Synchronized distortions of bicyclobutanes

The linear relationship between flap angle, θ, and bridging bond length, r₁₃, in bicyclobutanes, found empirically by Irngartinger through x-ray analysis, is reproduced by $\text{ab initio}$ STO-3G calculations. Additional distortions of the bicyclobutane geometry which are synchronized with flap angle variations are predicted.