Change-in-self-consistent-field theory of the work function

By analogy with the change-in-self-consistent-field ($\Delta \mathrm{SCF}$) method of atomic physics, the work function of a metal surface is computed as the difference between the total energy of the system in its final state, where one electron is missing from the metal and removed to a large distance from the surface, and its initial state, where the metal is charge neutral. Our $\Delta \mathrm{SCF}$ expression is a generalization of one given by Lang and Kohn, who assumed the electron density profile to be that of a jellium surface. The $\Delta \mathrm{SCF}$ expression also reduces in the appropriate limit to an expression derived by Mahan and Schaich. We show that the $\Delta \mathrm{SCF}$ expression is much less profile-sensitive than other exact expressions for the work function and is therefore well suited for use with approximate profiles. We apply our "variational self-consistent" profiles (more realistic than jellium profiles) to evaluate the $\Delta \mathrm{SCF}$ work function for a few selected surfaces of simple metals, among them the three low-index faces of Al, for which agreement with experiment is found to be good.