One number predicts how strongly atoms bond. We assign each element a single thermodynamic parameter — Pe (Péclet number) — derived from its effective nuclear charge, electron affinity, and shielding. Then we use Langevin dynamics to simulate how atoms move, collide, and form bonds. The result: Pe alone predicts bond dissociation energies across 56 known bonds with ρ = 0.881.
Electron shell theory is the gold standard for why bonds form (orbital overlap, electron sharing, quantum mechanics). We don't replace it.
What we show is that a single transport parameter (Pe) — computed from three atomic properties that electron shell theory already predicts — recovers bond strength rankings with ρ = 0.881. That's a convergence result: the full quantum picture compresses into one number for predicting how much energy it takes to break a bond.
Think of it like body mass index (BMI): it doesn't replace cardiology, but it captures a surprising amount of health variance with one number. Pe does the same for bond stability. And because it's a transport parameter, it naturally connects to reaction kinetics, thermal stability, and material behavior under stress — things that are harder to get from orbital diagrams alone.
Pe is not a new theory of chemistry. It's a thermodynamic lens on data that electron shell theory already explains at a deeper level. The interesting part is that the lens works — and generalizes to domains beyond chemistry.
| Bond | Predicted (kJ/mol) | Actual (kJ/mol) | Error % | Type |
|---|
Leave-30%-out splits (ATOM-04, N=56). Kill condition: CV ρ > 0.5. Mean = 0.785 — SURVIVES.
| Split | Train N | Test N | rho | RMSE | p-value |
|---|
Mapping: atomic (Z_eff, EA, sigma) to Langevin (alpha, gamma, c) with 8 free coefficients.