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The research aims to derive molecular structures and bond distances from first principles using semiclassical approaches.

March 10, 20260 citationsOpen Access

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The Dynamic Equilibrium Principle and The Geometry of Water: Semiclassical Coulomb Derivations from First Principles

AAAhmed Aboualy

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The research aims to derive molecular structures and bond distances from first principles using semiclassical approaches.
Developed a scaling law based on the dynamic equilibrium principle for analyzing molecular structure.
Calculated O–H bond length and hydrogen bond distance using semiclassical methods and the Bohr radius.
Applied the Lambert W function for analytical solutions without adjustable parameters.
O–H bond length derived at 1.810 a₀ with a 0.06% error.
H···O hydrogen bond distance derived at 3.820 a₀ with a 2.57% error.

Abstract

Two companion papers present semiclassical derivations of molecular structure from first principles. 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: derivation of the O–H bond length (1.810 a₀, 0.06% error) and H···O hydrogen bond distance (3.820 a₀, 2.57% error) using only the Bohr radius and Z=8, solved analytically via the Lambert W function. No adjustable parameters.

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The Dynamic Equilibrium Principle and The Geometry of Water: Semiclassical Coulomb Derivations from First Principles

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