Determination of Photochemical Quantum Yields via a Normalized Integrated Photokinetic Equation (NIPE)

The accurate determination of photochemical quantum yields ([[EQUATION]]) is often hindered by the inner-filter effect and the experimental difficulty of obtaining precise absorbance data at the reaction boundaries ([[EQUATION]] = 0 and [[EQUATION]] = [[EQUATION]]). Traditional kinetic methods typically address these challenges by either restricting analysis to the initial reaction time or by requiring complex corrections for competitive absorption. Herein, we present the Normalized Integrated Photokinetic Equation (NIPE) method, a generalized mathematical framework that solves the inner-filter problem for solutions with measurable transmittance of excitation light. This is achieved by applying a ratio-based normalization scheme, which relates [[EQUATION]] to the total absorbance changes between any two arbitrary reference times, [[EQUATION]] and [[EQUATION]]. This formulation accounts for the dynamic evolution of the solution's optical density, effectively decoupling quantum yield determination from physical boundary constraints and eliminating errors associated with mixing artifacts or incomplete reactions. We demonstrate the robustness and versatility of NIPE through three distinct case studies: the photodissociation of a ruthenium nitrosyl complex, the decomposition of riboflavin, and the reversible isomerization of azobenzene. The results confirm that NIPE yields accurate values consistent with established literature data, providing a rigorous and experimentally robust framework for quantum yield determination.