predictive evaluation of hydrogen diffusion coefficient on Pd(111) surface by path integral simulations using neural network potential

Quantum diffusion of hydrogen (H) on palladium (Pd) (111) was studied using two types of path integral simulations: quantum transition state theory (QTST) and ring polymer molecular dynamics (RPMD). The use of an artificial neural network potential trained by density functional theory calculations has made it feasible to perform path integral simulations considering nuclear quantum effects (NQEs) of a many-body Pd-H system with ab initio accuracy. The QTST result has shown a clear non-Arrhenius behavior in the diffusion coefficient (D) of H below the temperature of 150-200 K due to the NQEs. Comparing the D on Pd surface and bulk Pd, it was found that surface and bulk diffusion are competitive at high temperature. Consistent with this, it was observed in the RPMD simulation at 800 K that a part of the quantum trajectories of H on the surface bifurcates to the Pd subsurface. As the temperature decreases, the surface diffusion becomes much faster than the bulk diffusion. Furthermore, distinct quantum behaviors of H were identified at the surface and within the bulk. The D values obtained from this study using a "flexible" Pd surface model differed considerably from those previously reported using "frozen" Pd surface models, indicating an important contribution from Pd vibrations coupled with H diffusion.