Engineering Paramagnetic Spin Centers in Metal-Free Organic Frameworks

Tuning the density of paramagnetic spin centers (PSCs) in π-conjugated systems enables controllable magnetism, coherent spin transport, and molecular spin qubits, thereby opening new frontiers in metal-free quantum magnetism and spintronic technologies. Here, we investigate how key quantum-mechanical and structural parameters govern the balance between spin pairing and unpaired spin density in sp²-carbon-conjugated systems. A modified Hubbard-style Hamiltonian that incorporates electrostatic interactions and static disorder combined with combinatorial analysis and Monte Carlo simulations is employed to analyze how spin density can be tuned in linear polymers, two-dimensional (2D) Lieb-type monolayers, and π-stacked 2D Lieb lattices. We find that the interplay among spin-spin repulsion, spin-anion attraction, anion-anion repulsion, π-connectivity, building-block design, and pore geometry collectively determines whether systems favor spin pairing or stabilize unpaired PSCs. Our results show that 2D π-stacked systems can intrinsically suppress spin pairing, thereby enabling enhanced PSC densities relative to 2D monolayers and 1D linear polymers, consistent with experimental observations. Overall, these findings establish a series of robust design principles that can be used to tune PSC concentrations for applications ranging from isolated spin qubits to collective magnetic and spin-transport networks, thereby advancing the rational design of quantum-coherent, metal-free π-conjugated materials.