In Hartree-Fock / Kohn-Sham theory, the total energy of a system of electrons is the sum of single electron energies $\varepsilon_k$ plus some correction $C[\rho]$ depending on the electron density $\rho$, $$ E_\mathit{tot} = \sum_{k} \varepsilon_k + C[\rho], $$ see e.g. the formula at the bottom of this Wikipedia article.

However, it seems in applications the correction $C[\rho]$ is often ignored, see e.g. formula (15) in Stefan Goedecker's Linear scaling electronic structure methods. What is the justification for this?

My guesses are:

  • The correction is small and can hence be ignored.
  • We are mostly interested in energy differences where the correction cancels out.

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