Fully quantum mechanical calculation of the diffusivity of hydrogen in iron using the tight-binding approximation and path integral theory

We present calculations of free energy barriers and diffusivities as functions of temperature for the diffusion of hydrogen in alpha-Fe. This is a fully quantum mechanical approach since the total energy landscape is computed using a self-consistent, transferable tight binding model for interstitial impurities in magnetic iron. Also the hydrogen nucleus is treated quantum mechanically and we compare here two approaches in the literature both based in the Feynman path integral formulation of statistical mechanics. We find that the quantum transition state theory which admits greater freedom for the proton to explore phase space gives result in better agreement with experiment than the alternative which is based on fixed centroid calculations of the free energy barrier. This will have an impact on future modeling and the simulation of hydrogen trapping and diffusion.