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研究生： 許文一
Hsu, Wen-Yi
論文名稱： 天然鍵性軌域的應用：過渡金屬六羰基和單取代五羰基錯合物
Applications of Natural Bond Orbital (NBO) Analysis: Transition-metal hexacarbonyl and mono-substituted pentacarbonyl complexes
指導教授： 王小萍
Wang, Shao-Pin
學位類別： 博士
Doctor
系所名稱： 理學院 - 化學系
Department of Chemistry
論文出版年： 2008
畢業學年度： 96
語文別： 中文
論文頁數： 299
中文關鍵詞： 回饋貢獻 、天然鍵性軌域 、三中心四電子超越鍵 、配位子
外文關鍵詞： 3-center 4-electron hyperbond, back-donation, natural bond orbital, ligand
相關次數： 點閱：62  下載：0 
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    • 本文可以分成四個單元，而第一單元包含源始分子軌域理論；這裡介紹時間不相依Schrödinger方程式內的Hamiltonian和波函數，以及根據Schrödinger方程式所獲得的分子軌域；相關的軟體介紹則是以高斯套裝軟體為主。第二單元包含天然鍵性軌域分析，它可以根據分子軌域理論所獲得的密度矩陣來獲得量化版的Lewis結構；根據二級擾動理論，鍵結軌域和反鍵結軌域之間的donor-acceptor相互作用可以使分子整體變得更穩定，而此種相互作用所導致的軌域能量下降便稱為第二級能量下降[E(2)值]；相關的軟體介紹則是以NBO 5.0程式為主。第四單元所包含的一些計算則是跟離子液體溶液的性質有關。
    第三單包含實例應用；利用高斯98 Linux版和NBO 5.0程式，我們可以獲得過渡金屬六羰基M(CO)6和單取代五羰基M(CO)5X錯合物的2pi軌域分佈值（[2pi]）。在M(CO)6 (M = Cr, Mo, W)當中，由計算和NMR實驗所獲得的pi回饋貢獻顯示出相似的傾向：3d ~ 5d > 4d。根據NBO分析結果，M(CO)6包含有兩種donor-acceptor相互作用會對pi回饋貢獻有所影響：三中心四電子超越鍵 → pi*CO (3CHB超共軛)和M → pi*CO。從這裡可以發現3CHB超共軛是影響pi回饋貢獻的主要因素。在M(CO)5X錯合物當中（M = Cr, Mo, W），根據軸向[2pi]可以排列出配位子X的pi-acceptor能力順序：X = F– < Cl– < Br– < I– < CN– < Quinuclidine < NMe3 < Pyridine < Pyrazine < N2 < PPh3 < PPh2Me < PPhMe2 < PMe3 < H2 < P(OMe)3 < PI3 < PBr3 < PCl3 < PF3 < CO < SiO < CS < BF < NO+。

    This article includes four units and the first unit contains Ab Initio Molecular Orbital (MO) theory. Here it introduces the Hamiltonian and wavefunctions of the Schrödinger equation, and molecular orbitals obtained from the Schrödinger equation. The related software introduction is Gaussian package in chief. The second unit covers Natural Bond Orbital (NBO) analysis. It could acquire quantized Lewis structures on the basis of the density matrix obtained from MO theory. According to second-order perturbation theory, the donor-acceptor interaction between bonding and antibonding orbitals can stabilize a molecule on the whole, and the orbital energy lowing due to this interaction is called second-order energy lowing [E(2)]. The related software introduction is NBO 5.0 program in chief. The fourth unit involves some calculations about the properties of ionic liquid solutions.
    The third unit embraces applications for example. Using Linux version of Gaussian 98 and NBO 5.0 program, we can obtain 2pi orbital populations ([2pi]) of transition-metal hexacarbonyl [M(CO)6] and mono-substituted pentacarbonyl [M(CO)5X] complexes. In M(CO)6 (M = Cr, Mo, W), pi-back-donations of the calculated and NMR experiments show the similar trend: 3d ~ 5d > 4d. According to the results of NBO analysis, M(CO)6 contains two donor-acceptor interactions, 3-center, 4-electron hyperbond → pi*CO (3CHB hyperconjugation) and M → pi*CO, for pi-back-donation. The trend of M → pi*CO is 3d < 4d < 5d and that of 3CHB hyperconjugation is 3d > 5d ~ 4d. It could be found that the 3CHB hyperconjugation is the main factor that influences the pi-back-donation. In M(CO)5X complexes (M = Cr, Mo, W), we can arrange the pi-acceptor ability of ligands X in increasing order: X = F– < Cl– < Br– < I– < CN– < Quinuclidine < NMe3 < Pyridine < Pyrazine < N2 < PPh3 < PPh2Me < PPhMe2 < PMe3 < H2 < P(OMe)3 < PI3 < PBr3 < PCl3 < PF3 < CO < SiO < CS < BF < NO+, according to axial [2pi].

