  We propose a density functional to find the ground state energy and density
of interacting particles, where both the density and the pair density can
adjust in the presence of an inhomogeneous potential. As a proof of principle
we formulate an a priori exact functional for the inhomogeneous Hubbard model.
The functional has the same form as the Gutzwiller approximation but with an
unknown kinetic energy reduction factor. An approximation to the functional
based on the exact solution of the uniform problem leads to a substantial
improvement over the local density approximation.
