A nonlinear transformation performs the Levy-constrained search formulation of the density functional for the electronic energy through a minimization of the energy with respect to a set of variational coefficients. The construction requires a complete set of arbitrary functions as the auxiliary basis. Truncation of the basis set provides an upper bound to the energy functional. Practical approaches to obtain accurate upper bounds to this functional are discussed, and a density-functional alternative to the standard Hartree-Fock method is described.

• Received 9 December 1987

DOI:https://doi.org/10.1103/PhysRevLett.60.2141