In all TD-DFT calculations, the resolution of the identity (RI) approximation was employed to speed up the evaluation of Coulomb and exchange two-electron integrals, exploiting the chain-ofspheres method for the exact Hartree-Fock exchange. Moreover, to compare with the experimental measurements in solution, solvent effects were taken into account through the conductor-like polarizable continuum model (C-PCM) for cyclohexane, using equilibrium solvation. For the sake of clarity, in the following, the first two excited states of the pyrene monomer will be labeled as Lb (almost dark) and La (bright) according to Platt's notation, whereas the general Sn notation indicates excimer states.