The surface energy of a bounded electron gas

An exact expression for the exchange and correlation energy of an inhomogeneous electron gas, as defined by Hohenberg, Kohn and Sham (1966), is derived. This expression is separated into exchange and correlation terms and a formula linking the surface exchange energy of a half space to the Kohn-Sham one electron potential follows without approximation. For an infinite barrier model, the local density approximation gives a surface exchange energy 50% greater than the exact value, a large and previously unsuspected error. An exact evaluation of the surface correlation energy is not feasible, but the authors argue that the dominant contribution, arising from the difference in zero point energy between bounded and unbounded systems, can be estimated using a simple model. Numerical results, not dependent on the introduction of arbitrary plasmon wavevector cutoffs, give surface correlation energies larger than Lang and Kohn (1970), who work from a local formula, by a factor of six.