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When it comes to improving the accuracy of DFT calculations, there is a well known hierarchy:
starting from LDA using $E_{xc}[n]$,
proceeding with GGA and its $E_{xc}[ n, \nabla n]$ dependency
and finally meta-GGAs with $E_{xc}[ n, \nabla n, \nabla^2n~\text{or}~\nabla^2\phi_i]$
I always wonder...