Quantum size effects in equilibrium lithium ultrathin layers

The existence and extent of quantum size effects in simple metal ultrathin films are studied by a systematic local-density, all-electron, full-potential calculation of the cohesive properties of ν layers of hexagonal Li, with ν=1, 2, 3, 4, and 5. By ν=5, there is clear convergence of the a lattice parameter (intraplanar bond length) to very nearly the calculated crystalline value, with a distinction between the two films with a meaningful interior (a=5.68±0.01 a.u. for ν=4 and 5) and those with a minimal interior or none at all (ν=3 and ν=1 and 2, respectively; a=5.${75}_{\mathrm{-}0.01}^{+0.02\mathrm{}}$ a.u.). Equally clear stability of the interplanar spacings occurs at distinctly noncrystalline values (4.27 a.u. for ν=2; 4.38±0.01 a.u. for the inner spacing of ν=3, 4, and 5 versus 4.64 a.u. for the crystalline calculation). The cohesive energies of the 3, 4, and 5 layers are closely clumped at about 87% of the crystalline value. As the 2 and 1 layers are substantially less bound, both the cohesive properties and the inner interplanar spacing suggest a different grouping than suggested by the a lattice parameter. Rough extrapolation of the slowly increasing cohesion with ν suggests that ν≊20 would be needed to achieve even 90% of the crystalline cohesive energy.