Pith Number

pith:VOLYUDET

pith:2026:VOLYUDETDPT4JDZE6OVEWGN3BO

not attested not anchored not stored refs pending

DeepHartree: A Poisson-Coupled Neural Field for One-Shot Density Functional Theory

Chao Qian, Jiankun Wu, Jinming Fan, Shaodong Zhou

DeepHartree couples an equivariant neural network to the Poisson equation to predict consistent electron densities and Hartree potentials at near-linear cost.

arxiv:2604.22669 v4 · 2026-04-24 · physics.chem-ph

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\pithnumber{VOLYUDETDPT4JDZE6OVEWGN3BO}

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4 Citations open

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

Receipt and verification

First computed	2026-07-29T00:24:38.205414Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab978a0c931be7c48f24f3aa4b19bb0bbfe0aebedb6a912d6b61997e6f891357

Aliases

arxiv: 2604.22669 · arxiv_version: 2604.22669v4 · doi: 10.48550/arxiv.2604.22669 · pith_short_12: VOLYUDETDPT4 · pith_short_16: VOLYUDETDPT4JDZE · pith_short_8: VOLYUDET

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VOLYUDETDPT4JDZE6OVEWGN3BO \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ab978a0c931be7c48f24f3aa4b19bb0bbfe0aebedb6a912d6b61997e6f891357

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06222846f311a46e8d215f502b781d6300e316c293ff2dd162cda0eff2ac91ba",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.chem-ph",
    "submitted_at": "2026-04-24T15:48:38Z",
    "title_canon_sha256": "bf07e847ebce8cea6995517b2b468b0623e6ea8a2d46841a2947e97037a1c499"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.22669",
    "kind": "arxiv",
    "version": 4
  }
}