摘要
本研究主要利用量子力學之時間獨立密度泛函理論(time- independent density functional theory, TI-DFT)與時間相關密度泛函理論(time-dependent density functional theory, TD-DFT)兩種方法，模擬高分子發光二極體（polymer light-emitting diodes, PLED）之發光材料，利用微觀分析了解材料特性及其電子與光學性質。
高分子發光二極體，為有機電激發光(organic electroluminescent, OEL)元件的一種，其以高分子材料作為發光層，因此，了解發光層材料之特性在PLED研究中扮演極為重要的角色。本論文為研究PLED之常見高分子發光材料-聚噻吩(polythiophene, PT)及其衍生物，探討其特性。首先，建構噻吩(thiophene, T)之單體(monomer, T1)分子，接著逐步增加單體數量至十個(T10)，十五個(T15)，二十個單體(T20)，利用所計算之各別能隙，線性獲得聚噻吩之能隙與實驗值比較，可獲得適用此類分子的模擬參數，利用此參數計算各單體分子及其衍生物之最佳化結構，振動頻率、單點能量等資訊，可獲得鍵長（bond length）、鍵角(bond angle）、能隙(band gap)、分子軌域(molecular orbital）、游離能(ionization potential)、電子親和力(electron affinity)、電子與電洞重組能(reorganization energy)與紫外/可見光光譜(UV/Vis spectrum)等性質，了解單體增加後，材料性質的改變趨勢，以利預測高分子聚噻吩及其高分子衍生物之性質，此外亦進行激發態計算，可獲得放射光譜(emission spectrum)與史托克位移(Stokes shift)等放光特性。
在實驗部分，利用紫外/可見光光譜儀量測二單體噻吩(2, 2′-Bithiophene, T2)與模擬計算所獲得之吸收光譜進行比對，並可透過吸收光譜圖獲得材料之能隙，可驗證模擬的正確性。最後將聚噻吩及其衍生物各種性質進行比較與探討，推測取代基－Br之聚噻吩衍生物具有較佳的電子/電洞傳輸能力，應可有效增加發光性質，因此，此衍生物可做為未來設計新材料之參考。

In this thesis, we employ a time-independent and time-dependent density functional theory (TI-DFT and TD-DFT, respectively) to calculate the performance for polymer light-emitting diodes (PLEDs). Electronic and optical properties of PLEDs emission materials are analyzed and investigated.
PLEDs are one kind of “Organic Electroluminescenc”, OEL, devices. The materials of polythiophene (PT) are used to fabricate the emitting layer in PLEDs. Therefore, it is of prime importance to understand the characteristics of the emitting layer materials which play an important role in PLED research. The first step of this research is to set-up-thiophene (T1) monomer and 2, 2′-Bithiophene (T2, dimer), T3 (trimer), T4 (tetramer)…, T10, T15, T20 molecular models and then calculate their band gap. We can determine the best exchange-correlation functional and basis set for thiophene and thiophene derivatives by using linear extrapolation techniques to determine these band gap values and then performing a comparsion with experimental data. Then, the optimized structures, bond length, band gap, molecular orbital, ionization energies, electron affinities and reorganization energy were calculated by using the DFT. The corresponding UV/Vis spectrum and absorption/excitation energies can be evaluated from the TD-DFT simulation results. The Stokes shift can be observed by comparing the difference between absorption and emission spectrum.
In the experimental part, we took the 2, 2′-Bithiophene (dimer, T2) molecule, and its UV/Vis experimental spectrum data closely matches the simulation results. This is a good indication that we can use B3LYP/6-31G(d) to simulate other molecular units (T3, T4…, T10, T15, T20) and thiophene derivatives. It can be concluded that the derivatives, T_∞Br, may display a better performance than the polythiophene (PT) counterpart and can serve as the design reference for new emission materials of PLEDs devices.

參考文獻
[1] U.S. Energy Information Administration/International Energy Outlook 2010.
[2] http://zfacts.com/p/226.html (Modified: Mon, 21 May 2007).
[3] 城戶淳二，圖解有機EL (Organic Electroluminescence), 世茂出版社, 台灣新北市, 2004. (ISBN: 9577766161).
[4] Z. Li, H. Meng, Organic Light-Emitting Materials and Devices, CRC/Taylor & Francis, Boca Raton , 2007, (IBSN: 1-57444-574-X).
[5] J. L. Segura, “The Chemistry of Electroluminescent Organic Materials“, Acta Polym., Vol. 49, pp. 319-344, 1998.
