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In practice, the exchange-correlation term is difficult to capture, and is generally modeled by approximations known as the local density approximation (LDA) or generalized gradient approximation (GGA). Theoretical chemists have classified the introduced errors into two types. The delocalization error describes the tendency of LDA/GGA to distribute an electron added to a system over too large a spatial region, which leads to underestimation of band gaps. The static correlation error describes the poor treatment of spin states, which leads to an inability to capture the Mott insulating state ubiquitous in strongly correlated systems, including the superconducting cuprates.  Assuming we have the exact $V_\text{xc}$, DFT guarantees the correct ground state density and energy, but makes no claims about the electronic spectrum. For electrons moving in the lattice potential $\V_\text{ion}$ $V_\text{ion}$  of the nuclear ions, the general form of the Green's function is \begin{equation}  G(\omega) = \frac{1}{\omega + \nabla^2/2 + \mu - V_\text{ion} - V_\text{H} - \Sigma(\omega)}.  \end{equation}