Correlation energy of two electrons in a ball

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We study the ground-state correlation energy E c of two electrons of opposite spin confined within a D-dimensional ball (D ≥ 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 c⁽⁰⁾ = ᵣ → ₀ for various values of D, we test our recent conjecture [J. Chem. Phys. 131 (2009) 241101] that, in the large-D limit, E c⁽⁰⁾ -δ²/8 for any spherically-symmetric confining external potential, where δ=1/(D-1).