本研究推導出諧和與非諧和振子法蘭克-康登積分的公式，並開發其計算法。在諧 和振子 FCI 的計算方面，利用了張嘉麟教授於 2008 年所使用的公式化簡技巧做為基礎 [2]，以厄米多項式以及高斯積分的數學關係式，將法蘭克-康登積分式轉換成為可適用 於任意維度分子的 FCI 計算公式。由於此公式具有封閉型式且已化簡為一般化的通式，
對於計算程式上的編碼撰寫公式有所助益，並且可透過結合量子力學計算所得的平衡結 構、振動頻率、正規振動模式(normal mode)、激發能量以及躍遷偶極矩等數據，進行如 吸收、螢光、磷光與光電子等光譜的分析以及預測，對於理論光譜學具有重要的貢獻。
為了驗證公式實際執行的成效，本研究分別以具有 102 以及 132 個振動自由度的蔻 與卵苯分子進行光電子光譜模擬。我們透過 B3LYP 計算法及 6-31G(d)、6-31G(d,p)與 6-311G(d)等基組，獲得其分子與離子的平衡結構、振動頻率等數據，再用我們開發的方 法計算 FCF，並經繪製成模擬光譜。在與蔻和卵苯的實驗光譜比對後，我們發現基本上 模擬光譜與實驗光譜的外形是相符的。
然而，在蔻的低解析度模擬光譜中，雖然三個主要躍遷譜帶的相對能量與實驗圖譜 相似，但在相對強度的對應上，第二以及第三躍遷譜帶的強度較實驗值弱，推測與熱譜 帶的躍遷有關。由於本研究尚未進行熱譜帶的計算，將熱譜帶納入考量是否會於強度修 正上會有所幫助，建議可以進行後續的研究。而在卵苯分子的光電子光譜計算上，低解 析度的模擬光譜上亦具有三個主要的躍遷譜帶，類似於實驗光譜，但在強度上仍有落 差，尚須進行進一步的研究與計算。
而在非諧和的計算上，本研究採用張教授於 2005 年所發表計算諧和振子的公式[4]
做為基礎，並結合 Palma 等人在過去使用摩斯位能計算非諧和振子 FCF 的方式[29]，進 行一階微擾公式的推導。在過去張教授將此基礎公式推導到適用於多維度的諧振子 FCF 計算，在本研究中，則將其加入一階微擾因素的考量，將其延伸至非諧和振子 FCF 的計
譜的模擬。在實驗中，採用 aug-cc-pVTZ 以及 aug-cc-pVQZ 等兩種基組，透過 CCSD(T) 計算方進行 HCl、HCl+(X)以及 HCl+(A)量子與位能曲線計算，接著利用摩斯位能公式進 行位能曲線的擬合，如此可得一階微擾公式中所需的 a 、D 等參數，並將量子計算所得e 的平衡結構、振動頻率、正規振動模式等數據，一併代入計算式中，進行一階微擾非諧 和 FCF 計算。在計算結果比較上，aug-cc-pVTZ 以及 aug-cc-pVQZ 兩基組的結果相近。
在 HCl 躍遷至 HCl+(X)的光譜圖中，不論考慮諧和振子或是非諧和振子，兩者的結 果相近，且與實驗圖譜亦有類似的結果。而在 HCl 躍遷至 HCl+(A)的光譜圖中，僅考慮 諧和振子的計算結果，僅具有五根較為明顯的躍遷訊號，且最大值出現於第二根訊號110 的位置，此與實驗圖譜最大值出現於第三根的情況不符合。若將微擾因素加入考慮，進 行非諧和振子的計算，在結果圖上可見七根明顯的躍遷訊號，第三根訊號120為最大值，
且訊號的強弱順序皆與實驗值相符，顯然於此非諧和的計算法有更貼近於實際的描述能 力。至於非諧和計算在 HCl+(A)的躍遷上有較明顯的影響，原因推測在於 HCl+(A)相較 於 HCl+(X)有較大的結構變化(約六倍)，且在位能曲線的圖形中也明顯可見 HCl+(A)與另 兩者的差異，因此僅利用諧和振子的模型進行計算將產生較大的誤差。在本研究中，雖 已證明考慮一階微擾的優勢，但由圖 3.32 中，可知理論光譜圖在訊號強度上以及訊號的 相對能量位置與實驗值較不相符，而考慮二階微擾是否能帶來修正，值得後續的研究與 探討。
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附錄
一、 蔻的平衡結構與振動頻率
表 A1: coronene 平衡結構 1
coronene 鍵長(Angstroms)及鍵角(Degrees) 計算方法：B3LYP/6-31G(d)
分子態 離子態
Name Definition Value Name Definition Value R1 R(1,2) 1.4242 R1 R(1,2) 1.412 R2 R(1,6) 1.3725 R2 R(1,6) 1.3938 R3 R(1,19) 1.0875 R3 R(1,19) 1.0864 R4 R(2,3) 1.4219 R4 R(2,3) 1.421 R5 R(2,23) 1.4243 R5 R(2,23) 1.4294 R6 R(3,4) 1.4279 R6 R(3,4) 1.4246 R7 R(3,7) 1.428 R7 R(3,7) 1.4205 R8 R(4,5) 1.4219 R8 R(4,5) 1.4283 R9 R(4,8) 1.428 R9 R(4,8) 1.4171 R10 R(5,6) 1.4242 R10 R(5,6) 1.4058 R11 R(5,16) 1.4242 R11 R(5,16) 1.4385 R12 R(6,20) 1.0875 R12 R(6,20) 1.0862 R13 R(7,10) 1.428 R13 R(7,10) 1.4171 R14 R(7,25) 1.4217 R14 R(7,25) 1.4369 R15 R(8,9) 1.428 R15 R(8,9) 1.4205
R16 R(8,14) 1.4217 R16 R(8,14) 1.4369 R17 R(9,10) 1.4279 R17 R(9,10) 1.4246 R18 R(9,11) 1.4219 R18 R(9,11) 1.421 R19 R(10,30) 1.4219 R19 R(10,30) 1.4283 R20 R(11,12) 1.4243 R20 R(11,12) 1.4294 R21 R(11,33) 1.4242 R21 R(11,33) 1.412 R22 R(12,13) 1.3725 R22 R(12,13) 1.379 R23 R(12,21) 1.0875 R23 R(12,21) 1.0864 R24 R(13,14) 1.4243 R24 R(13,14) 1.4158 R25 R(13,22) 1.0875 R25 R(13,22) 1.0859 R26 R(14,15) 1.4242 R26 R(14,15) 1.4312 R27 R(15,16) 1.3725 R27 R(15,16) 1.3662 R28 R(15,18) 1.0875 R28 R(15,18) 1.0859 R29 R(16,17) 1.0875 R29 R(16,17) 1.0862 R30 R(23,24) 1.3725 R30 R(23,24) 1.379 R31 R(23,26) 1.0875 R31 R(23,26) 1.0864 R32 R(24,25) 1.4243 R32 R(24,25) 1.4158 R33 R(24,27) 1.0875 R33 R(24,27) 1.0859 R34 R(25,28) 1.4242 R34 R(25,28) 1.4312 R35 R(28,29) 1.3725 R35 R(28,29) 1.3662 R36 R(28,31) 1.0875 R36 R(28,31) 1.0859 R37 R(29,30) 1.4242 R37 R(29,30) 1.4385 R38 R(29,32) 1.0875 R38 R(29,32) 1.0862
R39 R(30,35) 1.4242 R39 R(30,35) 1.4058 R40 R(33,34) 1.0875 R40 R(33,34) 1.0864 R41 R(33,35) 1.3725 R41 R(33,35) 1.3938 R42 R(35,36) 1.0875 R42 R(35,36) 1.0862 A1 A(2,1,6) 121.2442 A1 A(2,1,6) 121.1864 A2 A(2,1,19) 118.631 A2 A(2,1,19) 119.1975 A3 A(6,1,19) 120.1248 A3 A(6,1,19) 119.6161 A4 A(1,2,3) 118.7542 A4 A(1,2,3) 118.8684 A5 A(1,2,23) 122.485 A5 A(1,2,23) 122.2895 A6 A(3,2,23) 118.7608 A6 A(3,2,23) 118.8421 A7 A(2,3,4) 120.0009 A7 A(2,3,4) 120.0031 A8 A(2,3,7) 119.9937 A8 A(2,3,7) 119.9896 A9 A(4,3,7) 120.0054 A9 A(4,3,7) 120.0074 A10 A(3,4,5) 120.0054 A10 A(3,4,5) 120.0155 A11 A(3,4,8) 120.0008 A11 A(3,4,8) 119.9959 A12 A(5,4,8) 119.9938 A12 A(5,4,8) 119.9886 A13 A(4,5,6) 118.7556 A13 A(4,5,6) 118.8996 A14 A(4,5,16) 118.765 A14 A(4,5,16) 118.8661 A15 A(6,5,16) 122.4794 A15 A(6,5,16) 122.2344 A16 A(1,6,5) 121.2397 A16 A(1,6,5) 121.027 A17 A(1,6,20) 120.1314 A17 A(1,6,20) 119.6422 A18 A(5,6,20) 118.6289 A18 A(5,6,20) 119.3308 A19 A(3,7,10) 119.9938 A19 A(3,7,10) 119.9967
A20 A(3,7,25) 120.0055 A20 A(3,7,25) 120.0092 A21 A(10,7,25) 120.0008 A21 A(10,7,25) 119.994 A22 A(4,8,9) 119.9938 A22 A(4,8,9) 119.9967 A23 A(4,8,14) 120.0008 A23 A(4,8,14) 119.994 A24 A(9,8,14) 120.0055 A24 A(9,8,14) 120.0092 A25 A(8,9,10) 120.0054 A25 A(8,9,10) 120.0074 A26 A(8,9,11) 119.9937 A26 A(8,9,11) 119.9896 A27 A(10,9,11) 120.0009 A27 A(10,9,11) 120.0031 A28 A(7,10,9) 120.0008 A28 A(7,10,9) 119.9959 A29 A(7,10,30) 119.9938 A29 A(7,10,30) 119.9886 A30 A(9,10,30) 120.0054 A30 A(9,10,30) 120.0155 A31 A(9,11,12) 118.7608 A31 A(9,11,12) 118.8421 A32 A(9,11,33) 118.7542 A32 A(9,11,33) 118.8684 A33 A(12,11,33) 122.485 A33 A(12,11,33) 122.2895 A34 A(11,12,13) 121.2426 A34 A(11,12,13) 121.3023 A35 A(11,12,21) 118.6269 A35 A(11,12,21) 118.7481 A36 A(13,12,21) 120.1305 A36 A(13,12,21) 119.9497 A37 A(12,13,14) 121.2346 A37 A(12,13,14) 120.9318 A38 A(12,13,22) 120.1443 A38 A(12,13,22) 120.0326 A39 A(14,13,22) 118.621 A39 A(14,13,22) 119.0356 A40 A(8,14,13) 118.7629 A40 A(8,14,13) 118.925 A41 A(8,14,15) 118.7666 A41 A(8,14,15) 118.915 A42 A(13,14,15) 122.4705 A42 A(13,14,15) 122.1599
