{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"808941dcbb2d4363d1705a1e2e040716a5b57a71c9efa4396423170f8fd29e1d","created":"2026-10-03T07:17:58Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"5212fb5dad793d7a34ca0b7013c1bacfb235959fb825e184fc17bd8b3f773164","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"chem.xc-functional-accuracy.self-interaction-free-functional","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Common approximations let an electron feel a push from its own charge, which spreads electrons out too much and spoils predictions of reaction barriers and charge transfer. Corrections that remove this self-repulsion usually make ordinary bond energies worse, and no approximation yet fixes the first without hurting the second.","posed_since":"1981","precise":"Construct an exchange-correlation functional $E_{\\mathrm{xc}}[n]$ that is exact for every one-electron density ($E_{\\mathrm{xc}}[n_1] = -J[n_1]$, with J the classical Coulomb self-energy), gives total energies $E(N)$ piecewise linear in fractional electron number N between integers, and retains main-group thermochemistry and barrier-height accuracy at least equal to the best hybrid functionals on a broad benchmark such as GMTKN55 (a set of 55 standard chemistry test databases). An answer is an explicit functional with these properties demonstrated numerically, or a proof that no functional of a given class (semilocal, hybrid, or orbital-dependent of fixed form) can satisfy them together.","problem_ref":null,"references":"","settled_by":"An explicit functional passing the one-electron, fractional-charge linearity and benchmark-accuracy tests together, or a no-go theorem for a stated functional class.","status_note":"Perdew-Zunger-type self-interaction corrections fix the one-electron limit but degrade equilibrium thermochemistry; the machine-learned DM21 functional (Kirkpatrick et al., Science 2021, https://doi.org/10.1126/science.abj6511) imposes fractional-charge and fractional-spin constraints approximately while keeping hybrid-level accuracy, but it is not exact for one-electron densities and its transferability was disputed (Gerasimov et al., Science 2022 comment, https://doi.org/10.1126/science.abq3385).","title":"A density functional free of self-interaction that keeps thermochemical 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