ACCURATE EXCHANGE-CORRELATION POTENTIALS AND TOTAL-ENERGY COMPONENTS FOR THE HELIUM ISOELECTRONIC SERIES

Starting from very accurate many-body wave functions, we have construc ted essentially exact densities, exchange-correlation potentials, and components of the total energy for helium and two-electron ions. These density-functional results are compared to the corresponding quantiti es obtained from a variety of commonly used approximate density functi onals, namely, the local-density approximation and various generalized gradient approximations, in order to test the accuracy of the approxi mate functionals. Although the generalized gradient approximations yie ld improved energies compared to the local-density approximation, the exchange and correlation potentials (especially the latter) obtained f rom the generalized gradient approximations are in poor agreement with the corresponding exact potentials. The large-distance asymptotic beh avior of the. exact exchange-correlation potential to O(1/r(4)) is fou nd to agree with theoretical predictions. The short-range behavior of the exchange-correlation potential is very close to quadratic. The pro spects for improved generalized gradient approximations are discussed.