A43 A(14,15,16) 121.2347 A43 A(14,15,16) 121.0136 A44 A(14,15,18) 118.6224 A44 A(14,15,18) 118.64 A45 A(16,15,18) 120.1429 A45 A(16,15,18) 120.3464 A46 A(5,16,15) 121.2391 A46 A(5,16,15) 121.2227 A47 A(5,16,17) 118.6255 A47 A(5,16,17) 118.4896 A48 A(15,16,17) 120.1354 A48 A(15,16,17) 120.2877 A49 A(2,23,24) 121.2426 A49 A(2,23,24) 121.3023 A50 A(2,23,26) 118.6269 A50 A(2,23,26) 118.7481 A51 A(24,23,26) 120.1305 A51 A(24,23,26) 119.9497 A52 A(23,24,25) 121.2346 A52 A(23,24,25) 120.9318 A53 A(23,24,27) 120.1443 A53 A(23,24,27) 120.0326 A54 A(25,24,27) 118.621 A54 A(25,24,27) 119.0356 A55 A(7,25,24) 118.7629 A55 A(7,25,24) 118.925 A56 A(7,25,28) 118.7666 A56 A(7,25,28) 118.915 A57 A(24,25,28) 122.4705 A57 A(24,25,28) 122.1599 A58 A(25,28,29) 121.2347 A58 A(25,28,29) 121.0136 A59 A(25,28,31) 118.6224 A59 A(25,28,31) 118.64 A60 A(29,28,31) 120.1429 A60 A(29,28,31) 120.3464 A61 A(28,29,30) 121.2391 A61 A(28,29,30) 121.2227 A62 A(28,29,32) 120.1354 A62 A(28,29,32) 120.2877 A63 A(30,29,32) 118.6255 A63 A(30,29,32) 118.4896 A64 A(10,30,29) 118.765 A64 A(10,30,29) 118.8661 A65 A(10,30,35) 118.7556 A65 A(10,30,35) 118.8996
A66 A(29,30,35) 122.4794 A66 A(29,30,35) 122.2344 A67 A(11,33,34) 118.631 A67 A(11,33,34) 119.1975 A68 A(11,33,35) 121.2442 A68 A(11,33,35) 121.1864 A69 A(34,33,35) 120.1248 A69 A(34,33,35) 119.6161 A70 A(30,35,33) 121.2397 A70 A(30,35,33) 121.027 A71 A(30,35,36) 118.6289 A71 A(30,35,36) 119.3308 A72 A(33,35,36) 120.1314 A72 A(33,35,36) 119.6422 表 A2 coronene 平衡結構 2
coronene 鍵長(Angstroms)及鍵角(Degrees) 計算方法：B3LYP/6-31G(d,p)
分子態 離子態
Name Definition Value Name Definition Value R1 R(1,2) 1.4242 R1 R(1,2) 1.4135 R2 R(1,6) 1.3723 R2 R(1,6) 1.3926 R3 R(1,19) 1.0869 R3 R(1,19) 1.086 R4 R(2,3) 1.4217 R4 R(2,3) 1.4204 R5 R(2,23) 1.4242 R5 R(2,23) 1.4277 R6 R(3,4) 1.4278 R6 R(3,4) 1.4242 R7 R(3,7) 1.4279 R7 R(3,7) 1.4209 R8 R(4,5) 1.4217 R8 R(4,5) 1.4292 R9 R(4,8) 1.4279 R9 R(4,8) 1.4168 R10 R(5,6) 1.4241 R10 R(5,6) 1.406 R11 R(5,16) 1.4242 R11 R(5,16) 1.4387
R12 R(6,20) 1.0869 R12 R(6,20) 1.0856 R13 R(7,10) 1.4279 R13 R(7,10) 1.4168 R14 R(7,25) 1.4216 R14 R(7,25) 1.4362 R15 R(8,9) 1.4279 R15 R(8,9) 1.4209 R16 R(8,14) 1.4216 R16 R(8,14) 1.4362 R17 R(9,10) 1.4278 R17 R(9,10) 1.4242 R18 R(9,11) 1.4217 R18 R(9,11) 1.4204 R19 R(10,30) 1.4217 R19 R(10,30) 1.4292 R20 R(11,12) 1.4242 R20 R(11,12) 1.4277 R21 R(11,33) 1.4242 R21 R(11,33) 1.4135 R22 R(12,13) 1.3722 R22 R(12,13) 1.3806 R23 R(12,21) 1.0869 R23 R(12,21) 1.086 R24 R(13,14) 1.4242 R24 R(13,14) 1.4142 R25 R(13,22) 1.0869 R25 R(13,22) 1.0853 R26 R(14,15) 1.4242 R26 R(14,15) 1.4328 R27 R(15,16) 1.3723 R27 R(15,16) 1.3651 R28 R(15,18) 1.0869 R28 R(15,18) 1.0853 R29 R(16,17) 1.0869 R29 R(16,17) 1.0856 R30 R(23,24) 1.3722 R30 R(23,24) 1.3806 R31 R(23,26) 1.0869 R31 R(23,26) 1.086 R32 R(24,25) 1.4242 R32 R(24,25) 1.4142 R33 R(24,27) 1.0869 R33 R(24,27) 1.0853 R34 R(25,28) 1.4242 R34 R(25,28) 1.4328
R35 R(28,29) 1.3723 R35 R(28,29) 1.3651 R36 R(28,31) 1.0869 R36 R(28,31) 1.0853 R37 R(29,30) 1.4242 R37 R(29,30) 1.4387 R38 R(29,32) 1.0869 R38 R(29,32) 1.0856 R39 R(30,35) 1.4241 R39 R(30,35) 1.406 R40 R(33,34) 1.0869 R40 R(33,34) 1.086 R41 R(33,35) 1.3723 R41 R(33,35) 1.3926 R42 R(35,36) 1.0869 R42 R(35,36) 1.0856 A1 A(2,1,6) 121.2458 A1 A(2,1,6) 121.2055 A2 A(2,1,19) 118.6319 A2 A(2,1,19) 119.1487 A3 A(6,1,19) 120.1224 A3 A(6,1,19) 119.6457 A4 A(1,2,3) 118.7526 A4 A(1,2,3) 118.8643 A5 A(1,2,23) 122.4882 A5 A(1,2,23) 122.295 A6 A(3,2,23) 118.7592 A6 A(3,2,23) 118.8407 A7 A(2,3,4) 120.0009 A7 A(2,3,4) 120.0007 A8 A(2,3,7) 119.9936 A8 A(2,3,7) 119.991 A9 A(4,3,7) 120.0055 A9 A(4,3,7) 120.0082 A10 A(3,4,5) 120.0054 A10 A(3,4,5) 120.0154 A11 A(3,4,8) 120.0008 A11 A(3,4,8) 119.9948 A12 A(5,4,8) 119.9938 A12 A(5,4,8) 119.9898 A13 A(4,5,6) 118.754 A13 A(4,5,6) 118.9036 A14 A(4,5,16) 118.7633 A14 A(4,5,16) 118.8695 A15 A(6,5,16) 122.4826 A15 A(6,5,16) 122.2269
A16 A(1,6,5) 121.2413 A16 A(1,6,5) 121.0103 A17 A(1,6,20) 120.1289 A17 A(1,6,20) 119.6815 A18 A(5,6,20) 118.6298 A18 A(5,6,20) 119.3082 A19 A(3,7,10) 119.9937 A19 A(3,7,10) 119.997 A20 A(3,7,25) 120.0055 A20 A(3,7,25) 120.0103 A21 A(10,7,25) 120.0008 A21 A(10,7,25) 119.9927 A22 A(4,8,9) 119.9937 A22 A(4,8,9) 119.997 A23 A(4,8,14) 120.0008 A23 A(4,8,14) 119.9927 A24 A(9,8,14) 120.0055 A24 A(9,8,14) 120.0103 A25 A(8,9,10) 120.0055 A25 A(8,9,10) 120.0082 A26 A(8,9,11) 119.9936 A26 A(8,9,11) 119.991 A27 A(10,9,11) 120.0009 A27 A(10,9,11) 120.0007 A28 A(7,10,9) 120.0008 A28 A(7,10,9) 119.9948 A29 A(7,10,30) 119.9938 A29 A(7,10,30) 119.9898 A30 A(9,10,30) 120.0054 A30 A(9,10,30) 120.0154 A31 A(9,11,12) 118.7592 A31 A(9,11,12) 118.8407 A32 A(9,11,33) 118.7526 A32 A(9,11,33) 118.8643 A33 A(12,11,33) 122.4882 A33 A(12,11,33) 122.295 A34 A(11,12,13) 121.2442 A34 A(11,12,13) 121.3011 A35 A(11,12,21) 118.6275 A35 A(11,12,21) 118.7889 A36 A(13,12,21) 120.1282 A36 A(13,12,21) 119.91 A37 A(12,13,14) 121.2362 A37 A(12,13,14) 120.9331 A38 A(12,13,22) 120.142 A38 A(12,13,22) 119.9933
