The theory of double bond fixation in conjugated hydrocarbons

A general method is given for treating the problem of bond fixation in conjugated hydrocarbons. Two effects are considered separately: first-order bond fixation from which bond-length-bond-order relationships may be derived, but which cannot lower the symmetry of the molecule; and second-order bond fixation which can lower the symmetry. It is shown that the most favourable distortion in the latter case is given by the lowest eigenvalue of the bond-bond polarizability matrix. The critical value for this eigenvalue appears to be about 1·8β -1. For values whose modulus is greater than this a distortion will occur which overcomes the σ-bond compression energy, and may lower the symmetry of the molecule.