<b>Difficulty of the evaluation of the barrier height of an open-shell transition state between closed shell minima: the case of small C_4n rings</b>

C 4n cyclacenes exhibit strong bond alternation in their equilibrium geometry. In the two equivalent geometries the system keeps an essentially closed-shell character. The two energy minima are separated by a transition state suppressing the bond alternation, where the wave function is strongly diradical. The paper discusses the physical factors involved in this energy difference and possible evaluations of the barrier height. The simple comparison between the restricted DFT/B3LYP for the equilibrium with the broken symmetry DFT/B3LYP of the transition state underestimates or cancels the barrier in comparison with the most reliable CASPT2 or NEVPT2 results. The minimal (2 electrons in 2 Molecular Orbitals) Complete Active Space SCF overestimates the barrier, the subsequent second-order perturbation cancels it. Due to the collective character of the spin-polarization effect, it is necessary to perform a full π CASSCF + second-order perturbation to reach a reasonable value of the barrier, but this type of treatment cannot be applied to large molecules. DFT procedures treating on an equal foot the closed-shell and open-shell geometries have been explored, such as MRSF-TDDFT and a new spin-decontamination proposal, namely DFT-dressed CI, but the results still depend on the density functional. The M06-2X without or with spin-decontamination gives the best agreement with the accurate wave function results.