The quest for cheap, light, flexible materials for use in electronics applications has resulted in the exploration of soft organic materials as possible candidates, and several polycyclic aromatic hydrocarbons (PAHs) have been shown to be versatile (semi)conductors. In this investigation, dispersion inclusive density functional theory is used to explore all of the current crystalline PAHs within the Cambridge Structure Database (CSD) from both structural and electronic standpoints. Agreement is achieved between the experimental and calculated crystalline structures, as well as the electronic properties. Specifically, variation between the mass densities, unit cell parameters, and intermolecular close contact fractions were within +5%, +/-2%, and +/-1% of experiment, respectively. It is found that a simple addition of a similar to 1 eV constant to the DFT-PBE gaps provides good agreement with the experimental optical gaps of both gas phase (within +/-2.6%) and crystalline (within +/-3.5%) PAHs. Structural and electronic analysis revealed several correlations/trends, where ultimately limits in the band gaps as a function of structure are established. Finally, analysis of the difference between band gaps of the isolated molecules and crystals (Delta E-g(Xtal-Mols)) demonstrates that Delta E-g(Xtal-Mols) can be captured qualitatively by PBE and PBE0 functionals, yet significant quantitative deviations remain between these functionals and experiment.