Modern valence-bond description of aromatic annulene ions

Abstract

Spin-coupled theory for ‘N electrons in M orbitals’ active spaces [SC(N,M)], an ab initio valence-bond (VB) approach which uses a compact and easy-to-interpret wave function comparable in quality to a ‘N in M’ complete-activespace self-consistent field [CASSCF(N,M)] construction, is used to obtain modern VB descriptions of the π-electron systems of the most important annulene rings with 4n + 2 π electrons: the cyclopropenium ion, the cyclobutadiene dication and dianion, the cyclopentadienide anion, benzene, the cycloheptatrienyl cation, and the cyclooctatetraene dication and dianion in their highest-symmetry nuclear conformations. The SC wave functions for the cyclopropenium ion, cyclopentadienide anion, cycloheptatrienyl cation, cyclooctatetraene dication and dianion are shown to closely resemble the well-known SC model of the classical example of an aromatic system, benzene. The SC orbitals for the cyclobutadiene dication and dianion are more delocalized and demonstrate the ways in which SC wave functions adjust to electron-deficient and electron-rich environments. The high levels of resonance observed in all annulene ions with 4n + 2 π electrons clearly demonstrate their aromaticity.