Convergence of the gradient expansion in metallic surface-energy calculations

The exchange contribution to the surface energy of a finite-barrier model (chosen to reproduce a physical density profile) is calculated for a Yukawa interparticle interaction. The above result is compared with the exchange contribution to the surface energy calculated from the gradient expansion and is found to give excellent agreement. This comparison gives a first clear assessment of the important question for the convergence rate of the gradient expansion in surface-energy calculations.