Strongly Correlated Electronic Structure of Some Graphene Nano Ribbons and Nano Flakes

An electronic structure study of carbon-based materials has become essential in recent times, as they emerge as promising materials for organic molecular devices. The active electrons residing in the π-molecular orbitals of these systems are strongly correlated, rendering the simple molecular orbital (MO) picture inadequate to accurately capture their electronic properties. The Pariser-Parr-Pople model, which incorporates long-range electron-electron repulsions, is the electronic model of choice for studying these systems. In this mini-review, we introduce the model Hamiltonian and discuss modern numerical methods such as the exact diagonalization and the highly accurate density matrix renormalization group (DMRG) methods, both of which are commonly employed to probe this model. We present our findings on organic molecules like pyrene, triphenylene, benzopyrene, perylene, 1,12-benzoperylene, coronene, and ovalene, considered as graphene nano flakes (GNFs), along with representative graphene nano ribbons (GNRs) such as 2-ZGNR, 3-ZGNR, 5-AGNR and 6-AGNR (Z for zigzag and A for armchair edges), as well as polychrysene and fused azulene. For GNFs, we examine fluorescence properties, singlet fission, and triplet-triplet annihilation in the context of organic light-emitting diodes and organic photovoltaic devices, based on the energies of the low-lying states. Our studies also reveal that previous predictions made using effective one-electron models regarding ZGNRs and AGNRs with $3p+2$ (where $p$ is an integer) dimer bonds across the width are incorrect. We further find that narrow ZGNRs, in the polymer limit, can exhibit a high-spin ground state, contradicting the one-electron picture of edge magnetism predicting a zero-spin ground state. Additionally, we predict that fused azulene structures, which may form along the grain boundaries of graphene layers, can exhibit a high-spin ground state in the polymer limit.