The quantum nature of hydrogen has long been observed to play an important role on its diffusion within metals.

Motivated by recent experimental work, diffusion rates were calculated for both hydrogen and deuterium on the nickel (111) surface across a range of temperatures (75 K to 250 K), taking into account quantum nuclear effects. This was achieved through the method of partially adiabatic centroid molecular dynamics, which places the Feynman path integral in a central role. This method makes the calculation of quantum time correlation functions possible through an extension to classical molecular dynamics.

The ab intio calculation of the quantum diffusion of hydrogen/deuterium on the nickel surface is computationally demanding, and a method for approximating these interactions, in the form of a static potential energy surface is presented. Implicit in this method is that there is an adiabatic separation between motion of the surface ions and the adsorbate, due to their large mass differences. The resulting potential energy surface allows for the accurate determination of the energies and forces acting on the adsorbate, at all positions along the static surface, with a significantly reduced cost when compared with density functional theory.

The quantum dynamics calculations showed that, for the temperature range studied, the inclusion of quantum nuclear effects acted to increase the diffusion rate of both adsorbates. At 250 K, the quantum diffusion coeffcients were found to be ~34 times larger than the classical result. At 75 K, the quantum contribution is significantly increased, and the diffusion coeffcient is ~4×10^6 times larger for deuterium and ~1×10^7 times larger for hydrogen. The classical and quantum treatments also give rise to qualitatively different diffusion profiles on an Arrhenius plot, especially in the low temperature regime, where there is a transition from classical (thermally activated) to quantum (tunnelling) diffusion.