Pith Number

pith:EV2ZDMSM

pith:2026:EV2ZDMSMGYOBPJJDRVZFDYTZCG

not attested not anchored not stored refs resolved

Explicitly Correlated Gaussian Basis Approach to Periodic Systems

Kalman Varga

Closed-form expressions for matrix elements are derived for variational electronic structure calculations of periodic solids using explicitly correlated Gaussian bases.

arxiv:2605.12781 v1 · 2026-05-12 · quant-ph · physics.chem-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EV2ZDMSMGYOBPJJDRVZFDYTZCG}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

Closed-form expressions for all matrix elements required for variational calculation of the electronic structure of periodic solids have been derived using a basis of explicitly correlated Gaussians (ECGs).

C2weakest assumption

The generalized unfolding theorem correctly reduces the double lattice sum to a single sum for overlap, kinetic energy, and Coulomb operators in the periodic ECG basis.

C3one line summary

Derives closed-form matrix elements for explicitly correlated Gaussian basis in periodic systems and validates on infinite 1D hydrogen chain.

References

161 extracted · 161 resolved · 0 Pith anchors

[1] Ewald decomposition (Secs. II H–III). The pe- riodic 1 /r potential is split into a short-range complementary-error-function part evaluated in real space and a long-range smooth part evaluated in reci

[2] Direct neutral-cell sum (Sec. III E). When the sim- ulation cell is charge-neutral the lattice sum over 1/r converges absolutely when shells are grouped by charge neutrality. Each matrix element re- d

[3] Dirac delta convolution (Sec. III F). The 1 /r ker- nel is the convolution of a Dirac delta density with the Green’s function of the Laplacian. The matrix element of δ(3)(ri − rj) gives the pair-conta

[4] Electron–electron reciprocal-space term The electron–electron reciprocal-space matrix element is (see Appendix D V (ee,G) kl = 4π Ω Skl n−1X i=1 nX j=i+1 X G̸=0 e−G2/4κ2 G2 × X M ωM e iG·PT ij¯rM−σ2 i

[5] Electron–electron real-space term For the real-space sum we define the t-augmented non- linear parameter matrix and its determinant ratio, A(t,ij) kl = Akl + t2(ei − ej)(ei − ej)T , (46) det A(t,ij) k

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:13.141363Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

257591b24c361c17a5238d7251e279119ffa62274e1b0b14976c5bad0797946f

Aliases

arxiv: 2605.12781 · arxiv_version: 2605.12781v1 · doi: 10.48550/arxiv.2605.12781 · pith_short_12: EV2ZDMSMGYOB · pith_short_16: EV2ZDMSMGYOBPJJD · pith_short_8: EV2ZDMSM

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/EV2ZDMSMGYOBPJJDRVZFDYTZCG \
  | 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: 257591b24c361c17a5238d7251e279119ffa62274e1b0b14976c5bad0797946f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e356e280d07a597132d76df024268cae20b096c123d5a78795e5bddb22417b6a",
    "cross_cats_sorted": [
      "physics.chem-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-12T21:50:41Z",
    "title_canon_sha256": "ae8d953553104754054e13cdf281c91689d02212ff70331143d0ac446b3fa530"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12781",
    "kind": "arxiv",
    "version": 1
  }
}