Quantum size effect in Pb(100) films: the role of symmetry and   implication for film growth
  We show from density-functional calculations that Pb(100) thin films exhibit quantum size effect with a bilayer periodicity in film energies, film relaxations, and work functions, which originate from different symmetry of the stacking geometry of odd and even layer films. The bilayer periodicity of the film energy is argued to survive on a semiconductor substrate, which should allow the growth of ``magically'' thick even-layer Pb(100) films. Furthermore, it is found that the quantum well states in a simple metal film can be classified into $\sigma$-bonded and $\pi$-bonded states, which quantize independently. 
Dengke Yu, Matthias Scheffler, and Mats Persson