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).
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China Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R ChinaChina Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R China
He, Hua
Sun, Xing
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China Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R ChinaChina Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R China
Sun, Xing
Wang, Xiaojuan
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China Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R ChinaChina Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R China
Wang, Xiaojuan
Sun, Yawei
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China Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R ChinaChina Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R China
Sun, Yawei
Xu, Hai
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China Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R ChinaChina Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R China
Xu, Hai
Lu, Jian R.
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Univ Manchester, Sch Phys & Astron, Biol Phys Lab, Manchester M13 9PL, Lancs, EnglandChina Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R China
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China Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R ChinaChina Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R China
He, Hua
Sun, Xing
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China Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R ChinaChina Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R China
Sun, Xing
Wang, Xiaojuan
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China Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R ChinaChina Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R China
Wang, Xiaojuan
Sun, Yawei
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China Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R ChinaChina Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R China
Sun, Yawei
Xu, Hai
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China Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R ChinaChina Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R China
Xu, Hai
Lu, Jian R.
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机构:
Univ Manchester, Sch Phys & Astron, Biol Phys Lab, Manchester M13 9PL, Lancs, EnglandChina Univ Petr East China, Ctr Bioengn & Biotechnol, Qingdao 266580, Peoples R China