All instances / Hydrogen chain
Hydrogen chain H12 chain, open, R = 1.88973, STO-3G
Exact energy and best values
(rules §6)
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 = 1.88973 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
- 1.88973
- 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).
Numerically exact (1)
Exact diagonalization, an exact solution, or sign-problem-free QMC where that is established. An exact energy is shown first, before the best of each other class. QMC is exact only within its error bar, which it must state, and reads exact (stochastic); an exact diagonalization outranks it. For a diagonalization resolved by symmetry sector only the ground state's sector is listed; the lowest energies of the other sectors are the instance's spectrum, in its JSON, and are not shown as the exact energy.
How these numbers were read
Where each number below was read, and how it was checked.
-0.5377347, ED
Checked 2026-10-20 · source text of arXiv:2505.08635 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. −6.452816 Ha per total; R = 1 Å = 1.88973 bohr
text Results; sources/2505.08635.txt line 233; version read: arXiv text; no journal version found | 'in the given basis is −6.452816 Hartree' (l.232-233); R = 1 A, STO-3G l.175-176 | boundary not stated (open assumed, H12 chain [45]); nuclear repulsion not stated; basis STO-3G on RHF orbitals; method of the exact value not named | reader confidence medium
Coverage
Newest published number here: 2026.