近年來，隨著光物理之研究領域蓬勃發展，相關機制也日益被重視，例如：生物顯影技術之遠紅外放光量子效率之提升與有機發光二極體效率提升之微觀光物理機制。本論文利用計算化學探索重組能對以上兩大光物理現象之影響，內容分別如下：
I. 為了提升遠紅外放光分子的放光量子效率，以Franck Condon Principle與Marcus Theory為根基，將基態與激發態兩能階之間的電子躍遷與遲豫至優化結構的能量差定為重組能，並以青色素分子（Cyanines）與電子予體－受體分子（Donor－acceptor compounds），兩類目前研究上最具遠紅外放光潛能之分子，以DFT以及TD－DFT計算結果比對分子差異，並探討分子結構對重組能的影響。
II. 以Fermi’s Golden Rule與Marcus Theory為基礎，將電子轉移速率推廣至第一單重激發態與第一參重激發態的轉換速率，並以絕熱狀態、低耦合為前提，在構象座標中，y軸表示以基態優化結構能量為零點的相對能量，x軸表示不同結構，兩能態得以兩拋物線表達。兩拋物線的相交點為由第一參重激發態轉換至第一單重激發態所需經過的能量障礙。透過DFT以及TD－DFT計算各能態能量並運用二次函數運算，計算不同分子之能障，討論熱延遲螢光放光現象計算上預測之判斷依據。

With booming researches in photophysics, the underlying mechanisms behind many interesting phenomena are attracting more attention, e.g. the quantum efficiency of near-IR emitting compounds used in bioimaging, and detailed mechanisms of thermally activated delayed fluorescence (TADF). In this thesis, we use computational methods to explore these two fundamental photophysical topics.
I. We explore the relation between the molecular structure and the reorganization energy. In principle, the quantum efficiency formula can be enhanced by reducing the nonradiation rate constant, which depends strongly on the magnitude of the reorganization energy. Based on Franck Condon Principle and Marcus theory, the reorganization energy is defined as the the first singlet excited state (S1) state in the ground state (S0) structure and in the optimized S1 structure. Using DFT and TD-DFT methods, we compute the reorganization energies of cyanine-related compounds and other donor-acceptor compounds. Our detailed analysis indicates that the reorganization energy may be effectively reduced by modifying the molecular structure.
II. We compute the intersystem crossing energy barrier between the first singlet excited state (S1) and the first triplet excited state (T1) for various systems, and discuss its effect on TADF. On the condition that S1 and T1 states are adiabatic and weakly coupled, these states may be simplified as parabolas on the conformation coordinate diagram based on Fermi’s Golden Rule and Marcus Theory. Using DFT and TD-DFT, we calculate the energy barrier by solving the quadratic function of the enegy parabola, and we attempt to propose rules for qualitative and quantitative predictions on the experimentally observed TADF phenomenon.

1. Berezin, M. Y.; Achilefu, S., Fluorescence Lifetime Measurements and Biological Imaging. Chemical Reviews 2010, 110 (5), 2641-2684.
2. Uoyama, H.; Goushi, K.; Shizu, K.; Nomura, H.; Adachi, C., Highly efficient organic light-emitting diodes from delayed fluorescence. Nature 2012, 492 (7428), 234-8.
3. Jones, R. O., Density functional theory: Its origins, rise to prominence, and future. Reviews of Modern Physics 2015, 87 (3), 897-923.
4. Bush, V.; Caldwell, S. H., Thomas-Fermi Equation Solution by the Differential Analyzer. Physical Review 1931, 38 (10), 1898-1902.
5. Thomas, L. H., The calculation of atomic fields. Mathematical Proceedings of the Cambridge Philosophical Society 1927, 23 (5), 542-548.
6. Frank, N. H., Note on the Hartree and Hartree-Fock Methods. Physical Review 1937, 51 (7), 577-583.
7. Hohenberg, P.; Kohn, W., Inhomogeneous Electron Gas. Physical Review 1964, 136 (3B), B864-B871.
8. Mardirossian, N.; Head-Gordon, M., Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals. Molecular Physics 2017, 115 (19), 2315-2372.
9. Chai, J. D.; Head-Gordon, M., Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections. Phys Chem Chem Phys 2008, 10 (44), 6615-20.
10. Davidson, E. R.; Feller, D., Basis set selection for molecular calculations. Chemical Reviews 1986, 86 (4), 681-696.
11. Tomasi, J.; Mennucci, B.; Cammi, R., Quantum Mechanical Continuum Solvation Models. Chemical Reviews 2005, 105 (8), 2999-3094.
