本研究針對含5-6-5 雜環硬桿式發色團分子(5-6-5 heterocyclic
rigid-rod chromophores) 的衍生物之二次非線性光學效應中的一階超極化率β(first hyperpolarizability) ，利用Gaussian03軟體來計算發色團的光學性質，並作有系統的計算分析，以期望能替未來合成此類發色團時，能掌握設計發色團的重點。本研究所著重的重點在於(1)了解含5-6-5 雜環硬桿式發色團分子與其他類似之硬桿式分子在非線性光學的情況 (2)了解各共軛組成對發色團的非線性光學影響 (3)了解電子施體、電子受體數量對發色團的非線性光學影響。
結果顯示，含5-6-5 雜環硬桿式結構必須在接近電子受體的狀況下發色團才會有好的非線性光學性質；若將含5-6-5 雜環硬桿式接近於電子施體，則會導致非線性光學性質的變差，之間的β差異最高可達30%，這種現象也是5-6-5 雜環硬桿式結構異於其他類似之硬桿式分子之處。共軛組成上也以雙鍵、Thiophene等結構上較柔軟或是含有雜質原子的共軛組成較好，以含有15個雙鍵構成之含5-6-5 雜環硬桿式發色團為例，β值可達1.44x10-26esu；最後在電子施體、受體數量上從一個電子施體─一個電子受體到兩個電子施體─兩個電子受體，β差異可達116%，但是這些多電子施體、多電子受體造成結構上的不穩定時，在本研究中的例子β僅差異5%。
透過CASTEP能帶解析的分析，發現β值受到電子施體的影響主要是在HOMO、受到電子受體的影響主要是在LUMO，而共軛橋的部分是在HOMO或LUMO之外的分子軌域；而這HOMO或LUMO之外的分子軌域會隨著共軛組成種類以及數量不同而有所差異，如雙鍵為HOMO-2以及LUMO+1，苯環為HOMO-2、HOMO-1及LUMO+1。而含5-6-5 雜環硬桿式結構的影響主要在HOMO以下的軌域，以含雙鍵為例則為HOMO-2。這些分子軌域與結構的關係可以進一步透過分子軌域圖形的分析加以確認。

A computational analysis on the first hyperpolarizability (β) of 5-6-5 heterocyclic rigid-rod benzobisthiazole-based chromophores and their derivatives has been systematically investigated in this study by the software Gaussian03, in an effort to provide a molecular design criterion for better opto-electonic properties. The specific objectives of this study have been focused on (1) understanding of 5-6-5 heterocyclic rigid-rod chromophores and other similar compounds in nonlinear optical property, (2) control on the nonlinear optical properties through the manipulation of the conjugated composition of the chromophores, (3) understanding the effect of the donor and acceptor of chromophore on the nonlinear optical property.
The results show that β value of a chromophore with its 5-6-5 heterocyclic rigid-rod structure near the acceptor is 30 % higher than the one with the same structure near the donor; this reflects a unique property of 5-6-5 heterocyclic rigid-rod structure quite different from other chromophores. In conjugated chromophores, those having double bonds or thiophenes, which have soft structures or heteroatoms, would offer higher β values. For example, a 5-6-5 heterocyclic rigid-rod chromophore with 15 double bonds has a β value up to 1.44 x 10-26esu. In the study of multi-donors and acceptors, from 1 donor- 1 acceptor to 2 donors- 2 acceptors, the difference in β could be up to 116%; however, this difference reduces to only 5% if the chromophere structure becomes unstable.
From the band-resolved analysis, it is found that β values of chromophores are affected by the electronic donor via its HOMO part, the electronic acceptor via its LUMO part, while the conjugated bridge via its molecular orbital exclusive of HOMO and LUMO, depending on the type and degree of conjugation, i.e., HOMO-2 and LUMO+1 for double bonds and HOMO-2, HOMO-1, and LUMO+1 for phenyl moieties. For the 5-6-5 heterocyclic rigid-rod structure, β value is mainly affected by those molecular orbital below HOMO, i.e., HOMO-2 for those containing double bonds. Further detailed elucidation on the relation between molecular orbital and molecular structure of chromophores can be ambiguously depicted through analyses of electronic distribution on the molecular orbital.

目錄
摘要 i
Abstract ii
目錄 iii
圖目錄 vi
表目錄 viii

壹、緒論 1
1-1 前言 1
1-2 研究動機 2
1-3 研究目標 2

貳、文獻回顧 5
2-1非線性光學 5
2-2 非線性光學材料發展 6
2-2-1 無機非線性光學材料 7
2-2-2 有機非線性光學材料 8
2-2-3 非線性光學發色團發展 9
2-3 計算化學方法 15
2-4 計算化學軟體 17

叁、計算軟體與硬體設備 19

肆、結果 22
4-1 計算測試 22
4-1-1 不同理論模型的測試 22
4-1-2 理論計算和實驗值比較的測試 22
4-1-3 不同計算模組和實驗值比較的測試 23
4-1-4 不同基底函數(basis set)的比較 24
4-1-5 和其他化學軟體(MOPAC)的比較 24
4-2 雜環及多環結構的極化率計算 26
4-3 位置效應 28
4-4 不同共軛組成及長度對一階超極化率之影響 30
4-4-1 trans-double bond 30
4-4-2 1,4-Phenyl 31
4-4-3 2,5-thiophene 32
4-4-4 Triple bond 33
4-4-5 1,4-phenylenevinylene 35
4-4-6 1,4-phenyleneethynylene 36
4-4-7 2,5-thienylenevinylene 36
4-5 結構軟硬對一階超極化率之影響 39
4.6 其他類型組成設計之發色團 41
4-6-1 具cyclohexene結構之發色團 41
4-6-2 具azo型結構之發色團 43
4-7 雙電子施體及雙電子受體型發色團 45
4-7-1 雙電子施體/雙電子受體的數量效應 46
4-7-2 雙電子施體或雙電子受體架橋分子 49

伍、討論 55
5-1 計算測試之誤差討論 55
5-2 發色團共軛系統變化討論 55
5-2-1 雙鍵、苯環、三鍵及Thiophene結構 56
5-2-2 1,4-phenylenevinylene、1,4-phenyleneethynylene以及2,5-thienylenevinylene結構 65
5-2-3 雙電子施體/雙電子受體型結構 71
5-3 能隙差異對β值的影響 86

陸、結論與未來工作 88
6-1 結論 88
6-2 未來工作 90

參考文獻 91

附錄 94
A-1 已發展之發色團合成流程 94
A-2 雜環作為電子施體或電子受體之非線性光學性質 96

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