| Summary: | 碩士 === 國立臺灣大學 === 化學研究所 === 106 === 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
|
|---|
