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We introduced a new electron density n({\epsilon}) by projecting the spatialelectron density n(r) onto the energy coordinate {\epsilon} defined with theexternal potential \upsion (r) of interest. Then, a density functional theory(DFT) was formulated, where n({\epsilon}) serves as a fundamental variable forthe electronic energy. It was demonstrated that the Kohn-Sham equation can alsobe adapted to the DFT that employs the density n({\epsilon}) as an argument tothe exchange energy functional. An important attribute of the energy density isthat it involves the spatially non-local population of the spin-adapted densityn(r) at the bond dissociation. By taking advantage of this property wedeveloped a prototype of the static correlation functional employing noempirical parameters, which realized a reasonable dissociation curve for H2molecule.

Density Functional Theory Based on the Electron Distribution on the Energy Coordinate