A39 A(14,13,22) 118.6217 A39 A(14,13,22) 119.0736 A40 A(8,14,13) 118.7612 A40 A(8,14,13) 118.9238 A41 A(8,14,15) 118.7649 A41 A(8,14,15) 118.9105 A42 A(13,14,15) 122.4738 A42 A(13,14,15) 122.1658 A43 A(14,15,16) 121.2364 A43 A(14,15,16) 121.0332 A44 A(14,15,18) 118.6233 A44 A(14,15,18) 118.6054 A45 A(16,15,18) 120.1403 A45 A(16,15,18) 120.3614 A46 A(5,16,15) 121.2407 A46 A(5,16,15) 121.2043 A47 A(5,16,17) 118.6263 A47 A(5,16,17) 118.4837 A48 A(15,16,17) 120.133 A48 A(15,16,17) 120.3121 A49 A(2,23,24) 121.2442 A49 A(2,23,24) 121.3011 A50 A(2,23,26) 118.6275 A50 A(2,23,26) 118.7889 A51 A(24,23,26) 120.1282 A51 A(24,23,26) 119.91 A52 A(23,24,25) 121.2362 A52 A(23,24,25) 120.9331 A53 A(23,24,27) 120.142 A53 A(23,24,27) 119.9933 A54 A(25,24,27) 118.6217 A54 A(25,24,27) 119.0736 A55 A(7,25,24) 118.7612 A55 A(7,25,24) 118.9238 A56 A(7,25,28) 118.7649 A56 A(7,25,28) 118.9105 A57 A(24,25,28) 122.4738 A57 A(24,25,28) 122.1658 A58 A(25,28,29) 121.2364 A58 A(25,28,29) 121.0332 A59 A(25,28,31) 118.6233 A59 A(25,28,31) 118.6054 A60 A(29,28,31) 120.1403 A60 A(29,28,31) 120.3614 A61 A(28,29,30) 121.2407 A61 A(28,29,30) 121.2043
A62 A(28,29,32) 120.133 A62 A(28,29,32) 120.3121 A63 A(30,29,32) 118.6263 A63 A(30,29,32) 118.4837 A64 A(10,30,29) 118.7633 A64 A(10,30,29) 118.8695 A65 A(10,30,35) 118.754 A65 A(10,30,35) 118.9036 A66 A(29,30,35) 122.4826 A66 A(29,30,35) 122.2269 A67 A(11,33,34) 118.6319 A67 A(11,33,34) 119.1487 A68 A(11,33,35) 121.2458 A68 A(11,33,35) 121.2055 A69 A(34,33,35) 120.1224 A69 A(34,33,35) 119.6457 A70 A(30,35,33) 121.2413 A70 A(30,35,33) 121.0103 A71 A(30,35,36) 118.6298 A71 A(30,35,36) 119.3082 A72 A(33,35,36) 120.1289 A72 A(33,35,36) 119.6815 表 A3: coronene 平衡結構 3
coronene 鍵長(Angstroms)及鍵角(Degrees) 計算方法：B3LYP/6-311G(d)
分子態 離子態
Name Definition Value Name Definition Value R1 R(1,2) 1.4221 R1 R(1,2) 1.4183 R2 R(1,6) 1.3694 R2 R(1,6) 1.385 R3 R(1,19) 1.0862 R3 R(1,19) 1.085 R4 R(2,3) 1.4196 R4 R(2,3) 1.4175 R5 R(2,23) 1.4223 R5 R(2,23) 1.4184 R6 R(3,4) 1.4258 R6 R(3,4) 1.421
R8 R(4,5) 1.4197 R8 R(4,5) 1.4312 R9 R(4,8) 1.4259 R9 R(4,8) 1.4145 R10 R(5,6) 1.4221 R10 R(5,6) 1.4065 R11 R(5,16) 1.4223 R11 R(5,16) 1.4357 R12 R(6,20) 1.0862 R12 R(6,20) 1.0846 R13 R(7,10) 1.4259 R13 R(7,10) 1.4145 R14 R(7,25) 1.4192 R14 R(7,25) 1.4313 R15 R(8,9) 1.426 R15 R(8,9) 1.421 R16 R(8,14) 1.4192 R16 R(8,14) 1.4313 R17 R(9,10) 1.4258 R17 R(9,10) 1.421 R18 R(9,11) 1.4196 R18 R(9,11) 1.4175 R19 R(10,30) 1.4197 R19 R(10,30) 1.4312 R20 R(11,12) 1.4223 R20 R(11,12) 1.4184 R21 R(11,33) 1.4221 R21 R(11,33) 1.4183 R22 R(12,13) 1.3693 R22 R(12,13) 1.3849 R23 R(12,21) 1.0861 R23 R(12,21) 1.085 R24 R(13,14) 1.4223 R24 R(13,14) 1.4065 R25 R(13,22) 1.0861 R25 R(13,22) 1.0846 R26 R(14,15) 1.4223 R26 R(14,15) 1.4357 R27 R(15,16) 1.3693 R27 R(15,16) 1.3605 R28 R(15,18) 1.0861 R28 R(15,18) 1.0846 R29 R(16,17) 1.0862 R29 R(16,17) 1.0846 R30 R(23,24) 1.3693 R30 R(23,24) 1.3849
R31 R(23,26) 1.0861 R31 R(23,26) 1.085 R32 R(24,25) 1.4223 R32 R(24,25) 1.4065 R33 R(24,27) 1.0861 R33 R(24,27) 1.0846 R34 R(25,28) 1.4223 R34 R(25,28) 1.4357 R35 R(28,29) 1.3693 R35 R(28,29) 1.3605 R36 R(28,31) 1.0861 R36 R(28,31) 1.0846 R37 R(29,30) 1.4223 R37 R(29,30) 1.4357 R38 R(29,32) 1.0862 R38 R(29,32) 1.0846 R39 R(30,35) 1.4221 R39 R(30,35) 1.4065 R40 R(33,34) 1.0862 R40 R(33,34) 1.085 R41 R(33,35) 1.3694 R41 R(33,35) 1.385 R42 R(35,36) 1.0862 R42 R(35,36) 1.0846
A1 A(2,1,6) 121.2617 A1 A(2,1,6) 121.2851 A2 A(2,1,19) 118.715 A2 A(2,1,19) 119.0561 A3 A(6,1,19) 120.0233 A3 A(6,1,19) 119.6588 A4 A(1,2,3) 118.7322 A4 A(1,2,3) 118.8317 A5 A(1,2,23) 122.5243 A5 A(1,2,23) 122.3368 A6 A(3,2,23) 118.7434 A6 A(3,2,23) 118.8315 A7 A(2,3,4) 120.0077 A7 A(2,3,4) 119.9937 A8 A(2,3,7) 119.9866 A8 A(2,3,7) 119.9935 A9 A(4,3,7) 120.0057 A9 A(4,3,7) 120.0128 A10 A(3,4,5) 120.0019 A10 A(3,4,5) 120.0121 A11 A(3,4,8) 120.0096 A11 A(3,4,8) 119.9943
A12 A(5,4,8) 119.9885 A12 A(5,4,8) 119.9935 A13 A(4,5,6) 118.7285 A13 A(4,5,6) 118.8978 A14 A(4,5,16) 118.7411 A14 A(4,5,16) 118.8639 A15 A(6,5,16) 122.5304 A15 A(6,5,16) 122.2382 A16 A(1,6,5) 121.268 A16 A(1,6,5) 120.9795 A17 A(1,6,20) 120.0149 A17 A(1,6,20) 119.7216 A18 A(5,6,20) 118.7171 A18 A(5,6,20) 119.299 A19 A(3,7,10) 119.9847 A19 A(3,7,10) 119.9929 A20 A(3,7,25) 120.0063 A20 A(3,7,25) 120.0127 A21 A(10,7,25) 120.009 A21 A(10,7,25) 119.9945 A22 A(4,8,9) 119.9847 A22 A(4,8,9) 119.9929 A23 A(4,8,14) 120.009 A23 A(4,8,14) 119.9945 A24 A(9,8,14) 120.0063 A24 A(9,8,14) 120.0127 A25 A(8,9,10) 120.0057 A25 A(8,9,10) 120.0128 A26 A(8,9,11) 119.9866 A26 A(8,9,11) 119.9935 A27 A(10,9,11) 120.0077 A27 A(10,9,11) 119.9937 A28 A(7,10,9) 120.0096 A28 A(7,10,9) 119.9943 A29 A(7,10,30) 119.9885 A29 A(7,10,30) 119.9935 A30 A(9,10,30) 120.0019 A30 A(9,10,30) 120.0121 A31 A(9,11,12) 118.7434 A31 A(9,11,12) 118.8315 A32 A(9,11,33) 118.7322 A32 A(9,11,33) 118.8317 A33 A(12,11,33) 122.5243 A33 A(12,11,33) 122.3368 A34 A(11,12,13) 121.2632 A34 A(11,12,13) 121.2855
