The one-electron states of (7,38) armchair graphene nanoribbon (AGNR) have been investigated in the ground and excited singlet electronic states by a multi-configuration ensemble density functional theory method. The quasiparticle energies for both electron removal and electron addition states were used to construct the electronic bands of the bulk and zigzag edge states of the ribbon. The zigzag edge states of the ribbon are dispersionless and localized at the ribbon termini. Energetically, the electron removal and electron addition edge states are separated by 2.4 eV, which is in good agreement with the experimentally measured splitting of 2.45±0.10 eV in AGNR of similar length. Excitation of the edge electrons results in a highly electrically polarized singlet excited state, where some of the delocalized bulk orbitals become confined within the structural units (anthracene), thus leading to the formation of Wannier–Stark ladder states.

Implications of the edge states for the band structure of armchair graphene nanoribbons
    Abstract
    1 Introduction
    2 Results and discussion
    3 Conclusions
    4 Methods
    Acknowledgements 
    References

• Michael Filatov(Center for Multidimensional Carbon Materials, Institute for Basic Science (IBS), UNIST‑gil 50, Ulsan 44919, Republic of Korea) Corresponding author
• Seung Kyu Min(Center for Multidimensional Carbon Materials, Institute for Basic Science (IBS), UNIST‑gil 50, Ulsan 44919, Republic of Korea, Department of Chemistry, Ulsan National Institute of Science and Technology (UNIST), UNIST‑gil 50, Ulsan 44919, Republic of Korea)
• Anna Pomogaeva(Institute of Chemistry, Saint Petersburg State University, Universitetskaya emb. 7/9, St. Petersburg 199034, Russia)