{"paper":{"title":"Practical and Rigorous reduction of the Many-Electron Quantum-Mechanical Coulomb Problem to O(N^(2/3) Storage","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"physics.chem-ph","authors_text":"Mark R. Pederson","submitted_at":"2015-02-27T20:23:32Z","abstract_excerpt":"It is tacitly accepted that, for practical basis sets consisting of N functions, solution of the two-electron Coulomb problem in quantum mechanics requires storage of O(N^4) integrals in the small N limit. For localized functions, in the large N limit, or for planewaves, due to closure, the storage can be reduced to O(N^2) integrals. Here, it is shown that the storage can be further reduced to O(N^{2/3}) for separable basis functions. A practical algorithm, that uses standard one-dimensional Gaussian-quadrature sums, is demonstrated. The resulting algorithm allows for the simultaneous storage,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.08043","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"}