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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/105245


    Authors: 闕子翔;Chueh, Tsu-Hsiang
    Contributors: 淡江大學物理學系碩士班
    李明憲;Lee, Min-Hsien
    Date: 2015
    Abstract: 分析方法發展:鍵結密度分析法與孤立電子分析法,能夠對使用密度泛函理論計算、解Kohn-Sham薛丁格方程式得出了系統的總電子雲的結果後,作電子雲的貢獻類型的分解。在此指的是能區分出固體材料或者分子中不同鍵結類型的電子雲(鍵結密度分析法),以及能找出不參與鍵結的電子雲(孤立電子分析法)。
    簡介:
    孤立電子與非線性光學現象─「二倍頻」的關係密切。
    以往實驗與理論計算發現,二倍頻係數(second harmonic coefficient)大部分的貢獻是來自於陰離子基團。這些陰離子基團存在於硼氧化物β-BaB2O4(BBO)、LiB3O5(LBO)、CsB3O5(CBO)、CsLiB6O10(CLBO) (因為非線性光學材料中氧化物的種類不少)中。陰離子基團指的是這些硼氧化物晶體中硼氧共價鍵結形成的各種不同的「子結構」。這些「子結構」對於二倍頻有相當的貢獻。然而藉由我們研究群發展的分析方法(倍頻係數能帶解析方法與孤立電子分析工具)分析,其解析度更好,已能鎖定「就是硼氧基團中的氧原子的孤立電子貢獻了二倍頻」。所以將來孤立電子分析工具將有助於在材料設計上,專門找有這種孤立電子存在的結構。
    另外,目前仍在發展中的鍵結密度分析法,正好與孤立電子分析法相反,是用來分析晶體或是分子的鍵結電子貢獻的工具,能夠將總電子雲作類型分解 (分類為σ鍵、π鍵、δ鍵、φ鍵以及其各自的反鍵anti-bonding)。將來也能夠將態密度(Density of states)、吸收能譜等作貢獻分解。上述分析方法須將原子軌域函數轉動到特定鍵的自然座標軸上,以利對稱性的浮現。過去研究群已經實作了數值轉動,目前新採用了Wigner-D 矩陣對原子軌域基底函數作轉動。但是,有興趣的系統之電荷密度究竟長得像哪種鍵結類型呢?數學上就是和有興趣的系統算出來的波函數做投影的動作(類似Mulliken population)。
    總言之,以上兩種分析方法將來都有助於分子、晶體(固體)材料的設計,提高電子結構分析的「解析度」。

    [1]Z.H. Lin, X.X. Jiang ,L. Kang , P. Gong, S. Luo ,M.H. Lee. (2014). J. Phys. D: Appl. Phys, Vol.47, No.25
    [2] Chun-Hung Lo. (2005). Master''s thesis. New Taipei City: Tamkang University, Department of Physics.
    [3] R.N.Rashkeev, W.R.L. Lamberrecht, B. Segall. (1998). PRB, Vol.57, No.7, p3905-3919
    [4] M.H.Lee, C.H. Yang, and J.H. Jan, (2004). PRB, Vol.70, 235110
    [5] R. S.Mulliken. (1955). J.ChemPhys. Vol.23, No.10, p1833-1840
    Over the past few years, more and more calculation results [1] revealed that the connection between nonbonding (lone-pair) electrons and the second harmonic generation (SHG) which is a phenomenon that the frequency of incident laser light can be doubled after the light pass through some materials called non-linear crystals such as β-BaB2O4(BBO), LiB3O5(LBO), CsB3O5(CBO), CsLiB6O10(CLBO), etc.
    Hence, professor Ming-Hsien Lee first proposed a new method named Lone-pair Density Analysis (LPDOS)[2] for calculating the density of states as well as the electron number of nonbonding. In this thesis, one of my two works is establishing this new method and atempts to use it to show that SHG is really comes from the nonbonding electrons.
    Therefore, once this work is done, utilizing both of SHG calculation[3][4] and LPDOS method can benefit to the scientists and engeneers to find more new, useful nonlinear materials.

    On the other hand, my second work is rotating Atomic Orbitals (AO) with Wigner-D matrix or Wigner-D functions in Bonding Density Analysis (BD) which is a method that can classify the Kohn-Sham electron density with different bond types such as σ bonding, π bonding, δ bonding, φ bonding, and also the anti-bonding of each of them based on Mulliken population [5].
    This new rotation method is necessary because of the directionality of covalent bonding.In molecules or solids, it exist a particular natural bonding direction (bonding axis) that the AO must be rotated along this direction in mathematics for the combination of each two atoms.

    At last, the conclusion is that improving and implementing these works (BD and LPDOS methods) may facilitate the resolution of the study of electronic structures in the future.
    [1]Z.H. Lin, X.X. Jiang ,L. Kang , P. Gong, S. Luo ,M.H. Lee. (2014). J. Phys. D: Appl. Phys, Vol.47, No.25
    [2] Chun-Hung Lo. (2005). Master''s thesis. New Taipei City: Tamkang University, Department of Physics.
    [3] R.N.Rashkeev, W.R.L. Lamberrecht, B. Segall. (1998). PRB, Vol.57, No.7, p3905-3919
    [4] M.H.Lee, C.H. Yang, and J.H. Jan, (2004). PRB, Vol.70, 235110
    [5] R. S.Mulliken. (1955). J.ChemPhys. Vol.23, No.10, p1833-1840.
    Appears in Collections:[物理學系暨研究所] 學位論文

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