Density functional theory DFT is a widely used computational method in quantum chemistry and solid-state physics to investigate the electronic structure and properties of materials. In the case of graphene nanoribbons GNRs with zigzag edges, DFT calculations can be employed to predict their electronic transport properties, such as conductance and current-voltage I-V curves.To perform a DFT calculation for a zigzag graphene nanoribbon, one would need to consider the following steps:1. Construct a model of the zigzag graphene nanoribbon, including the atomic positions and lattice structure.2. Choose an appropriate exchange-correlation functional, such as the local density approximation LDA or the generalized gradient approximation GGA .3. Perform a self-consistent field SCF calculation to obtain the ground-state electron density and energy.4. Calculate the band structure and density of states DOS to analyze the electronic properties of the GNR.5. Employ a non-equilibrium Green's function NEGF formalism combined with DFT to compute the electronic transport properties, such as the conductance and I-V curves.The DFT calculations for zigzag graphene nanoribbons typically predict that they exhibit unique electronic properties, such as edge states and a tunable bandgap. These features make them promising candidates for various nanoelectronic applications, such as field-effect transistors, sensors, and spintronic devices.However, it is essential to note that DFT calculations have certain limitations, such as the choice of exchange-correlation functional and the treatment of van der Waals interactions, which can affect the accuracy of the predicted electronic properties.When comparing DFT predictions to experimental measurements, it is crucial to consider the effects of factors such as edge roughness, defects, and environmental factors e.g., substrate interactions and temperature on the electronic transport properties of zigzag GNRs. These factors can lead to discrepancies between the DFT predictions and experimental results. Nevertheless, DFT calculations can provide valuable insights into the fundamental electronic properties of zigzag GNRs and guide the design of novel nanoelectronic devices based on these materials.