This study investigates the effects of edge hydrogenation and length changes on the electronic and magnetic properties of armchair PSI (Ψ)-graphene nanoribbons (AΨGNRBs) and zigzag PSI (Ψ)- graphene nanoribbons (ZΨGNRBs) with changing the length and a repetition number from 1 to 10. Density Functional Theory (DFT) and Generalized Gradient Approximation (GGA-1/2) were used for this purpose. The Perdew-Burke-Ernzerhof (PBE) method was used to calculate the exchange-correlation energy. Results demonstrated that hydrogenation of AΨGNRBs causes a band gap of about 0.73 eV with slight changes due to the varied length of the nanoribbon (NRB), but with a constant value of 0.7366 in repetitions from 4 to 10. They are utilized in the fields of optoelectronics, photonics, LEDs, lasers, sensors, and photonic devices. This NRB is a non-magnetic N-type semiconductor. It is used in transistors, and quantum devices that require precise electronic (rather than spintronic) control. However, ZΨGNRBs with changing the length and a repetition number from 1 to 10 are non-magnetic conductors, and edge hydrogenation does not cause a band gap. These nanostructures are compatible with conventional electronic (non-spintronic) devices. The formation energy of hydrogen-passivated AΨGNRBs and ZΨGNRBs is lower than that of the non-passivated counterparts, indicating greater stability of the passivated NRBs. Moreover, the formation energy of AΨGNRBs from 1 to 10 repetitions is lower than that of ZΨGNRBs. This significant reduction in the formation energy indicates greater stability and a more optimal structure of AΨGNRBs compared to ZΨGNRBs. This issue is of critical importance in the design of nanomaterials.
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