Engineering Paramagnetic Spin Centers in Metal-Free Organic Frameworks

Tuning the density of paramagnetic spin centers (PSCs) in π-conjugated systems en- ables coherent quantum dynamics, controllable magnetism, and molecular spin qubits, thereby opening new frontiers in molecular-scale quantum technologies. We investi- gate the fundamental mechanisms governing spin pairing and PSC concentration in sp2-carbon-conjugated polymeric systems using a Hubbard-style Hamiltonian, mod- ified to incorporate electrostatic interactions and static defects, in combination with combinatorial analysis and Monte Carlo simulations. By analyzing linear polymers, 2D Lieb-type monolayers, and π-stacked Lieb structures, we elucidate how the interplay of various quantum-mechanical interactions such as spin–spin repulsion, spin–anion attraction, and anion–anion repulsion along with structural features such as 2D π- connectivity, building-block design, and pore size, collectively influence the propensity for spin-paired bipolaron formation and, consequently, the concentration of PSCs. Our results reveal that π-stacked 2D organic frameworks intrinsically suppress spin pairing, thereby facilitating enhanced PSC densities compared to monolayers and linear poly- mers consistent with experimental observations. Building upon good agreement with experiments, we identify key design principles that provide experimentally actionable guidelines for engineering high-spin-density organic materials and lay the foundation for the rational design of metal-free magnets and spin-active semiconductors for next- generation organic spintronics and quantum information technologies.