Density-functional theory based on the electron distribution on the energy coordinate

We developed an electronic density functional theory utilizing a novel electron distribution n(ϵ) as a basic variable to compute ground state energy of a system. n(ϵ) is obtained by projecting the electron density $n\left(r\right)$ defined on the space coordinate $r$ onto the energy coordinate ϵ specified with the external potential ${\upsilon }_{ext}\left(r\right)$ of interest. It was demonstrated that the Kohn–Sham equation can also be formulated with the exchange-correlation functional E _xc[n(ϵ)] that employs the density n(ϵ) as an argument. It turned out an exchange functional proposed in our preliminary development suffices to describe properly the potential energies of several types of chemical bonds with comparable accuracies to the corresponding functional based on local density approximation. As a remarkable feature of the distribution n(ϵ) it inherently involves the spatially non-local information of the exchange hole at the bond dissociation limit in contrast to conventional approximate functionals. By taking advantage of this property we also developed a prototype of the static correlation functional E _sc including no empirical parameters, which showed marked improvements in describing the dissociations of covalent bonds in $H_2,C_2{H}_4$ and ${CH}_4$ molecules. (paper)