Density Functional Theory of Atomic Structure. I. Exchange and Correlation Potentials for Two-Electron Atoms

The density functional theory of Hohenberg, Kohn, and Sham would be capable of giving exact energies, and densities if realistic exchange and correlation potentials could be used in the density functional SCF equations rather than approximations based on the uniform electron gas model. Instead of looking for ways to improve the uniform electron gas expressions for the exchange and correlation potentials, we adopt the point of view that a knowledge of the form of realistic potentials should be the basis for constructing approximate potentials to be used in computational work, and could transform the density functional method into the powerfully accurate tool it is capable of becoming. A helium wavefunction was constructed with sufficient accuracy so that the exchange and correlation potentials implied by it would not be grossly affected by known errors in the wavefunction. The resulting "exact" exchange and correlation potentials differ widely from those currently used in density functional calculations, and this points out the need for a systematic study of good atomic wavefunctions in order to learn how to parametrize exchange and correlation potentials for use in accurate work.