What question did this study set out to answer?

The research aims to unify molecular structures through a semiclassical approach to equilibrium and geometry, particularly for water.

March 10, 20260 citationsOpen Access

The Dynamic Equilibrium Principle and The Geometry of Water: Semiclassical Coulomb Derivations and Unification of Structural Scales

AAAhmed Aboualy

Key Points

The research aims to unify molecular structures through a semiclassical approach to equilibrium and geometry, particularly for water.
Present a scaling law based on the dynamic equilibrium principle
Derive structures using semiclassical models including Slater screening and Coulomb–Pauli balance
Analyze O–H and H···O bond lengths using the Lambert W function
Achieved accurate modeling of O–H bond length with 0.06% error
Predicted H···O hydrogen bond distance with 2.57% error
Showed convergence of multiple theoretical frameworks on a logarithmic scale anchored to the Bohr radius

Abstract

Two companion papers present a semiclassical unification of molecular structure. Paper 1 — The Dynamic Equilibrium Principle: a structural scaling law showing that competing forces generate a discrete hierarchy of equilibrium scales anchored to a confinement radius. Paper 2 — The Geometry of Water: a semiclassical unification of its structural scales, demonstrating that Slater screening, the H₂⁺ Bohr–Sommerfeld treatment, and a Coulomb–Pauli balance model all converge on the same logarithmic ladder of distances anchored to the Bohr radius and Z=8. The O–H bond length (1.810 a₀, 0.06% error) and H···O hydrogen bond distance (3.820 a₀, 2.57% error) are recovered without water-specific adjustable parameters, solved analytically via the Lambert W function.

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Ahmed Aboualy (Sat,) studied this question.

synapsesocial.com/papers/69af954870916d39fea4cac2 https://doi.org/https://doi.org/10.5281/zenodo.18909249

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