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Electron work functions, surface potentials, and electron number density distributions and electric fields in the surface region of 26 metals are calculated from first principles within the free-electron model. The number of free electrons per atom is taken as the group number as listed in the Periodic Table. Grain orientation effects are not considered. The calculation proceeds from an expression of the total energy as a functional of the electron number density including exchange and correlation energies as well as a first inhomogeneity term. The self-consistent solution is then obtained via a variational procedure akin to the Ritz method. Surface barriers are found, in most cases, to be due principally to many-body effects, but dipole barriers are small only for a number of alkali metals, becoming quite large for the transition metals. As one might expect, surface energies are found to be inadequately described by this model which neglects atomistic effects. Considering the simplicity of the model, reasonable results are obtained for electron work functions and surface potential characteristics for all metals studied, maximum electron densities varying by a factor of over 60.
John R. Smith (Sat,) studied this question.