Almost Exact Exchange At Almost No Cost
  A recently developed semiclassical approximation to exchange in one dimension is shown to be almost exact, with essentially no computational cost. The variational stability of this approximation is tested, and its far greater accuracy relative to local density functional calculations demonstrated. Even a fully orbital-free potential-functional calculation (no orbitals of any kind) yields little error relative to exact exchange, for more than one orbital. 
Peter Elliott, Attila Cangi, Stefano Pittalis, E.K.U. Gross, Kieron   Burke
physics.chem-ph cond-mat.mtrl-sci cond-mat.other