Development of static correlation functional using electron distribution on the energy coordinate

Abstract

A static correlation error (SCE) inevitably emerges when the dissociation of a covalent bond is described with a conventional density-functional theory (DFT) for electrons. The SCE gives rise to a serious overshoot in the potential energy (PE) at the dissociation limit even in the simplest molecules. The error is attributed to the basic framework of the approximate functional for the exchange correlation energy E xc which refers only to local properties at coordinate r , namely, the electron density n( r ) and its derivatives. To solve the problem we developed a functional that uses the energy electron distribution n e(ϵ) as a fundamental variable in DFT. n e(ϵ) is obtained by projecting the density n( r ) onto an energy coordinate ϵ defined by the external potential of interest. The functional was applied to the dissociations of single, double, and triple bonds in small molecules, showing reasonable agreement with the results given by a high-level molecular orbitals theory. We also applied the functional to the computation of the energy change associated with spin depolarization and symmetrization in a carbon atom, which made an improvement over the conventional functional. This work opens the way to develop a tougher functional that necessitates nonlocal properties of electrons, such as a kinetic energy functional.