{"paper":{"title":"Linear scaling computation of the Fock matrix. VIII. Periodic boundaries for exact exchange at the $\\Gamma$-point","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.mtrl-sci","authors_text":"C. J. Tymczak, Eric Schwegler, Matt Challacombe, Val\\'ery T. Weber","submitted_at":"2004-05-21T18:02:51Z","abstract_excerpt":"A translationally invariant formulation of the Hartree-Fock (HF) $\\Gamma$-point approximation is presented. This formulation is achieved through introduction of the Minimum Image Convention (MIC) at the level of primitive two-electron integrals, and implemented in a periodic version of the ONX algorithm [J. Chem. Phys, {\\bf 106} 9708 (1997)] for linear scaling computation of the exchange matrix. Convergence of the HF-MIC $\\Gamma$-point model to the HF ${\\bf k}$-space limit is demonstrated for fully periodic magnesium oxide, ice and diamond. Computation of the diamond lattice constant using the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0405500","kind":"arxiv","version":1},"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"}