  We introduced a new electron density n({\epsilon}) by projecting the spatial
electron density n(r) onto the energy coordinate {\epsilon} defined with the
external potential \upsion (r) of interest. Then, a density functional theory
(DFT) was formulated, where n({\epsilon}) serves as a fundamental variable for
the electronic energy. It was demonstrated that the Kohn-Sham equation can also
be adapted to the DFT that employs the density n({\epsilon}) as an argument to
the exchange energy functional. An important attribute of the energy density is
that it involves the spatially non-local population of the spin-adapted density
n(r) at the bond dissociation. By taking advantage of this property we
developed a prototype of the static correlation functional employing no
empirical parameters, which realized a reasonable dissociation curve for H2
molecule.
