Contributions to the work function of crystals

We consider a simple model of the work function based on the overlapping spherical atomic charge-density approximation to the potential (the so-called Mattheiss construct). We show analytically that the dipole barrier of nonpolar crystals is simply related to a moment of the spherical densities, and hence there is no face dependence of the work function in this model. For the polar faces of polar crystals there is an additional face-dependent term that was found previously by different means. We calculate the bulk contributions to the work function for the metals with atomic number less than 50. The dipole barriers obtained from free-atomic densities result in work functions which are on the average {~}80% too large. The use of contracted atomic densities, while leaving the bulk density virtually unchanged, decreases the dipole barriers and yields work functions in reasonable agreement with experiment. Some implications for surface calculations, electronegativity scales, and charge-transfer and bonding trends are briefly discussed.