    中文摘要...................................................... I 英文摘要..................................................... II 謝誌........................................................ III 目錄......................................................... IV 表目錄....................................................... IX 圖目錄...................................................... XIV 元素週期表................................................. XVII 中英文對照表.............................................. XVIII 第一單元 源始分子軌域理論..................................... 1 第一章 序論................................................... 2 1-1 理論模型.................................................. 2 1-2 分子軌域模型.............................................. 3 第二章 理論背景............................................... 6 2-1 Schrödinger 方程式........................................ 6 2-2 原子核運動的分離：位能曲面................................ 7 2-3 原子單位.................................................. 8 2-4 分子軌域理論.............................................. 9 2-5 基底集合擴展............................................. 11 2-6 變異特性方法和Hartree-Fock 理論.......................... 14 2-6-1 封閉殼層系統........................................... 15 2-6-2 開放殼層系統........................................... 17 2-6-3 Koopmans’定理和游離能................................. 18 2-7 對稱性性質............................................... 19 2-8 Mulliken 分佈分析........................................ 19 2-9 多重行列式波函數......................................... 22 2-9-1 完全組態相互作用....................................... 25 2-9-2 有限組態相互作用....................................... 27 2-9-3 Møller-Plesset 擾動理論................................ 30 2-10 單電子性質：電子二偶極距................................ 33 第三章 計算上的問題.......................................... 35 3-1 序論..................................................... 35 3-2 電腦問題的邏輯結構....................................... 35 3-3 計算上的方法............................................. 39 3-3-1 用於積分值解的方法..................................... 39 3-3-2 用於求解自我滿足方程式的方法........................... 41 3-3-3 用於值解能量梯度的方法................................. 43 3-3-4 用於積分轉型的方法..................................... 44 3-3-5 分子對稱性的使用....................................... 46 3-3-6 用於產生3-D 分子軌域和總電子密度製圖的方法............. 48 第四章 模型的選擇............................................ 50 4-1 序論..................................................... 50 4-2 Hartree-Fock 方法........................................ 50 4-2-1 封閉殼層行列式波函數................................... 50 4-2-2 開放殼層行列波函數..................................... 51 4-3 高斯函數的原子基底集合................................... 52 4-3-1 最小基底集合........................................... 53 4-3-2 向外延伸的sp 基底集合.................................. 57 4-3-3 極化基底集合........................................... 65 4-3-4 用於超共價分子的有效基底集合........................... 68 4-3-5 整合擴散函數的基底集合................................. 71 4-3-6 使用高斯基底集合之Hartree-Fock 模型的相對計算時間...... 72 4-4 電子相關性方法........................................... 72 4-4-1 有限組態相互作用....................................... 73 4-4-2 Møller-Plesset 擾動處理方式............................ 73 4-4-3 相關性方法的相對計算時間............................... 74 4-5 分子對稱性............................................... 74 4-5-1 標準分子幾何........................................... 75 4-5-2 分子幾何的不完全最佳化................................. 76 4-5-3 分子幾何的完整最佳化................................... 77 4-5-4 使用從較低階理論水準所獲得的幾何....................... 79 4-6 命名..................................................... 80 4-7 結論..................................................... 80 第五章 輸入和輸出............................................ 82 5-1 高斯03 基本輸入與操作介面................................ 82 5-2 輸出數據說明............................................. 84 5-3 GaussView 的操作方法..................................... 