Electron gas, 3D sc cell, N = 246, rs = 20, unpolarized

Record

-0.031375(5) E/N (Ha)

Slater-Jastrow

10.1103/PhysRevB.58.6800 · lowest unflagged energy published, a strict variational 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_↑ = 123, N_↓ = 123 in a periodic sc cell at r_s = 20 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: 246
boundary: periodic
N_up: 123
N_dn: 123
rs: 20
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.

Strict variational upper bounds (1)

Where the instance is not solved, the record is the lowest unflagged energy in this group or among the projected and extrapolated ones, with or without an error bar; where it is solved, the exact energy is the record and the lowest of these is the closest challenger.

E/N (Ha)	distance to record	σ	Var(E)	V-score	method	source	year
-0.031375record	0	5.0e-6	n/a	n/a	Slater-Jastrow peer reviewed	10.1103/PhysRevB.58.6800	1998

How these numbers were read

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

-0.031375(5) — Slater-Jastrow

Checked 2026-10-17 · source text of arXiv:cond-mat/9803092 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. -0.06275(1)

Table III, row N=246, rs=20.0; sources/cond-mat-9803092.txt line 660; printed in Ry per electron; version read: arXiv text (sources/cond-mat-9803092.txt), Tables II and III; APS copy not read | Ry per electron (converted × 1/2), N electrons in a cube with periodic boundary conditions (simple cubic). Checked against arXiv:0801.0518 on the same instance: the fixed-node DMC energy with backflow nodes, 1.0601(2) Ry = 0.53005 Ha at N = 54, rs = 1, agrees with its 0.52989(1) Ha, 0.0376 Ha below QMBL's HF energy 0.569245.

Coverage

Newest published number here: 1998.

This instance as data

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