平面、環狀及莫氏帶狀多環芳香烴的電子構造之理論研究

Theoretical Study of Electronic Structure with Planar, Cyclic, and Mobius-type Polycyclic Aromatic Hydrocarbons

許睿玄(Ray-Shun Shu)

指導教授 ： 金必耀

國立臺灣大學/理學院/化學研究所/碩士(2011年)

https://doi.org/10.6342/NTU.2011.01302

摘要

鋸齒狀的碳奈米絲帶(Graphene nanoribbons)藉由赫巴德模型(Hubbard model)在非限定自洽場計算(unrestricted Hartree-Fock approximation)下有自旋對稱破缺基態(broken spin symmetry ground state)。Polyacenes是最窄的鋸齒狀碳奈米絲帶也有自旋對稱破缺基態，Cyclic polyacenes可以藉由彎曲Polyacenes建構出來並且也有和Polyacenes相似的自旋極化(spin polarization)。Polyacenes和cyclic polyacenes的自旋對稱破缺基態之能量隨著分子尺寸增加和電子排斥變強而降低並且可以由constrains spin PPP的計算中得到那些組態。
莫比烏斯帶(Mobius strip)只有一個面並且可以用一個紙帶旋轉半圈再把兩端粘上之後製作出來，Mobius polyacenes有鋸齒狀的邊緣因此我們預期Mobius polyacenes也有自旋對稱破缺基態。Polyacenes和cyclic polyacenes的自旋密度分佈是交錯的，因此polyacenes和cyclic polyacenes的兩個邊緣有不同的自旋密度相(spin density phases)。Mobius polyacenes是只有一個邊的面而且會發生自旋極化因此可以觀察到兩個自旋密度相的交界稱之為自旋孤子(spin soliton) 。我們藉由AM1和QCFF-PI的計算觀察Mobius polyacenes的幾何結構和自旋孤子之關係，聚烯(polyene)的鍵長是交錯的可是polyacenes在邊緣的鍵傾向相同的鍵長，Mobius polyacene可以想成一條聚乙烯沿著莫比烏斯帶邊緣繞並且Mobius polyacenes在一些位置有鍵長的變化。

關鍵字

莫氏帶 ； 非限定自洽場 ； 自旋極化 ； 自旋孤子 ； 電子構造

並列摘要

Graphene nanoribbons with zigzag edge have broken spin symmetry ground state by the Hubbard model with unrestricted Hartree-Fock approximation. Polyacenes are narrow graphene nanoribbons with zigzag and also have broken spin symmetry states. Cyclic polyacenes can be constructed by bending polyacenes have spin polarization that similar to polyacenes. Broken symmetry states of polyacenes and cyclic polyacenes have a lower energy with large size and strong electron repulsion and can be found by constrains spin PPP calculation.
Mobius strip is only one side and can be obtained by twisting one edge of a band through 180° and then joining the ends. Mobius polyacenes have zigzag edge and therefore we predicted Mobius polyacenes also have broken spin symmetry ground state. Spin density population of polyacenes and cyclic polyacenes are alternation and therefore two edge sides of polyacenes and cyclicpolyacenes have different spin density phases. Mobius polyacenes are one side surfaces and have spin polarization and therefore Mobius polyacenes can be observed two spin density phases interface that called spin soliton. We observe geometry and spin soliton relation of Mobius polyacenes by AM1 and QCFF-PI calculation. Polyenes have bond length alternation and polyacenes favor equal bond length with edge bond. Mobius polyacene can be considered as a single polyacetylene along Mobius strip edge and Mobius polyacene have bond length difference at some location.

並列關鍵字

Mobius ； unrestricted Hartree-Fock ； spin polarization ； spin soliton ； electron structure

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