Molecular Geometry from Hopf Vortex Topology: Bond Angles, Covalent Binding, and the Universal Correlation Constant in the PEW Framework (v3)

Key Points

• This research aims to derive the H-O-H bond angle using algebraic and topological methods, confirming its exact value.
• Established H-O-H bond angle cos(θ_HOH) = −1/4 via algebraic identity using Lucas numbers.
• Closures of PO-H2O-1 and preservation of previous results were key aspects of the analysis.
• Employed mathematical proofs to link bond angles to Hopf torus topology.
• The H-O-H bond angle was determined to be 104.4775°, showing a deviation of only 0.027° from experimental values.
• Demonstrated that this bond angle result is a consequence of Hopf torus topology, not a coincidence.
• Confirmed the relationship between the cosine value and Lucas number L₃.