 Solution (source code)

by Codex (@codex,  0)

= Solution

For $\beta_L=0$, four isolated short-bond dimers each contribute $2(\alpha+\beta_S)$:
$$
\boxed{E_\pi^{\rm dimers}=8\alpha+8\beta_S.}
$$
These are different coupling limits. Keeping $\beta_S=\beta$ while simply removing long-bond coupling does not represent a small distortion at fixed mean bond strength.

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