Loos, Pierre-FrancoisGill, Peter2015-12-100009-2614http://hdl.handle.net/1885/60823We review our recent progress in the determination of the high-density correlation energy Ec in two-electron systems. Several two-electron systems are considered, such as the well known helium-like ions (helium), and the Hooke's law atom (hookium). We also present results regarding two electrons on the surface of a sphere (spherium), and two electrons trapped in a spherical box (ballium). We also show that, in the large-dimension limit, the high-density correlation energy of two opposite-spin electrons interacting via a Coulomb potential is given by Ec∼-1/(8D2) for any radial external potential V(r), where D is the dimensionality of the space. This result explains the similarity of Ec in the previous two-electron systems for D=3.Keywords: Coulomb potential; External potential; Helium-like ion; High-density; Hooke's Law; Recent progress; Spin electrons; Two-electron systems; Electric fields; Helium; Spheres; Electrons201010.1016/j.cplett.2010.09.0192016-02-24