Quadripartite bond length rule applied to two prototypical aromatic and antiaromatic molecules

Context In 2000, a remarkably simple relationship was introduced, which connected the calculated geometries of isomolecular states of three different multiplicities. These encompass a ground single state, the first excited triplet state, as well as related radical anion and radical cation. The rule allows the prediction of the geometry of one of the species if the three remaining ones are known. Here, we verify the applicability of this bond length rule for two small planar cyclic organic molecules, i.e., benzene and cyclobutadiene, which stand as prototypical examples of, respectively, aromatic and antiaromatic systems. We see that the rule works fairly well to benzene, and it works independently for quinoid as well as for anti-quinoid minima, despite the fact that radical anion species poses challenges for correct theoretical description. Methods To obtain chosen electronic state equilibrium geometries, three types of computational approaches were utilized: fast and efficient density functional theory DFT, the coupled cluster method CC2, the complete active space self-consistent field (CASSCF) approach, and the most accurate but also resource-consuming perturbation theory with multireference wavefunction (CASPT2) with a default value and without IPEA-shift. Dunning and co-workers correlation-consistent basis sets (aug-)cc-pVXZ (X = D, T, Q) were employed. Gaussian 16 revision A.03, Turbomole 7.1, and Molcas 8.0 computational software were used.