Geodesic costs on a scalar field over the periodic table predict diatomic bond dissociation energies

We construct a scalar configuration field Φ on the periodic table lattice from z -score-normalized first ionization energy and covalent radius, with a single coupling parameter λ fixed a priori . Geodesic costs computed on this field via Dijkstra’s algorithm predict experimental diatomic bond dissociation energies D₀ for 201 diatomics at Spearman ρ = -0.325 ( $$95%$$ CI: $$[-0.462,\,-0.180]$$ , p < 10⁻⁵ ), outperforming both Manhattan and Euclidean distance baselines without molecular orbital theory, fitted regression, or element-pair-specific parameters. On the sparser gradient-magnitude cost field, the correlation strengthens to ρ = -0.633 ( p < 10⁻⁷ , $$N = 60$$ ). The field’s curvature (second difference along atomic number) also correlates with Pearson–Parr chemical hardness at $$r = -0.830$$ ( $$95%$$ CI: $$[-0.947,\,-0.604]$$ , p < 10⁻⁹ , $$N = 35$$ ) and with atomic polarizability at $$r = -0.600$$ ( α -1/3 transform, 95% CI: $$[-0.858,\, -0.263]$$ , p = 1.3 × 10⁻⁹ , $$N = 85$$ ), a property that shares no input variable with the field. A 16-configuration ablation study confirms robustness across λ ∈ [0.5,\,2.0] , connectivity, and cost-field choices. We do not propose this framework as a competitor to quantum chemical calculations of bond energies; rather, we present it as evidence that the periodic table possesses intrinsic differential-geometric structure from which chemical observables can be recovered without reference to electronic wavefunctions.