Spin-Flip Density Functional Theory for the Redox Properties of Organic Photoredox Catalysts in Excited States

Photoredox catalysts (PCs) have contributed to the advancement of organic chemistry by accelerating conventional reactions and enabling new pathways through the use of reactive electrons in excited states. With a number of successful applications, chemists continue to seek new promising organic PCs to achieve their objectives. Instead of labor-intensive manual experimentation, quantum chemical simulations could explore the enormous chemical space more efficiently. The reliability and accuracy of quantum chemical simulations have become important factors for material screening. We designed a theoretical protocol capable of predicting redox properties in excited states with high accuracy for a selected model system of dihydroquinoxalino[2,3-b]quinoxaline derivatives. Herein, three factors were considered as critical to achieving reliable predictions with accurate physics: the solvent medium effect on excited-state geometries, an adequate amount of Hartree-Fock exchange (HFX), and the consideration of double-excitation character in excited states. We determined that it is necessary to incorporate solvent medium during geometry optimizations to obtain planar excited-state structures that are consistent with the experimentally observed modest Stokes shift. While density functionals belonging to the generalized gradient approximation family perform well for the prediction of photoelectrochemical properties, an incorrect description of exciton boundedness (spontaneous dissociation of excitons or extremely weak boundedness) on small organic molecules was predicted. The inclusion of an adequate amount of Hartree-Fock exchange was suggested as one approach to obtain bound excitons, which is physically reasonable. The last consideration is the double-excitation character in S-1 states. As revealed by the second-order algebraic diagrammatic construction theory, non-negligible double excitations exist in S-1 states in our model systems. Time-dependent density functional theory (TDDFT) is blind to doubly excited states, and this motivated us to use spin-flip DFT (SF-DFT). We established a theoretical protocol that could provide highly accurate estimations of photophysical properties and ground-/excited-state redox properties, focusing on the three factors mentioned above. Geometry optimization with DFT and TDDFT employing the B3LYP functional (20% HFX) in solution and energy refinement by SF-DFT reproduced the experimental redox properties in the excited and ground states remarkably well with mean signed deviations (MSDs) of 0.01 and -0.15 V, respectively. This theoretical protocol is expected to contribute to the understanding of exciton behavior in organic PCs and to the efficient design of new promising PC candidates.