Electron gas, 3D sc cell, N = 54, rs = 4, unpolarized

Record

-0.0774134 E/N (Ha)

mCCD (mosaics only (a self-consistent Brueckner MP2); extrapolated: 1/M → 0 (complete basis))

10.1063/1.4867783 · lowest unflagged energy published, an approximate method, the only kind published here (rules §6)

The Hamiltonian

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

Homogeneous electron gas in 3D: N_↑ = 27, N_↓ = 27 in a periodic sc cell at r_s = 4 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: 54
boundary: periodic
N_up: 27
N_dn: 27
rs: 4
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.

Approximate methods (no bound) (1)

Methods built on a fixed approximation that converges to that approximation, not to the exact energy: RPA, finite-order perturbation theory, coupled cluster restricted to some of its terms. Their error has no known sign, so they are listed but rank only where nothing else is published (rules §4).

E/N (Ha)	distance to record	σ	Var(E)	V-score	method	source	year
-0.0774134record	0	n/a	n/a	n/a	mCCD (mosaics only (a self-consistent Brueckner MP2); extrapolated: 1/M → 0 (complete basis)) peer reviewed	10.1063/1.4867783	n/a

How these numbers were read

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

-0.0774134 — mCCD (mosaics only (a self-consistent Brueckner MP2);...

Checked 2026-10-19 · source text of arXiv:1310.6806 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 = -1.098

Table II, rs=4.0, column mCCD; sources/1310.6806.txt line 464; printed in Ha, total; printed correlation energy -1.098, E = E_HF + E_c with E_HF = -0.0570800676622 Ha per electron (QMBL, checks/heg-hf/hf.mjs); version read: arXiv text in sources/; journal copy not read | Sec. II (txt line 64-81): HF eigenvalues with the zero-momentum integral given by 'vM, the Madelung constant ... defined uniquely for a cell geometry and box length, and here we calculate it to be vM L ~ 2.8372'. No Ewald-sum statement beyond that. The paper prints correlation energies only, which do not depend on the Madelung term, and no Hartree-Fock energy.

Coverage

No row here carries a publication year.

This instance as data

JSON · source file on GitHub · add a result · open an issue about this instance