= Hückel square-to-trapezium distortion
{c}
For a four-site cycle with site <energy> $\alpha$, three resonance integrals $\beta<0$ and one weakened integral $n\beta$, $0<n<1$, put $D=\sqrt{(n-1)^2+4}$. In the independent-electron <Hückel method>, filling the two or four lowest spin orbitals gives total electronic energies $E_2=2\alpha+\beta(n+1+D)$ and $E_4=4\alpha+2\beta D$. At the square limit $n=1$, these become $2\alpha+4\beta$ and $4\alpha+4\beta$. The weakened-edge distortion raises the two-electron sum but lowers the four-electron sum. Near $n=1$ the latter change is $\beta(1-n)^2/2+O((1-n)^4)$, so its first-order term cancels. This electronic comparison omits structural repulsion and other restoring forces, and does not determine the open-shell spin at the square limit.
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