A35 A(11,12,21) 118.6935 A35 A(11,12,21) 119.0558 A36 A(13,12,21) 120.0434 A36 A(13,12,21) 119.6587 A37 A(12,13,14) 121.2498 A37 A(12,13,14) 120.9791 A38 A(12,13,22) 120.0633 A38 A(12,13,22) 119.7208 A39 A(14,13,22) 118.6869 A39 A(14,13,22) 119.3 A40 A(8,14,13) 118.7506 A40 A(8,14,13) 118.8977 A41 A(8,14,15) 118.7457 A41 A(8,14,15) 118.8642 A42 A(13,14,15) 122.5037 A42 A(13,14,15) 122.2381 A43 A(14,15,16) 121.2558 A43 A(14,15,16) 121.1413 A44 A(14,15,18) 118.7065 A44 A(14,15,18) 118.587 A45 A(16,15,18) 120.0377 A45 A(16,15,18) 120.2718 A46 A(5,16,15) 121.26 A46 A(5,16,15) 121.1426 A47 A(5,16,17) 118.6952 A47 A(5,16,17) 118.5853 A48 A(15,16,17) 120.0448 A48 A(15,16,17) 120.272 A49 A(2,23,24) 121.2632 A49 A(2,23,24) 121.2855 A50 A(2,23,26) 118.6935 A50 A(2,23,26) 119.0558 A51 A(24,23,26) 120.0434 A51 A(24,23,26) 119.6587 A52 A(23,24,25) 121.2498 A52 A(23,24,25) 120.9791 A53 A(23,24,27) 120.0633 A53 A(23,24,27) 119.7208 A54 A(25,24,27) 118.6869 A54 A(25,24,27) 119.3 A55 A(7,25,24) 118.7506 A55 A(7,25,24) 118.8977 A56 A(7,25,28) 118.7457 A56 A(7,25,28) 118.8642 A57 A(24,25,28) 122.5037 A57 A(24,25,28) 122.2381
A58 A(25,28,29) 121.2558 A58 A(25,28,29) 121.1413 A59 A(25,28,31) 118.7065 A59 A(25,28,31) 118.587 A60 A(29,28,31) 120.0377 A60 A(29,28,31) 120.2718 A61 A(28,29,30) 121.26 A61 A(28,29,30) 121.1426 A62 A(28,29,32) 120.0448 A62 A(28,29,32) 120.272 A63 A(30,29,32) 118.6952 A63 A(30,29,32) 118.5853 A64 A(10,30,29) 118.7411 A64 A(10,30,29) 118.8639 A65 A(10,30,35) 118.7285 A65 A(10,30,35) 118.8978 A66 A(29,30,35) 122.5304 A66 A(29,30,35) 122.2382 A67 A(11,33,34) 118.715 A67 A(11,33,34) 119.0561 A68 A(11,33,35) 121.2617 A68 A(11,33,35) 121.2851 A69 A(34,33,35) 120.0233 A69 A(34,33,35) 119.6588 A70 A(30,35,33) 121.268 A70 A(30,35,33) 120.9795 A71 A(30,35,36) 118.7171 A71 A(30,35,36) 119.299 A72 A(33,35,36) 120.0149 A72 A(33,35,36) 119.7216 表 A4: coronene 振動頻率 1
coronene 振動頻率(cm-1) coronene 離子振動頻率(cm-1) 振動模式 B3LYP/6-31G(d) B3LYP/6-31G(d,p) B3LYP/6-31G(d) B3LYP/6-31G(d,p)
1 90.89 90.85 56.88 49.27
2 91.18 91.14 86.03 86.66
3 131.18 130.94 89.67 90.37
4 168.08 167.91 125.32 126.11
5 230.89 231.04 161.28 161.55
6 303.76 303.28 221.94 222.89
7 304.11 303.64 285.21 285.42
8 306.23 306.19 295.21 295.78
9 306.7 306.66 299.04 299.66
10 370 369.99 301.78 302.04
11 370.08 370.06 370.99 371.01
12 384.63 384.62 380.35 380.45
13 385.18 385.17 384.77 384.88
14 458.28 458.41 437.88 438.45
15 459.16 459.28 444.68 445.18
16 480.68 480.55 468.29 468.21
17 486.35 486.37 476.81 477.04
18 496.67 496.67 487.22 487.14
19 496.92 496.91 495.88 496.19
20 529.5 529.83 500.64 501.11
21 558.43 557.97 531.19 531.02
22 559.32 558.86 554.04 553.89
23 563.67 563.55 557.59 557.81
24 570.15 568.75 569.74 569.28
25 640.2 639.24 629.25 628.07
26 644.3 643.7 637.15 636.57
27 675.03 673.67 665.71 664.87
28 675.21 673.85 670.49 669.69
29 681.34 681.17 677.89 677.74
30 691.3 690.88 681.66 681.05
31 691.37 690.95 689.19 688.74
32 778.05 775.25 751.26 748.78
33 778.08 775.26 758.02 755.41
34 780.31 780.28 764.63 758.06
35 784.79 783.97 774.49 771.9
36 784.99 784.17 775.12 773.85
37 800 793.81 777.96 777.31
38 821.31 820.06 790.98 793.19
39 821.98 820.75 807.23 806.94
40 825.96 825.83 820.1 820.86
41 826 825.88 828.47 828.22
42 858.68 857.68 833.74 834.92
43 858.79 857.81 871.48 872.17
44 879.49 878.01 874.12 875.01
45 937.29 936.41 896 896.22
46 950.77 955.28 936.96 936.19
47 958.09 962.34 969.46 973.75
48 958.27 962.54 977.24 980.95
49 969.13 973.07 984.09 987.89
50 969.72 973.65 993.42 996.13
51 977.18 980.2 997.06 1000.6
52 1012.23 1011.5 1003.21 1005.6
53 1012.3 1011.56 1009.86 1009.2
54 1054.51 1053.54 1030.29 1029.01
55 1166.47 1162.83 1062.32 1061.63
56 1167.21 1163.57 1160.94 1157.9
57 1173.11 1167.57 1170.24 1166.72
58 1182.43 1180.81 1174.99 1171.87
59 1191.95 1187.03 1181.94 1180.6
60 1192 1187.08 1190.13 1186.56
61 1223.38 1222.69 1213.03 1210.56
62 1245.94 1242.19 1239.17 1236.1
63 1246.16 1242.41 1248.94 1245.96
64 1253.89 1249.85 1252.3 1248.88
65 1259.72 1257.02 1254.78 1252.14
66 1259.79 1257.08 1265.31 1261.52
67 1263.76 1259.07 1275.56 1272.52
68 1345.83 1343.05 1338.86 1335.2
69 1345.9 1343.11 1345.65 1343.01
70 1386.31 1385.27 1356.07 1353.19
71 1386.97 1386.06 1397.78 1396.32
72 1435.8 1432.69 1403.12 1402.02
73 1436.07 1432.97 1411.03 1410.14
74 1437.98 1436.98 1434.61 1433.44
75 1438.31 1437.32 1439.61 1436.88
76 1459.87 1453.05 1446.75 1443.42
77 1476.65 1475.65 1461.48 1455.78
78 1476.71 1475.69 1472.56 1468.4
79 1494.53 1490.62 1496.89 1494.94
80 1494.81 1490.9 1511.06 1507.97
81 1532.52 1531.72 1513.2 1510.47
82 1548.48 1544.63 1527.51 1523.96
83 1548.7 1544.84 1547.56 1547.3
84 1587.63 1584.25 1553.35 1550.69
85 1591.84 1591.32 1573.83 1572.03
86 1654.7 1652.23 1584.89 1581.85
87 1666.29 1665.28 1616.18 1614.22
88 1666.43 1665.43 1627.93 1625
89 1668.11 1666.15 1644.95 1642.42
90 1668.37 1666.4 1674.03 1672.69
91 3174.63 3172.1 3208.02 3198.32
92 3175.35 3172.8 3208.55 3198.81
93 3175.87 3173.32 3209.02 3199.35
94 3177.44 3174.8 3210.11 3200.37
95 3177.58 3174.95 3210.22 3200.45
96 3178.49 3175.77 3210.92 3201.13
97 3192.33 3189.83 3222.14 3212.46
98 3193.36 3190.78 3222.55 3212.78
