Static electronic susceptibility,χ(q∥,z,z′), of the Lang-Kohn jellium surface

We present the first accurate values of $\chi (q_{\parallel },z,z^{\prime })$, the static susceptibility of a jellium surface, including (i) finite surface wave vector $q_{\parallel }$; (ii) Friedel oscillations (from an exact kinetic energy functional); (iii) Kohn-Sham exchange-correlation effects (Wigner form); (iv) self-consistent screening; (v) realistic Lang-Kohn zero-order profile; and (vi) comparison, for $r_s=2.07\mathrm{}$, with a useful approximation.