Pith Number

pith:JFXJPGQH

pith:2026:JFXJPGQHYDV7KWHZ3LE5EKFUPL

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A density-functional perspective on force fields

Nan Sheng

Exact force fields are induced by pulling back the DFT external-potential energy functional along the nuclear-to-Coulomb-potential map.

arxiv:2604.25215 v3 · 2026-04-28 · physics.chem-ph · math-ph · math.MP

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Claims

C1strongest claim

exact force fields are variationally induced by DFT: the Born-Oppenheimer potential-energy surface is the pullback of the external-potential energy functional along the map from nuclear configurations to Coulomb potentials.

C2weakest assumption

The Lieb formulation of DFT is valid and the map from nuclear configurations to external Coulomb potentials is sufficiently regular for the pullback and functional derivatives to be well-defined.

C3one line summary

The Born-Oppenheimer PES is the pullback of the DFT energy functional from external potentials to nuclear configurations, placing force fields, DFT, and response theory in a single derivative hierarchy.

Cited by

1 paper in Pith

Full-State and Reduced-Moment Encodings: A Representation-Level View of Equilibrium Quantum Many-Body Theory

Receipt and verification

First computed	2026-06-09T02:07:27.477767Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

496e979a07c0ebf558f9dac9d228b47ade762a60ef46996d9911c4c716da656f

Aliases

arxiv: 2604.25215 · arxiv_version: 2604.25215v3 · doi: 10.48550/arxiv.2604.25215 · pith_short_12: JFXJPGQHYDV7 · pith_short_16: JFXJPGQHYDV7KWHZ · pith_short_8: JFXJPGQH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JFXJPGQHYDV7KWHZ3LE5EKFUPL \
  | 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: 496e979a07c0ebf558f9dac9d228b47ade762a60ef46996d9911c4c716da656f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05c11f3e0e309372aa637b440f19fffb6cafece54d86abd4c0087ba7d33b728e",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.chem-ph",
    "submitted_at": "2026-04-28T04:37:43Z",
    "title_canon_sha256": "b5be1db611052d7e5bc9e34f072f8250660b2526e71ca5e202d36336fd470caf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.25215",
    "kind": "arxiv",
    "version": 3
  }
}