[6] Z. H. Kafafi, Organic Electroluminescence, CRC/Taylor & Francis, Boca Raton , 2005, (IBSN: 0824759060).
[7] M. Pope, H. Kallmann and P. Magnante, ”Electroluminescence in Organic Crystals”, J .Chem. Phys., Vol. 38, pp. 2042-2043, 1993.
[8] H. Shirakawa, A. J. Heeger and A. G. MacDiarmid, ”Synthesis of Electrically Conducting Organic Polymers : Halogen Derivatives of Polyacetylene, (CH)x”, J. C. S. Chem. Comm., pp. 578-580, 1977.
[9] H. Shirakawa, A. J. Heeger and A. G. MacDiarmid, “Conductive Polymers”, The Nobel Prize in Chemistry, 2000.
[10] C. W. Tang and S. A. VanSlyke, “Organic Electroluminescent Diodes”, Appl. Phys. Lett., Vol. 51, pp. 913-914, 1987.
[11] C. W. Tang, S. A. VanSlyke and C. H. Chen, “Electroluminescence of Doped Organic Thin Films”, J. Appl. Phys., Vol. 65, pp. 3610-3616, 1989.
[12] J. H. Burroughes, D. D. C. Bradley, A. R. Brown, R. N. Marks, K. Mackay, R. H. Friend, P. L. Burns and A. B. Holmes, “Light-Emitting Diodes Based on Conjugated Polymers”, Nature, Vol. 347, pp. 539-541, 1990.
[13] I. F. Perpichka, D. F. Perepichka, H. Meng and F. Wudl, “Light-Emitting Polythiophenes”, Adv. Mater., Vol. 17, pp. 2281-2305, 2005.
[14] M. R. Andersson, M. Berggren, G. Gustafsson, J. C. Gustafsson-Carlberg, D. Selse T. Hjertberg and O. Wennerstroem,” Electroluminescence from Substituted Poly(thiophenes): From Blue to Near-Infrared”, Macromolecules, Vol. 27, pp.7525-7529. 1995.
[15] H. A. M. van Mullekoma, J. A . J. M. Vekemans, E. E. Havinga and E.W. Meijer,”Developments in The Chemistry and Band Gap Engineering of Donor–Acceptor Substituted Conjugated Polymers”, Mater. Sci. Eng., Vol. 32, pp. 1-40, 2001.
[16] R. V. Stanton, and K. M. Merz, “Density Functional Study of Symmetric Proton Transfers”, J. Chem. Phys., Vol. 101, pp. 6658-6663, 1994.
[17] J. P. Perdew and W. Yue, “Accurate and Simple Density Functional for The Electronic Exchange Energy: Generalized Gradient Approximation”, Phys. Rev. B, Vol. 33, pp. 8800-8802, 1986.
[18] J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson and D. J. Singh, “Atoms, molecules, solids, and Surfaces: Applications of The Generalized Gradient Approximation for Exchange and Correlation”, Phys. Rev. B, Vol. 46, pp. 6671-6687, 1992.
[19] P. Gomes da Costa, R. G. Dandrea, and E. M. Conwell, “First-Principles Calculation of The Three-Dimensional Band Structure of Poly(phenylene vinylene)”, Phys. Rev. B, Vol. 47, pp. 1800-1810, 1993.
[20] J. Cornil, D. Beljonne, D. A. dos Santos and J. L. Bredas, “Poly(p-phenylene vinylene) as Active Layer in Light-Emitting Diodes: A Theoretical Investigation of The Effects of Derivatization”, Synth. Met., Vol. 76, pp. 101-104, 1996.
[21] W. Förner, F. Bogar and R. Knab, “Energy Bands and Bond Alternation Potential in Poly(para-phenylene vinylene): A Comparative Ab Initio Quantum Chemical and Density Functional Theory Study”, Mol. Struct. Vol. 430, pp. 73-84, 1998.
[22] C. H. Yu , J. S. K. Yu and W. C. Chen, “Time-Dependent Density Functional Study of Electroluminescent Polymers”, J. Phys. Chem. A , Vol. 107, pp. 4268- 4275, 2003.
[23] S. Rentsch , R. Colditz , D. Grebner , and M. Helbig, ”Theoretical Studies and Spectroscopic Investigations of Ground and Excited Electronic States of Thiophene Oligomers”, Chem. Phys. Vol. 201, pp. 309-320, 1995.
