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Additional info for A primer in density functional theory
LSD is a controlled extrapolation because, even when applied to a density that varies rapidly over space, it preserves many features of the exact Exc , as discussed in Sect. 1. LSD has worked well in solid state applications for thirty years. Our conservative philosophy of GGA construction is to try to retain all the correct features of LSD, while adding others. In particular, we retain the correct uniform-gas limit, for two reasons: (1) This is the only limit in which the restricted GGA form can be exact.
203). 15 is only semi-empirical since f ≈ 1/6 was estimated theoretically. Extension of the Langreth-Mehl EcGGA beyond the random phase approximation was made by Perdew  in 1986. 203)). , exp(−κu) as κ → 0). This suggested that the required cutoﬀs should be done in real space, not in wavevector space. 94). 92) then provided a numerically-deﬁned GGA for Ex , which turned out to be more accurate than either LSD or GEA. In 1986, Perdew and Wang  simpliﬁed this GGA in two ways: (1) They replaced nGEA (r, r+u), which depends upon both ﬁrst and second derivatives x (r, r+u), an equivalent expression found through integration of n(r), by n ˜ GEA x by parts, which depends only upon ∇n(r).
J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, Phys. Rev. Lett. 49, 1691 (1982). 50. J. P. Perdew, in Density Functional Methods in Physics, Vol. B123 of NATO ASI Series, edited by R. M. Dreizler and J. da Providencia (Plenum Press, New York, 1985), p. 265. 51. J. F. Janak, Phys. Rev. B 18, 7165 (1978). 52. M. Levy, J. P. Perdew, and V. Sahni, Phys. Rev. A 30, 2745 (1984). 53. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart, and Winston, New York, 1976). 54. M. Gell-Mann and K.