Since the work of Forster on excited state proton transfer, chemists have used approximate thermodynamic cycles to estimate the equilibrium constants for excited state reactions. In these approximate cycles, quantum energies from spectroscopy have been substituted for thermodynamic free energies. Forster’s approximate cycle leads to typical errors of one pK unit for excited state acidities, but errors of up to 4 pK units are known. The same approximations are used in the approximate cycles for excited state electron transfer put forth by Marcus and by Rehm and Weller. Last year, Ryu et al. showed how to measure the standard free energy change for an electronic transition using femtosecond 2D spectroscopy and generalized Einstein relations between absorption and emission. We discuss related 1D experimental approaches that use the generalized Einstein relations to determine the standard free energy change for homogeneous electronic transitions. Experimental absorption and emission lineshapes for a single molecular form of rhodamine B satisfy the generalized Einstein relations to within about 1%. Measurements on the rhodamine B cation (acid) and rhodamine B zwitterion (its conjugate base) have been used to construct a true thermodynamic cycle and calculate the excited state acid dissociation constant. Sources of experimental uncertainty in spectroscopic determinations of excited state standard free energies will be discussed.

Spectroscopic measurement of free energies: Thermodynamic cycles for excited state chemistry

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ACS Fall 2022

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