In this computational study, we investigate the electronic properties of zigzag graphene nano-parallelograms (GNPs), which are parallelogram-shaped graphene nanoribbons of various widths and lengths, using thermally-assisted-occupation density functional theory (TAO-DFT). Our calculations reveal a monotonic decrease in the singlet-triplet energy gap as the GNP length increases. The GNPs possess singlet ground states for all the cases examined. With the increase of GNP length, the vertical ionization potential and fundamental gap decrease monotonically, while the vertical electron affinity increases monotonically. Besides, as the GNP length increases, the symmetrized von Neumann entropy increases monotonically, denoting an increase in the degree of multi-reference character associated with ground-state GNPs. The occupation numbers and real-space representation of active orbitals indicate that there is a transition from the nonradical nature of the shorter GNPs to the increasing polyradical nature of the longer GNPs. In addition, the edge/corner localization of active orbitals is found for the wider and longer GNPs.
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