Time-Dependent Differential and Integral Quantum Yields for Wavelength-Dependent [4+4] Photocycloadditions

The [4+4] photocycloaddition of anthracene is one of most relevant photoreactions and is widely applied in materials science, as it allows to remote-control soft matter material properties by irradiation. However, highly energetic UV irradiation is commonly applied, which limits its application. Herein, the wavelength dependence of the photodimerization of anthracene is assessed for the first time, revealing that the reaction is induced just as effectively with mild visible light (410 nm). To fully establish [4+4] cycloadditions within defined chemical environments, a conceptual framework for the solution kinetics of the photo-dimerization up to long reaction times is established by developing a novel photoreaction rate law that is dependent on individual rate coefficients of the key reaction steps. These coefficients can be determined based on low conversion photochemical experiments. Both differential and integral quantum yields can subsequently be predicted that are strongly time-dependent, highlighting the need for a detailed reaction pathway analysis. The presented approach simplifies a complex photochemical scenario, making the photochemical anthracene dimerization, or potentially any other photochemical dimerization, amenable to a time-dependent understanding at the elementary reaction level.