ominance of broken bonds and unpaired nonbonding 冟-electrons in the band gap expansion and edge states generation in graphene nanoribbons

Incorporating the bond-order-length-strength (BOLS) correlation theory to the density-functional-theory calculations and experimental observations has led to consistent insight into the electronic behavior of graphene nanoribbons (GNRs) from the perspective of bond formation, dissociation and relaxation and the associated dynamics and energetics of charge densification, localization and polarization. The consistency between the BOLS predictions and the observed coordination dependence of bond contraction and the associated thermal instability, mechanical strength and band structure variation in various situations evidences the significance of the broken bond that induces local strain and quantum trapping. The inconsistency between the theoretically and experimentally observed band gap expansions in GNRs indicates particularly the impact of the unpaired nonbonding (or called 冟-bond) electrons and the adsorbate-induced inhomogeneous repulsion along the edges. A perturbation to the Hamiltonian by the local strain and edge trapping dictates intrinsically the band structure yet the presence and polarization of the nonbonding states by the nearby densely-trapped bonding electrons and the adsorbate-induced inhomogeneous repulsion along the edges dominate the observed edge states.