Visualizing Electronic Vibrations on the Wave Function Tiles of the Low-Lying Singlet Excited States of Benzene.

The representation of the electronic structure of benzene is important for understanding the properties of planar and monocyclic organic carbon compounds. Resonant Kekulé and conjugated structures based on localized and delocalized electronic theories, respectively, can be used to depict the ground state of benzene; however, depictions of its electrons vibrating in the excited states remain to be clarified. This paper presents a novel algorithm for exploring the three lowest lying vertically singlet excited states of benzene, focusing on the electronic excitations between occupied π and unoccupied π* orbitals. We show that electronic vibrations between neighboring carbon nuclei on the wave function tile of benzene undergo excitation in the π → π* transition. Furthermore, we reveal that electronic vibrations from the ground state can explain the optical dark or bright properties of the relevant excited states, as well as transition dipole moments (TDMs) calculated from the centroid of electron densities. Moreover, our method shows the potential intramolecular change of the molecular structures in the bright excited states. This study provides new insights into the singlet excited states of benzene and validates the algorithm as a useful tool for introducing the high-dimensional wave function to the general chemical community.