All instances / Hydrogen chain
Hydrogen chain H20 chain, open, R = 3.6, STO-6G
Best values
(rules §6)
| best projected |
-0.481978(1) |
FCIQMC10.1063/5.0005754 · the lowest unflagged projected energy, a projected estimate, which depends on its node or constraint |
Energies as E/N (Ha). Classes are different claims and are not ranked against each other.
The Hamiltonian
H = −½ ∑i ∇i2 − ∑i,I 1/|ri − RI| + ∑i<j 1/|ri − rj| + ∑I<J 1/|RI − RJ|
Hydrogen chain: 20 protons equally spaced on a line, spacing R = 3.6 bohr, open (a finite molecule); N↑ = 10, N↓ = 10. Projected onto the STO-6G basis set; full CI in it is this instance's exact energy. Hartree atomic units, nuclear repulsion included; the energy per atom is E/N.
- geometry
- chain
- atoms
- 20
- boundary
- open
- N_up
- 10
- N_dn
- 10
- R
- 3.6
- basis
- STO-6G
- energies
- 1
Stored as a total energy in Hartree, nuclear repulsion included (rules §13); quoted here as
E/N (Ha), the energy per atom
(how the conversion works).
Every published energy
Grouped by what the number is. The exact energy comes first where there is one; in every other group the lowest unflagged energy is its best value, and each row's distance is to that best (rules §6).
Projected or fixed-node estimates (1)
Variational only within a constraint: fixed-node, constrained-path, GFMC on a trial state. Each depends on its node or constraint, so two of them are not cleanly comparable to each other or to strict bounds.
How these numbers were read
Where each number below was read, and how it was checked.
-0.481978(1), FCIQMC
Checked 2026-10-20 · source text of arXiv:2006.14956 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading (Sonnet reader)
Reported as. -0.481978(1) Ha per atom
Table II; sources/2006.14956.txt line 1480; version read: arXiv text; journal copy not reached (publisher returned HTTP 403 or a login page, 2026-10-21); read again when reachable (RULES.md §8) | Table II caption line 1471: 'energy per site E/L'; columns '[Eh]'; 'r = 3.6 a0' (line 1473); 'STO-6G' (line 1471) | Boundary not stated; linear chain of Motta et al. taken as open. Per-atom value, total = N x value by loader. Nuclear repulsion not stated (Eref per site -0.48 at 3.6 bohr suggests included). | reader confidence medium
Coverage
Newest published number here: 2020.