Electron gas, 3D sc cell, N = 38, rs = 2, unpolarized

Record

-0.01422(5) E/N (Ha)

FCIQMC (initiator (n_add = 3), run at 922 spin orbitals; extrapolated: 1/M → 0 (complete basis))

10.1063/1.4720076 · lowest unflagged energy published, an extrapolation, not a bound (rules §6)

The Hamiltonian

H = −½ ∑_i ∇_i² + ∑_i<j v_E(r_i − r_j) + Nξ/2

Homogeneous electron gas in 3D: N_↑ = 19, N_↓ = 19 in a periodic sc cell at r_s = 2 bohr, Γ point. v_E is the Ewald-summed Coulomb interaction with a uniform neutralizing background, ξ the Madelung term. Hartree atomic units; the energy per electron is E/N.

cell: sc
electrons: 38
boundary: periodic
N_up: 19
N_dn: 19
rs: 2
twist: Gamma
energies: 1

Stored as a total energy in Hartree (rules §12); quoted here as E/N (Ha), the energy per electron (how the conversion works).

Every published energy

Grouped by what the number is. Where the instance is not solved, the lowest unflagged energy of any group is the record.

Extrapolations (1)

Zero-variance, bond-dimension or Trotter-error extrapolations. Not a bound: no ansatz reached the number itself. Like any unflagged energy, one holds the record where it is the lowest on an unsolved instance.

E/N (Ha)	distance to record	σ	Var(E)	V-score	method	source	year
-0.01422record	0	5.3e-5	n/a	n/a	FCIQMC (initiator (n_add = 3), run at 922 spin orbitals; extrapolated: 1/M → 0 (complete basis)) peer reviewed	10.1063/1.4720076	2012

How these numbers were read

Where each number below was read, and how it was checked.

-0.01422(5) — FCIQMC (initiator (n_add = 3), run at 922 spin orbitals;...

Checked 2026-10-19 · source text of arXiv:1201.4691 read locally (arXiv HTML or pypdf layout text); value copied from the harvested cell and the text, no LLM transcription of numbers; single reading

Reported as. E_c = -1.225(2) (total, Ha)

Table II, rs=2.0, N=38, column Ecorr (a.u.); sources/1201.4691.txt line 21005; printed correlation energy -1.225(2) Ha for 38 electrons; E = E_HF + E_c with E_HF = 0.0180198722521 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text, Tables I and II; AIP copy not read | Correlation energy E_c = E - E_HF, total for the cell, Hartree; 14, 38 or 54 electrons in a simple cubic cell at the Gamma point, a closed shell, so E_HF is the unique plane-wave determinant's. Stored E = E_HF + E_c with E_HF from QMBL (checks/heg-hf/hf.mjs; RULES.md 12.3, 2026-10-19).

Coverage

Newest published number here: 2012.

This instance as data

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