Molecular Periodic Table: Unified Chemical Theory via Φ-Open-Branch Undertaking

This paper constructs a Molecular Periodic Table within the Energy Ontology framework. The undertaking tightness S, defined as S = (1 − d̂₁·d̂₂) · f(ΔS), unifies covalent, ionic, metallic, hydrogen, and van der Waals bonds as different intervals of a single continuous spectrum. Six benchmark molecules calibrate the S-value function using publicly available NIST data. Bond angles are derived from Φ-open-branch directionality, deviating from measured values by less than two degrees. Catalysis is unified as a low-S interface operation. Complete quantitative data—diatomic molecules, polyatomic molecules, giant covalent networks, transition metal d-orbital branch numbers, and catalytic S-value/efficiency relationships—are submitted as Supplementary Material, with all entries marked by data status. The Molecular Periodic Table upgrades chemistry from empirical rules to a quantitative framework derived from first-principle physical laws.