Reducing Systematic Uncertainty in Computed Redox Potentials for Aqueous Transition-Metal-Substituted Polyoxotungstates

Polyoxometalates have attracted significant interest owing to their structural diversity, redox stability, and functionality at the nanoscale. In this work, density functional theory calculations have been employed to systematically study the accuracy of various exchange-correlation functionals in reproducing experimental redox potentials, U⁰_Red in [PW₁₁M(H₂O)O₃₉]^q- M = Mn(III/II), Fe(III/II), Co(III/II), and Ru(III/II). U⁰_Red calculations for [PW₁₁M(H₂O)O₃₉]^q- were calculated using a conductor-like screening model to neutralize the charge in the cluster. We explicitly located K⁺ counterions which induced positive shifting of potentials by > 500 mV. This approximation improved the reproduction of redox potentials for K_x[XW₁₁M(H₂O)O₃₉]^q-x M = Mn(III/II)/Co(III/II). However, uncertainties in U⁰_Red for K_x[PW₁₁M(H₂O)O₃₉]^q-x M = Fe(III/II)/Ru(III/II) were observed because of the over-stabilization of the ion-pairs. Hybrid functionals exceeding 25% Hartree-Fock exchange are not recommended because of large uncertainties in ΔU⁰_Red attributed to exaggerated proximity of the ion-pairs. Our results emphasize that understanding the nature of the electrode and electrolyte environment is essential to obtain a reasonable agreement between theoretical and experimental results.