A simple effective potential for exchange

The optimized effective potential (OEP) for exchange was introduced some time ago by Sharp and Horton and by Talman and Shadwick. The integral equation for the OEP is difficult to solve, however, and a variety of approximations have therefore been proposed. These are explicitly orbital dependent and require the same two-electron integrals as Hartree-Fock theory. We have found a remarkably simple approximate effective potential that closely resembles the Talman-Shadwick potential in atoms. It depends only on total densities and requires no two-electron integrals.