The science
What’s modelled, how well, and what isn’t.
The short version of how the sandbox works, how it’s checked, and where it’s still wrong.
The molecule sandbox
A reactive field where nothing is named.
CLASSICAL_FF
A reactive force field that knows elements, not molecules. There’s no list of molecules, shapes or reactions anywhere in the code.
- Valence competition. Atoms share out bonds by competing for partners, so one bond can form while another breaks.
- Shapes from electrons. Bond angles come from counting the electrons around each atom.
- Charges that balance. Partial charges flow by electronegativity; press + or − to make an ion.
- Real dynamics. Atoms move under the exact forces of the model, in a heat bath you control.
Validation
The 0.5.0 release, against measurement.
20 molecules, relaxed in the model and compared with measurement. Average bond-length error 2.5 %, worst 7.6 %. The bad rows stay in.
| Molecule | Bond | Valence (Å) | Measured (Å) | Error | Angle: Valence / measured |
|---|---|---|---|---|---|
| H₂ | H–H | 0.745 | 0.741 | +0.5 % | · |
| N₂ | N–N | 1.109 | 1.098 | +1.0 % | · |
| O₂ | O–O | 1.264 | 1.208 | +4.6 % | · |
| F₂ | F–F | 1.428 | 1.412 | +1.1 % | · |
| Cl₂ | Cl–Cl | 1.997 | 1.988 | +0.5 % | · |
| S₂ | S–S | 1.835 | 1.889 | −2.9 % | · |
| HF | H–F | 0.921 | 0.917 | +0.4 % | · |
| HCl | H–Cl | 1.282 | 1.275 | +0.6 % | · |
| CO | C–O | 1.214 | 1.128 | +7.6 % | · |
| NO | N–O | 1.212 | 1.151 | +5.3 % | · |
| H₂O | O–H | 1.003 | 0.958 | +4.7 % | 105.0° / 104.5° |
| NH₃ | N–H | 1.026 | 1.012 | +1.4 % | 107.2° / 106.7° |
| CH₄ | C–H | 1.117 | 1.087 | +2.7 % | 109.5° / 109.47° |
| CO₂ | C–O | 1.219 | 1.160 | +5.1 % | 180.0° / 180° |
| C₂H₆ | C–C | 1.500 | 1.535 | −2.3 % | · |
| C₂H₄ | C–C | 1.308 | 1.339 | −2.3 % | · |
| C₂H₂ | C–C | 1.201 | 1.203 | −0.2 % | · |
| N₂H₄ | N–N | 1.422 | 1.447 | −1.7 % | · |
| N₂H₂ | N–N | 1.211 | 1.252 | −3.3 % | 116.1° / 106.8° |
| H₂O₂ | O–O | 1.444 | 1.475 | −2.1 % | · |
Source: the app’s 0.5.0 release record, charge equilibration on. Rows in amber are the largest misses.
Reaction barriers
| Reaction | Valence | Measured |
|---|---|---|
| H + H₂ | 8.0 | 9.7 |
| Cl + H₂ | 8.1 | 8.0 |
| OH + H₂ | 8.5 | 5.2 |
| F + H₂ | 0.7 | 1.6 |
| CH₃ + H₂ | 12 | 11.9 |
kcal/mol. These calibrate the bond model and were measured with charge equilibration off. With it on, as it is by default, chlorine, hydroxyl, fluorine and oxygen meet no barrier when they attack H₂.
Also measured
- Atomization energies: average error 5.4 % over 12 molecules, against reference values still waiting to be independently checked.
- Tests: 1,414 automated tests passing at the last full run (27 September 2026).
Provenance
Every number says where it came from.
Every result in the app carries one of six labels saying what kind of model produced it.
| Tier | Meaning | Used for |
|---|---|---|
| EXACT_ANALYTIC | Exact analytical solution | Hydrogen spectrum |
| NUMERICAL | Numerical solution of the stated equation | Numerov radial solver |
| APPROXIMATE_QM | Approximate many-electron electronic structure | Kohn–Sham DFT, LCAO, Gamow tunnelling |
| EMPIRICAL | Phenomenological or empirically fitted model | Mass formula, Cornell potential |
| CLASSICAL_FF | Classical mechanics with an empirical force field | The molecule sandbox |
| REFERENCE | Measured or published reference data | Element data, measured binding energies |
Open problems
What comes next.
Each of these is a gap in 0.5.0, and a direction the model can grow in. The app lists them itself, under Show the science.
- Give oxygen its spin. Today the model’s oxygen is spin-free: it inserts into H₂ side-on, which real ground-state oxygen does not, and its reaction rates are not validated yet.
- Keep reaction barriers from vanishing. With charge equilibration on, the charge model’s pre-reactive well is deeper than the bond model’s ridge, so chlorine, hydroxyl, fluorine and oxygen attacking H₂ react too readily when heated.
- Make N₄ as sturdy as theory says. The nitrogen tetrahedron is held by a barrier of 4.3 kcal/mol in the model, against about 61 in theory.
- Hold nitric acid and nitro compounds. Nitrogen stops at three bonds today, so these are not held yet.
- Let electrons move between atoms. Today ions are what you label them: charge spreads and protons transfer, but electrons stay with their atoms, and there are no oxidation-state changes.
- Add hydrogen bonds and torsion. 0.5.0 has neither, and nothing condenses beyond the van der Waals well. Double bonds that resist twisting are already in the development build.
- Bigger scenes. Up to 400 atoms today.
Also in 0.5.0
The other four scales.
They ship as they are; new work goes into the molecule sandbox.
- ~10 nmBulk matterClassical molecular dynamics. Energy drift below 10⁻⁴ over 3,000 steps.
- ~100 pmAtomExact hydrogen orbitals and density-functional theory. All 118 electron configurations match NIST.
- ~10 fmNucleusMeasured binding energies and alpha decay by tunnelling. The binding curve peaks at nickel-62.
- ~1 fmQuarksA confining potential that predicts the Υ(1S) mass to within 0.6 %.