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研究生:李睿哲
研究生(外文):Jui-Che Lee
論文名稱:運用密度泛函理論計算材料束縛能
論文名稱(外文):Theoretical Study on the Exciton Binding Energy from Density Functional Theory Methods
指導教授:林祥泰
口試委員:蔡政達謝介銘張博凱
口試日期:2015-07-22
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:化學工程學研究所
學門:工程學門
學類:化學工程學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:英文
論文頁數:96
中文關鍵詞:束縛能fundamental gap激發能量游離能電子親和力密度泛函理論CCSD
外文關鍵詞:exciton binding energyfundamental gapoptical gapionization potentialelectron affinityCCSDDFT
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束縛能的定義是把束縛的電子電洞對變成自由電荷所需要的能量,束縛能對於有機光電材料和裝置來說,是一個影響表現好壞的因素,然而,對於現在運用密度泛函理論(Density Functional Theory)的量子計算是不是可以信賴是一個很重要的議題,在本研究中,我們分成兩部份去討論。
我們用9種常用的密度泛函理論方法和參考方法(CCSD)去計算121個小分子的束縛能,把9種密度泛函理論方法和參考方法比較找出最精準的方法,這些方法包括LSDA、PBE、M06L、B3LYP、ωB97、ωB97X、ωB97X-D、M06-HF、M06-2X,他們的平均絕對誤差依序為ωB97X 是0.38 eV、ωB97是0.39 eV、ωB97X-D是0.40 eV、M06-2X是0.48 eV、B3LYP是0.53 eV、M06L是0.57 eV、PBE和LSDA是0.66 eV、M06-HF是0.80 eV,在本研究中還有計算其他的光電性質,例如:frontier orbitals和HOMO-LUMO gap,比較所有光電性質的計算結果,ωB97是最精準的,所以我們預期ωB97是有潛力去預測更複雜分子的束縛能。
根據前面的結果,顯示ωB97方法可能可以預測有機半導體材料的束縛能,另一方面,Pabitra K. Nayak暗示B3LYP方法也可以預測有機半導體材料的束縛能,所以我們計算了19個有機半導體材料的adiabatic ionization potential, adiabatic electron affinity and vertical optical gap,並把ωB97和B3LYP計算結果和實驗值做比較,這證明了ωB97和B3LYP是有能力預測有機半導體材料的束縛能,所以我們預期ωB97和B3LYP有能力預測出新設計的光電裝置材料的束縛能。


The exciton binding energy, the energy required to separate an excited electron-hole pair to free charge carriers, is one of the key performance factors of organic photoactive materials and devices. However, it is questionable whether modern quantum mechanical calculations based on the density functional theory (DFT) can provide reliable predictions for this physical quantity. In this study, we use two parts to discuss it.
we compared the results from 9 common DFT methods, including LDA, PBE, M06L, B3LTP, ωB97, ωB97X, ωB97X-D, M06-HF, M06-2X, to the benchmark method, CCSD, for 121 small to medium sized molecules. The mean absolute errors in the exciton binding energy are found to be 0.38 eV from ωB97X, 0.39 from ωB97X, 0.40 eV from ωB97X-D, 0.48 eV from M06-2X, 0.53 eV from B3LYP, 0.57 eV from M06L, 0.66 eV from PBE and LSDA, and 0.80 eV from M06-HF. The ωB97-methods are also found to be accurate for many other optoelectronic properties such as the energy of frontier orbitals and the HOMO-LUMO gap. Our results indicate that the ωB97-method has the potential of predicting the exciton binding energy for more complex systems.
From previous work, our results show ωB97 method is possible to estimate the exciton binding energy of molecular organic semiconductors. On the other hand, Pabitra K. Nayak implies B3LYP is possible to estimate the exciton binding energy of molecular organic semiconductors. We compared adiabatic ionization potential, adiabatic electron affinity and vertical optical gap from ωB97 and B3LYP methods to experimental values for 19 molecular organic semiconductors. It verifies ωB97 and B3LYP methods have good prediction for molecular organic semiconductors. Our results indicate that the ωB97 and B3LYP methods have the potential to predict the exciton binding energy for designing new organic optoelectronic materials.


致謝 i
中文摘要 ii
ABSTRACT iii
Contents v
List of Figures vii
List of Tables xii
Chapter 1 Introduction 1
1.1 Research Background and Motivation 1
1.2 Exciton Binding Energy 3
1.3 Literature Review 5
1.4 Polarization Energy 7
Chapter 2 Theory 9
2.1 Born-Oppenheimer Approximation 9
2.2 Coupled-Cluster Theory 10
2.3 Density Functional Theory 12
2.3.1 Approximation for Exchange-Correlation Energy 15
2.4 Basis Set 17
2.5 The Polarizable Continuum Model 19
2.6 The Ionization Potential and Electron Affinity 20
2.7 The Fundamental Gap 21
2.8 The Exciton Binding Energy 22
Chapter 3 Computational Detail 24
3.1 Molecular structure of organic semiconductors 26
Chapter 4 Result and Discussion 29
4.1 Exciton Binding Energy of Elements and Small Organic Molecules 29
4.1.1 The benchmark method 29
4.1.2 The DFT performance 35
4.2 Exciton Binding Energy of Organic Semiconductor molecules 45
4.2.1 Organic Molecules 45
4.2.2 Polymer 71
4.2.3 The correlation between Eb, Eg and Eopt 78
Chapter 5 Conclusion 86
Chapter 6 References 89


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