We consider a five-electron system in the Hubbard model with a coupling between nearest-neighbors. The structure of essential spectrum and discrete spectrum of the systems in the third and fourth doublet states in a &...We consider a five-electron system in the Hubbard model with a coupling between nearest-neighbors. The structure of essential spectrum and discrete spectrum of the systems in the third and fourth doublet states in a <em>v</em>-dimensional lattice is investigated. We prove that the essential spectrum of the system in a third doublet state consists is the union of at most four segments, and discrete spectrum of the system is empty. We show that the essential spectrum of the system in a fourth doublet state consists of the union of at most seven segments, and discrete spectrum of the system consists of no more than one point.展开更多
The synthesis of stable open-shell hydrocarbon system comprising of pentagon defects and zigzag edges remains unexplored,which can be considered as model compounds for unraveling the spin-localized states in graphene ...The synthesis of stable open-shell hydrocarbon system comprising of pentagon defects and zigzag edges remains unexplored,which can be considered as model compounds for unraveling the spin-localized states in graphene edges.With concise synthetic approaches,twoπ-extended fluorenyl radicals were synthesized and isolated in their crystalline state.X-ray crystallographic analysis and studies on the magnetic,optical and electrochemical properties of neutral and charged species have revealed an interesting edge-dependence of the spin/charge distribution,that is,the spin and charge distribution shifted from the pentagon defects to the zigzag edges with the elongation of conjugation.Such phenomenon was unprecedented for hydrocarbon radicals and can be rationalized by the recovery of Clar Sextets in the dominant resonance structures.Remarkably,one of the radicals exhibited exceptional stability in air-saturated solutions with the half-life time up to 260 d,thus providing opportunities for the applications as electronic materials.展开更多
文摘We consider a five-electron system in the Hubbard model with a coupling between nearest-neighbors. The structure of essential spectrum and discrete spectrum of the systems in the third and fourth doublet states in a <em>v</em>-dimensional lattice is investigated. We prove that the essential spectrum of the system in a third doublet state consists is the union of at most four segments, and discrete spectrum of the system is empty. We show that the essential spectrum of the system in a fourth doublet state consists of the union of at most seven segments, and discrete spectrum of the system consists of no more than one point.
基金support from the National Natural Science Foundation of China(Grant No.21971187)the Natural ScienceFoundationof Tianjin(19JCJQJC62700)the Haihe Laboratory of Sustainable Chemical Transformations。
文摘The synthesis of stable open-shell hydrocarbon system comprising of pentagon defects and zigzag edges remains unexplored,which can be considered as model compounds for unraveling the spin-localized states in graphene edges.With concise synthetic approaches,twoπ-extended fluorenyl radicals were synthesized and isolated in their crystalline state.X-ray crystallographic analysis and studies on the magnetic,optical and electrochemical properties of neutral and charged species have revealed an interesting edge-dependence of the spin/charge distribution,that is,the spin and charge distribution shifted from the pentagon defects to the zigzag edges with the elongation of conjugation.Such phenomenon was unprecedented for hydrocarbon radicals and can be rationalized by the recovery of Clar Sextets in the dominant resonance structures.Remarkably,one of the radicals exhibited exceptional stability in air-saturated solutions with the half-life time up to 260 d,thus providing opportunities for the applications as electronic materials.
