All instances / Electron gas, 3D
Electron gas, 3D fcc cell, N = 178, rs = 2, unpolarized
Record
0.00892(2)
E/N (Ha)
Fixed-node DMC (Slater-Jastrow wave function, Ewald interaction; DMC time step 0.003 a.u., target population 800, expansion orders Nu=Neta=8)
10.1088/0953-8984/22/6/065501 · 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↑ = 89, N↓ = 89 in a periodic fcc cell at rs = 2 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
- fcc
- electrons
- 178
- boundary
- periodic
- N_up
- 89
- N_dn
- 89
- 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.
How these numbers were read
Where each number below was read, and how it was checked.
0.00892(2) — Fixed-node DMC (Slater-Jastrow wave function, Ewald...
Checked 2026-10-19 · source text of arXiv:1001.5002 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. 0.00892(2)
Table 1, N=178, column 'SJ DMC Ewald'; sources/1001.5002.txt line 275; printed in Ha per electron; version read: arXiv text in sources/; journal copy not read | No Hartree-Fock energy is printed. The text states the interaction used: 'Coulomb finite-size effects were reduced by using the MPC scheme, where the Hartree energy is calculated with the Ewald interaction while the xc energy is calculated using 1/r within the minimum image convention' (txt lines 234-238). The MPC columns are therefore NOT the Ewald Hamiltonian of RULES 12.2. The 'Ewald' column of Table 1 (SJ-DMC) is the usual Ewald interaction (txt line 264 and text lines 'using the usual 1/r Ewald interaction'). The Madelung term is not mentioned. Indirect check with QMBL hf.mjs (3 fcc N/2 N
Coverage
No row here carries a publication year.