99 3193.84 3191.27 3223.31 3213.67
100 3195.56 3192.88 3223.83 3214.11
101 3195.81 3193.13 3225.19 3215.54
102 3197.24 3194.45 3225.55 3215.84
表 A5: coronene 振動頻率 2
coronene 振動頻率 計算方法：B3LYP/6-311G(d)
振動模式 分子態(cm-1) 離子態(cm-1)
1 88.14 84.4
2 88.29 88.5
3 127.06 100.24
4 164.76 123.69
5 226.54 159
6 297.2 219.02
7 297.41 280.24
8 301.69 291.87
9 302.01 296.41
10 369.94 297.52
11 370.01 370.61
12 385.1 380.97
13 385.79 385.46
15 456.59 442.32
16 481.23 468.66
17 484.85 478.19
18 498.47 485.5
19 498.85 497.89
20 529.22 500.03
21 552.22 524.13
22 553.18 549.09
23 563.55 559.74
24 565.53 565.11
25 620.54 583.93
26 646.84 639.56
27 669.62 661.57
28 670.3 662.88
29 681.26 677.74
30 691.21 684.52
31 691.34 688.52
32 767.33 715.23
33 771.09 747.12
34 771.6 753.97
35 785.47 764.67
36 786.33 775.38
37 786.58 779.57
38 812.02 785.81
39 813.12 804.99
40 823.87 812.4
41 824.05 826.7
42 847.36 829.08
43 847.51 865.86
44 868.06 868.69
45 937.99 890.06
46 942.93 942.3
47 944.51 965.81
48 945 972.94
49 955.14 979.77
50 956.32 988.45
51 964.34 992.42
52 1010.31 998.34
53 1010.56 1012
54 1051.14 1022.28
55 1163.02 1059.37
56 1163.4 1159.43
57 1164.06 1163.8
58 1186.14 1172.77
59 1186.89 1185.34
60 1187.12 1194.35
61 1213.96 1202.36
62 1241.09 1236.13
63 1241.21 1239.38
64 1249.18 1248.24
65 1251.79 1249.57
66 1251.98 1265.32
67 1262.65 1270.57
68 1341.04 1331.09
69 1341.09 1341.11
70 1371.63 1349.44
71 1375.83 1382.64
72 1425.41 1393.58
73 1425.68 1393.88
74 1425.99 1423.53
75 1426.29 1433.28
76 1452.88 1437.32
77 1467.58 1456.81
78 1467.82 1466.68
79 1485.98 1490.81
80 1486.45 1504.8
81 1521.25 1507.02
82 1538.69 1516.22
83 1539.24 1532.36
84 1578.12 1552.58
85 1583.9 1557.93
86 1643.78 1576.1
87 1655.86 1608.13
88 1656.51 1618.16
89 1657.66 1635.52
90 1657.88 1671.48
91 3155.1 3183.36
92 3155.95 3184.02
93 3156.36 3184.36
94 3158.24 3185.52
95 3158.35 3186.17
96 3159.47 3186.82
97 3173.29 3197.9
98 3174.5 3198.71
99 3174.88 3198.83
100 3176.87 3199.95
101 3177.06 3200.65
102 3178.64 3201.25
二、 卵苯的平衡結構與振動頻率
表 A6: ovalenee 平衡結構 1
ovalene 鍵長(Angstroms)及鍵角(Degrees) 計算方法：B3LYP/6-31G(d)
分子態 離子態
Name Definition Value Name Definition Value R1 R(1,2) 1.4329 R1 R(1,2) 1.4212 R2 R(1,6) 1.3651 R2 R(1,6) 1.3759 R3 R(1,18) 1.0874 R3 R(1,18) 1.0862 R4 R(2,3) 1.4226 R4 R(2,3) 1.4256 R5 R(2,20) 1.415 R5 R(2,20) 1.4281 R6 R(3,4) 1.4272 R6 R(3,4) 1.4198 R7 R(3,7) 1.4266 R7 R(3,7) 1.4239 R8 R(4,5) 1.4321 R8 R(4,5) 1.4282 R9 R(4,8) 1.418 R9 R(4,8) 1.4229 R10 R(5,6) 1.4346 R10 R(5,6) 1.4266 R11 R(5,16) 1.4014 R11 R(5,16) 1.4082 R12 R(6,19) 1.0873 R12 R(6,19) 1.0863 R13 R(7,10) 1.4272 R13 R(7,10) 1.4198 R14 R(7,22) 1.4226 R14 R(7,22) 1.4256 R15 R(8,9) 1.435 R15 R(8,9) 1.4226 R16 R(8,14) 1.4178 R16 R(8,14) 1.4228
R17 R(9,10) 1.418 R17 R(9,10) 1.4229 R18 R(9,11) 1.4178 R18 R(9,11) 1.4228 R19 R(10,27) 1.4321 R19 R(10,27) 1.4282 R20 R(11,12) 1.4273 R20 R(11,12) 1.4198 R21 R(11,30) 1.4321 R21 R(11,30) 1.4281 R22 R(12,13) 1.4266 R22 R(12,13) 1.4239 R23 R(12,41) 1.4224 R23 R(12,41) 1.4254 R24 R(13,14) 1.4273 R24 R(13,14) 1.4199 R25 R(13,36) 1.4226 R25 R(13,36) 1.4255 R26 R(14,15) 1.4321 R26 R(14,15) 1.4282 R27 R(15,16) 1.401 R27 R(15,16) 1.4081 R28 R(15,33) 1.4351 R28 R(15,33) 1.4269 R29 R(16,17) 1.088 R29 R(16,17) 1.0874 R30 R(20,21) 1.3801 R30 R(20,21) 1.3711 R31 R(20,23) 1.0874 R31 R(20,23) 1.0862 R32 R(21,22) 1.415 R32 R(21,22) 1.4281 R33 R(21,24) 1.0874 R33 R(21,24) 1.0862 R34 R(22,25) 1.4328 R34 R(22,25) 1.4212 R35 R(25,26) 1.3651 R35 R(25,26) 1.3759 R36 R(25,28) 1.0874 R36 R(25,28) 1.0862 R37 R(26,27) 1.4346 R37 R(26,27) 1.4267 R38 R(26,29) 1.0873 R38 R(26,29) 1.0863 R39 R(27,31) 1.4014 R39 R(27,31) 1.4083
R40 R(30,31) 1.401 R40 R(30,31) 1.4081 R41 R(30,44) 1.4349 R41 R(30,44) 1.4268 R42 R(31,32) 1.088 R42 R(31,32) 1.0874 R43 R(33,34) 1.365 R43 R(33,34) 1.3759 R44 R(33,45) 1.0871 R44 R(33,45) 1.0863 R45 R(34,35) 1.0874 R45 R(34,35) 1.0862 R46 R(34,36) 1.4333 R46 R(34,36) 1.4215 R47 R(36,37) 1.4147 R47 R(36,37) 1.4279 R48 R(37,38) 1.0874 R48 R(37,38) 1.0862 R49 R(37,39) 1.3804 R49 R(37,39) 1.3712 R50 R(39,40) 1.0874 R50 R(39,40) 1.0862 R51 R(39,41) 1.4147 R51 R(39,41) 1.4279 R52 R(41,42) 1.4333 R52 R(41,42) 1.4215 R53 R(42,43) 1.0874 R53 R(42,43) 1.0862 R54 R(42,44) 1.3648 R54 R(42,44) 1.3757 R55 R(44,46) 1.0871 R55 R(44,46) 1.0863 A1 A(2,1,6) 121.4442 A1 A(2,1,6) 121.1791 A2 A(2,1,18) 118.3807 A2 A(2,1,18) 118.8585 A3 A(6,1,18) 120.1751 A3 A(6,1,18) 119.9624 A4 A(1,2,3) 118.6812 A4 A(1,2,3) 118.9837 A5 A(1,2,20) 122.4702 A5 A(1,2,20) 122.2061 A6 A(3,2,20) 118.8486 A6 A(3,2,20) 118.8102 A7 A(2,3,4) 120.0879 A7 A(2,3,4) 119.9932
