Since Lewis proposed the electron pair model of the covalent bond in 1916and Pauling established the quantum mechanical theory of the chemical bondin 1939, covalent, ionic, metallic, hydrogen, and van der Waals bonds havebeen regarded as five fundamentally distinct types of interactions. Thispaper proves that these five types of chemical bonds are in fact differentmanifestations of a single continuous variable, the undertaking tightness S,across five natural intervals. S is defined as S = (1 − d̂₁·d̂₂) · f(ΔS),where d̂₁·d̂₂ is the directional dot product of the Φ-open-branches on bothsides, and f(ΔS) is the correction factor for the sealing field strengthdifference. Starting from the rigorous mathematical foundations of ConstraintNetwork dynamics, this paper proves the existence, uniqueness, and continuityof S (Theorems 1–2), establishes the dynamical convergence mechanism by whichS attains its steady-state value, derives the analytical functionalrelationships between the S-value and bond energy and bond length(Theorems 3–4), proves the chemical bond unification theorem (Theorem 5),and proves that the geometry of polyatomic molecules is rigorously determinedby the angles between the direction vectors of the Φ-open-branches of thecentral node (Theorem 6). The predicted values of all theorems are consistentwith experimental data from the NIST database within chemical accuracy. Onthis basis, this paper constructs a Molecular Periodic Table—starting fromthe axioms, one reads out the number and directionality of Φ-open-branchesfor each nuclear node, arranges and combines all possible undertakingnetworks according to the Φ-complementarity rule, and directly outputs thebond energy, bond length, bond angle, and reactivity for each combination.This result provides chemistry with its first unified axiomatic foundation.
Menggang Yu (Wed,) studied this question.