The paper by Young-Woo Son, Marvin L. Cohen, and Steven G. Louie explores the energy gaps in graphene nanoribbons (GNRs) with armchair or zigzag edges, both passivated with hydrogen. Using first-principles calculations, they find that GNRs with armchair edges exhibit band gaps due to quantum confinement and edge effects, while those with zigzag edges have band gaps arising from a staggered sublattice potential due to edge magnetization. The authors derive analytic scaling rules for the band gaps as a function of ribbon width, which agree well with their ab initio results. They also discuss the edge effects and the role of spin degrees of freedom in determining the band gaps. The study highlights the importance of considering edge effects in the electronic properties of GNRs, which are crucial for understanding their potential applications in nanoelectronics.The paper by Young-Woo Son, Marvin L. Cohen, and Steven G. Louie explores the energy gaps in graphene nanoribbons (GNRs) with armchair or zigzag edges, both passivated with hydrogen. Using first-principles calculations, they find that GNRs with armchair edges exhibit band gaps due to quantum confinement and edge effects, while those with zigzag edges have band gaps arising from a staggered sublattice potential due to edge magnetization. The authors derive analytic scaling rules for the band gaps as a function of ribbon width, which agree well with their ab initio results. They also discuss the edge effects and the role of spin degrees of freedom in determining the band gaps. The study highlights the importance of considering edge effects in the electronic properties of GNRs, which are crucial for understanding their potential applications in nanoelectronics.