A8 A(2,3,7) 119.9393 A8 A(2,3,7) 120.0073 A9 A(4,3,7) 119.9728 A9 A(4,3,7) 119.9994 A10 A(3,4,5) 120.1106 A10 A(3,4,5) 120.0536 A11 A(3,4,8) 120.0359 A11 A(3,4,8) 120.0429 A12 A(5,4,8) 119.8535 A12 A(5,4,8) 119.9035 A13 A(4,5,6) 118.3294 A13 A(4,5,6) 118.7335 A14 A(4,5,16) 119.2151 A14 A(4,5,16) 119.0743 A15 A(6,5,16) 122.4555 A15 A(6,5,16) 122.1922 A16 A(1,6,5) 121.3468 A16 A(1,6,5) 121.0568 A17 A(1,6,19) 120.2947 A17 A(1,6,19) 120.0804 A18 A(5,6,19) 118.3585 A18 A(5,6,19) 118.8628 A19 A(3,7,10) 119.9728 A19 A(3,7,10) 119.9986 A20 A(3,7,22) 119.9422 A20 A(3,7,22) 120.0099 A21 A(10,7,22) 120.085 A21 A(10,7,22) 119.9915 A22 A(4,8,9) 119.9918 A22 A(4,8,9) 119.9583 A23 A(4,8,14) 120.0143 A23 A(4,8,14) 120.0821 A24 A(9,8,14) 119.9939 A24 A(9,8,14) 119.9596 A25 A(8,9,10) 119.9904 A25 A(8,9,10) 119.9578 A26 A(8,9,11) 119.9958 A26 A(8,9,11) 119.9616 A27 A(10,9,11) 120.0138 A27 A(10,9,11) 120.0806 A28 A(7,10,9) 120.0363 A28 A(7,10,9) 120.043 A29 A(7,10,27) 120.1115 A29 A(7,10,27) 120.0534 A30 A(9,10,27) 119.8522 A30 A(9,10,27) 119.9036
A31 A(9,11,12) 120.0354 A31 A(9,11,12) 120.0406 A32 A(9,11,30) 119.8527 A32 A(9,11,30) 119.9051 A33 A(12,11,30) 120.1118 A33 A(12,11,30) 120.0543 A34 A(11,12,13) 119.97 A34 A(11,12,13) 119.9986 A35 A(11,12,41) 120.0897 A35 A(11,12,41) 119.9918 A36 A(13,12,41) 119.9403 A36 A(13,12,41) 120.0096 A37 A(12,13,14) 119.97 A37 A(12,13,14) 119.9993 A38 A(12,13,36) 119.9372 A38 A(12,13,36) 120.0074 A39 A(14,13,36) 120.0928 A39 A(14,13,36) 119.9933 A40 A(8,14,13) 120.0348 A40 A(8,14,13) 120.0403 A41 A(8,14,15) 119.8508 A41 A(8,14,15) 119.9043 A42 A(13,14,15) 120.1143 A42 A(13,14,15) 120.0554 A43 A(14,15,16) 119.2313 A43 A(14,15,16) 119.0803 A44 A(14,15,33) 118.3251 A44 A(14,15,33) 118.734 A45 A(16,15,33) 122.4436 A45 A(16,15,33) 122.1857 A46 A(5,16,15) 121.8349 A46 A(5,16,15) 121.9554 A47 A(5,16,17) 119.0751 A47 A(5,16,17) 119.0238 A48 A(15,16,17) 119.09 A48 A(15,16,17) 119.0208 A49 A(2,20,21) 121.2119 A49 A(2,20,21) 121.1825 A50 A(2,20,23) 118.8008 A50 A(2,20,23) 118.6929 A51 A(21,20,23) 119.9873 A51 A(21,20,23) 120.1245 A52 A(20,21,22) 121.2106 A52 A(20,21,22) 121.1811 A53 A(20,21,24) 119.9898 A53 A(20,21,24) 120.1269
A54 A(22,21,24) 118.7996 A54 A(22,21,24) 118.6921 A55 A(7,22,21) 118.8474 A55 A(7,22,21) 118.8089 A56 A(7,22,25) 118.6849 A56 A(7,22,25) 118.9871 A57 A(21,22,25) 122.4678 A57 A(21,22,25) 122.204 A58 A(22,25,26) 121.4455 A58 A(22,25,26) 121.1787 A59 A(22,25,28) 118.3832 A59 A(22,25,28) 118.8599 A60 A(26,25,28) 120.1712 A60 A(26,25,28) 119.9614 A61 A(25,26,27) 121.3432 A61 A(25,26,27) 121.0543 A62 A(25,26,29) 120.2981 A62 A(25,26,29) 120.0833 A63 A(27,26,29) 118.3587 A63 A(27,26,29) 118.8624 A64 A(10,27,26) 118.3299 A64 A(10,27,26) 118.7349 A65 A(10,27,31) 119.2156 A65 A(10,27,31) 119.0739 A66 A(26,27,31) 122.4545 A66 A(26,27,31) 122.1912 A67 A(11,30,31) 119.2301 A67 A(11,30,31) 119.0813 A68 A(11,30,44) 118.3269 A68 A(11,30,44) 118.7342 A69 A(31,30,44) 122.443 A69 A(31,30,44) 122.1845 A70 A(27,31,30) 121.8356 A70 A(27,31,30) 121.9555 A71 A(27,31,32) 119.0753 A71 A(27,31,32) 119.0221 A72 A(30,31,32) 119.0891 A72 A(30,31,32) 119.0224 A73 A(15,33,34) 121.3482 A73 A(15,33,34) 121.0569 A74 A(15,33,45) 118.3222 A74 A(15,33,45) 118.845 A75 A(34,33,45) 120.3296 A75 A(34,33,45) 120.0981 A76 A(33,34,35) 120.2055 A76 A(33,34,35) 119.9814
A77 A(33,34,36) 121.4364 A77 A(33,34,36) 121.1732 A78 A(35,34,36) 118.3581 A78 A(35,34,36) 118.8454 A79 A(13,36,34) 118.6831 A79 A(13,36,34) 118.9873 A80 A(13,36,37) 118.8517 A80 A(13,36,37) 118.8113 A81 A(34,36,37) 122.4651 A81 A(34,36,37) 122.2014 A82 A(36,37,38) 118.8092 A82 A(36,37,38) 118.7033 A83 A(36,37,39) 121.2061 A83 A(36,37,39) 121.1784 A84 A(38,37,39) 119.9847 A84 A(38,37,39) 120.1183 A85 A(37,39,40) 119.9837 A85 A(37,39,40) 120.118 A86 A(37,39,41) 121.2098 A86 A(37,39,41) 121.1793 A87 A(40,39,41) 118.8064 A87 A(40,39,41) 118.7027 A88 A(12,41,39) 118.8548 A88 A(12,41,39) 118.814 A89 A(12,41,42) 118.6864 A89 A(12,41,42) 118.9901 A90 A(39,41,42) 122.4588 A90 A(39,41,42) 122.1959 A91 A(41,42,43) 118.3589 A91 A(41,42,43) 118.8421 A92 A(41,42,44) 121.4388 A92 A(41,42,44) 121.1733 A93 A(43,42,44) 120.2024 A93 A(43,42,44) 119.9846 A94 A(30,44,42) 121.3465 A94 A(30,44,42) 121.0562 A95 A(30,44,46) 118.3261 A95 A(30,44,46) 118.8422 A96 A(42,44,46) 120.3274 A96 A(42,44,46) 120.1016
表 A7 ovalene 平衡結構 2
ovalene 鍵長(Angstroms)及鍵角(Degrees) 計算方法：B3LYP/6-311G(d)
分子態 離子態
Name Definition Value Name Definition Value R1 R(1,2) 1.4314 R1 R(1,2) 1.4193 R2 R(1,6) 1.362 R2 R(1,6) 1.3729 R3 R(1,18) 1.0862 R3 R(1,18) 1.0848 R4 R(2,3) 1.4204 R4 R(2,3) 1.4234 R5 R(2,20) 1.413 R5 R(2,20) 1.4263 R6 R(3,4) 1.4255 R6 R(3,4) 1.4179 R7 R(3,7) 1.4248 R7 R(3,7) 1.4221 R8 R(4,5) 1.43 R8 R(4,5) 1.4261 R9 R(4,8) 1.4161 R9 R(4,8) 1.421 R10 R(5,6) 1.4331 R10 R(5,6) 1.4249 R11 R(5,16) 1.3993 R11 R(5,16) 1.4061 R12 R(6,19) 1.086 R12 R(6,19) 1.0849 R13 R(7,10) 1.4255 R13 R(7,10) 1.4179 R14 R(7,22) 1.4204 R14 R(7,22) 1.4234 R15 R(8,9) 1.4332 R15 R(8,9) 1.4205 R16 R(8,14) 1.4159 R16 R(8,14) 1.4209 R17 R(9,10) 1.4161 R17 R(9,10) 1.421
R19 R(10,27) 1.43 R19 R(10,27) 1.4261 R20 R(11,12) 1.4256 R20 R(11,12) 1.4179 R21 R(11,30) 1.43 R21 R(11,30) 1.426 R22 R(12,13) 1.4248 R22 R(12,13) 1.4221 R23 R(12,41) 1.4203 R23 R(12,41) 1.4232 R24 R(13,14) 1.4257 R24 R(13,14) 1.418 R25 R(13,36) 1.4205 R25 R(13,36) 1.4233 R26 R(14,15) 1.43 R26 R(14,15) 1.426 R27 R(15,16) 1.3988 R27 R(15,16) 1.406 R28 R(15,33) 1.4337 R28 R(15,33) 1.4252 R29 R(16,17) 1.0867 R29 R(16,17) 1.0859 R30 R(20,21) 1.3775 R30 R(20,21) 1.368 R31 R(20,23) 1.0861 R31 R(20,23) 1.0849 R32 R(21,22) 1.413 R32 R(21,22) 1.4264 R33 R(21,24) 1.0861 R33 R(21,24) 1.0849 R34 R(22,25) 1.4313 R34 R(22,25) 1.4193 R35 R(25,26) 1.362 R35 R(25,26) 1.3729 R36 R(25,28) 1.0862 R36 R(25,28) 1.0848 R37 R(26,27) 1.4332 R37 R(26,27) 1.425 R38 R(26,29) 1.086 R38 R(26,29) 1.0849 R39 R(27,31) 1.3993 R39 R(27,31) 1.4061 R40 R(30,31) 1.3988 R40 R(30,31) 1.4059 R41 R(30,44) 1.4336 R41 R(30,44) 1.4251
