TY - JOUR
T1 - Correlation energy of two electrons in a ball
AU - Loos, Pierre Fraņois
AU - Gill, Peter M.W.
PY - 2010/6/21
Y1 - 2010/6/21
N2 - We study the ground-state correlation energy Ec 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 Ec(0) = limR→0 Ec for various values of D, we test our recent conjecture [P.-F. Loos and P. M. W. Gill, J. Chem. Phys. 131, 241101 (2009)] that in the large- D limit, Ec(0) ∼- δ2 /8 for any spherically symmetric confining external potential, where δ=1/ (D-1).
AB - We study the ground-state correlation energy Ec 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 Ec(0) = limR→0 Ec for various values of D, we test our recent conjecture [P.-F. Loos and P. M. W. Gill, J. Chem. Phys. 131, 241101 (2009)] that in the large- D limit, Ec(0) ∼- δ2 /8 for any spherically symmetric confining external potential, where δ=1/ (D-1).
UR - http://www.scopus.com/inward/record.url?scp=77953830818&partnerID=8YFLogxK
U2 - 10.1063/1.3455706
DO - 10.1063/1.3455706
M3 - Article
SN - 0021-9606
VL - 132
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
IS - 23
M1 - 234111
ER -