Reproducible to the Last Digit

How do you know a quantum-chemistry number is right? Not by trusting the program that printed it. A calculation is only as trustworthy as your ability to reproduce it and to check it against reality. Hilbeon earns that trust two ways — determinism and experiment — and neither of them needs a second program to vouch for the first.

1. Bit-identical, every time

Run the same molecule, from the same input, on two different machines — a laptop and a 16-core server — and Hilbeon returns the same wavefunction to the last bit. We converged orforglipron, a 113-atom oral drug, over 1006 basis functions on two separate computers, and the total energies matched digit for digit. There is no hidden randomness in the path: no stochastic grids, no random seeds in the SCF, nothing that shifts from one run to the next. Re-run a Hilbeon calculation tomorrow, on any machine, and you get the identical number. A result you can reproduce exactly is a result you can build a program on.

2. It lands on the bench

Reproducible means consistent; it does not yet mean correct. For correct, we check against measured reality — and this is the test that matters most, because the world does not care which program you used.

• Dipole moments. Caffeine's dipole is well measured, in the 3.58–3.83 D range; Hilbeon computes 3.56 D — right on the experimental band. Aspirin, salicylic acid, and a dozen other molecules land where the instruments say they should.
• Structure. Aspirin's two carbonyls come back at 1.20 and 1.22 Å — the textbook ester and carboxylic-acid C=O bond lengths. Salicylic acid folds into an intramolecular hydrogen bond (O···H 1.80 Å) that masks its polarity to a mere 0.72 D — exactly the “molecular chameleon” behaviour medicinal chemists exploit for permeability.
• Spectra and energetics. Excitation energies, tautomer preferences, reaction shifts — each is quoted against the experimental or thermodynamic fact it is meant to reproduce, with the level of theory stated openly.

When the number agrees with the thermometer and the diffractometer, you are looking at physics, not a fit.

3. Converged, not approximated

Every energy is driven to tight convergence — the SCF residual pushed to ~10⁻⁸ Hartree, orders of magnitude below chemical accuracy. Analytic gradients are checked, component by component, against an independent finite-difference calculation before they ship. When Hilbeon hands you a minimum, it is a genuine stationary point on the energy surface, not a loosely-converged guess that happened to stop.

4. We built the engine

Hilbeon runs on a two-electron integral engine written from scratch — McMurchie–Davidson and Rys quadrature, no third-party integral libraries in the hot path. That is not a boast; it is why we can make the promises above. We know exactly what every number went through, from the first integral to the last SCF cycle. There is no black box we cannot open, and no dependency whose behaviour we cannot account for.

The receipts

Test	Hilbeon result	What it proves
Two-machine determinism	orforglipron, 1006 bf — identical to the last digit	reproducible, run to run
Caffeine dipole	3.56 D	matches experiment (3.58–3.83 D)
Salicylic acid dipole	0.72 D	matches the H-bond-masked "chameleon"
Aspirin carbonyls	1.20 / 1.22 Å	matches textbook ester / acid C=O
SCF convergence	~10⁻⁸ Ha residual	converged, not approximate

References

• Caffeine dipole moment (experimental ~3.58–3.83 D) — Sci. Rep. (caffeine properties).
• Aspirin structure — PubChem: Aspirin.
• Salicylic acid intramolecular H-bond — Seeing hydrogen bonds with NCI.