Measuring Theoretical Descriptors of Water Oxidation: Free Energy Differences Between Intermediates Using Time-Resolved Optical Spectroscopy

Theoretical descriptions differentiate catalytic activity of material surfaces for the water oxidation reaction by the stability of the reactive oxygen (O*) intermediate. The underlying conjecture is that there are several meta-stable steps of the reaction, each connected by free energy differences critically dependent on O*. Recently in-situ, time-resolved spectroscopy of the (photo)-electrochemical water oxidation reaction identified the vibrational and optical signatures of O* time-evolution. However, there has been little connection between these inherently kinetic experiments and the underlying thermodynamic parameters of the theory. Here, we discover that picosecond optical spectra of the O* population modulated by a shift in reaction equilibria defines an effective equilibrium constant (K_eff) containing the relevant free-energy differences. A Langmuir isotherm as a function of electrolyte pH extracts K_eff using a model titania system (SrTiO₃). The results show how to obtain equilibrium constants of individual reaction steps on material surfaces, which had not been experimentally accessible previously. Further, we find that for a photo-excited reaction on a semiconductor surface tuning past a pH defined by K_eff doubles the initial O* population. That the free energies of the catalytic surface are definable through a time-resolved spectroscopy, alongside the finding that the surface recollects its explicit equilibrium with the electrolyte, provides a new and critical connection between theory and experiment by which to tailor the pathway of water oxidation and other surface reactions.