87 第六章 參考文獻.............................................. 89 第二單元 天然鍵性軌域分析................................... 124 第一章 序論................................................. 125 第二章 理論背景............................................. 128 2-1 簡介.................................................... 128 2-2 主要能力與限制.......................................... 130 2-3 天然定域化軌域之間的轉型................................ 131 2-3-1 原子軌域轉型成天然原子軌域（ AOs → NAOs）............ 131 2-3-2 天然原子軌域轉型成天然混成軌域（NAOs → NHOs）........ 133 2-3-3 天然混成軌域轉型成天然鍵性軌域（NHOs → NBOs ）....... 135 2-3-4 天然鍵性軌域轉型成天然定域化分子軌域（NBOs → NLMOs ） 137 2-4 以NBOs 為基礎的增補模組................................. 138 2-4-1 天然共振理論（NRT）分析............................... 138 2-4-2 天然鍵性-鍵性極化特性（NBBP）分析..................... 141 2-4-3 天然立體分析（NSA）................................... 142 2-4-4 天然能量分解分析（NEDA）.............................. 143 2-4-5 傳統分子軌域（CMO）分析............................... 144 2-4-6 天然化學遮蔽（NCS）分析............................... 145 2-4-7 天然J-耦合（NJC）分析................................. 147 2-4-8 三中心四電子超越鍵（3CHB）搜尋分析.................... 149 第三章 輸入和輸出........................................... 151 3-1 基本分析的輸入與輸出.................................... 151 3-1-1 天然分佈分析（NPA）................................... 151 3-1-2 天然鍵性軌域（NBO）分析............................... 152 3-1-3 天然混成軌域（NHO）方向性分析......................... 154 3-1-4 擾動理論能量分析...................................... 154 3-1-5 天然鍵性軌域（NBO）摘要............................... 155 3-2 額外分析的輸入和輸出.................................... 155 3-2-1 二偶極距分析.......................................... 156 3-2-2 天然定域化分子軌域（NLMO）分析........................ 157 3-2-3 天然共振理論（NRT）分析............................... 157 3-2-4 天然鍵性-鍵性極化特性（NBBP）分析..................... 160 3-2-5 天然立體分析（NSA）................................... 160 3-2-6 天然能量分解分析（NEDA）.............................. 161 3-2-7 傳統分子軌域（CMO）分析............................... 161 3-2-8 天然化學遮蔽（NCS）分析............................... 162 3-2-9 天然J-耦合（NJC）分析................................. 163 3-2-10 三中心四電子超越鍵（3CHB）搜尋分析................... 166 第四章 參考文獻............................................. 168 第三單元 實例應用........................................... 188 第一章 序論................................................. 189 第二章 計算方法............................................. 191 第三章 結果與討論........................................... 194 3-1 鍵結模型與電子分佈...................................... 194 3-2 合適的基底集合搭配...................................... 197 3-3 針對特殊Lewis 結構的天然鍵性軌域分析描述................ 199 3-4 合適基底集合搭配的計算可靠度............................ 200 3-5 TM(CO)6q 內各種性質的列傾向和族傾向..................... 202 3-6 TM(CO)6q 的天然鍵性軌域分析和天然分佈分析結果........... 204 3-7 第六族TM(CO)5L（含自由配位基）的各種計算結果............ 209 第四章 結論................................................. 215 第五章 參考文獻............................................. 216 第四單元 附錄............................................... 280 實例應用-離子液體（ionic liquid）........................... 281

    第一單元 源始分子軌域理論
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    58. (a) first-row: Hehre, W. J.; Stewart, R. F.; Pople, J. A. J. Chem. Phys. 1969, 51, 2657; (b) second-row: Hehre, W. J.; Ditchfield, R.; Stewart, R. F.; Pople, J. A. ibid. 1970, 52, 2769; (c) third-row, main group: Pietro, W. J.; Levi, B. A.; Hehre, W. J.; Stewart, R. F. Inorg. Chem. 1980, 19, 2225; (d) fourth-row, main group: Pietro, W. J.; Hout, Jr., R. F.; Blurock, E. S.; Hehre, W. J.; DeFrees, D. J.; Stewart, R. F. ibid. 1981, 20, 3650; (e) first- and second-row transition metals: Pietro, W. J.; Hehre, W. J. J. Comput. Chem. 1983, 4, 241.
    59. (a) Clementi, E.; Raimondi, D. L. J. Chem. Phys. 1963, 38, 2686; (b) Clementi, E.; Raimondi, D. L.; Reinhartdt, W. P. ibid. 1967, 47, 1300; (c) Clementi, E.; Roetti, C. Atomic and Nuclear Data Tables 1974, 14.
