A Physical Expression of Electrons in Density Functional Theory

17 January 2022, Version 1
This content is a preprint and has not undergone peer review at the time of posting.


We present a formally exact density functional theory (DFT) determination of the average electron energy. Our orbital-free theory, which is based on a different accounting of energy functional terms, partially solves one well known downside of Kohn-Sham (KS) DFT: that orbital energies have but tenuous connections to physical quantities. Our computed average electron energies are close to experimental ionization potentials in one-electron systems, demonstrating a surprisingly small effect of self-interaction and other exchange- correlation errors in established DFT methods. We argue for the use of the average electron energy as a physics condition on otherwise fictitious KS energy levels and as a design criterion for density functional approximations.


Experimental Quantum Chemistry
Self-interaction energy
Orbital Correction
Kinetic-Energy Functional

Supplementary materials

Supporting Information for "A Physical Expression of Electrons in Density Functional Theory"
Materials and Methods, Supplementary Text, References and Notes (31-62), Tables S1 to S9.


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