Kinetic energy density functional based on electron distribution on the energy coordinate to describe covalent bond

Abstract The development of kinetic energy functional (KEF) is known as one of the most difficult subjects in the electronic density functional theory (DFT). In particular, the sound description of chemical bonds using a KEF is a matter of great significance in the field of theoretical physics and chemistry. It is well known, however, that the Thomas–Fermi (TF) model or the TF model corrected with a generalized gradient approximation (GGA) cannot realize the bound state of a covalent bond in general. In this work, a new KEF is developed on the basis of the novel DFT (Takahashi 2018 J. Phys. B: At. Mol. Opt. Phys. 51 055102) that utilizes the electron distribution on the energy coordinate as the fundamental variable. It is demonstrated for an H 2 molecule that the bound state can be realized by the KEF by virtue of the property of the electron density on the energy coordinate. The mechanism underlying the formation of the bound state is the same as that for the realization of the static correlation in the exchange energy described with the new DFT. We also developed a method termed potential gradient approximation (PGA) to make a correction to the TF model instead of the GGA approach. The functional with the PGA correction is used to describe the dissociation of the double bond in an ethene molecule.