The Geometry and Electronic Topology of Higher-Order Charged Möbius Annulenes

Higher-order aromatic charged Möbius-type annulenes have been <i>L</i>_krealized computationally. These charged species are based on strips with more than one electronic half-twist, as defined by their linking numbers. The B3LYP/6-311+G(d,p) optimized structures and properties of annulene rings with such multiple half-twists (C₁₂H₁₂²⁺, C₁₂H₁₂²⁻, C₁₄H₁₄, C₁₈H₁₈²⁺, C₁₈H₁₈²⁻, C₂₁H₂₁⁺, C₂₄H₂₄²⁻, C₂₈H₂₈²⁺, and C₂₈H₂₈²⁻) have the nearly equal C−C bond lengths, small dihedral angles around the circuits, stabilization energies, and nucleus-independent chemical shift values associated with aromaticity. The topology and nature of Möbius annulene systems are analyzed in terms of the torus curves defined by electron density functions (ρ(<i>r</i>)_π, ELF_π) constructed using only the occupied π-MOs. The π-torus subdivides into a torus knot for annulenes defined by an odd linking number (<i>L</i>_k = 1, 3π) and a torus link for those with an even linking number (<i>L</i>_k = 2, 4π). The torus topology is shown to map onto single canonical π-MOs only for even values of <i>L</i>_k. Incomplete and misleading descriptions of the topology of π-electronic Möbius systems with an odd number of half twists result when only signed orbital diagrams are considered, as is often done for the iconic single half twist system.