Restatement of conventional electronic wave function determination as a density functional procedure

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Abstract
It is shown how any conventional ground‐state electronic wave function determination starting from a basis set of orthonormal spatial orbitals fk may be restated as a density functional procedure. Write fk=(ρ/N)1/2exp(iθk), with ρ the total electron density, N the number of electrons, and θk a function which may have complex as well as real parts. All matrix elements then are expressible as functionals of ρ and the θk. Orthonormalization gives ∫ρ exp[−i(θ*k−θl)]dτ=Nδkl. With these conditions imposed as constraints, the variational process for determining the energy is equivalent to a procedure for starting from a guessed ρ, determining the θk, determining ρ again, and iterating, with the energy decreasing at each stage. The equations are given and discussed in detail for the four‐electron Hartree–Fock problem for which the two orbitals are φ1=(ρ/4)1/2exp(iθ) and φ2=(ρ/4)1/2exp(−iθ), with θ real. A graph of θ is given for the atom Be.

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