Surface correlation energy—An interpolation formula

Abstract

In this paper we obtain an interpolation formula for the surface correlation energy. We do this as follows. We first calculate the correlation energy in the low-density limit where the electrons are expected to crystallize. It is shown thatE ∝1/r s asr s →∞. We have shown elsewhere that asr s →0, $$E_c^s \propto 1/\sqrt {r_s } $$ . Hence we try an interpolation formula of the type $$E_c^s = (a/\sqrt {r_s } )(\sqrt {r_s } + b)$$ that reduces to the exact functional form at the high- and low-density limits. The main conclusion we draw from the behaviour of the interpolation formula is that thesurface may be more unstable against charge density waves than the bulk. Also, we feel that RPA may be a worse approximation for surface problems (2<r s <6) than has been suspected up to now.