Functional constructions with specified functional derivatives

A bifunctional construction depending on a specified density–potential pair and an approximate guiding electron density functional is presented. The proposed bifunctional construction properly transforms under homogeneous coordinate scaling and yields the specified functional derivative, which determines the electron density. Whereas the method is general and applicable to all functional types, it will prove especially helpful in the context of orbital-free density functional theory, where most existing approximate density functionals predict inaccurate potentials.