由富勒烯之共振結構探討其穩定度與合成起始物

Kekulé Structures of Fullerenes: a Theoretical View of Stability and Precursors

林映廷(Ying-Ting Lin)

指導教授 ： 金必耀

國立臺灣大學/理學院/化學研究所/碩士(2018年)

https://doi.org/10.6342/NTU201801874

摘要

本論文分成兩大章，第一章討論富勒烯的共振結構個數及其穩定度之關係。富勒烯的共振結構可以對應到數學上的完美匹配，故我們使用數學上計算完美匹配個數的FKT演算法來計算C120以內所有的富勒烯異構物，及C160以內所有IPR富勒烯的共振結構個數。IPR富勒烯之共振能與共振結構個數有相當良好的線性關係，亦即IPR富勒烯之共振結構個數能拿來測定其π電子穩定度，而穩定能與共振結構個數的關係則相對不明朗，C80以前的IPR異構物之共振結構個數相對穩定能，在排除某些例外之後，有相對強的線性關係，但在較高碳數的富勒烯，還必須加上對稱來進一步排除立體張力的差異，才有較強的線性關係，這代表在適當的條件下，富勒烯的共振結構個數確實能作為穩定性的測度。
第二章則提供了一套能夠系統性建構富勒烯全合成之起始物的策略。合成上的起始物可以被視為一種富勒烯的分子展開圖，將富勒烯沿著邊剪開攤開在平面上，但保留所有的頂點。我們注意到富勒烯的共振結構包含了所有可能的單雙鍵排列方式，藉由移除共振結構上適當的雙鍵，我們便能系統性地建構所有可能的分子展開圖，而這些展開圖都是可能的起始物。我們也實際建構了巴克球的分子展開圖。這套以拆解共振結構建構起始物的方法，為實驗上的全合成提供了更多起始物的可能。

關鍵字

富勒烯 ； 共振結構 ； 完美匹配 ； FKT演算法 ； 展開圖

並列摘要

Two topics are included in this thesis. In the first topic, the relation between number of Kekulé structures and fullerene’s stability is studied. Kekulé structures in fullerene chemistry correspond to perfect matchings in mathematics, so that we could introduce the FKT algorithm in mathematics on fullerenes to enumerate their Kekulé structures. The number of Kekulé structures in distinct fullerene isomers up to C120 and IPR isomers up to C160 are counted, demonstrating the relatively strong correlation between resonance energy, which is an index of π- electronic stability, and raw Kekulé counts for IPR fullerenes. Although the relation between internal energy and Kekulé counts for fullerenes is quite poor, after some steric factors such as pentagon adjacency and symmetry are considered , the relatively good correlation are shown, and this points out that the Kekulé counts for fullerene could be a measurement of stability in certain condition.
In the second topic, a strategy to obtain potentially sensible precursors of fullerene is studied. The precursors can be considered as a particular form of Dürer’s polyhedral net, which will be called molecular Dürer’s net, lying flat on a plane and can be folded back to become the original fullerene. Moreover, many chemically sensible fullerene nets that could become potential precursors for the chemical synthesis of fullerene can be deduced from Kekulé structures of fullerene. The distribution of single and double bonds in Kekulé structures form different kinds of interesting labyrinth patterns on a fullerene polyhedron. Systematically removing some of these double bonds, the remaining structures then form unfolded molecular Dürer’s nets. We believe that these fullerene nets derived from Kekulé structures are potentially sensible precursors which can be used as a guide of the total synthesis of fullerene for chemists.
Keywords: fullerene; Kekulé structures; perfect matching; FKT algorithm; Dürer's net

並列關鍵字

fullerene ； Kekulé structures ； perfect matching ； FKT algorithm

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