Pith Number

pith:NJQYNSPH

pith:2023:NJQYNSPHYPAOLCKWQFWP6JS7NN

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Four-component relativistic calculations in a multiwavelet basis with improved convergence

Christian Tantardini, Jacopo Masotti, Luca Frediani, Roberto Di Remigio Eik{\aa}s

Squaring the Dirac operator turns the four-component problem into a convex one that multiwavelets can solve to controlled precision.

arxiv:2311.03290 v6 · 2023-11-06 · physics.chem-ph

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\pithnumber{NJQYNSPHYPAOLCKWQFWP6JS7NN}

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4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The squared Dirac operator, combined with a multiwavelet basis, yields a convex four-component relativistic eigenvalue problem whose negative-energy solutions are folded onto the positive side, and this scheme can be implemented and validated against analytic and GRASP references for one- and two-electron systems with increasing Z.

C2weakest assumption

That folding the negative-energy spectrum via D̂² genuinely eliminates variational collapse and spurious solutions in practice, rather than merely re-encoding them at higher energies that can still contaminate excited states or two-electron correlations. Also implicit: that the multiwavelet adaptive refinement near the nuclear cusp resolves the squared operator (which involves derivatives of the potential, e.g. ∇·E-type terms producing delta-function-like contributions at point nuclei) without introducing controlled but quantitatively significant artifacts. Neither of these can be checked from the abstract alone.

C3one line summary

A multiwavelet implementation of the squared Dirac equation gives convex, bounded-below 4-component relativistic calculations validated for one- and two-electron atoms against analytic and GRASP references.

Receipt and verification

First computed	2026-06-25T01:18:33.456079Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a6186c9e7c3c0e58956816cff265f6b7aa75373815ccdca7b76020269f553e1

Aliases

arxiv: 2311.03290 · arxiv_version: 2311.03290v6 · doi: 10.48550/arxiv.2311.03290 · pith_short_12: NJQYNSPHYPAO · pith_short_16: NJQYNSPHYPAOLCKW · pith_short_8: NJQYNSPH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/NJQYNSPHYPAOLCKWQFWP6JS7NN \
  | 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: 6a6186c9e7c3c0e58956816cff265f6b7aa75373815ccdca7b76020269f553e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7582ac46e7748fa638cc11417e4dcc7f2d52ee16d670d67facd849eb698a14b1",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "physics.chem-ph",
    "submitted_at": "2023-11-06T17:30:50Z",
    "title_canon_sha256": "1fcd1eca053c66de2869db174a3e73808daa68493292019ea3f8eb8664e1abc9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2311.03290",
    "kind": "arxiv",
    "version": 6
  }
}