Topological classification of cycloadditions occurring on-surface and in the solid-state

The study of cycloaddition mechanisms is central to the fabrication of extended sp² carbon nanostructures such as graphene nanoribbons and spin chains. Reaction modeling in this context has focused mostly on putative, energetically preferred, exothermic products with limited consideration for symmetry allowed or forbidden mechanistic effects. To classify and optimize allowed reaction mechanisms, modern topological tools can be explored. Here, we introduce a scheme for classifying symmetry-forbidden reaction coordinates in Woodward-Hoffmann correlation diagrams. We show that topological classifiers grant access to the study of reaction pathways and correlation diagrams in the same footing, for the purpose of elucidating mechanisms and products of polycyclic aromatic azomethine ylide (PAMY) cycloadditions of pentacene-yielding polycyclic aromatic hydrocarbons with an isoindole core in the solid-state and on surfaces, as characterized by mass spectrometry and scanning tunneling microscopy, respectively. By means of a tight-binding reaction model and broken-symmetry density functional theory (DFT), we find topologically-allowed pathways for an endothermic reaction mechanism. Our work unveils topological classification as a crucial element of reaction modeling for nanographene engineering, and highlights its fundamental role in the design of cycloadditions in on-surface and solid-state chemical reactions, while underscoring that exothermic pathways can be topologically-forbidden.