Comment on “Nonanalyticity of the optimized effective potential with finite basis sets”

Abstract

In a recent paper [Phys. Rev. A 85, 052508 (2012)], Gidopoulos and Lathiotakis discuss difficulties in solving the optimized effective potential (OEP) equation in a finite basis. We show that these difficulties are resolved by choosing basis sets that fulfill a balance condition. In particular, the nonanalyticity of the finite-basis OEP equation disappears in basis-set convergence. In connection with the basis-set balance, we also discuss the role of small eigenvalues. The approximate treatment of them with a common energy denominator suggested by the authors requires care in order to avoid spurious oscillations in the potential. We briefly discuss an alternative scheme that overcomes the aforementioned difficulties and enables OEP calculations with a minimal orbital basis.