{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"537aa4e2ef49d762532cdf4b8242122d6ab2925748f8fd071959202ed589608a","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["a754ae190f8564c40dd02646a107d8f5d95bab993397c1b6076b67fb059fbeb2","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"fdedd70405f1aef8cd4d387fb95ecb1c4b4cdda1dc0881f9b7349ce53622501c","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":"2","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 $\\mathrm{H_2}$ 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":"a754ae190f8564c40dd02646a107d8f5d95bab993397c1b6076b67fb059fbeb2","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":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"901c6ec71611867d2baaef004d454c51ce4eec8f943a6fc94f042cab564d2e8c","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"bd347014ca33d06f036b820a302ae34c33b7708e98ac718647db72b8e0ddecc6","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"heuFBf1M45x0f7quNW1DqjXBIjpMJ-PVoo9aBDqEPxW0whmmXwfrhsHwVc7ukB1Jn9IsgeSHnekM6kNAuSY1Bw"},"schema":"pubphys.envelope/1"},"record_hash":"901c6ec71611867d2baaef004d454c51ce4eec8f943a6fc94f042cab564d2e8c","leaf_index":2660}