Tests of functionals for systems with fractional electron number

In the exact theory, the ground state energy of an open system varies linearly when the electron number is changed between two adjacent integers. This linear dependence is not reproduced by common approximate density functionals. Deviation from linearity in this dependence has been suggested as a basis for the concept of many-electron self-interaction error (SIE). In this paper, we quantify many-electron SIE of a number of approximations by performing calculations on fractionally charged atoms. We demonstrate the direct relevance of these studies to such problems of common approximate functionals as instabilities of anions, spurious fractional charges on dissociated atoms, and poor description of charge…

• NS
  National Science Foundation
• WF
  Welch Foundation
• DO
  Division of Materials Research