POINT-TRANSFORMATIONS APPLIED TO DENSITY-FUNCTIONAL CALCULATIONS

The method of point transformations enables us to generate an unknown wave function ({rk}) from a given electron density (r) based on a reference wave function 0({rk}) initially chosen for the system. The generated wave function ({rk}) can be used to evaluate the energy E associated with the given density (r). This procedure constitutes a rigorous density-functional theory, if the density (r) and reference function 0({rk}) are varied. Within the Hartree-Fock framework numerical applications are presented for the ground-state helium atom and its analogs both in position and momentum spaces. Simple position and momentum densities are reported that well reproduce the Hartree-Fock limit energy. A few calculations beyond the Hartree-Fock approximation are also given. © 1990 The American Physical Society.