Evolution of the energy gaps of stacked polycyclic aromatic hydrocarbons

π-Conjugated molecules with large highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO-LUMO) energy gaps Δ E H − L have been extensively studied due to their unique optoelectronic properties. In this work, we focus on polycyclic aromatic hydrocarbon (PAH) stacks exhibiting significantly reduced Δ E H − L values. We derive a two-parameter formula for the evolution of the HOMO-LUMO gap Δ E H − L ( N ) of ideal stacked PAHs as the number of N of monomers in the stack increases and validate the formula by comparing it with density-functional-theory (DFT) simulations of stacks of up to N = 15 . This means that measurement of the energy gaps of a monomer and dimer alone can be used to predict the energy gaps of longer stacks. The electronic properties were primarily calculated using the generalized gradient approximation (GGA) method. To reinforce our findings, additional DFT calculations were performed using both the HONPAS and Gaussian packages.