Gradient expansion of the exchange-energy density functional: Effect of taking limits in the wrong order

We show that if one uses a screened Coulomb potential V(K)=4{π}/(K²+Kₛ²) to calculate γₓ, the exchange-energy density-functional gradient expansion coefficient, one obtains Sham's result if one takes K{→}0 before taking Kₛ{→}0. The exchange energy is by its very definition an unscreened quantity so that the correct order of the limits is Kₛ{→}0 before K{→}0, in which case γₓ=1.42γₓSham. .AE