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    63. (a) first-row: Binkley, J. S.; Pople, J. A.; Hehre, W. J. J. Am. Chem. Soc. 1980, 102, 939; (b) second-row: Gordon, M. S.; Binkley, J. S.; Pople, J. A.; Pietro, W. J.; Hehre, W. J. ibid. 1982, 104, 2797; (c) third- and fourth-row main-group: Dobbs, K. D.; Hehre, W. J. J. Comput. Chem. 1986, 7, 359; (d) first- and second- row transition metals: Dobbs, K. D.; Hehre, W. J. J. Comput. Chem. 1987, 8, 861, 880.
    64. van Duijneveldt, F. B. Gaussian Basis Sets for the Atoms H-Ne for Use in Molecualr Calculations; I.B.M. Publication RJ945 (#16437).
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    66. carbon to fluorine: Ditchfield, R.; Hehre, W. J.; Pople, J. A. J. Chem. Phys. 1971, 54, 724; (b) boron: Hehre, W. J.; Pople, J. A. ibid. 1972, 56, 4233; (c) lithium, beryllium: Dill, J. D.; Pople, J. A. ibid. 1975, 62, 2912; (d) phosphorous to chlorine: Hehre, W. J.; Lathan, W. A. ibid. 1972, 56, 5255.
    67. (a) carbon to fluorine: Hehre, W. J.; Ditchfield, R.; Pople, J. A. J. Chem. Phys. 1972, 56, 2257; (b) lithium, beryllium, and boron: Binkley, J. S.; Pople, J. A. ibid. 1977, 66, 879; (c) second-row: Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. A. J. Chem. Phys. 1982, 77, 3654.
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    69. Hariharan, P. C.; Pople, J. A. Chem. Phys. Lett. 1972, 66, 217.
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    71. See for example: (a) DeFrees, D. J.; Levi, B. A.; Pollack, S. K.; Hehre, W. J.; Binkley, J. S.; Pople, J. A. J. Am. Chem. Soc. 1979, 101, 4085; (b) Dykstra, C. E.; Schaefer III, H. F. in The Chemistry of Ketenes and Allenes; Patai, S. ed.; Wiley: New York, 1980, p. 1.
    72. Collins, J. B.; Schleyer, P. v. R.; Binkley, J. S.; Pople, J. A. J. Chem. Phys. 1976, 64, 5142.
    73. Pietro, W. J.; Francl, M. M.; Hehre, W. J.; DeFrees, D. J.; Pople, J. A.; Binkley, J. S. J. Am. Chem. Soc. 1982, 104, 5039. 3-21G(*) basis sets for third- and fourth- row main-group elements: see ref. 63c.
    74. (a) Random, L. Modern Theoretical Chemistry; Schasfer III, H. F. ed.; Plenum Press: New York, 1977, vol. 4, p. 333; (b) Hopkinson, A. C. Progress in Theoretical Organic Chemistry; Csizmada, I. G. ed.; Elsevier: New York, 1977, vol. 2, p. 194.; (c) Simons, J. Ann. Rev. Phys. Chem. 1977, 28, 15.
    75. (a) Janousek, B. K.; Brauman, J. I. Gas Phase Ion Chemistry; Bowers, M. T. ed.; Academic Press: New York, 1979, vol. 2, p.53; (b) Bartmess, J. E.; McIver, Jr., R. T. ibid., vol. 2, p. 88.
