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\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 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.  A good rule We can crudely categorize the effects  of thumb for a correlated material is strong frequency dependence correlations by considering the dominant term  in $\Sigma(\omega)$ 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 less than below  $\sim 1$~eV. A simple examples is that of 1$~eV, we have  a correlated metal, where interactions renormalize 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 mass linear term dominates, the main effect  of electrons the self-energy is to flatten the bands  near the Fermi surface and transfer energy while transferring the residual  spectral weight to higher energies. This appears as large linear $\omega$-term in $\Sigma(\omega)$, with a coefficient related These mass-enhanced systems corresponds  to correlated metals and require techniques such as  the renormalization factor.  Sigma must either be observed GW approximation  or computed using more sophisticated methods. 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}