Redox Control in a Conducting MOF through Coupled Electronic-Vibronic Effects

Redox control in electrically conducting metal-organic frameworks (MOFs) requires understanding how intercalated cations reshape both electronic structure and lattice thermodynamics. In the nominal A₂-Mn-DOBDC anionic framework (A = Li⁺, Na⁺, K⁺), redox potentials and electronic conductivities follow K < Li < Na, contradicting an electrostatic polarization model. Finite-temperature free-energy partitioning shows competing contributions: ΔF_EL (electronic term) decreases along Li > Na > K, whereas ΔF_VIB (vibrational term) increases along Li < Na < K, producing a maximum stabilization that favors Na and rationalizes the nonintuitive potential ordering. FTIR band shifts track cation-induced systematic mode shifts consistent with cation-dependent vibrational reorganization, and DFT vibrational densities of states with Helmholtz free energies reproduce ΔF_VIB trends. Mixed-valence charge transfer with cation-modulated electronic coupling accounts for the conductivity ordering. Na₂-Mn-DOBDC delivers a median discharge voltage of ∼3.0 V vs Na⁺/Na while retaining measurable electronic conductivity, providing a general electronic-vibronic route to tune redox energetics in conducting MOFs.