We have systematically investigated a series of polycyclic aromatic hydrocarbons (PAHs) with armchair edges that maximize the aromaticity, denoted as Clar PAHs, using density functional theory. Their structures fall into three major categories: branched, intermediate, and armchair. Branched PAHs contain up to 60 carbons, they are eroded and the least stable, and their spectra are the most complex. Armchair PAHs are the most stable and their spectra differ from the nominal PAH spectra by lacking a 11.2 μm band and having their 7.8 and 8.2 μm bands coalesce as their size increases. Only intermediate and armchair PAHs have 12.7/13.5 μm PAH band intensity ratios that are consistent with observations. The fitting results show that Clar PAH spectra are more consistent with class B than class A sources, with only a few small Clar PAHs contributing to the fit of the class A source IRAS 23133+6050 and large Clar PAHs contributing to the fit of the class B source IRAS 17347−3139, and NGC 7027. Overall, our study suggests that large Clar PAHs are potential emitters in class B sources.