Developing Scaling Relationships for Molecular Electrocatalysis through Studies of Fe-Porphyrin-Catalyzed O₂...

The oxygen reduction reaction (ORR) is a multiproton/multielectron transformation in which dioxygen (O₂) is reduced to water or hydrogen peroxide and serves as the cathode reaction in most fuel cells. The ORR (O₂ + 4e^- + 4H⁺ → 2H₂O) involves up to nine substrates and thus requires navigating a complicated reaction landscape, typically with several high-energy intermediates. Many catalysts can perform this reaction, though few operate with fast rates and at low overpotentials (close to the thermodynamic potential). Attempts to optimize these parameters, both in homogeneous and heterogeneous electrocatalytic systems, have focused on modifying catalyst design and understanding kinetic/thermodynamic relationships between catalytic intermediates. One such method for analyzing and predicting catalyst reactivity and efficiency has been the development of "molecular scaling relationships". Here, we share our experience deriving and utilizing molecular scaling relationships for soluble, iron-porphyrin-catalyzed O₂ reduction in organic solvents. These relationships correlate turnover frequencies (TOF_max) and effective overpotentials (η_eff), properties uniquely defined for homogeneous catalysts. Following a general introduction of scaling relationships for both homogeneous and heterogeneous electrocatalysis, we describe the components of such scaling relationships: (i) the overall thermochemistry of the reaction and (ii) the rate and rate law of the catalyzed reaction. We then show how connecting these thermodynamic and kinetic parameters reveals multiple molecular scaling relationships for iron-porphyrin-catalyzed O₂ reduction. For example, the log(TOF_max) responds steeply to changes in η_eff that result from different catalyst reduction potentials (18.5 decades in TOF_max/V in η_eff) but much less dramatically to changes in η_eff that arise from varying the pK_a of the acid buffer (5.1 decades in TOF_max/V in η_eff). Thus, a single scaling relationship is not always sufficient for describing molecular electrocatalysis. This is particularly evident when the catalyst identity and reaction conditions are coupled. Using these multiple scaling relationships, we demonstrate that the metrics of turnover frequency and effective overpotential can be predictably tuned to achieve faster rates at lowered overpotentials. This Account uses a collection of related stories describing our research on soluble iron-porphyrin-catalyzed ORR to show how molecular scaling relationships can be derived and used for any electrocatalytic reaction. Such scaling relationships are powerful tools that connect the thermochemistry, mechanism, and rate law for a catalytic system. We hope that this collection shows the utility and simplicity of the molecular scaling approach for understanding catalysis, for enabling direct comparisons between catalyst systems, and for optimizing catalytic processes.