In this work, two different classes of poly aromatic hydrocarbon (PAH) systems have been investigated in order to characterize the amount of polyradical character and to localize the specific regions of chemical reactivity: (a) the non-Kekule triangular structures phenalenyl, triangulene and a yr-extended triangulene system with high-spin ground state and (b) PAHs based on zethrenes, p-quinodimethane-linked bisphenalenyl, and the Clar goblet containing varying polyradical character in their singlet ground state. The first class of structures already have open-shell character because of their high-spin ground state, which follows from the bonding pattern, whereas for the second class the open-shell character is generated either because of the competition between the closed-shell quinoid Kekule and the open-shell singlet biradical resonance structures or the topology of the a-electron arrangement of the non-Kekule form. High-level ab initio calculations based on multireference theory have been carried out to compute singlet triplet splitting for the above-listed compounds and to provide insight into their chemical reactivity based on the polyradical character by means of unpaired densities. Unrestricted density functional theory and Hartree-Fock calculations have been performed for comparison also in order to obtain better insight into their applicability to these types of complicated radical systems.