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\begin{equation}  G(\omega) = \frac{1}{\omega + \nabla^2/2 + \mu - V_\text{ion} - V_\text{H} - \Sigma(\omega)}.  \end{equation}  We have used atomic units, included a chemical potential $\mu$, and separated the large Hartree component out from the self-energy $\Sigma$. The self-energy is generally frequency-dependent, and we have omitted the argument $\vec{r}$ from all quantities. The eigenenergies that are the result diagonalizing the Kohn-Sham hamiltonian $H_\text{KS} = -\frac{1}{2}\vec{\nabla}^2- \mu  + V_\text{KS}(\vec{r})$ does not capture the frequency-dependent effects of many-body interactions, and should not be interpreted as physical eigenvalues. Nevertheless, we often ignore the lack of formal justification and compute the Green's function using the Kohn-Sham solution anyway: \begin{equation}  G_\text{KS}(\omega) = \frac{1}{\omega + \mu  - H_\text{KS}}. \end{equation}  Thus, we find the self-energy in DFT $\Sigma_\text{KS} = V_\text{xc}$ is in fact frequency independent. In comparing with experiment, we always expect deviations at high frequencies because the non-interacting Kohn-Sham framework should only work well near the Fermi surface, where the quasiparticles of Fermi liquid theory are well-defined. However, at low frequencies (which for this section we take to mean $\omega \lesssim 1$~eV, a typical chemical scale) we can hope the DFT spectrum will resemble observations, and in many cases it does. We call these materials weakly correlated.