本研究目的在利用量子計算的方法，研究三氟化硼正離子基態及激發態的結構和光譜。我們利用密度泛函理論的B3LYP 泛函數和6-311G(d)、6-311+G(d)及6-311+G(2d)三種基組，計算出三氟化硼分子及正離子的平衡結構、振動頻率與法蘭克－康登因子，進而模擬出三氟化硼的光電子光譜並與實驗光譜比對，結果發現兩種光譜頗為吻合。另外，選取6-311+G(2d)基組，我們計算出三氟化硼正離子在2A1， 2B1 ， 2B2, 及 2A2 四個離子態（C2V點群）的平衡結構及振動頻率。離子的游離能則使用CCSD 及CCSD（T）兩種方法獲得。結果發現三氟化硼正離子的2B1態為正離子的基態，但第一激發態（2B2）的垂直激發能低於2B1態的垂直激發能。同時，我們也計算出分子基態與四個離子態之間的法蘭克－康登因子，並模擬了三氟化硼的光電子光譜。

The purpose of this study is to investigate the properties and spectra of boron trifluoride in the cationic ground state and in the excited states by using quantum calculation methods. The equilibrium geometries, harmonic vibrational frequencies, and Frank-Condon factors of neutral and cationic boron trifluoride have been calculated by means of density functional theory and the B3LYP functional with the basis sets of 6-311G(d,), 6-311+G(d,), and 6-311+G(2d). The ionization spectra of boron trifluoride were stimulated and compared with experimental photoelectron spectra. The agreement between stimulated and experimental spectra turns out to be satisfactory. On the other hand, the equilibrium geometries, harmonic vibrational frequencies for the 2A1，2B1 ，2B2, and 2A2 ionic states (C2v point group) of boron trifluoride have been calculated with at the B3LYP/6-311+G(2d) level. The ionization energies for these excited states have also been obtained using the CCSD and CCSD(T) methods. We have found that the 2B1 state is the cationic ground state, but the vertical ionization energy of the first excited state (2B2) is lower than that of the 2B1. Meanwhile, Frank-Condon factors between the molecular ground state and these four ionic states have been computed in order to simulate the photoelectron spectra of boron trifluoride.

目錄
第一章 緒論..............................................................................................................1
1.1 研究動機與目的..................................................................................1
1.2 文獻探討..............................................................................................2
1.3 論文架構..............................................................................................3
第二章 研究方法......................................................................................................5
2.1 密度泛函理論......................................................................................5
2.2 三氟化硼分子與正離子的計算..........................................................7
2.3三氟化硼正離子激發態的計算...........................................................8
2.4 法蘭克-康登因子................................................................................9
2.5 光譜模擬............................................................................................11
第三章 結果與討論果............................................................................................12
3.1 三氟化硼分子與正離子的計算........................................................12
3.1.1平衡結構.....................................................................................12
3.1.2振動頻率.....................................................................................13
3.1.3 法蘭克－康登因子與光譜模擬................................................14
3.2三氟化硼正離子激發態的計算.........................................................15
3.2.1三氟化硼2A1態...........................................................................16
3.2.2三氟化硼2B1態...........................................................................16
3.2.3三氟化硼2B2態...........................................................................17
3.2.4三氟化硼2A2態...........................................................................18
3.3游離能與模擬光譜.............................................................................18
第四章 結論............................................................................................................20
參考文獻...................................................................................................................21
附錄...........................................................................................................................23

表目錄

表一 三氟化硼分子在不同計算基組與其它計算和實驗值的差異...............26
表二 三氟化硼正離子在不同計算基組的結構...............................................27
表三 三氟化硼分子的正規振動模式...............................................................28
表四 三氟化硼正離子的正規振動模式...........................................................29
表五 三氟化硼分子基態各計算層級之振動頻率...........................................30
表六 三氟化硼正離子之振動頻率...................................................................31
表七 三氟化硼正離子相對於分子基態之幾何結構改變（△Q）.................32
表八 三氟化硼正離子相對於分子基態之 S因子..........................................33
表九 三氟化硼從分子電離成離子基態的法蘭克－康登因子.......................34
表十 三氟化硼從分子電離成離子基態的法蘭克－康登因子.......................35
表十一 三氟化硼從分子電離成離子基態的法蘭克－康登因子.......................36
表十二 三氟化硼離子基態與四個離子態的幾何結構..................................37
表十三 三氟化硼離子基態與四個離子態的振動頻率....................................38
表十四 三氟化硼四個離子態相對於分子基態之幾何結構改變（△Q）..39
表十五 三氟化硼四個離子態相對於分子基態之S因子..............................40
表十六 三氟化硼2A1激發態的法蘭克－康登因子.........................................41
表十七 三氟化硼2B1激發態的法蘭克－康登因子.........................................42
表十八 三氟化硼2B2激發態的法蘭克－康登因子.........................................43
表十九 三氟化硼正離子激發態的游離能........................................................44


圖目錄

圖一 三氟化硼分子與正離子結構..................................................................45
圖二 三氟化硼在6-311G(d)計算基組的模擬光譜.......................................46
圖三 三氟化硼在6-311+G(d)計算基組的模擬光譜.....................................47
圖四 三氟化硼在6-311+G(2d)計算基組的模擬光譜...................................48
圖五 三氟化硼之模擬光譜與實驗光譜的比較..............................................49
圖六 三氟化硼2A1激發態之模擬光譜............................................................50
圖七 三氟化硼2B1激發態之模擬光譜............................................................51
圖八 三氟化硼2B2激發態之模擬光譜............................................................52
圖九 三氟化硼光電子光譜之模擬圖（CCSD）.............................................53
圖十 三氟化硼光電子光譜之模擬圖（CCSD(T)）.......................................54
圖十一 實驗光譜.................................................................................................55

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