{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"2027ce2ce13512d002e7112166b007d8f9a2cb807d7a6b55af8cba036105ad84","created":"2026-10-03T07:17:58Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"c6291c7bebc386c7724edb3d3838842163360d6b5ca438efb5b9c043986d63b9","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"identification","assisted_by":[],"external_id":"chem.dft-functionals.flat-plane-functional","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"The exact energy changes in straight lines when a fraction of an electron is added or when spin is fractionally shared, and approximate functionals bend those lines. Bending one way spreads electrons out too much; bending the other way mistreats stretched bonds.","posed_since":"","precise":"Construct an exchange-correlation approximation, at cost no higher than a global hybrid, whose energy $E(N, S_z)$ is piecewise linear in fractional electron number N (no delocalization error) and constant in fractional spin at fixed N (no static correlation error), as tested on H2+ and H2 dissociation, fractional-charge atoms and the stretched-bond benchmark sets, while keeping main-group thermochemistry errors below 3 kcal/mol. An answer is such a functional, or a proof that no functional of a given class can satisfy both conditions.","problem_ref":null,"references":"","settled_by":"A functional passing fractional-charge, fractional-spin and standard thermochemistry benchmarks simultaneously, or a no-go theorem for a defined functional class.","status_note":"In 2021 the DM21 learned functional, trained on fractional-charge and fractional-spin data, reduced both errors for small systems; no functional satisfies both conditions in general.","title":"A practical functional that obeys the flat-plane condition","topic_ref":"3c4f63964447b45aecf4c4997f101268b15cc64d8f6c4f7f7f8c32e958440823"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"a754ae190f8564c40dd02646a107d8f5d95bab993397c1b6076b67fb059fbeb2","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"058243729be7fe3e7fe4de2b4ef1f4204e6295f41902fa77e9c7d4d1b9d5abdf","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"1OqA3Q7sIS1BZwmGdHEWQRMhJRNO8xIARzU2f8zwdPDVqmwD_FwN9KlEDVuERvefJOAGTikLkI9lO-zImbU5Aw"},"schema":"pubphys.envelope/1"},"record_hash":"a754ae190f8564c40dd02646a107d8f5d95bab993397c1b6076b67fb059fbeb2","leaf_index":858}