Geometry-Dependent Linker Spin States and Real-Space Band Topology in Two-Dimensional Conductive Metal–Organic Frameworks

Two-dimensional (2D) conductive metal–organic frameworks (MOFs) based on phenylenediamine linkers typically exhibit higher conductivity for Ni nodes than for Cu analogues. Here, density functional theory analyses at both framework and molecular levels reveal that this contrast originates from structure–spin–topology interplay. In tritopic triphenylene-based frameworks, square-planar Ni nodes stabilize the quartet state of linker, which couples via superexchange to generate double kagome bands. In contrast, Jahn–Teller distortion at Cu centers favors the doublet state of linker, suppresses kagome-type dispersion, and drives the system toward open-gap honeycomb bands. Extension to tetratopic porphyrin-based frameworks confirms analogous structure–spin interplay in 4-fold lattices. Comparison between 3-fold and 4-fold systems shows that stronger superexchange broadens Dirac bandwidths and enhances in-plane transport. These findings establish coordination geometry and linker spin state as key design parameters for emergent electronic topology in 2D MOFs.