In recent years, polycyclic aromatic hydro-carbons (PAHs) have been studied for their electronic properties as they are viewed as nanodots of graphene. They have also been of interest as functional molecules for applications such as light-emitting diodes and solar cells. Since the last few years, varying structural and chemical properties corresponding to the size and geometry of these molecules have been studied both theoretically and experimentally. Here, we carry out a systematic study of the electronic states of several PAHs using the Pariser-Parr-Pople model, which incorporates long-range electron correlations. In all of the molecules studied by us, we find that the 2A state is below the 1B state and hence none of them will be fluorescent in the gaseous phase. The singlet-triplet gap is more than half of the singlet-singlet gap in all cases, and hence, none of these PAHs can be candidates for improved solar cell efficiencies in a singlet fission. We discuss in detail the properties of the electronic states, which include bond orders and spin densities (in triplets) of these systems.