Since Lewis introduced the electron-pair model of the covalent bond in 1916 and Pauling established the quantum mechanical theory of chemical bonding in 1939, covalent, ionic, metallic, hydrogen, and van der Waals bonds have been regarded as five fundamentally distinct interactions. In this paper, starting from a minimal set of mathematical axioms, we rigorously prove that these five bond types are, in fact, manifestations of a single continuous variable—the junction tightness S—in 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 both sides, and f(ΔS) is a correction factor for the sealing field strength difference. We strictly prove the existence, uniqueness, and continuity of S (Theorems 1-2), derive the analytical functional relationships between S and bond energy and bond length (Theorems 3-4), prove the Chemical Bond Unification Theorem (Theorem 5), and prove that the geometry of polyatomic molecules is strictly determined by the angle between the Φ open branch vectors of the central node (Theorem 6). The predictions of all theorems are consistent with experimental data from the NIST database within chemical accuracy. This result provides chemistry with its first unified axiomatic foundation, ending the history of chemistry as a purely empirical science.
Menggang Yu (Thu,) studied this question.