Study of a neutrally charged electron gas with a surface

A charge-neutral electron-gas system with a surface is studied over a wide range of densities including the metallic range, by application of certain theoretical and physical constraints to a model surface effective potential. The properties derived are metallic surface dipole barriers, work functions, and surface energies, the behavior of the work function for densities higher than those existing in metals, and low-density surface energies. The finite-linear-potential model employed is one which varies linearly over a finite region and is constant beyond some point, the parameters of the system being the edge of the neutralizing positive charge (jellium) background, the field strength, and the barrier height. For this model effective potential the determination of all properties is primarily analytic. The jellium edge and barrier height are determined by the condition of charge neutrality and requirement of self-consistency of the surface dipole barrier, respectively, whereas the field strength is either adjusted so as to satisfy the constraint set on the electrostatic potential by the Budd-Vannimenus theorem (BVT) or varied in an application of the variational principle for the energy. The results obtained on use of the BVT constraint indicate that although the work function decreases with increasing density, it does not saturate at some finite value in the high-density limit as concluded by Peuckert, but rather that it vanishes at a density corresponding to rₒ0. 4. For metallic densities, the surface dipole barriers and work functions thus determined lie within three tenths of an electron volt of the fully self-consistent calculations of Lang and Kohn (LK). The upper bounds obtained by a variational-self-consistent calculation of metallic surface energies as determined within the local-density approximation (LDA) are within 5 ergs/cm^2 of the LK values for rₒ2. 5 and differ by less than 3% for rₒ=2. Surface energies for metallic and lower densities are also determined by use of the Vannimenus-Budd theorem in conjunction with the physical criterion of the vanishing of the surface energy in the low-density limit. For the same choice of single-particle Hamiltonian, determined by the BVT sum rule, these results lie significantly below those of a LDA calculation over the entire range of densities considered.