Correlation energy of two electrons in the high-density limit

Details Correlation energy of two electrons in the high-density limit Correlation energy of two electrons in the high-density limit

2010-02-17

arxiv.org/abs/1002.3402v1

J. Chem. Phys. 131, 241101 (2009)

Physics

Condensed Matter

Other Condensed Matter

4 pages, 0 figure

Scientific paper

10.1063/1.3275519

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 $\delta = 1/(D-1)$.

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