請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/90986完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 蔡政達 | zh_TW |
| dc.contributor.advisor | Jeng-Da Chai | en |
| dc.contributor.author | 蔡弘毅 | zh_TW |
| dc.contributor.author | Hung-Yi Tsai | en |
| dc.date.accessioned | 2023-10-24T16:37:12Z | - |
| dc.date.available | 2023-12-01 | - |
| dc.date.copyright | 2023-10-24 | - |
| dc.date.issued | 2023 | - |
| dc.date.submitted | 2023-08-12 | - |
| dc.identifier.citation | [1] W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
[2] J.-D. Chai, The Journal of Chemical Physics 136, 154104 (2012). [3] J.-D. Chai, The Journal of Chemical Physics 140, 18A521 (2014). [4] J.-D. Chai, The Journal of Chemical Physics 146, 044102 (2017). [5] Y. Zhu and J. M. Herbert, The Journal of Chemical Physics 156, 204123 (2022). [6] S.-H. Yeh, A. Manjanath, Y.-C. Cheng, J.-D. Chai, and C.-P. Hsu, The Journal of Chemical Physics 153, 084120 (2020). [7] M. Born and R. Oppenheimer, Annalen der Physik 389, 457 (1927). [8] C. Ullrich, Time-Dependent Density-Functional Theory: Concepts and Applications, Oxford Graduate Texts (OUP Oxford, 2012), ISBN 9780199563029. [9] P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964). [10] E. Engel and R. M. Dreizler, Foundations of Density Functional Theory: Existence Theorems (Springer Berlin Heidelberg, Berlin, Heidelberg, 2011), pp. 11–56, ISBN 978-3-642-14090-7. [11] T. L. Gilbert, Phys. Rev. B 12, 2111 (1975). [12] M. Levy, Proceedings of the National Academy of Sciences 76, 6062 (1979). [13] E. H. Lieb, International Journal of Quantum Chemistry 24, 243 (1983). [14] R. M. Dreizler and E. K. U. Gross, Density Functional Theory: An Approach to the Quantum ManyBody Problem (Springer Berlin Heidelberg, Berlin, Heidelberg, 1990), ISBN 978-3-642-86105-5. [15] M. Levy, Phys. Rev. A 26, 1200 (1982). [16] P. Schipper, O. Gritsenko, and E. Baerends, Theoretical Chemistry Accounts 99, 329 (1998), ISSN 1432-881X. [17] R. C. Morrison, The Journal of Chemical Physics 117, 10506 (2002). [18] J. Katriel, S. Roy, and M. Springborg, The Journal of Chemical Physics 121, 12179 (2004). [19] A. D. Becke, The Journal of Chemical Physics 138, 074109 (2013). [20] N. D. Mermin, Phys. Rev. 137, A1441 (1965). [21] V. V. Flambaum, F. M. Izrailev, and G. Casati, Phys. Rev. E 54, 2136 (1996). [22] V. V. Flambaum and F. M. Izrailev, Phys. Rev. E 55, R13 (1997). [23] V. V. Flambaum and F. M. Izrailev, Phys. Rev. E 56, 5144 (1997). [24] F. Xuan, J.-D. Chai, and H. Su, ACS Omega 4, 7675 (2019), pMID: 31459859. [25] C.-Y. Lin, K. Hui, J.-H. Chung, and J.-D. Chai, RSC Adv. 7, 50496 (2017). [26] B.-J. Chen and J.-D. Chai, RSC Adv. 12, 12193 (2022). [27] S. Li and J.-D. Chai, Frontiers in Chemistry 8 (2020), ISSN 2296-2646. [28] C.-S. Wu and J.-D. Chai, Journal of Chemical Theory and Computation 11, 2003 (2015). [29] C.-N. Yeh and J.-D. Chai, Scientific Reports 6, 30562 (2016). [30] S. Seenithurai and J.-D. Chai, Scientific Reports 6 (2016). [31] C.-S. Wu, P.-Y. Lee, and J.-D. Chai, Scientific Reports 6, 37249 (2016). [32] S. Seenithurai and J.-D. Chai, Scientific Reports 7, 4966 (2017). [33] S. Seenithurai and J.-D. Chai, Scientific Reports 8 (2018). [34] C.-N. Yeh, C. Wu, H. Su, and J.-D. Chai, RSC Adv. 8, 34350 (2018). [35] J.-H. Chung and J.-D. Chai, Scientific Reports 9, 2907 (2019). [36] S. Seenithurai and J.-D. Chai, Scientific Reports 9, 12139 (2019). [37] Q. Deng and J.-D. Chai, ACS Omega 4, 14202 (2019), pMID: 31508542. [38] H.-J. Huang, S. Seenithurai, and J.-D. Chai, Nanomaterials 10 (2020), ISSN 2079-4991. [39] S. Seenithurai and J.-D. Chai, Scientific Reports 10, 13133 (2020). [40] S. Seenithurai and J.-D. Chai, Nanomaterials 11 (2021), ISSN 2079-4991. [41] C.-C. Chen and J.-D. Chai, Nanomaterials 12 (2022), ISSN 2079-4991. [42] E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984). [43] R. van Leeuwen, Phys. Rev. Lett. 82, 3863 (1999). [44] T.-c. Li and P.