{"paper":{"title":"A differential derivation of the Obara-Saika relation for Gaussian electron repulsion integrals","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"physics.chem-ph","authors_text":"Charles C. Forgy, David A. Mazziotti","submitted_at":"2026-06-30T19:42:12Z","abstract_excerpt":"The Obara-Saika (OS) method is one of the most widely used techniques in quantum chemistry for evaluating electron repulsion integrals (ERIs) via a set of recurrence relations that build higher angular momentum integrals from lower-order ones. The original derivation by Obara and Saika proceeded by directly relating integrals of differing angular momentum. In this work, we present a compact novel derivation of the OS vertical recurrence relation based solely on differential relations between Gaussian basis functions, expanding on a method suggested in earlier work. By explicitly deriving the r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00102","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.00102/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}