Conclusions Made from Computations of WDA

If one chooses the formula for the Fermi vector that is appropriate for the uniform electron gas (Equation 1.113), one recovers the TF + W (A, = 1) functional. Although 

The conventional WDA for the kinetic energy results when the effective Fermi vector is determined by substituting the asymmetric one-matrix (Equation 1.110) into the diagonal idempotency condition (Equation 1.115). This functional is also exact for the uniform electron gas, but the kinetic energies of atoms and molecules are still predicted to be far too high. Indeed, this functional is only slightly more accurate than the Thomas-Fermi functional. This is surprising, since the WDA and the TF functional were derived from the same formula for the one-matrix, but the WDA adds an additional exact constraint. 

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