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_-0.01+0.02 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.The calculated surface energies do not exhibit any strong size effect, in striking contrast to Al films. The equilibrium intraplanar force constant a²E/da² has a minimum at {ν}=3, with its maximum at {ν}=5 almost 2.5 times larger. The calculated work functions give only a hint, at the very most, of the quantum size oscillations predicted from jellium models. A significant quantum size effect occurs, however, in the occupied portion of the density of states, which exhibits a step-function increase for each integer increase in {ν}. The density of states at EF has a maximum at {ν}=3 with a variation over the series of about 10%. The unrelaxed films do not exhibit a stronger quantum size effect than the equilibrium films, again with the barely possible exception of the work function.