Global Lifetime Analysis on Excited Three-State Reactions

Studying excited-state chemical kinetics offers not only benchmark platforms for understanding chemical reactions in the ground state, but is essential for advancing light-energy harvesting/conversion in catalysis, photovoltaics, and biology. For investigating complex reactions with multiple species and reversibility, global lifetime analysis on time-resolved spectral data is useful because it offers an intuitive measure for identifying reactants, products, and intermediates, if any, with the rate constants for their relaxation and interconversion. Based on the global lifetime analysis, here, we present analytical solutions for three-state reactions in the excited state with partial or full reversibility. Our analytical approach was applied to time-resolved fluorescence spectra of a photoacid undergoing collisional excited-state proton transfer to a cosolvent base in binary solvent mixtures, where the rates of collisional processes can be controlled with the concentration of the base expanding the data set for validating our approach. Based on the general solutions, we elucidated all the rate constants and kinetic order in each step, thus, the full reaction mechanism. Also, we determined the emission spectral shape and initial amount of each emitting species. The presented analytical protocol offers a guideline for systematically investigating excited three-state reactions beyond the demonstrated proton-transfer reaction.