    76. (a) Duke, A. J. Chem. Phys. Lett. 1973, 21, 275; (b) Ahlrich, R. ibid. 1972, 15, 609; 1973, 18, 512; (c) Driessler, F.; Ahlrichs, R.; Staemmler, V.; Kutzelnigg, W. Theor. Chim. Acta. 1973, 30, 315; (d) Webster, B. J. Phys. Chem. 1975, 79, 2809; (e) Dunning, T. H.; Hay, P. J. Modern Theoretical Chemistry; Schaefer, III, H. F. ed.; Plenum Press: New York, 1977, vol. 3, p. 1;(f) Dykstra, C. E.; Hereld, M.; Lucchese, R. R.; Schaefer III, H. F.; Meyer, W. J. Chem. Phys. 1977, 67, 4071; (g) Davidson, R. B.; Hudak, M. L. J. Am. Chem. Soc. 1977, 99, 3918; (h) Jönsson, B.; Karlstrom, G.; Wennerström, H. ibid. 1978, 100, 1658; (i) Kollmar, H. ibid. 1978, 100, 2665; (j) Dykstra, C. E.; Arduengo, A. J.; Fukunaga, T. ibid. 1978, 100, 6007; (k) Jordon, K. D. Acc. Chem. Res. 1979, 12, 36; (l) Wilmshurst, J. K.; Dykstra, C. E. J. Am. Chem. Soc. 1980, 102, 4668; (m) Eades, R. A.; Gaussian, P. G.; Dixon, D. A. ibid. 1981, 103, 1066; (n) Bonaccorsi, R.; Petrongolo, C.; Scrocco, E.; Tomasi, J. Chem. Phys. Lett. 1969, 3, 473; (o) Survatt, G. T.; Goddard, III, W. A. Chem. Phys. 1977, 23, 39; (p) Marynick, D. S.; Dixon, D. A. Proc. Natl. Acad. Sci., USA 1977, 74, 410. (q) Cársky, P.; Zahradnik, R.; Urban, M.; Kello, V. Chem. Phys. Lett. 1979, 61, 85; (r) Cársky, P.; Urban, M. Lecture Notes in Chemistry, 16, Ab Initio Calculation Methods and Applications in Chemistry; Springer-Verlag: Berlin 1980, p. 50, and references cited therein; (s) Chandrasekhar, J.; Andrade, J. G.; Schleyer, P. v. R. J. Am. Chem. Soc. 1981, 103, 5609; (t) Spitznagel, G. W.; Clark, T.; Chandrasekhar, J.; Schleyer, P. v. R. J. Comput. Chem. 1982, 3, 353; (u) Clark, T.; Schleyer, P. v. R.; Houk, K. N.; Rondan, N. G. J. Chem. Soc., Chem. Commu. 1981, 579; (v) Schleyer, P. v. R.; Chandrasekhar, J.; Kos, A. J.; Clark, T.; Spitznagel, G. W. ibid. 1981, 882; (w) Chandrasekhar, J.; Andrade, J. G.; Schleyer, P. v. R. J. Am. Chem. Soc. 1981, 103, 5612; (x) Wrthwein, E.-U.; Krogh-Jespersen, M.-B.; Schleyer, P. v. R. Inorg. Chem. 1981, 20, 3663; (y) Rondan, N. G.; Houk, K. N.; Beak, P.; Zajdel, W. J.; Chandrasekhar, J.; Schleyer, P. v. R. J. Org. Chem. 1981, 46, 4108; (z) Chandrasekhar, J.; Kahn, R. A.; Schleyer, P. v. R. Chem. Phys. Lett. 1982, 85, 493.
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    第二單元 天然鍵性軌域分析
    1. 在此主要是以NBO 5.0程式為主，相關文獻可以見Weinhold, F.; Landis, C. R. Chem. Educ. Res. Pract. Eur. 2001, 2, 91.
    2. (a) Reed, A. E.; Weinhold, F. J. Chem. Phys. 1983, 78, 4066; (b) Reed, A. E.; Weinstock, R. B.; Weinhold, F. J. Chem. Phys. 1985, 83, 735.
    3. (a) Foster, J. P.; Weinhold, F. J. Am. Chem. Soc. 1980, 102, 7211; (b) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88, 899; (c) Weinhold, F.; Natural Bond Orbital Methods. In Encyclopedia of Computational Chemistry; Schleyer, P. v. R.; Allinger, N. L.; Clark, T.; Gasteiger, J.; Kollman, P. A.; Schaefer, III, H. F.; Schreiner, P. R., Eds. John Wiley & Sons: UK, 1998; Vol. 3, p. 1792; (d) Weinhold. F.; Carpenter, J. E.; In The structure of Small Molecules and Ions; Naaman, R.; Vager, Z., Eds. Plenum: New York, 1988; p. 227.
