Exact high-density limit of correlation potential for two-electron density

Abstract

Present approximations to the correlation energy, Ec[n], in density functional theory yield poor results for the corresponding correlation potential, vc([n];r)=δEc[n]δ/n(r). Improvements in vc([n];r), are especially needed for high-quality Kohn–Sham calculations. For a two-electron density, the exact form of vc([n];r) in its high-density limit is derived in terms of the density of the system and the first-order wave function from the adiabatic perturbation theory. Our expression leads to a formula for the difference 2Ec[n]−∫vc([n];r)n(r)dr, valid for any two-electron density in the high-density limit, thus generalizes previous results. Numerical results (both exact and approximate) are presented for both Ec[n] and ∫vc([n];r)n(r)dr in this limit for two electrons in a harmonic oscillator external potential (Hooke’s atom).