Quantum mechanical theory of isotope effect on thermally activated hydrogen migration on W(110)

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Abstract
A quantum mechanical model is introduced to explain the exponential increase with isotopic mass of the preexponential factor for the thermally activated diffusion rate for atomic hydrogen and its isotopes on the W(110) surface as recently observed by Gomer and co-workers. The adsorbed hydrogen atom is taken to have self-trapped quantum levels at low energies, with mobile ones above the barrier to hopping. The kinetics of transitions among these levels is analyzed using a master equation, and the individual transition rates are evaluated from a model of the coupling between the adsorbed hydrogen atom and its environment. The preexponential factor is found to vary exponentially with terms having a −1/2 and −1 power of the hydrogen mass (the latter is multiplied by a more slowly varying function of mass), in excellent agreement with the experiments on hydrogen, deuterium, and tritium.