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

Abstract

Abstract We construct a scalar configuration field $$\Phi $$ on the periodic table lattice from z -score-normalized first ionization energy and covalent radius, with a single coupling parameter $$\lambda $$ fixed a priori . Geodesic costs computed on this field via Dijkstra’s algorithm predict experimental diatomic bond dissociation energies $$D_0$$ for 201 diatomics at Spearman $$\rho = -0.325$$ ( $$95\%$$ 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 $$\rho = -0.633$$ ( $$p < 10^{-7}$$ , $$N = 60$$ ). 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 $$r = -0.600$$ ( $$\alpha ^{-1/3}$$ transform, 95% CI: $$[-0.858,\, -0.263]$$ , $$p = 1.3 \times 10^{-9}$$ , $$N = 85$$ ), a property that shares no input variable with the field. A 16-configuration ablation study confirms robustness across $$\lambda \in [0.5,\,2.0]$$ , 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.