The π-Electrons Set Apart: Hückel's Settings, Priced
Year: 2026
Type: preprint
Abstract: In 1931 Hueckel produced the first derivable theory of aromaticity: split the molecule by fiat — sigma-electrons frozen into a rigid framework, pi-electrons treated alone — set every Coulomb integral equal to one alpha, every neighbour resonance integral equal to one beta, every other resonance integral and every overlap integral to zero, and inside those settings the level pattern E_k = alpha + 2 beta cos(2 pi k / N) and the 4n+2 rule follow as genuine derivations. I credit those derivations at full strength, and my bench reproduces their arithmetic exactly (benzene total pi-energy 6 alpha + 8.000000 beta against the localized 6 alpha + 6.000000 beta — the famous 2 beta of delocalization). What I evaluate is the derivation status of the settings: the sigma/pi separation is a split by fiat, and alpha, beta, and S = 0 are adopted values, not derived ones. My bench evaluates the deleted overlap in the theory's own headline currency, restoring ring and localized reference together: the benzene delocalization energy falls from D(0) = 2.000000 |beta| to D(0.25) = 1.066667 |beta| at S = 0.250000 — a loss of 0.933333 |beta|, 0.466667 of the headline, from one deleted number — with only 0.480769 of the headline surviving at S = 0.300000 and a beta-refit factor of 1.875000 at S = 0.25. Counted plainly: 1 sigma/pi separation carrying 2 parametrized integrals and 2 exact deletions, 0 derivations in 1931 of the separation or of any setting's value. Grade: REASON FOUND / STILL TURNING — PREMISE-ONLY, explicitly not a kill and not a falsification. Program headline: vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.
Author: Aldred, William Alexander
Language: English
Subfield: Organic Chemistry
Field: Chemistry
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225381112