    4. Reed, A. E.; Weinhold, F. J. Chem. Phys. 1985, 83, 1736.
    5. Carpenter, J. E.; Weinhold, F. J. Mol. Struct. (Theochem) 1988, 169, 41.
    6. 然而要注意的是，有些電子結構套裝程式並沒有針對特定類型的開放殼層波函數（例如，以GUGA數學式子所計算出來的MCSCF或CASSCF波函數）提供自旋密度矩陣。在這些情況當中NBO分析程式就只能應用於『最大自旋配對（maximum spin-paired，MSPNBO）』的數學式子。
    7. Löwdin, P.-O. Phys. Rev. 1955, 97, 1474.
    8. 並非絕對是如此。若是所計算的波函數並不是使用以原子為中心的基底集合，則首先就必須針對每一個獨立的原子去計算出所需要的波函數（根據分子計算的真實基底集合以及幾何），並且選用高度佔有的天然軌域作為適合那個原子的『原子軌域』。
    9. 這些是Linux版的NBO 5.0程式所擁有的增補模組，視窗版高斯98或是高斯03內附的NBO 3.1程式並沒有這些增補模組。
    10. (a) Glendening, E. D.; Weinhold, F. J. Comput. Chem. 1998, 19, 593; (b) Glendening, E. D.; Weinhold, F. J. Comput. Chem. 1998, 19, 610; (c) Glendening, E. D.; Badenhoop, J. K.; Weinhold, F. J. Comput. Chem. 1998, 19, 628; (d) Feldgus, S.; Landis, C. R.; Glendening, E. D.; Weinhold, F. J. Comput. Chem. 2000, 21, 411.
    11. Zimmerman, H. E.; Weinhold, F. J. Am. Chem. Soc. 1994, 116, 1579.
    12. (a) Badenhoop, J. K.; Weinhold, F. J. Chem. Phys. 1997, 107, 5406; (b) Badenhoop, J. K.; Weinhold, F. J. Chem. Phys. 1997, 107, 5422; (c) Badenhoop, J. K.; Weinhold, F. Int. J. Quantum Chem. 1999, 72, 269.
    13. (a) Glendening, E. D.; Streitwieser, A. J. Chem. Phys. 1994, 100, 2900; (b) Glendening, E. D. J. Am. Chem. Soc. 1996, 118, 2473; (c) Schenter, G. K.; Glendening, E. D. J. Phys. Chem. 1996, 100, 17152.
    14. Bohmann, J. A.; Weinhold, F.; Farrar, T. C. J. Chem. Phys. 1997, 107, 1173.
    15. Wilkens, S. J.; Westler, W. M.; Markley, J. L.; Weinhold, F. J. Am. Chem. Soc. 2001, 123, 12026.
    16. 視窗版高斯98或是高斯03內附的NBO 3.1程式最大只能計算到100個原子，而且也無法將此限制解除。
    17. Levine, I. N. Quantum Chemistry, 5th ed.; Prentice-Hall, Inc.: New York, 1991, 2000.
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    第三單元 實例應用
    1. 網址：http://nobelprize.org/chemistry/laureates/1998/index.html。
    2. 網址：http://www.chem.ccu.edu.tw/~consult/jnl8907.htm#1998年諾貝爾化學獎。
    3. Kohn, W.; Electronic Structure of Matter - Wave Functions and Density Functionals In Nobel Lectures, Chemistry 1996-2000; Grenthe, I., Ed. World Scientific Publishing Co.: Singapore, 2003, p. 213.
    4. Pople, J. A.; Quantum Chemical Models In Nobel Lectures, Chemistry 1996-2000; Grenthe, I., Ed. World Scientific Publishing Co.: Singapore, 2003, p. 246.
    5. 官方網址：http://www.gaussian.com/。
    6. 官方網址：http://www.hyper.com/。
    7. 官方網址：http://www.wavefun.com/。
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    17. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, Jr., J. A.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, Revision A.11; Gaussian, Inc.: Pittsburgh, PA, 1998. 原始碼編譯環境：Mandrake Linux operating systems，release 10.1，kernel 2.6.8.1-24mdksmp。
    18. Glendening, E. D.; Badenhoop, J. K.; Reed, A. E.; Carpenter, J. E.; Bohmann, J. A.; Morales, C. M.; Weinhold, F. NBO, Version 5.0; Theoretical Chemistry Institute, University of Wisconsin, Madison, WI, 2001 (http://www.chem.wisc. edu/~nbo5). 一般高斯98套裝軟體內附的NBO程式是以3.1版本為主，若需要換成5.0版本，則必須先以NBO 5.0程式原始碼取代高斯98內附的NBO 3.1程式原始碼，之後在Linux作業系統下進行整體高斯98套裝軟體的編譯過程，編譯完後的高斯98就會含有NBO 5.0程式。
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