Can Li, Ying Wang, Yashi Jiang, Yufeng Liu, Yi Wu, Yanjie Han, Zhenqiang Chen, Liang Liu, Xiaoxue Liu, Dandan Guan, Yaoyi Li, Hao Zheng, Canhua Liu, Pei Nian Liu, Jinfeng Jia, Deng‐Yuan Li, Shiyong Wang
Metal-organic frameworks (MOFs) offer remarkable structural and functional tunability across chemistry, physics and materials science, yet most MOFs built from closed-shell ligands remain wide-gap insulators, limiting their electronic functionality. Here we introduce a general strategy for imparting programmable topology to MOFs by leveraging open-shell ligands. Integrating radical nanographene linkers─featuring singly occupied molecular orbitals─into cobalt-coordination networks via on-surface synthesis, we create MOFs on Au(111) with emergent electronic states spanning the Fermi level. As a proof of concept, we synthesize Sierpiński-triangle fractal MOFs and directly observe topologically protected corner modes─the hallmarks of higher-order topological phases─using low-temperature scanning tunneling microscopy/spectroscopy. Through precise, molecule-by-molecule tip-induced assembly, we systematically tune the fractal hierarchy and monitor the evolution of topological states, supported by tight-binding simulations that align with experimental data. Our work establishes open-shell ligand chemistry as a versatile route to topological MOFs, paving the way for designer molecular quantum materials with programmable electronic and quantum properties.