Fast estimation of intersystem crossing rate constants of radical pairs

Abstract

The spin–flip or intersystem crossing (ISC) process plays a main role in photophysics and photochemistry. ISC is the radiationless electronic transition between singlet and triplet states. ISC is responsible for phosphorescence and the chemical reaction which happens only in the electronic state with the specific spin. One specific and challenging case is the formation of accretion products in peroxy radical cross-reactions, recently demonstrated to be important in atmospheric chemistry. Here, the ISC or spin–flip occurs between triplet and singlet states of a complex of two alkoxy radicals (RO˙⋯R′O˙). The complex is initially formed in a triplet state, while the formation of the ROOR′ accretion product can only happen on the singlet surface. Therefore, the ISC rate dictates the rate of this reaction. We developed a fast algorithm to calculate ISC rate constants (k_ISC) between the lowest electronic states of alkoxy radical pairs. The k_ISC calculation requires the spin-orbital coupled interaction matrix elements (SOCME) and the excitation energies (E) of the involved electronic states. The E and SOCME are calculated quickly using the CASSCF level of theory, and a novel analytical expression, respectively. Finally, the k_ISC calculation is performed efficiently; within 5–60 seconds even for radical pairs with the large substituents such as CH₃(CO)CH₂O˙ and HOCH₂CH(O˙)CH₂CH₃. This algorithm is applied to a large number of radical pairs with different substituents, and the k_ISC is calculated for 95 875 radical pair conformers using this algorithm. It provides an opportunity to generate large amounts of data (input and output values, e.g. geometries and associated ISC rates) quickly. Therefore, we believe that the fast algorithm can be useful not only for photophysical calculations, but also for Big Data creation to implement machine learning methods.