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This argument can be taken a step further, and applied to the system-average in Eq. (22). For r near a nucleus, the Laplacian of the density becomes large, and LSD does not work so well. However, the phase space factor 411'r2 unweights such a region in the average (see Figs. 1-3 of Ref. [15]). Also, at large distances from finite systems, in the evanescent tail regions, LSD performs poorly, but now the density weighting ensures this makes little contribution. Similar arguments apply to the large u behavior in finite systems, which LSD misses entirely (see the discussion of exact behavior above).
3. 4. 5. 6. 7. R. M. Dreizler and E. K. U. Gross, Density Functional Theory (Springer-Verlag, Berlin, 1990). R. G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford University Press, Oxford, 1989). R. O. Jones and O. Gunnarsson, Rev. Mod. Phys. 61,689 (1989). Recent Developments and Applications of Modem Density Functional Theory, edited by J. M. Seminario, Theoretical and Computational Chemistry (Elsevier, Amsterdam, 1996). J. P. Perdew and A. Zunger, Phys. Rev. B 23,5048 (1981), and references therein.