ON-TOP PAIR-DENSITY INTERPRETATION OF SPIN-DENSITY FUNCTIONAL THEORY,WITH APPLICATIONS TO MAGNETISM

The on-top pair density P(r, r) gives the probability that one electro n will be found on top of another at position r. We find that the loca l spin density (LSD) and generalized gradient (GGA) approximations for exchange and correlation predict this quantity with remarkable accura cy. We show how this fact and the usual sum-rule arguments explain the success of these approximations for real atoms, molecules, and solids , where the electron spin densities do not vary slowly over space. Sel f-consistent LSD or GGA calculations make realistic predictions for th e total energy E, the total density n(r), and the on-top pair density P(r,r), even in those strongly ''abnormal'' systems (such as stretched H-2) where these approximations break symmetries and yield unrealisti c spin magnetization densities m(r). We then suggest that ground-state ferromagnetic iron is a ''normal'' system, for which for LSD or GGA m (r) and the related local spin moment are trustworthy, but that iron a bove the Curie temperature and antiferromagnetic clusters at all tempe ratures are abnormal system for which the on-top pair density interpre tation is more viable than the standard physical interpretation. As an example of a weakly abnormal system, we consider the four-electron io n with nuclear charge Z --> infinity. (C) 1997 John Wiley & Sons, Inc.