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)=4π/($K^2$+$K_s^2$) to calculate ${\gamma }_x$, the exchange-energy density-functional gradient expansion coefficient, one obtains Sham’s result if one takes K→0 before taking $K_s$→0. The exchange energy is by its very definition an unscreened quantity so that the correct order of the limits is $K_s$→0 before K→0, in which case ${\gamma }_x$=1.42${\gamma }_x^{\mathrm{Sham}}$. .AE