Formally exact integral equation theory of the exchange-only potential in density functional theory: Refined closure approximation

A formally exact integral equation theory for the exchange-only potential Vx(r)Vx(r) in density functional theory was recently set up by Howard and March [I.A. Howard, N.H. March, J. Chem. Phys. 119 (2003) 5789]. It involved a ‘closure’ function P(r)P(r) satisfying the exact sum rule ∫P(r)dr=0. The simplest choice P(r)=0P(r)=0 recovers then the approximation proposed by Della Sala and Görling [F. Della Sala, A. Görling, J. Chem. Phys. 115 (2001) 5718] and by Gritsenko and Baerends [O.V. Gritsenko, E.J. Baerends, Phys. Rev. A 64 (2001) 042506].Here, refined choices of P(r)P(r) are proposed, the most direct being based on the KLI (Krieger–Li–Iafrate) approximation. A further choice given some attention is where P(r)P(r) involves frontier orbital properties. In particular, the introduction of the LUMO (lowest unoccupied molecular) orbital, along with the energy separation between HOMO (highest occupied molecular orbital) and LUMO levels, should prove a significant step beyond current approximations to the optimized potential method, all of which involve only single-particle occupied orbitals.