Excited-state Free Energies from an Exact Thermodynamic Cycle

Previous methods to spectroscopically study excited-state reaction thermodynamics have been limited by approximations of free energies as photon energies. For example, Förster added standard enthalpy differences—approximated from electronic spectra and neglecting entropy changes—to the ground‑state standard Gibbs free energy change to estimate the standard Gibbs free energy change and pKa* for excited-state proton transfer. I will present a theory that connects the excited-state Gibbs free energy from an exact thermodynamic cycle to standard chemical potential differences for spectroscopic transitions. The standard chemical potential differences for homogeneous solutions of the reaction components can be obtained by applying generalized Einstein relations to transformed absorption and photoluminescence spectra. We apply this method to aqueous Rhodamine B, a xanthene laser dye that acts as a photobase. By measuring the excited-state equilibrium constant for the Rhodamine B proton acquisition, we show that the thermodynamic cycle is an order of magnitude more accurate than Förster’s method.