Algorithmic Design of Metal-Free Fully π-Conjugated Organic Polyradicals with Any Ground-State Multiplicity

Polyradicals, molecules with multiple unpaired electrons, exhibit unique magnetic properties and are promising candidates for applications in organic electronics, photonics, spintronics, and quantum devices. However, polyradicals with more than two unpaired electrons (beyond diradicals) remain underexplored, and the principles governing their design have been elusive. In this work, we develop a comprehensive framework for the rational design of polyradicals with any number of unpaired electrons and a ground-state multiplicity. Our approach allows precise control over the spin state spectrum, including the ability to specify the multiplicity of the highest-energy spin state. Using high-level quantum chemical calculations, we demonstrate how the polyradical character can be tuned based on a set of simple rules, including the topological control of π-conjugation and the use of cross-conjugation to set a lower-bound restriction on polyradical behavior/identity. Our chemical model requires that the designed polyradicals possess a fully conjugated π-system (including unpaired electrons), ensuring stabilization through delocalization and aromaticity. Each pair of directly π-conjugated unpaired electrons should be bridged by a system possessing an aromatic resonance energy equivalent to at least two benzene-like rings, which may be shared among different such pairs. We explore polyradicals built from synthetically accessible building blocks up to hexaradicals with various ground-state multiplicities. Through multiconfigurational quantum chemical validation, we confirm the accuracy of our design rules and show how to systematically tailor the magnetic properties of these systems. Finally, we propose an algorithmic approach to polyradical design and introduce general homologous series that can be extended to generate novel structural frameworks for future research.