{"paper":{"title":"DeepHartree: A Poisson-Coupled Neural Field for One-Shot Density Functional Theory","license":"http://creativecommons.org/licenses/by/4.0/","headline":"DeepHartree couples an equivariant neural network to the Poisson equation to predict consistent electron densities and Hartree potentials at near-linear cost.","cross_cats":[],"primary_cat":"physics.chem-ph","authors_text":"Chao Qian, Jiankun Wu, Jinming Fan, Shaodong Zhou","submitted_at":"2026-04-24T15:48:38Z","abstract_excerpt":"Linear-combination-of-atomic-orbital (LCAO) density functional theory (DFT) incurs steep costs when it constructs Coulomb terms and iterates the self-consistent field (SCF) equations. Matrix-learning approaches can bypass parts of this workflow, but their outputs inherit the dimensions and conventions of a fixed orbital basis. We introduce DeepHartree, a Poisson-coupled neural field that connects continuous real-space prediction to LCAO electronic structure. An E(3)-equivariant network predicts the Hartree potential, and the Poisson equation converts this potential into electron density. Atom-"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"By coupling an E(3)-equivariant neural network with the Poisson equation through automatic differentiation and mitigating nuclear singularities via delta-learning, DeepHartree simultaneously predicts mutually consistent real-space electron densities and Hartree potentials. This resolves the Coulomb bottleneck by substituting O(N^4) analytical integrals with GPU-accelerated, near-linear O(N) numerical inference.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That a model trained solely on small molecules will maintain physical consistency and achieve robust zero-shot transferability to systems up to 168 atoms across diverse basis sets, functionals, and properties without post-hoc adjustments that compromise the claimed rigor.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"DeepHartree is a Poisson-coupled E(3)-equivariant neural field that predicts consistent real-space densities and Hartree potentials to accelerate LCAO DFT with near-linear scaling and zero-shot transfer to larger systems.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"DeepHartree couples an equivariant neural network to the Poisson equation to predict consistent electron densities and Hartree potentials at near-linear cost.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9f7c730f9ec7d3549cf9c99704946b57df75be0eccd9be3ca47ef78fd64ac039"},"source":{"id":"2604.22669","kind":"arxiv","version":4},"verdict":{"id":"c2556156-a135-42f3-9dfb-bf393febd13b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T02:47:57.045542Z","strongest_claim":"By coupling an E(3)-equivariant neural network with the Poisson equation through automatic differentiation and mitigating nuclear singularities via delta-learning, DeepHartree simultaneously predicts mutually consistent real-space electron densities and Hartree potentials. This resolves the Coulomb bottleneck by substituting O(N^4) analytical integrals with GPU-accelerated, near-linear O(N) numerical inference.","one_line_summary":"DeepHartree is a Poisson-coupled E(3)-equivariant neural field that predicts consistent real-space densities and Hartree potentials to accelerate LCAO DFT with near-linear scaling and zero-shot transfer to larger systems.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That a model trained solely on small molecules will maintain physical consistency and achieve robust zero-shot transferability to systems up to 168 atoms across diverse basis sets, functionals, and properties without post-hoc adjustments that compromise the claimed rigor.","pith_extraction_headline":"DeepHartree couples an equivariant neural network to the Poisson equation to predict consistent electron densities and Hartree potentials at near-linear cost."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.22669/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T10:35:58.427513Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:45:36.402393Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"63f359da214eb2caf96d78574c09fb703f1eee1b149a744fe1c468007e73ee6f"},"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"}