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We present a novel and systematic fragmentation scheme to treat polycyclic aromatic hydrocarbons (PAHs) built off the molecules-in-molecules composite method. Our algorithm generates a set of biphenyl and naphthalene subsystems overlapping by whole sextet rings, ensuring all calculations are performed on aromatic molecules. Hence, our method is called Aromatic Fragmentation Based on a Ring Overlap Scheme (AroBOROS), and the generated fragments may be combined to form a hierarchy of subsystems to reduce errors for more complex PAHs. Error