溶劑對電子光譜影響的新方法：阻尼諧振法蘭克康登理論和模擬

New Approach of Solvent Effects on Electronic Spectroscopy: Damped Harmonic Franck-Condon Theory and Simulation

王辰文(Chen-Wen Wang)

指導教授 ： 朱超原

國立交通大學/理學院/應用化學系所/博士(2020年)

摘要

本論文中我們開發了阻尼法蘭克-康登諧振子法並應用於實驗觀測的溶劑化光譜。
我們證明了這套新方法對苝和咔唑等類型的多環芳香烴和雜環芳香化合物實驗溶劑增益光譜模擬得相當好。這兩種化合物皆具獨特的物理和化學以及吸收和螢光特性。此先天特性讓其廣泛應用於各領域學門中。我們於此展示這套新式阻尼諧振法的重要性和有效性以運用於這兩例的溶劑增益光譜模擬。透過阻尼法蘭克-康登簡諧方法我們描述了電振光譜增益以及貢獻光譜的關鍵振動模式。為了適當擬合實驗溶劑增益光譜，我們首先利用位移諧振法蘭克近似搭配各式全始計算法來模擬氣相光譜。我們也描繪和指認出貢獻氣相光譜譜峰的主要振動模式。在完成氣相模擬光譜分析之後，我們緊接著按氣相模擬和實驗光譜最吻合的最佳化光譜將重心放在模擬溶劑增益譜峰上。這裡我們認為在該兩例經由氣相轉到溶劑相所出現的顯著譜帶強度增益歸因於溶劑和溶質分子之間的阻尼作用力所致。該效應導致某些活性正則模式產生特定的改變。另外我們也運用全新開發的阻尼法蘭克諧振法說明溶劑效應反應在這兩化學分子其電振光譜的不同影響。
首先對於苝分子，我們進行包含 HF-CIS，(TD) B3LYP，(TD) B3LYP-35以及(TD) BHandHLYP 的全始計算法來判估模擬光譜的穩定性並擬合實驗氣相光譜含苯環的溶劑化光譜。我們發現有六個黃瑞斯因子數值明顯的振動模式主要貢獻於氣相電振(電子振動)光譜中。在這六個振動模式之中我們又發現具有複合式C-H彎曲和C-C伸縮運動的第10振動模式(1410 cm-1)在苯溶液中會對作用於未擾動苯溶液裡溶質分子之標定參數的改變產生相當高的活性。我們的數據顯示第10振動模式的黃瑞斯因子從氣相中的HR = 0.077上升到了凝相的HR = 0.359，反應了實驗光譜觀測到的溶劑增益特性。另外一項我們發現的特性為每個C-H模式在阻尼近似下的氫原子經驗標定參數皆為等值標定，並且我們的數據模擬資料也證實和實驗結果一致。
對於咔唑分子，我們比較了四種不同類型的全始計算法並發現(TD) B3LYP-35能適切描述氣相實驗光譜以及進一步的阻尼簡諧溶劑增益光譜。由於單一標定參數會使得模擬的光譜低估了實驗光譜譜帶強度而產生不一致，所以會使此法對於該體系模擬失效。因而我們利用歸納性多重標定阻尼近似法來再度研究極端溶液增益光譜。我們的數據資料顯示有四至五個包含複合式環伸縮以及環呼吸運動的代表性振動模式主要各別對吸收和發射光譜的電子振動譜帶造成增益。另外我們也發現在基態下振動模式的型態會和激發態下的振動模式型態有明顯出入，這也說明了為何我們在實驗觀測的溶劑增益光譜會看到鏡像破缺，而在基態下吸收和發射光譜卻仍為鏡像。

