Communication: Near-locality of exchange and correlation density functionals for 1-and 2-electron systems

 Jianwei Sun,1John P. Perdew,1,2Zenghui Yang,1and Haowei Peng1 

1Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA

 2Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, USA

 (Received 26 March 2016; accepted 6 May 2016; published online 17 May 2016)

 

 The uniform electron gas and the hydrogen atom play fundamental roles in condensed matter physicsand quantum chemistry. The former has an infinite number of electrons uniformly distributed overthe neutralizing positively charged background, and the latter only one electron bound to the proton.The uniform electron gas was used to derive the local spin density approximation to the exchange-correlation functional that undergirds the development of the Kohn-Sham density functional theory.We show here that the ground-state exchange-correlation energies of the hydrogen atom and manyother 1- and 2-electron systems are modeled surprisingly well by a different local spin densityapproximation (LSDA0). LSDA0 is constructed to satisfy exact constraints but agrees surprisinglywell with the exact results for a uniform two-electron density in a finite, curved three-dimensionalspace. We also apply LSDA0 to excited or noded 1-electron densities, where it works less well.Furthermore, we show that the localization of the exact exchange hole for a 1- or 2-electron groundstate can be measured by the ratio of the exact exchange energy to its optimal lower bound.

 

 https://www.osti.gov/pages/servlets/purl/1471104