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\begin{equation}  G_\text{KS}(\omega) = \frac{1}{\omega - H_\text{KS}}.  \end{equation}  Thus, we find the self-energy in DFT $\Sigma_\text{KS} = V_\text{H} + V_\text{xc}$ 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 we take to mean $\omega \lesssim 1$~eV, a typical chemical scale)  we may hope the DFT spectrum may resemble observations, and in many cases it does. We call these materials weakly correlated. Strongly correlated materials are those compounds where the actual self-energy $\Sigma(\omega)$ deviates strongly from the DFT reference $V_\text{H} + V_\text{xc}$ at low frequencies. We can crudely categorize the effects of correlations by considering the dominant term in the low-order expansion of the self-energy deviation  \begin{equation}  \Sigma(\omega) - \Sigma_\text{KS} \sim \Sigma_0 + \omega \Sigma_1 + \ldots  \end{equation}  If $\Sigma_0$ is large compared to the linear term for frequencies below $\sim 1$~eV, low frequencies,  we have a large static shift which typically corresponds to materials in the Mott insulating regime with magnetic order. Extensions to DFT known as LDA+U describe these systems well. If the linear term dominates, the main effect of the self-energy is to flatten the bands near the Fermi energy while transferring the residual spectral weight to higher energies. These mass-enhanced systems corresponds to correlated metals and require techniques such as the GW approximation or dynamical mean field theory (DMFT) for accurate description. % It starts with the Kohn-Sham formulation~\cite{Kohn_1965} of density functional theory. It states the existence of a potential $V_{KS}(r)$, which is itself a functional of the density. One should write $V_{KS}(\vec{r})[\{ \rho(\vec{r}') \}]$ to indicate this dependence, but we omit this in the following. The exact (but unknown) functional is such that the solution of the set of self-consistent equations,  % \begin{equation}