關鍵字

法蘭克-康登因子 ； 黃瑞斯因子 ； 阻尼諧振法 ； 紫外吸收光譜 ； 發射光譜 ； 位移諧振子 ； 苝 ； 咔唑

並列摘要

In this thesis we developed the damped Franck-Condon harmonic oscillator method and applied it on solvent-enhanced electronic spectroscopy observed in experiments. We demonstrated that this new method works fairly well in solvent-enhanced vibronic spectra of polycyclic hydrocarbons and heterocyclic compounds such as perylene and carbazole, both of which are physically and chemically unique and of highly absorbance and fluorescence properties. Such these intrinsic characters have been brought into wide applications in various areas of subjects. We here present the importance and effectiveness of this new damped harmonic method that could be applied to solvent-enhanced spectral simulations with these two examples. Vibronic spectral enhancement and the key vibrational normal-modes contributing to the spectra were also illustrated via damped Franck-Condon harmonic oscillator method. In order to adequately interpret experimentally observed solvent-enhanced spectra, simulated gas-phase spectra were initially performed using the displaced harmonic Franck-Condon approach in combination with various ab-initio quantum chemistry computational methods. The dominant vibrational modes contributing to the gas-phase vibronic bands were also assigned and depicted. After completing the simulated gas-phase analysis, we then turned our attention to simulate solvent-enhanced vibronic bands based on the most optimized gas-phase simulation that nicely interpreted the experiment. Here we suggest significant enhancements of experimental spectral band intensities of both examples from gaseous to condensed phase are ascribed to the damping force between solute and solvent molecules. Such an effect results in specific changes in certain active normal modes. In addition, different influences of the solvent effect reflected on the vibronic spectrum of these two chemical species were illustrated using newly developed damped Franck-Condon harmonic oscillator approach.
For perylene molecule, we carried out the study with ab-initio methods including HF-CIS, (TD) B3LYP and (TD) B3LYP-35 as well as (TD) BHandHLYP to assess the robustness of the simulated spectra and reproduce the experimental data in gas-phase and benzene solution. We found six vibrational normal modes with noticeable values of Huang-Rhys factors mainly contribute to vibronic spectra in gas-phase. Among these modes, v10 (1410 cm-1) mode with the C-H bending plus C-C stretching motion was found to be highly active to varied scaling parameters acting on un-damped solute molecules in benzene. It reveals that the Huang-Rhys factor of v10 increases from un-damped HR = 0.077 in the gaseous phase to damped HR = 0.359 in the condensed phase, reflecting the significant solvent enhancement of the experimental vibronic spectrum. An additional feature is that the empirical scaling parameters were equally scaled to each hydrogen atom of C-H mode, and the resulting data was shown to be consistent with the experiment.
For carbazole molecule, by comparing four different types of ab-initio methods, we found (TD) B3LYP-35 methods can pertinently describe the gas-phase experimental spectrum, and also the further damped harmonic solvent-enhanced spectrum. It was found the damped harmonic approach with merely one-set scaling was no longer valid for fitting the experimental spectrum in solution due to underestimations of the fitted band intensities. Hence, we utilized a generalized multi-scaling damped approach to investigate the extremely solvent-enhanced spectra. Our data show that five and four representative normal-modes involving combined ring-stretching and ring-breathing vibrational motions mostly cause enhancement of vibronic bands in absorbance and fluorescence, respectively. Additionally, we found that vibrational mode patterns in the ground state evidently differ from those in the excited state, showing why mirror image break of the observed solvent-enhanced spectra occurs as opposed to that of the gaseous phase spectra.

並列關鍵字

Franck-Condon factor ； Huang-Rhys factor ； Damped harmonic oscillator approach ； UV-vis spectra ； Fluorescence spectra ； Displaced harmonic oscillator ； Perylene ； Carbazole

參考文獻

Chapter One

Chapter Two

1. Born, M.; Oppenheimer, R., Zur Quantentheorie der Molekeln. Annalen der Physik 1927, 389 (20), 457-484.

2. Fock, V., Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems. Zeitschrift für Physik 1930, 61 (1), 126-148.

3. Slater, J. C., Note on Hartree's Method. Physical Review 1930, 35 (2), 210-211.