# Total electronic energy as the sum of single particle energies

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.