All instances / Hydrogen chain
Hydrogen chain H12 chain, open, R = 1.51178, STO-3G
Best values
(rules §6)
| best variational |
-0.5268575 |
VQE |
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: 12 protons equally spaced on a line, spacing R = 1.51178 bohr, open (a finite molecule); N↑ = 6, N↓ = 6. Projected onto the STO-3G 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
- 12
- boundary
- open
- N_up
- 6
- N_dn
- 6
- R
- 1.51178
- basis
- STO-3G
- 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).
Strict variational upper bounds (1)
Energies that a variational state reached (VMC, DMRG and MPS at finite bond dimension, PEPS, NQS, VQE). Each is an upper bound on the ground-state energy.
How these numbers were read
Where each number below was read, and how it was checked.
-0.5268575, VQE
Checked 2026-10-20 · source text of arXiv:2303.10825 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. -6,322.29 mHa per total; R = 0.8 Å = 1.51178 bohr
Table 1; sources/2303.10825.txt line 660; 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 1 header line 650 'Energy Error (mH) (mH)'; line 636-637 'STO-3G ... interatomic distance set to 0.8 Å'; thousands separator comma: -2,167.55 mH = -2.16755 Ha | Unit mH printed in header only; inferred from magnitude and header. Boundary not stated, open assumed. Nuclear repulsion not stated. Table also prints error vs FCI in mH (would imply FCI = energy - error, not printed itself). | reader confidence medium
Coverage
Newest published number here: 2023.