{"paper":{"title":"Correlation energy of two electrons in a ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","physics.chem-ph","physics.comp-ph"],"primary_cat":"cond-mat.other","authors_text":"Peter M. W. Gill, Pierre-Fran\\c{c}ois Loos","submitted_at":"2010-04-07T22:15:44Z","abstract_excerpt":"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)} \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1200","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}