R42 R(31,32) 1.0867 R42 R(31,32) 1.0859 R43 R(33,34) 1.3619 R43 R(33,34) 1.3729 R44 R(33,45) 1.0858 R44 R(33,45) 1.0849 R45 R(34,35) 1.0861 R45 R(34,35) 1.0848 R46 R(34,36) 1.4319 R46 R(34,36) 1.4196 R47 R(36,37) 1.4127 R47 R(36,37) 1.4262 R48 R(37,38) 1.0861 R48 R(37,38) 1.0849 R49 R(37,39) 1.3778 R49 R(37,39) 1.3682 R50 R(39,40) 1.0861 R50 R(39,40) 1.0849 R51 R(39,41) 1.4127 R51 R(39,41) 1.4262 R52 R(41,42) 1.4319 R52 R(41,42) 1.4196 R53 R(42,43) 1.0861 R53 R(42,43) 1.0848 R54 R(42,44) 1.3617 R54 R(42,44) 1.3727 R55 R(44,46) 1.0858 R55 R(44,46) 1.0849 A1 A(2,1,6) 121.4645 A1 A(2,1,6) 121.1979 A2 A(2,1,18) 118.4671 A2 A(2,1,18) 118.9327 A3 A(6,1,18) 120.0684 A3 A(6,1,18) 119.8694 A4 A(1,2,3) 118.66 A4 A(1,2,3) 118.9649 A5 A(1,2,20) 122.512 A5 A(1,2,20) 122.2499 A6 A(3,2,20) 118.828 A6 A(3,2,20) 118.7852 A7 A(2,3,4) 120.0905 A7 A(2,3,4) 119.9944 A8 A(2,3,7) 119.941 A8 A(2,3,7) 120.0098 A9 A(4,3,7) 119.9685 A9 A(4,3,7) 119.9958
A10 A(3,4,5) 120.1133 A10 A(3,4,5) 120.0589 A11 A(3,4,8) 120.0396 A11 A(3,4,8) 120.0452 A12 A(5,4,8) 119.8472 A12 A(5,4,8) 119.8958 A13 A(4,5,6) 118.3038 A13 A(4,5,6) 118.7028 A14 A(4,5,16) 119.2195 A14 A(4,5,16) 119.0813 A15 A(6,5,16) 122.4767 A15 A(6,5,16) 122.2159 A16 A(1,6,5) 121.3679 A16 A(1,6,5) 121.081 A17 A(1,6,19) 120.1774 A17 A(1,6,19) 119.9711 A18 A(5,6,19) 118.4547 A18 A(5,6,19) 118.9478 A19 A(3,7,10) 119.9685 A19 A(3,7,10) 119.9949 A20 A(3,7,22) 119.9441 A20 A(3,7,22) 120.0125 A21 A(10,7,22) 120.0875 A21 A(10,7,22) 119.9926 A22 A(4,8,9) 119.9925 A22 A(4,8,9) 119.9597 A23 A(4,8,14) 120.0127 A23 A(4,8,14) 120.0793 A24 A(9,8,14) 119.9948 A24 A(9,8,14) 119.961 A25 A(8,9,10) 119.9907 A25 A(8,9,10) 119.9589 A26 A(8,9,11) 119.9966 A26 A(8,9,11) 119.9629 A27 A(10,9,11) 120.0128 A27 A(10,9,11) 120.0782 A28 A(7,10,9) 120.0402 A28 A(7,10,9) 120.0455 A29 A(7,10,27) 120.1144 A29 A(7,10,27) 120.0588 A30 A(9,10,27) 119.8453 A30 A(9,10,27) 119.8957 A31 A(9,11,12) 120.0397 A31 A(9,11,12) 120.0434 A32 A(9,11,30) 119.8468 A32 A(9,11,30) 119.8977
A33 A(12,11,30) 120.1136 A33 A(12,11,30) 120.0589 A34 A(11,12,13) 119.965 A34 A(11,12,13) 119.9945 A35 A(11,12,41) 120.0935 A35 A(11,12,41) 119.9936 A36 A(13,12,41) 119.9414 A36 A(13,12,41) 120.0118 A37 A(12,13,14) 119.9652 A37 A(12,13,14) 119.9954 A38 A(12,13,36) 119.9385 A38 A(12,13,36) 120.0098 A39 A(14,13,36) 120.0963 A39 A(14,13,36) 119.9949 A40 A(8,14,13) 120.0387 A40 A(8,14,13) 120.0428 A41 A(8,14,15) 119.8452 A41 A(8,14,15) 119.8971 A42 A(13,14,15) 120.1161 A42 A(13,14,15) 120.0601 A43 A(14,15,16) 119.236 A43 A(14,15,16) 119.0872 A44 A(14,15,33) 118.3004 A44 A(14,15,33) 118.7041 A45 A(16,15,33) 122.4636 A45 A(16,15,33) 122.2087 A46 A(5,16,15) 121.8396 A46 A(5,16,15) 121.9592 A47 A(5,16,17) 119.0722 A47 A(5,16,17) 119.0218 A48 A(15,16,17) 119.0882 A48 A(15,16,17) 119.0189 A49 A(2,20,21) 121.2308 A49 A(2,20,21) 121.2051 A50 A(2,20,23) 118.8831 A50 A(2,20,23) 118.7749 A51 A(21,20,23) 119.886 A51 A(21,20,23) 120.0201 A52 A(20,21,22) 121.2296 A52 A(20,21,22) 121.2037 A53 A(20,21,24) 119.8884 A53 A(20,21,24) 120.0222 A54 A(22,21,24) 118.882 A54 A(22,21,24) 118.7742 A55 A(7,22,21) 118.8266 A55 A(7,22,21) 118.7838
A56 A(7,22,25) 118.6637 A56 A(7,22,25) 118.9683 A57 A(21,22,25) 122.5098 A57 A(21,22,25) 122.2479 A58 A(22,25,26) 121.4658 A58 A(22,25,26) 121.1974 A59 A(22,25,28) 118.4696 A59 A(22,25,28) 118.934 A60 A(26,25,28) 120.0646 A60 A(26,25,28) 119.8685 A61 A(25,26,27) 121.3643 A61 A(25,26,27) 121.0785 A62 A(25,26,29) 120.1803 A62 A(25,26,29) 119.9737 A63 A(27,26,29) 118.4554 A63 A(27,26,29) 118.9478 A64 A(10,27,26) 118.3043 A64 A(10,27,26) 118.7044 A65 A(10,27,31) 119.22 A65 A(10,27,31) 119.0807 A66 A(26,27,31) 122.4757 A66 A(26,27,31) 122.2149 A67 A(11,30,31) 119.2345 A67 A(11,30,31) 119.0882 A68 A(11,30,44) 118.3021 A68 A(11,30,44) 118.7043 A69 A(31,30,44) 122.4634 A69 A(31,30,44) 122.2075 A70 A(27,31,30) 121.8406 A70 A(27,31,30) 121.9595 A71 A(27,31,32) 119.072 A71 A(27,31,32) 119.0197 A72 A(30,31,32) 119.0874 A72 A(30,31,32) 119.0208 A73 A(15,33,34) 121.3691 A73 A(15,33,34) 121.081 A74 A(15,33,45) 118.4156 A74 A(15,33,45) 118.9284 A75 A(34,33,45) 120.2154 A75 A(34,33,45) 119.9907 A76 A(33,34,35) 120.1006 A76 A(33,34,35) 119.8899 A77 A(33,34,36) 121.4567 A77 A(33,34,36) 121.1916 A78 A(35,34,36) 118.4427 A78 A(35,34,36) 118.9185
