Single-Ion Reorganization Free Energy of Aqueous Ru(bpy)32+/3+ and Ru(H2O)62+/3+ from Photoemission Spectroscopy and Density Functional Molecular Dynamics Simulation

Photoelectron spectroscopy and density functional molecular dynamics simulations are combined to quantify and characterize the redox properties of Ru(bpy)(3)(2+/3+) and Ru(H2O)(6)(2+/3+) in aqueous solution. We report the energy-resolved photoelectron spectrum of aqueous Ru(bpy)(3)(2+) at 200 eV photon energy. From the peak position of the highest molecular orbital at 6.81 eV, an experimental value for the single-ion reorganization free energy of Ru(bpy)(3)(3+) is determined to be 1.21 +/- 0.04 eV. Density functional molecular dynamics calculations give a value of 0.84-1.20 eV for Ru(bpy)(3)(3+) and 1.92-2.42 eV for Ru(H2O)(6)(3+) depending on the method used to extrapolate the results to the infinite dilution limit. Since linear response is an excellent approximation for these systems, we report the same reorganization free energies for the divalent ions. The relatively small reorganization free energy of Ru(bpy)31 is a consequence of the small changes in the Ru-N bond lengths upon reduction (0.04 eV inner sphere contribution) and of the large hydrophobic cavity formed by the bulky bipyridine ligands, which effectively reduces the dipolar response of the solvent in qualitative agreement with continuum theory. The large difference in redox potential between Ru(bpy)(3)(2+/3+) and Ru(H2O)(6)(2+/3+) (1 eV) is mainly associated with the difference in reorganization free energy rather than vertical ionization energy. Finally, the measured photoelectron spectrum of Ru(bpy)(3)(2+) is compared with the Kohn-Sham density of states for interpretation of occupied as well as computed virtual energy levels. This computational approach, in conjunction with first-ever photoelectron spectroscopy measurements of an aqueous transition metal ion, provides a quantitative benchmark for understanding the effect of water on metal redox potential and lays the groundwork for future studies of redox properties.