Conjugated Molecules Described by a One-Dimensional Dirac Equation

被引:8
作者
Ernzerhof, Matthias [1 ]
Goyer, Francois [1 ]
机构
[1] Univ Montreal, Dept Chim, Montreal, PQ H3C 3J7, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
ZIGZAG GRAPHENE NANORIBBONS; EDGE; DOTS;
D O I
10.1021/ct1000044
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
Starting from the Huckel Hamiltonian of conjugated hydrocarbon chains (ethylene, allyl radical, butadiene, pentadienyl radical, hexatriene, etc.), we perform a simple unitary transformation and obtain a Dirac matrix Hamiltonian. Thus already small molecules are described exactly in terms of a discrete Dirac equation, the continuum limit of which yields a one-dimensional Dirac Hamiltonian. Augmenting this Hamiltonian with specially adapted boundary conditions, we find that all the orbitals of the unsaturated hydrocarbon chains are reproduced by the continuous Dirac equation. However, only orbital energies close to the highest occupied molecular orbital/lowest unoccupied molecular orbital energy are accurately predicted by the Dirac equation. Since it is known that a continuous Dirac equation describes the electronic structure of graphene around the Fermi energy, our findings answer the question to what extent this peculiar electronic structure is already developed in small molecules containing a delocalized pi-electron system. We illustrate how the electronic structure of small polyenes carries over to a certain class of rectangular graphene sheets and eventually to graphene itself. Thus the peculiar electronic structure of graphene extends to a large degree to the smallest unsaturated molecule (ethylene).
引用
收藏
页码:1818 / 1824
页数:7
相关论文
共 33 条
  • [31] CdS-modified one-dimensional g-C3N4 porous nanotubes for efficient visible-light photocatalytic conversion
    Chong, Ben
    Chen, Lei
    Han, Dezhi
    Wang, Liang
    Feng, Lijuan
    Li, Qin
    Li, Chunhu
    Wang, Wentai
    CHINESE JOURNAL OF CATALYSIS, 2019, 40 (06) : 959 - 968
  • [32] Cyclic arginyl-glycyl-aspartic acid (RGD) peptide-induced synthesis of uniform and stable one-dimensional CdTe nanostructures in aqueous solution
    He, Hua
    Sun, Xing
    Wang, Xiaojuan
    Sun, Yawei
    Xu, Hai
    Lu, Jian R.
    RSC ADVANCES, 2014, 4 (23): : 11794 - 11797
  • [33] Rb8Nb10Ge6O41: a new niobium-germanate crystal featuring unique one-dimensional [Nb7O30]∞ chains and wide mid-IR transparency
    Chai, Jing
    She, Yuheng
    Jiao, Jinmiao
    Li, Lili
    Ye, Ning
    Hu, Zhanggui
    Wu, Yicheng
    Li, Conggang
    DALTON TRANSACTIONS, 2024, 53 (06) : 2696 - 2702