Correlation energy of two electrons in the high-density limit

TL;DR

This paper investigates the high-density-limit correlation energy of two-electron systems across different external potentials and dimensions, revealing a universal behavior as the dimension increases.

Contribution

It demonstrates that the correlation energy depends mainly on the dimension and is nearly independent of the external potential, proposing a universal asymptotic form for large dimensions.

Findings

Correlation energies are similar across different systems in high-density limit.

Dependence of correlation energy on dimension is strong, on potential is weak.

Proposes a universal asymptotic formula for large dimensions.

Abstract

We consider the high-density-limit correlation energy $\Ec$ in $D \ge 2$ dimensions for the $^1S$ ground states of three two-electron systems: helium (in which the electrons move in a Coulombic field), spherium (in which they move on the surface of a sphere), and hookium (in which they move in a quadratic potential). We find that the $\Ec$ values are strikingly similar, depending strongly on $D$ but only weakly on the external potential. We conjecture that, for large $D$, the limiting correlation energy $\Ec \sim -\delta^2/8$ in any confining external potential, where $\delta = 1/(D-1)$.