A79 A(13,36,34) 118.6614 A79 A(13,36,34) 118.9684 A80 A(13,36,37) 118.8315 A80 A(13,36,37) 118.7867 A81 A(34,36,37) 122.5071 A81 A(34,36,37) 122.245 A82 A(36,37,38) 118.8907 A82 A(36,37,38) 118.7853 A83 A(36,37,39) 121.2252 A83 A(36,37,39) 121.2009 A84 A(38,37,39) 119.884 A84 A(38,37,39) 120.0138 A85 A(37,39,40) 119.8833 A85 A(37,39,40) 120.0137 A86 A(37,39,41) 121.2287 A86 A(37,39,41) 121.2016 A87 A(40,39,41) 118.8879 A87 A(40,39,41) 118.7848 A88 A(12,41,39) 118.8345 A88 A(12,41,39) 118.7892 A89 A(12,41,42) 118.664 A89 A(12,41,42) 118.9709 A90 A(39,41,42) 122.5014 A90 A(39,41,42) 122.2399 A91 A(41,42,43) 118.4441 A91 A(41,42,43) 118.9156 A92 A(41,42,44) 121.459 A92 A(41,42,44) 121.1916 A93 A(43,42,44) 120.0969 A93 A(43,42,44) 119.8928 A94 A(30,44,42) 121.3678 A94 A(30,44,42) 121.0806 A95 A(30,44,46) 118.4204 A95 A(30,44,46) 118.9261 A96 A(42,44,46) 120.2118 A96 A(42,44,46) 119.9933 表 A8: ovalene 振動頻率 1
ovalene 振動頻率(cm-1) ovalene 離子振動頻率(cm-1) 振動模式 B3LYP/6-311G(d) B3LYP/6-31G(d) B3LYP/6-311G(d) B3LYP/6-31G(d)
1 60.74 62.4 61.78 63.27
3 107.52 110.3 104.31 106.68
4 126.62 129.14 124.57 126.96
5 153.94 156.82 153.1 155.88
6 198.47 203.04 194.15 198.06
7 213.49 216.71 213.36 216.33
8 258.29 262.04 254 257.54
9 273.85 278.82 268.07 272.64
10 280.31 280.33 278.49 278.43
11 317.32 317.51 311.91 312.21
12 324.36 324.65 321.74 324.12
13 328.85 332.91 323.89 325.77
14 339.26 345.36 334.77 340.22
15 346.25 350.36 344.24 347.74
16 347.44 353.34 349.69 354.85
17 398.36 398.12 397.98 397.69
18 421.77 422.43 422.69 423.13
19 430.35 429.97 425.95 425.56
20 434.3 436.17 431.18 433.29
21 455.35 455.39 455.14 455.18
22 477.61 479.87 465.94 468.84
23 482.34 481 479.64 478.41
24 498.08 497.24 487.07 492.76
25 504.53 505.26 494.11 496.25
26 532.86 537.66 497.17 522.62
27 544.06 541.67 517.42 540.47
28 546.36 544.28 542.92 541.65
29 556.48 561.54 543.84 549.44
30 561.67 573.22 544.57 574.99
31 577.09 583.51 573.15 583.85
32 585.54 584.79 579.12 583.89
33 586.33 586.41 583.83 584.65
34 588.44 621.15 584.71 616.15
35 610.59 638.18 600.69 626.85
36 640.71 644.68 636.71 641.6
37 650.06 648.21 649.99 647.93
38 662.33 664.08 661.49 661.63
39 665.38 667.68 662.95 667.61
40 683.23 685.29 665.17 683.38
41 693.6 715.83 681.51 695.15
42 716.72 715.91 715.09 713.99
43 716.87 716.24 717.05 716.35
44 747.03 752.8 737.3 744.47
45 766.9 768.85 746.91 760.77
46 768.6 774 755.33 765
47 770.4 778.19 756.63 768.99
48 779.88 789.35 766.65 779.85
49 787.07 790.07 787.95 786.71
50 791.4 794.72 790.84 798.36
51 793 797.62 796.2 799.41
52 795.26 804.67 803.26 811.97
53 811.9 821.03 827.26 834.81
54 825.43 836.76 843.05 851.07
55 843.24 855.03 863.44 871.56
56 855.82 867.1 874.28 878.09
57 884.78 882.09 880.49 882.59
58 885.87 897.7 906.59 908.16
59 887.49 900.01 914.96 918.6
60 902.5 904.43 916.27 922.32
61 921.91 921.94 918.08 923.23
62 926.47 924.42 927.98 925.94
63 938.51 951.8 970.96 977.58
64 939.57 952.91 974.24 981.04
65 955 968.22 979.45 986.38
66 957.32 970.43 983.21 990.11
67 960.26 973.29 991.5 998.54
68 964.34 976.65 994.01 999
69 993.49 996.67 996.2 1000.86
70 1063.46 1067.03 1071.36 1074.49
71 1086.71 1087.01 1082.18 1082.68
72 1091.2 1095.37 1098.11 1101.7
73 1132.61 1134.09 1141.1 1141.78
74 1161.77 1171.62 1171.15 1174.86
75 1167.33 1171.9 1177.71 1180.87
76 1176.41 1179.2 1179.16 1185.36
77 1187.99 1190.99 1187.43 1189.98
78 1188.07 1193.39 1194.2 1198.58
79 1196.05 1202.96 1210.5 1216.87
80 1224.22 1228.98 1217.01 1221.12
81 1233.55 1240.3 1241.89 1249.31
82 1241.02 1248.99 1247.84 1251.55
83 1250.66 1254.44 1250.73 1254.2
84 1251.99 1256.35 1251.85 1259.14
85 1267.16 1273.47 1264.96 1269.64
86 1280.66 1290.01 1276.07 1283.53
87 1298.37 1304.8 1293.85 1299.49
88 1334.84 1340.55 1324.19 1328.02
89 1340.33 1346.29 1348.26 1354.14
90 1341.02 1347.9 1350.54 1355.25
91 1343.94 1356.96 1362.89 1376.95
92 1385.32 1396.53 1390.52 1402.22
93 1397.54 1411.43 1405.67 1416.6
94 1409.82 1418.62 1410.02 1421.95
95 1412.36 1425.19 1413.81 1422.05
96 1413.69 1427.08 1414.23 1425.66
97 1427.91 1437.44 1414.57 1427.21
98 1443.41 1454.67 1439.45 1450.39
99 1446.13 1455.31 1452.58 1461.96
100 1451.33 1461.88 1456.32 1463.69
101 1469.07 1477.66 1468.58 1476.06
102 1469.7 1478.23 1470.78 1479.12
103 1473.69 1482.36 1475.95 1482.59
104 1485.48 1495.63 1481.62 1488.56
105 1502.23 1513.34 1504.95 1514.99
106 1519.22 1529.23 1519.6 1527.81
107 1530.33 1542.46 1527.51 1537.98
108 1541.65 1550.51 1529.89 1538.62
109 1548.77 1558.85 1544.64 1552.76
110 1566.76 1576.98 1549.73 1557.92
111 1594.88 1603.58 1586.91 1595.18
112 1621.89 1633.12 1591.01 1600.49
113 1636.09 1646.48 1597.17 1606.17
114 1640.5 1651.27 1609.19 1618.19
115 1652.64 1663.71 1630.05 1639.07
116 1656.03 1667.7 1638.37 1648.28
117 1658.14 1669.47 1639.83 1649.98
118 1668.91 1680.32 1654.56 1664.41
119 3156.08 3175.92 3178.27 3195.97
120 3156.59 3176.47 3178.51 3196.15
121 3157.04 3176.65 3179.97 3199.93
122 3158.44 3177.74 3180.41 3200.17
123 3158.62 3178.47 3181.72 3201.31
124 3160.05 3179.71 3182.67 3201.87
125 3161.05 3179.99 3182.69 3202.17
126 3161.55 3180.61 3183.3 3202.5
127 3174.86 3194.45 3195.14 3214.63
128 3175.24 3194.69 3195.38 3214.8
129 3177.19 3196.69 3196.63 3215.88
130 3178.33 3197.61 3197.12 3216.25
131 3178.38 3197.69 3197.58 3216.84
132 3179.49 3198.67 3198.04 3217.19
三、平衡結構圖(單位:Angstroms)
圖 A1 coronene 分子態平衡結構圖(以 6-31G(d)為例)
圖 A2 coronene 離子態平衡結構圖(以 6-31G(d)為例) C=C 鍵皆為 1.3725 C-H 鍵皆為 1.0875
圖 A3 ovalene 分子態平衡結構圖(以 6-31G(d)為例)
圖 A4 ovalene 分子態平衡結構圖(以 6-31G(d)為例)
四、bq3v，以及gq4v分解式推導過程：
2. gq4 v