The kinetic model for AB(1ϕ) systems: A closed-form integration of the differential equation with a variable photokinetic factor

A kinetic law, the log–exp model, that describes the evolution of a unimolecular photochemical reaction, AB(1ϕ), has been realised for the first time through a closed-form integration of the differential equation that involves a time-dependent photokinetic factor. As a consequence, a novel analytical formula for the efficiency of AB(1ϕ) photoreactions has been established. The theoretical log–exp model has been successfully tested against numerical integration data for simulated kinetics. It has been applied to the direct determination of the absolute values of the quantum yields, at different visible irradiation wavelengths, for the photoisomerization of a diarylethene derivative in an organic medium.