Electron gas, 3D sc cell, N = 114, rs = 2, unpolarized

Record

0.00487(6) E/N (Ha)

ph-AFQMC (RHF trial, time step 0.005 a.u., 2880 walkers; basis M=2109)

10.1063/1.5109572 · lowest unflagged energy published, a projected estimate (rules §6)

The Hamiltonian

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

Homogeneous electron gas in 3D: N_↑ = 57, N_↓ = 57 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: 114
boundary: periodic
N_up: 57
N_dn: 57
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.

Projected or fixed-node estimates (1)

Variational only within a constraint: fixed-node, constrained-path, GFMC on a trial state. Node- or constraint-dependent, so not cleanly comparable to each other or to strict bounds. 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
0.00487record	0	6.0e-5	n/a	n/a	ph-AFQMC (RHF trial, time step 0.005 a.u., 2880 walkers; basis M=2109) peer reviewed	10.1063/1.5109572	n/a

How these numbers were read

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

0.00487(6) — ph-AFQMC (RHF trial, time step 0.005 a.u., 2880 walkers;...

Checked 2026-10-19 · source text of arXiv:1905.04361 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. 0.00487(6)

Table VI, rs=2.0; sources/1905.04361.txt line 677; printed in Ha per electron; version read: arXiv text in sources/; journal copy not read | Eq. (19) (txt line 210): H = T + Vee + E_M; txt lines 232-237: 'the Madelung energy E_M is included to account for the self-interaction of the Ewald sum under periodic boundary conditions. For simplicity we use the formula proposed by Schoof and co-workers' E_M ~ -2.837297 (3/4pi)^(1/3) N^(2/3)/rs (Eq. 22, txt line 238-239). So the Madelung term is included, but through the approximate closed form (Ref 76: T. Schoof, S. Groth, J. Vorberger, M. Bonitz, PRL 115, 130402 (2015)), not through a stated Ewald sum. No Hartree-Fock energy is printed. Reader's own check (python, scratch-R8/hf.py, NOT QM

Coverage

No row here carries a publication year.

This instance as data

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