Accurate prediction of the electronic properties of zigzag graphene nanoribbons (ZGNRs) has been very challenging for conventional electronic structure methods due to the presence of strong static correlation effects. To meet the challenge, we study the singlet-triplet energy gaps, vertical ionization potentials, vertical electron affinities, fundamental gaps, and symmetrized von Neumann entropy (i.e., a measure of polyradical character) of hydrogen-terminated ZGNRs with different widths and lengths using our recently developed thermally-assistedoccupation density functional theory (TAO-DFT) [Chai, J.-D. J. Chem. Phys. 2012, 136, 154104], a very efficient method for the study of large strongly correlated systems. Our results are in good agreement with the available experimental and high-accuracy ab initio data. The ground states of ZGNRs are shown to be singlets for all the widths and lengths investigated. With the increase of ribbon length, the singlet-triplet energy gaps, vertical ionization potentials, and fundamental gaps decrease monotonically, while the vertical electron affinities and symmetrized von Neumann entropy increase monotonically. On the basis of the calculated orbitals and their occupation numbers, the longer ZGNRs are shown to possess increasing polyradical character in their ground states, where the active orbitals are mainly localized at the zigzag edges.
Owing to the presence of strong static correlation effects, accurate prediction of the electronic properties (e.g., the singlet-triplet energy gaps, vertical ionization potentials, vertical electron affinities, fundamental gaps, symmetrized von Neumann entropy, active orbital occupation numbers, and real-space representation of active orbitals) of cyclacenes with n fused benzene rings (n = 4–100) has posed a great challenge to traditional electronic structure methods. To meet the challenge, we study these properties using our newly developed thermally-assisted-occupation density functional theory (TAO-DFT), a very efficient method for the study of large systems with strong static correlation effects. Besides, to examine the role of cyclic topology, the electronic properties of cyclacenes are also compared with those of acenes. Similar to acenes, the ground states of cyclacenes are singlets for all the cases studied. In contrast to acenes, the electronic properties of cyclacenes, however, exhibit oscillatory behavior (for n ≤ 30) in the approach to the corresponding properties of acenes with increasing number of benzene rings. On the basis of the calculated orbitals and their occupation numbers, the larger cyclacenes are shown to exhibit increasing polyradical character in their ground states, with the active orbitals being mainly localized at the peripheral carbon atoms.
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