Band Gap Energy of Some Kekuléan Polycyclic Aromatic Hydrocarbon as Finite-Size Graphene: A DFT Study

The effect of size and shapes of some Kekuléan Polycyclic Aromatic Hydrocarbon (PAH) were studied using the density functional theory with B3LYP hybrid function and LANL2DZ basis set using Gaussian09 software program. Four different geometries of PAH: Linear (L), Hexagonal (H), Zigzag (Z) and Rhombus (R) were evaluated. The results showed that band gap energy (Eg) tends to decrease as the size of the increase, but some geometry decrease faster. Simple analysis also showed that |log(N)| = o(Eg(N)) for L, H and R geometries, indicating that Eg will become 0 for a finite size. These trends indicate that PAH size and shape can be tuned to modulate electronic properties and redox behavior, offering routes to optimize PAH-based anodes for LIBs. In terms of industrial relevance, the ability to tailor Eg through geometry provides design guidelines to achieve higher energy density, faster charging, and improved cycling stability, while potentially enabli ng scalable and cost-effective synthesis and processing of carbon-based organic electrode materials. The findings support the development of PAH-based anodes as a viable pathway to enhance performance and manufacturability in lithium-ion battery technology.