[24] D. R. Ferro, W. Porzio, S. Destri and M. Ragaui, ”Application of Molecular Mechanics to Refine and Understand The Crystal Structure of Polythiophene and its Oligomers”, Macrmol. Theor. Simul., Vol. 6, pp. 713-727, 1997.
[25] J. Ma, S. Li and Y. Jiang, ”A Time-Dependent DFT Study on Band Gaps and Effective Conjugation Lengths of Polyacetylene, Polyphenylene, Polypentafulvene,Polycyclopentadiene, Polypyrrole, Polyfuran, Polysilole, Polyphosphole,and Polythiophene”, Macromolecules, Vol. 35, pp. 1109-1115, 2002.
[26] R. Colle, G. Grosso, A. Ronzani and C. M. Zicovich-Wilson, ”Structure and X-ray Spectrum of Crystalline Poly(3-hexylthiophene) from DFT-van der Waals Calculations”, Phys. Status Solidi B., Vol. 248, pp. 1360–1368, 2011.
[27] E. Lewars, Computational Chemistry: introduction to the theory and applications of molecular and quantum mechanics, 2nd edition, Springer Science+Business Media, Dordrecht, 2011, (ISBN: 978904813823)
[28] S. F. Nelsen and F. Blomgren, “Estimation of Electron Transfer Parameters from AM1 Calculations”, J. Org. Chem., Vol. 66, pp. 6551-6559, 2001.
[29] M. A. L. Marques, “Time-Dependent Density Functional Theory”, Berlin: Springer, 2006.
[30] E. Frisch, M. J. Frisch, G. W. Trucks, Gaussian 03 User’s Reference, 2nd edition, Gaussian, Inc., Wallingford, CT, 2005. (ISBN: 0972718702).
[31] A. D. Becke, “Density-Functional Thermochemistry. III: The Role of Exact Exchange”, J. Chem. Phys, Vol. 98, pp. 5648-5652, 1993.
[32] C. Lee, W. Yang and R. G. Parr, “Development of The Colle-Salvetti Correlation-Energy Formula into A Functional of The Electron Density”, Phys. Rev. B., Vol. 37, pp. 785-789, 1988.
[33] D. A. Skoog, F. J. Holler and T. A. Nieman, Principles of Instrumental Analysis, 5th edition, Thomson Learning, Boston, 1998. (ISBN: 9814066516).
[34] P. B. Kelter S. S. Zumdahl, Chemical Principles, 4th edition, Baker & Taylor Books , Boston, 2002. (ISBN: 0618120785).
[35] Z. Q. You, H. C. Chen and C. P. Hsu, “Ab Initio Quantum Chemistry Methods for Calculating Electronic Couplings in Electron Transfer Reactions”, Chemistry (The Chinese. Soc. Taipei), Vol. 63, pp. 623-634, 2005.
[36] R. A. Marcus, “On The Theory of Oxidation-Reduction Reactions Involving Electron Transfer. 1”, J. Chem. Phys., Vol. 24, pp. 966, 1956.
[37] L. G. Wade, Organic Chemistry, 5th edition , Prentice-Hall , N.J , 2003. (ISBN: 013033832X).
[38] Sadler Handbook of Ultraviolet Spectra; Sadler Research Labo- ratories, Philadelphia, PA, 1979.
[39] R. Colditz, D. Grebner, M. Helbig and S. Rentsch, ”Theoretical Studies and Spectroscopic Investigations of Ground and Excited Electronic States of Thiophene Oligomers”, Chem Phys., Vol. 201, pp. 309, 1995.
[40] M. Kobayashi, J. Chen, T.C. Chung, F. Moraes, A. J. Heeger and F. Wudl, “Synthesis and Properties of Chemically Coupled Poly(thiophene)“, Synth. Met., Vol. 9, pp. 77-86, 1984.
[41] S. A. Mcdonald, G. Konstantatos, S. Zhang, P. W. Cyr, E. J. D. Klem, L. Levina and E.H. Sargent, “Solution-Processed PbS Quantum Dot Infrared Photodetectors and Photovoltaics”, Nature Materials, Vol. 4, pp. 138-142, 2005.
[42] S. Hotchandani and P. V. Kamat, “Charge-Transfer Processes in Coupled Semiconductor Systems Photochemistry and Photo- Electrochemistry of The Colloidal Cadmium Sulfide-Zinc Oxide System”, J. Chem. Phys., Vol. 96, pp. 6834-6839, 1992.