A Paradigm for Density Functional Theory Using Electron Distribution on the Energy Coordinate

TL;DR

This paper introduces a new density functional based on electron distribution over an energy coordinate to better describe static correlation errors in bond dissociation, showing improved results over traditional methods.

Contribution

The authors developed a novel functional using electron energy distribution as a fundamental variable, addressing static correlation errors in DFT.

Findings

Reasonable agreement with high-level molecular orbital results.

Improved accuracy in spin depolarization and symmetrization energies.

Potential for developing more advanced functionals with non-local electron properties.

Abstract

Static correlation error(SCE) inevitably emerges when a dissociation of a covalent bond is described with a conventional denstiy-functional theory (DFT) for electrons. SCE gives rise to a serious overshoot in the potential energy 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 Exc 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 Ee which uses xc the energy electron distribution ne(e) as a fundamental variable in DFT. ne(e) is obtained by the projection of the density n(r) onto an energy coordinate e defined with the external potential of interest. The functional was applied to the dissociations of single, double, and triple bonds in small molecules showing reasonable agreements 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 Carbon atom, which made an improvement over the conventional functional. This work opens the way for development of tougher functional that necessitates non-local properties of electrons such as kinetic energy functional.