A Density Functional Theory for the Average Electron Energy.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Conventional Kohn-Sham density functional theory (DFT) methods often lack direct connections between calculated electronic energies and physical quantities.
• Addressing this limitation is crucial for improving the predictive power of theoretical chemistry and materials science.

Purpose of the Study:

• To present a formally exact density functional theory (DFT) determination of the average electron energy.
• To demonstrate the utility of average electron energy as a metric for evaluating and designing density functional approximations.

Main Methods:

• Developed a novel DFT framework with a distinct approach to energy functional terms.
• Calculated average electron energies for various systems.

Main Results:

• Average electron energies closely matched experimental ionization potentials in one-electron systems.
• Showcased minimal self-interaction and exchange-correlation errors in established DFT methods.
• Achieved remarkable agreement with ab initio quantum mechanical calculations for multielectron systems.

Conclusions:

• The average electron energy provides a more physically meaningful quantity than conventional DFT energies.
• This approach offers a viable design criterion for developing improved density functional approximations.
• The findings suggest a path towards more accurate and reliable electronic structure calculations.