12. Martin, R. L., Natural transition orbitals. The Journal of Chemical Physics 2003, 118 (11), 4775-4777.
13. Scrocco, E.; Tomasi, J. In The electrostatic molecular potential as a tool for the interpretation of molecular properties, New Concepts II, Berlin, Heidelberg, 1973//; Springer Berlin Heidelberg: Berlin, Heidelberg, 1973; pp 95-170.
14. Marcus, R. A., Electron transfer reactions in chemistry. Theory and experiment. Reviews of Modern Physics 1993, 65 (3), 599-610.
15. Marcus, R. A.; Sutin, N., Electron transfers in chemistry and biology. Biochimica et Biophysica Acta (BBA) - Reviews on Bioenergetics 1985, 811 (3), 265-322.
16. Libby, W. F., Theory of Electron Exchange Reactions in Aqueous Solution. The Journal of Physical Chemistry 1952, 56 (7), 863-868.
17. Franck, J.; Dymond, E. G., Elementary processes of photochemical reactions. Transactions of the Faraday Society 1926, 21 (February), 536-542.
18. Wu, Q.; Van Voorhis, T., Direct Calculation of Electron Transfer Parameters through Constrained Density Functional Theory. The Journal of Physical Chemistry A 2006, 110 (29), 9212-9218.
19. Hush, N. S., Adiabatic theory of outer sphere electron-transfer reactions in solution. Transactions of the Faraday Society 1961, 57 (0), 557-580.
20. Deng, G.; Li, S.; Sun, Z.; Li, W.; Zhou, L.; Zhang, J.; Gong, P.; Cai, L., Near-infrared fluorescence imaging in the largely unexplored window of 900-1,000 nm. Theranostics 2018, 8 (15), 4116-4128.
21. Antaris, A. L.; Chen, H.; Diao, S.; Ma, Z.; Zhang, Z.; Zhu, S.; Wang, J.; Lozano, A. X.; Fan, Q.; Chew, L.; Zhu, M.; Cheng, K.; Hong, X.; Dai, H.; Cheng, Z., A high quantum yield molecule-protein complex fluorophore for near-infrared II imaging. Nature Communications 2017, 8 (1), 15269.
22. Englman, R.; Jortner, J., The energy gap law for radiationless transitions in large molecules. Molecular Physics 1970, 18 (2), 145-164.
23. Wang, C.; Li, X.-L.; Gao, Y.; Wang, L.; Zhang, S.; Zhao, L.; Lu, P.; Yang, B.; Su, S.-J.; Ma, Y., Efficient Near-Infrared (NIR) Organic Light-Emitting Diodes Based on Donor–Acceptor Architecture: An Improved Emissive State from Mixing to Hybridization. Advanced Optical Materials 2017, 5 (20), 1700441.
24. Xie, J.-Y.; Li, C.-Y.; Li, Y.-F.; Fei, J.; Xu, F.; Ou-Yang, J.; Liu, J., Near-Infrared Fluorescent Probe with High Quantum Yield and Its Application in the Selective Detection of Glutathione in Living Cells and Tissues. Analytical Chemistry 2016, 88 (19), 9746-9752.
25. Bixon, M.; Jortner, J.; Cortes, J.; Heitele, H.; Michel-Beyerle, M. E., Energy Gap Law for Nonradiative and Radiative Charge Transfer in Isolated and in Solvated Supermolecules. The Journal of Physical Chemistry 1994, 98 (30), 7289-7299.
26. Chen, W.-C.; Chou, P.-T.; Cheng, Y.-C., Low Internal Reorganization Energy of the Metal–Metal-to-Ligand Charge Transfer Emission in Dimeric Pt(II) Complexes. The Journal of Physical Chemistry C 2019, 123 (16), 10225-10236.
27. Duong, T.; Li, X.; Yang, B.; Schumann, C.; Albarqi, H. A.; Taratula, O.; Taratula, O., Phototheranostic nanoplatform based on a single cyanine dye for image-guided combinatorial phototherapy. Nanomedicine 2017, 13 (3), 955-963.
28. Zhang, Z.; Lin, F.; Chen, H.-C.; Wu, H.-C.; Chung, C.-L.; Lu, C.; Liu, S.-H.; Tung, S.-H.; Chen, W.-C.; Wong, K.-T.; Chou, P.-T., A silole copolymer containing a ladder-type heptacylic arene and naphthobisoxadiazole moieties for highly efficient polymer solar cells. Energy & Environmental Science 2015, 8 (2), 552-557.
29. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H.; Li, X.; Caricato, M.; Marenich, A. V.; Bloino, J.; Janesko, B. G.; Gomperts, R.; Mennucci, B.; Hratchian, H. P.; Ortiz, J. V.; Izmaylov, A. F.; Sonnenberg, J. L.; Williams; Ding, F.; Lipparini, F.; Egidi, F.; Goings, J.; Peng, B.; Petrone, A.; Henderson, T.; Ranasinghe, D.; Zakrzewski, V. G.; Gao, J.; Rega, N.; Zheng, G.; Liang, W.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Throssell, K.; Montgomery Jr., J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M. J.; Heyd, J. J.; Brothers, E. N.; Kudin, K. N.; Staroverov, V. N.; Keith, T. A.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A. P.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Millam, J. M.; Klene, M.; Adamo, C.; Cammi, R.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Farkas, O.; Foresman, J. B.; Fox, D. J. Gaussian 16 Rev. C.01, Wallingford, CT, 2016.
30. Imahori, H.; Yamada, H.; Guldi, D. M.; Endo, Y.; Shimomura, A.; Kundu, S.; Yamada, K.; Okada, T.; Sakata, Y.; Fukuzumi, S., Comparison of Reorganization Energies for Intra- and Intermolecular Electron Transfer. Angewandte Chemie International Edition 2002, 41 (13), 2344-2347.
31. Mujumdar, R. B.; Ernst, L. A.; Mujumdar, S. R.; Lewis, C. J.; Waggoner, A. S., Cyanine dye labeling reagents: Sulfoindocyanine succinimidyl esters. Bioconjugate Chemistry 1993, 4 (2), 105-111.
32. Xue, L.; He, J.; Gu, X.; Yang, Z.; Xu, B.; Tian, W., Efficient Bulk-Heterojunction Solar Cells Based on a Symmetrical D-π-A-π-D Organic Dye Molecule. The Journal of Physical Chemistry C 2009, 113 (29), 12911-12917.
33. He, C.; He, Q.; He, Y.; Li, Y.; Bai, F.; Yang, C.; Ding, Y.; Wang, L.; Ye, J., Organic solar cells based on the spin-coated blend films of TPA-th-TPA and PCBM. Solar Energy Materials and Solar Cells 2006, 90 (12), 1815-1827.
34. Huang, C.-Y.; Ho, S.-Y.; Lai, C.-H.; Ko, C.-L.; Wei, Y.-C.; Lin, J.-A.; Chen, D.-G.; Ko, T.-Y.; Wong, K.-T.; Zhang, Z.; Hung, W.-Y.; Chou, P.-T., Insights into energy transfer pathways between the exciplex host and fluorescent guest: attaining highly efficient 710 nm electroluminescence. Journal of Materials Chemistry C 2020, 8 (17), 5704-5714.
35. Zhang, Q.; Kelly, M. A.; Bauer, N.; You, W., The Curious Case of Fluorination of Conjugated Polymers for Solar Cells. Accounts of Chemical Research 2017, 50 (9), 2401-2409.
36. Osaka, I.; Kakara, T.; Takemura, N.; Koganezawa, T.; Takimiya, K., Naphthodithiophene–Naphthobisthiadiazole Copolymers for Solar Cells: Alkylation Drives the Polymer Backbone Flat and Promotes Efficiency. Journal of the American Chemical Society 2013, 135 (24), 8834-8837.
37. Becquerel, E., Report on a memoir by MM. F. Lucas and A. Cazin, on the duration of the electric spark. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 1872, 44 (293), 316-319.
38. Marriott, G.; Clegg, R. M.; Arndt-Jovin, D. J.; Jovin, T. M., Time resolved imaging microscopy. Phosphorescence and delayed fluorescence imaging. Biophys J 1991, 60 (6), 1374-1387.
39. Delorme, R.; Perrin, F., Durées de fluorescence des sels d'uranyle solides et de leurs solutions. 1929, 10 (5), 177-186.
40. Parker, C. A.; Hatchard, C. G., Triplet-singlet emission in fluid solutions. Phosphorescence of eosin. Transactions of the Faraday Society 1961, 57 (0), 1894-1904.
41. Maciejewski, A.; Szymanski, M.; Steer, R. P., Thermally activated delayed S1 fluorescence of aromatic thiones. The Journal of Physical Chemistry 1986, 90 (23), 6314-6318.
42. Endo, A.; Ogasawara, M.; Takahashi, A.; Yokoyama, D.; Kato, Y.; Adachi, C., Thermally Activated Delayed Fluorescence from Sn4+–Porphyrin Complexes and Their Application to Organic Light Emitting Diodes — A Novel Mechanism for Electroluminescence. Advanced Materials 2009, 21 (47), 4802-4806.
43. Higginbotham, H. F.; Yi, C.-L.; Monkman, A. P.; Wong, K.-T., Effects of Ortho-Phenyl Substitution on the rISC Rate of D–A Type TADF Molecules. The Journal of Physical Chemistry C 2018, 122 (14), 7627-7634.
44. Ravinson, D. S. M.; Thompson, M. E., Thermally assisted delayed fluorescence (TADF): fluorescence delayed is fluorescence denied. Materials Horizons 2020, 7 (5), 1210-1217.
