Hydrogen chain H102 chain, open, R = 1.4, STO-6G

Best values (rules §6)

best projected	-0.51125(1)	ph-AFQMC 10.1103/PhysRevX.7.031059 · 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

Hydrogen chain: 102 protons equally spaced on a line, spacing R = 1.4 bohr, open (a finite molecule); N_↑ = 51, N_↓ = 51. 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: 102
boundary: open
N_up: 51
N_dn: 51
R: 1.4
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.

E/N (Ha)	distance to class best	σ	Var(E)	V-score	method	source	code	year	comment
-0.51125best projected	0	1.2e-5	n/a	n/a	ph-AFQMC peer reviewed	10.1103/PhysRevX.7.031059		2017

How these numbers were read

Where each number below was read, and how it was checked.

-0.51125(1), ph-AFQMC

Checked 2026-10-20 · dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0; source text of arXiv:1705.01608 read locally (pypdf layout text; the generator finds every value again on its line), no LLM transcription of numbers; single reading

Reported as. -52.1479 0.0012 (total for N = 102; second number the stated uncertainty)

dataset github.com/simonsfoundation/hydrogen-benchmark-PRX, commit b99a183 (2017-10-09, uploaded by the authors), CC BY 4.0, file N_102_OBC/R_1.4/AFQMC_basis-STO in sources/1705.01608-data-b99a183.tsv; number first printed in the dataset (RULES.md §8), the paper is the method reference | Hartree, lengths in bohr (Appendix B). Total energies with nuclear repulsion: FCI/STO-6G H10 at R = 1.8 is -5.42438538 in the dataset and -0.542439 per atom in Table II, and the paper's FCI E_inf = -0.471039 is the STO-6G hydrogen-atom energy per atom.

Coverage

Newest published number here: 2017.

This instance as data

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