A Density Functional Theory for the Average Electron Energy

A formally exact density functional theory (DFT) determination of the average electron energy is presented. Our theory, which is based on a different accounting of energy functional terms, partially solves one well-known downside of conventional Kohn-Sham (KS) DFT: that electronic energies have but tenuous connections to physical quantities. Calculated average electron energies are close to experimental ionization potentials (IPs) in one-electron systems, demonstrating a surprisingly small effect of self-interaction and other exchange-correlation errors in established DFT methods. Remarkable agreement with ab initio quantum mechanical calculations of multielectron systems is demonstrated using several flavors of DFT, and we argue for the use of the average electron energy as a design criterion for density functional approximations.

Automated summary

In this article, a different calculation method based on energy functional terms is proposed, which partly solves the problem of weak connection between electronic energy and physical quantities in traditional Kohn-Sham (KS) density functional theory (DFT). The calculated average electron energy is close to the experimental ionization potentials (IPs) in one-electron systems, indicating a small impact of self-interaction and other exchange-correlation errors in established DFT methods. Remarkable agreement with ab initio quantum mechanical calculations of multielectron systems is demonstrated using several flavors of DFT, and the average electron energy is argued to be a design criterion for density functional approximations.