Exact electron-gas response functions at high density

Abstract

We calculate the Hohenberg-Kohn-Sham energy response kernel $K_{\mathrm{xc}\left(\mathrm{q}\right)}$ exactly for the high-density electron gas, and thus generalize the classic work of Ma and Brueckner to finite wave vector. The results are relevant to (1) density-functional theory, where we verify that one of the key assumptions used in the Langreth-Mehl functional was qualitatively correct and suggest possible improvements; (2) dielectric response theory, where we exactly calculate the leading correction to the static Lindhard screening function; and (3) a static attractive 1/$r^6$-like interaction between like-charged point particles—we verify the recent suggestion of Maggs and Ashcroft that such an interaction exists and calculate its value.