Record
0.57290(3)
E/N (Ha)
Fixed-node DMC (Slater-Jastrow (SJ) trial function, Jastrow factor not stated for this table (J1 Eq. 36 or J2 Eq. 39; conclusions, line 1543, say the pseudo)
10.1140/epjb/e2013-40204-3 · lowest unflagged energy published, a projected estimate
(rules §6)
The Hamiltonian
H = −½ ∑i ∇i2 + ∑i<j vE(ri − rj) + Nξ/2
Homogeneous electron gas in 3D: N↑ = 33, N↓ = 33 in a periodic sc cell at rs = 1 bohr, Γ point. vE 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
- 66
- boundary
- periodic
- N_up
- 33
- N_dn
- 33
- rs
- 1
- twist
- Gamma
- energies
- 3
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.
Projected or fixed-node estimates (2)
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.
How these numbers were read
Where each number below was read, and how it was checked.
0.57290(3) — Fixed-node DMC (Slater-Jastrow (SJ) trial function, Jastrow...
Checked 2026-10-19 · source text of arXiv:1304.7298 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. 1.14579(7)
Table II, row rs = 1, column a; sources/1304.7298.txt line 984; printed in Ry per electron; version read: arXiv text in sources/; journal copy not read | Eq. (11) line 277: 'V = sum_{i<j} e^2 v_I(r_ij) + sum_i e^2 v_M', v_M = 1/2 lim_{r->0}[v_I(r) - v(r)] 'a Madelung constant ... interaction of a particle with its own images'; Ewald sums in Sec. III after Natoli and Ceperley (ref 34), background included (Eq. 8, 'uniform background of the same density but opposite charge'). Energies 'given in Rydbergs' (line 196-197). No Hartree-Fock energy is printed anywhere, so the convention cannot be fixed from the paper; the reader's check (see row notes) gives implied E-E_HF of -0.033 Ry (rs 10), -0.049 Ry (rs 5), -0.072 Ry (rs 2), -0.089 Ry (rs 1) per e
0.57305(3) — Fixed-node DMC (SJ trial function; time step tau = 0.01...
Checked 2026-10-19 · source text of arXiv:1304.7298 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. 1.14609(6)
Table III, row rs = 1, column a; sources/1304.7298.txt line 1001; printed in Ry per electron; version read: arXiv text in sources/; journal copy not read | Eq. (11) line 277: 'V = sum_{i<j} e^2 v_I(r_ij) + sum_i e^2 v_M', v_M = 1/2 lim_{r->0}[v_I(r) - v(r)] 'a Madelung constant ... interaction of a particle with its own images'; Ewald sums in Sec. III after Natoli and Ceperley (ref 34), background included (Eq. 8, 'uniform background of the same density but opposite charge'). Energies 'given in Rydbergs' (line 196-197). No Hartree-Fock energy is printed anywhere, so the convention cannot be fixed from the paper; the reader's check (see row notes) gives implied E-E_HF of -0.033 Ry (rs 10), -0.049 Ry (rs 5), -0.072 Ry (rs 2), -0.089 Ry (rs 1) per e
0.5748(3) — 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. 1.1496(5)
Table III, row N=66, rs=1.0; sources/cond-mat-9803092.txt line 657; 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.