Excitation Symmetry and Origin of Dark States in \pi-Conjugated Molecules

Utilizing the exact diagonalization method, the optical absorption spectra of two\begindocument\pi\enddocument-conjugated molecules, anthracene and pyrene, are calculated in various dielectric environments. In a confined quantum system with an anisotropic geometry, it is commonly believed that the first excited state is localized along the elongated direction. In the meantime, the dipole approximation says that the transitions to those states localized along the elongated direction shall generally have higher intensities. In this work we report that anthracene and pyrene would respectively fail these intuitive expectations. It is found that the first active transition in anthracene is always polarized along its short axis direction. For pyrene, it is revealed that the transition of the highest intensity is the one polarized along the short axis direction of the molecule. Furthermore, the first excited state in either anthracene or pyrene is often found to be optically inactive, which is successfully attributed to the short-range interactions by examining the energy spectra in varying interaction environments.