Structure of [18]Annulene Revisited: Challenges for Computing Benzenoid Systems

For cyclic conjugated structures, erratic computational results have been obtained with Hartree-Fock (HF) molecular orbital (MO) methods as well as density functional theory (DFT) with large HF-exchange contributions. In this work, the reasons for this unreliability are explored. Extensive computations on [18]annulene and related compounds highlight the pitfalls to be avoided and the due diligence required for such computational investigations. In particular, a careful examination of the MO singlet-stability eigenvalues is recommended. The appearance of negative eigenvalues is not (necessarily) problematic, but near-zero (positive or negative) eigenvalues can lead to dramatic errors in vibrational frequencies and related properties. DFT approaches with a lower HF admixture generally appear more robust in this regard for the description of benzenoid structures, although they may exaggerate the tendency toward planarity and C-C bond-equalization. For the iconic [18]annulene, the results support a nonplanar equilibrium structure. The density-fitted frozen natural orbital coupled-cluster singles and doubles with perturbative triples [DF-FNO CCSD(T)] method of electron correlation with an aug-pVQZ/aug-pVTZ basis set places the C₂ global minimum 1.1 kcal mol^-1 below the D₆ stationary point.