Correlation energy of two electrons in a ball

Details Correlation energy of two electrons in a ball Correlation energy of two electrons in a ball

2010-04-07

arxiv.org/abs/1004.1200v3

J. Chem. Phys. 132, 234111 (2010)

Physics

Condensed Matter

Other Condensed Matter

6 pages, 2 figures

Scientific paper

10.1063/1.3455706

We study the ground-state correlation energy $E_{\rm c}$ of two electrons of opposite spin confined within a $D$-dimensional ball ($D \ge 2$) of radius $R$. In the high-density regime, we report accurate results for the exact and restricted Hartree-Fock energy, using a Hylleraas-type expansion for the former and a simple polynomial basis set for the latter. By investigating the exact limiting correlation energy $E_{\rm c}^{(0)} = \lim_{R \to 0} \Ec$ for various values of $D$, we test our recent conjecture [J. Chem. Phys. {\bf 131} (2009) 241101] that, in the large-$D$ limit, $E_{\rm c}^{(0)} \sim -\delta^2/8$ for any spherically-symmetric confining external potential, where $\delta=1/(D-1)$.

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