Quantum rate theory of the trapping of hydrogen and deuterium by a   vacancy in iron
  We apply quantum rate theory to calculate the transition rates as hydrogen or deuterium atoms escape from a vacancy trap in iron into a neighbouring metastable site. We determine transition rates and corresponding activation energies over a wide range of temperatures covering both the quantum and classically dominated regimes. We find that quantum effects lead to an increase of the transition rate activation energy and to very significant recrossing of the transition state dividing surface. As a result of recrossing quantum transition state theory overestimates the rate of proton transfer by more than an order of magnitude and the rate of deuteron transfer by a factor of two. 
Ivaylo H. Katzarov and Anthony T. Paxton
cond-mat.mtrl-sci