Symmetry-Induced Topological Obstructions in Woodward-Hoffmann Forbidden Reactions: A Molecular Qubit Representation

Woodward-Hoffmann (WH) rules for electrocyclic reactions remain to date one of the most successful predictive tools in theoretical organic chemistry. At the heart of these rules is the simple idea that preserving bonding continuity in the highest occupied molecular orbital (HOMO) confers a kinetic advantage compared to a pathway that involves bonding disruption. However, this interpretation has been challenged by a few examples of symmetry-forbidden reactions that exhibit similar or lower kinetic barriers than corresponding allowed pathways. In this study, we develop a generalization of the WH rules through two complementary group-theoretic formulations: the Unitary Evolution Inaccessibility Theorem (UEIT) and the Topological Obstruction to Bonding Disruption Theorem (TOBDT). UEIT establishes that symmetry-forbidden reactions correspond to dynamical inaccessibility between the initial and target states under symmetry-preserving unitary evolution, while the TOBDT demonstrates that disruption in bonding continuity in a forbidden reaction constitutes a symmetry-induced topological obstruction. Within the frontier orbital subspace, the TOBDT is realized through a molecular qubit framework in which the orbital mixing angle Θ serves as a geometric descriptor of topological obstruction. This framework is verified through DFT and CASSCF calculations on four prototype 6π-electrocyclization reactions spanning diradicaloid and zwitterionic classes of transition states (TSs). Our results demonstrate that ΔΘ─the change in Θ between the reactant and the TS─correctly distinguishes diradicaloid from zwitterionic pathways. Additionally, computed nucleus-independent chemical shift (NICSzz) profiles confirm the antiaromatic character of diradicaloid TSs and the nonaromatic character of zwitterionic TSs, suggesting that the orbital symmetry restrictions may not be applicable in the latter.