Model Hamiltonian for Predicting the Bandgap of Conjugated Systems
Committee Members: Advisor: Xi Lin, MSE/ME; Srikanth Gopalan, MSE/ME; David J. Bishop,
MSE/ECE/Physics; David Campbell, ECE/Physics; Appointed Chair: Harold Park, MSE/ME
Abstract: Fundamental to developing novel organic electronics is the ability to model and understand the relationship between the chemical structure and electronic properties of π -conjugated systems. We develop the adapted Su-Schrieffer-Heeger Hamiltonian to calculate the bandgaps for conjugated systems and obtain new insights. We find that structures with aromatic rings fused along the direction of the conjugation path, such as thienoacene, may planarize the structure but does not significantly decrease the bandgap of the individual chains, simultaneously demonstrating that ring torsion angle effects are negligible. Fusing rings perpendicular to the chain direction creates monomers with lower bandgaps to polymerize, but the electronic hopping between units in the polymer is reduced due to increased unit aromatization and the system does not fully take advantage of band formation from polymerization to lower the bandgap. Copolymers of perpendicular and parallel fused ring monomers are a good compromise that takes advantage of the lower bandgap of perpendicular fused ring monomers but still allows enough hopping between units due to spacing of the parallel fused units to lower the polymer bandgap significantly. Polyacene is known to be unique in that its conjugated path is not strictly one dimensional so its bandgap tends to zero, but short oligomers have edge defects and a non-zero bandgap. Using insights from our model we propose modifications to finite sized oligoacenes to remove edge defects from the electronic structure and lower the bandgap to less than half of their original values. The excellent agreement obtained with 180 independent experimental points is achieved by fitting each new heteroatom using a single representative system, showing the transferability of the model. The model has a computational efficiency eight orders of magnitude better than ab-initio calculations and can also generate geometric structural data.