First-principles density-functional theory has been used to investigate equilibrium geometries, total energies, and diffusion barriers for H as an interstitial impurity absorbed in $\alpha \text{-Fe}$. Internal strains/stresses upon hydrogen absorption are a crucial factor to understand preferred absorption sites and diffusion. For high concentrations, H absorbs near the octahedral site favoring a large tetragonal distortion of the bcc lattice. For low concentration, H absorbs near the tetrahedral site minimizing the elastic energy stored on nearby cells. Diffusion paths depend on the concentration regime too; hydrogen diffuses about ten times faster in the distorted body-centered-tetragonal (bct) lattice. External stresses of several GPa modify barriers by $\approx 10\%$, and diffusion rates by $\approx 30\%$.

First-principles atomistic molecular-dynamics simulation in the microcanonical and canonical ensembles has been used to study the diffusion of interstitial hydrogen in $\alpha${}-iron. Hydrogen to iron ratios between $\theta${}=116 and 12 have been considered by locating interstitial hydrogen atoms at random positions in a 2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2 supercell. We find that the average optimum absorption site and the barrier for diffusion depend on the concentration of interstitials. Iron Debye temperature decreases monotonically for increasing concentration of interstitial hydrogen, proving that iron-iron interatomic potential is significantly weakened in the presence of a large number of diffusing hydrogen atoms.