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

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.