Surface Reactivity and Quantum-Size effects on the Electronic Density   Decay Length of ultrathin Metal Films
  The origin of the correlation between surface reactivity and quantum-size effects, observed in recent experiments on the oxidation of ultrathin magnesium films, is addressed by means of ab-initio calculations and model predictions. We show that the decay length in vacuum of the electronic local density of states at the Fermi energy exhibits systematic oscillations with film thickness, with local maxima induced when a quantum well state at k// = 0 crosses the Fermi energy. The predicted changes in the decay length are expected to have a major impact on the electron transfer rate by tunneling, which has been proposed to control the initial sticking of O2 in the oxidation process. 
N. Binggeli and M. Altarelli