First-Principles Derivation of van der Waals Parameters from the Electron Localization Function

The van der Waals parameters a (intermolecular cohesion) and b (excluded volume) are conventionally treated as empirical constants fitted to experimental data. We show that both can be derived analytically from a three-sector decomposition of intermolecular forces, without fitting to gas-phase PVT data. The excluded-volume parameter satisfies b = σst Ω3 v0, where σst ≈ 0.110 is a universal steric compressibility constant, Ω3 = 2π2 is a geometric volume factor, and v0 is the intrinsic molar volume; this reproduces experimental b for 18 gases with R2 = 0.985. The cohesion parameter splits additively into three physical sectors: a quantum dispersion term modulated by σe = α/2 (half the fine-structure constant) and the Electron Localization Function (ELF); a classical Keesom/Debye electrostatic term; and a hydrogen-bond network term governed by the Egelstaff-Widom solvent rigidity. Applied to 18 gases spanning nonpolar, polar, and hydrogen-bonding classes, the unified formula predicts a with R2 = 0.978 and mean absolute error 0.62 L2 atm mol−2, with zero fitted parameters. The same framework analytically recovers the empirical temperature function α(Tr, ω) of the Soave–Redlich–Kwong equation of state, explaining the sign and structure of its ω-polynomial from first-principles vibrational ELF saturation.