45. Lv, L.; Yuan, K.; Si, C.; Zuo, G.; Wang, Y., Mechanism study of TADF and phosphorescence in dinuclear copper (I) molecular crystal using QM/MM combined with an optimally tuned range-separated hybrid functional. Organic Electronics 2020, 81, 105667.
46. Peng, Q.; Niu, Y.; Shi, Q.; Gao, X.; Shuai, Z., Correlation Function Formalism for Triplet Excited State Decay: Combined Spin-Orbit and Nonadiabatic Couplings. J Chem Theory Comput 2013, 9 (2), 1132-43.
47. El‐Sayed, M. A., Spin—Orbit Coupling and the Radiationless Processes in Nitrogen Heterocyclics. The Journal of Chemical Physics 1963, 38 (12), 2834-2838.
48. Endo, A.; Sato, K.; Yoshimura, K.; Kai, T.; Kawada, A.; Miyazaki, H.; Adachi, C., Efficient up-conversion of triplet excitons into a singlet state and its application for organic light emitting diodes. Applied Physics Letters 2011, 98 (8), 083302.
49. Gao, Y.; Su, T.; Zhao, L.; Geng, Y.; Wu, Y.; Zhang, M.; Su, Z.-M., How does a little difference in structure determine whether molecules have thermally activated delayed fluorescence characteristic or not? Organic Electronics 2017, 50, 70-76.
50. Kim, D.-H.; D’Aléo, A.; Chen, X.-K.; Sandanayaka, A. D. S.; Yao, D.; Zhao, L.; Komino, T.; Zaborova, E.; Canard, G.; Tsuchiya, Y.; Choi, E.; Wu, J. W.; Fages, F.; Brédas, J.-L.; Ribierre, J.-C.; Adachi, C., High-efficiency electroluminescence and amplified spontaneous emission from a thermally activated delayed fluorescent near-infrared emitter. Nature Photonics 2018, 12 (2), 98-104.
51. Eyring, H., The Activated Complex in Chemical Reactions. The Journal of Chemical Physics 1935, 3 (2), 107-115.
52. Kitamoto, Y.; Namikawa, T.; Suzuki, T.; Miyata, Y.; Kita, H.; Sato, T.; Oi, S., Dimesitylarylborane-based luminescent emitters exhibiting highly-efficient thermally activated delayed fluorescence for organic light-emitting diodes. Organic Electronics 2016, 34, 208-217.
53. Mamada, M.; Inada, K.; Komino, T.; Potscavage, W. J., Jr.; Nakanotani, H.; Adachi, C., Highly Efficient Thermally Activated Delayed Fluorescence from an Excited-State Intramolecular Proton Transfer System. ACS Cent Sci 2017, 3 (7), 769-777.
54. Sun, H.; Zhong, C.; Brédas, J.-L., Reliable Prediction with Tuned Range-Separated Functionals of the Singlet–Triplet Gap in Organic Emitters for Thermally Activated Delayed Fluorescence. Journal of Chemical Theory and Computation 2015, 11 (8), 3851-3858.
55. Tanaka, H.; Shizu, K.; Miyazaki, H.; Adachi, C., Efficient green thermally activated delayed fluorescence (TADF) from a phenoxazine-triphenyltriazine (PXZ-TRZ) derivative. Chem Commun (Camb) 2012, 48 (93), 11392-4.
56. Yersin, H.; Mataranga-Popa, L.; Czerwieniec, R.; Dovbii, Y., Design of a New Mechanism beyond Thermally Activated Delayed Fluorescence toward Fourth Generation Organic Light Emitting Diodes. Chemistry of Materials 2019, 31 (16), 6110-6116.
57. Chen, X. K.; Bakr, B. W.; Auffray, M.; Tsuchiya, Y.; Sherrill, C. D.; Adachi, C.; Bredas, J. L., Intramolecular Noncovalent Interactions Facilitate Thermally Activated Delayed Fluorescence (TADF). J Phys Chem Lett 2019, 10 (12), 3260-3268.
58. Cheng, D.; Xu, D.; Wang, Y.; Zhou, H.; Zhou, Z.; Liu, X.; Han, A.; Zhang, C., 9,9-Dimethyl-9,10-dihydroacridine-based donor–acceptor cruciform luminophores: Envident aggregation-induced emission and remarkable mechanofluorochromism. Dyes and Pigments 2020, 173.
59. Dereka, B.; Svechkarev, D.; Rosspeintner, A.; Aster, A.; Lunzer, M.; Liska, R.; Mohs, A. M.; Vauthey, E., Solvent tuning of photochemistry upon excited-state symmetry breaking. Nat Commun 2020, 11 (1), 1925.