-q. Tong, Phys. Rev. A 31, 1950 (1985). [45] T. Li and Y. Li, Phys. Rev. A 31, 3970 (1985). [46] A. Pribram-Jones, P. E. Grabowski, and K. Burke, Phys. Rev. Lett. 116, 233001 (2016). [47] J. Dufty, K. Luo, and S. B. Trickey, Phys. Rev. E 98, 033203 (2018). [48] J. P. Solovej (2014), https://web.math.ku.dk/solovej/MANYBODY/mbnotes-ptn-5-3-14.pdf. [49] R. Seiringer, Cold Quantum Gases and Bose–Einstein Condensation (Springer Berlin Heidelberg, Berlin, Heidelberg, 2012), pp. 55–92, ISBN 978-3-642-29511-9. [50] M. Greiner, P. Carrier, and A. Görling, Phys. Rev. B 81, 155119 (2010). [51] R. Shankar, Principles of Quantum Mechanics, 经典英文物理学教材系列 (Springer, 1994), ISBN 9780306447907. [52] C. Heunen and J. Vicary, Categories for Quantum Theory: An Introduction, Oxford Graduate Texts in Mathematics (OUP Oxford, 2019), ISBN 9780191060069. [53] N. Dunford and J. Schwartz, Linear Operators: General theory, Linear Operators (Interscience Publishers, 1958), ISBN 9780470226056. [54] R. Martin, Electronic Structure: Basic Theory and Practical Methods (Cambridge University Press, 2020), ISBN 9781108429900. [55] gigo318 (https://physics.stackexchange.com/users/297482/gigo318), Operator expectation value for system of non-interacting particles (fermions), Physics Stack Exchange, uRL:https://physics.stackexchange.com/q/653616 (version: 2021-07-27). [56] P. Beale, Statistical Mechanics (Elsevier Science, 2011), ISBN 9780123821898. [57] R. G. Parr and Y. Weitao, in Density-Functional Theory of Atoms and Molecules (Oxford University Press, 1995), ISBN 9780195092769. [58] Y. Zhu and J. M. Herbert, The Journal of Chemical Physics 148, 044117 (2018). [59] M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, Phys. Rev. A 49, 2117 (1994). [60] P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993). [61] F. Bedurke, T. Klamroth, P. Krause, and P. Saalfrank, The Journal of Chemical Physics 150, 234114 (2019). [62] E. Epifanovsky, A. T. B. Gilbert, X. Feng, J. Lee, Y. Mao, N. Mardirossian, P. Pokhilko, A. F. White, M. P. Coons, A. L. Dempwolff, et al., The Journal of Chemical Physics 155, 084801 (2021). [63] B. P. Pritchard, D. Altarawy, B. Didier, T. D. Gibson, and T. L. Windus, Journal of Chemical Information and Modeling 59, 4814 (2019), pMID: 31600445. [64] T. H. Dunning, The Journal of Chemical Physics 90, 1007 (1989). [65] R. A. Kendall, T. H. Dunning, and R. J. Harrison, The Journal of Chemical Physics 96, 6796 (1992). [66] F. Bedurke, T. Klamroth, and P. Saalfrank, Phys. Chem. Chem. Phys. 23, 13544 (2021). [67] C. W. Murray, N. C. Handy, and G. J. Laming, Molecular Physics 78, 997 (1993). [68] P. A. M. Dirac, Mathematical Proceedings of the Cambridge Philosophical Society 26, 376–385 (1930). [69] J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992). [70] J. Maurer and U. Keller, Journal of Physics B: Atomic, Molecular and Optical Physics 54, 094001 (2021). [71] Y. Zhu, B. Alam, and J. Herbert, ChemRxiv (2021). [72] X. Li, S. M. Smith, A. N. Markevitch, D. A. Romanov, R. J. Levis, and H. B. Schlegel, Phys. Chem. Chem. Phys. 7, 233 (2005). [73] A. J. Cohen, P. Mori-Sánchez, and W. Yang, Science 321, 792 (2008). | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/90986 | - |
| dc.description.abstract | 密度泛函理論，特別是Kohn--Sham(KS)密度泛函理論，因其高計算效率成為量子計算領域被廣泛應用的方法。然而，KS密度泛函理論假設了基態密度具有非交互作用純態勢可代表性，這甚至限制了精確的KS密度泛函理論處理多參考系統的能力。為了從根本擺脫此限制，熱輔助佔據密度泛函理論已被開發。模擬結果顯示，熱輔助佔據密度泛函理論在單參考系統表現類似KS密度泛函理論，在多參考系統則優於KS密度泛函理論。其中，熱輔助佔據密度泛函理論展現了藉由分數佔據軌域描述靜態關聯能的能力。
如同線性響應含時密度泛函理論和即時含時密度泛函理論，線性響應含時熱輔助佔據密度泛函理論已被提出並應用於獲取激發能。這篇論文將把熱輔助佔據密度泛函理論擴展為即時熱輔助佔據密度泛函理論，不做線性響應理論常見的微擾近似以求更廣的適用性。過去作品中未完好定義的Hartree交換關聯theta作用量泛函也會一併修正。我們應用模擬氫分子系統，並討論線性響應理論無法處理的高諧波產生。模擬結果顯示，適當θ的即時熱輔助佔據密度泛函理論在單參考系統表現類似即時含時密度泛函理論。在多參考系統，足夠大θ的即時熱輔助佔據密度泛函理論則修復了限制自旋表述與非限制自旋表述被破壞的對稱。 | zh_TW |
| dc.description.abstract | Density functional theory (DFT), specifically Kohn--Sham DFT (KS-DFT), is a widespread method in the field of quantum computation due to its high computational efficiency. However, KS-DFT assumes the ground-state density to be non-interacting pure-state (NI-PS) v_s-representable, which limits the ability of even exact KS-DFT to handle multi-reference systems. To relieve this limitation, thermally assisted-occupation DFT (TAO-DFT) has been developed. Simulation results suggest that TAO-DFT performs similarly to KS-DFT for single-reference systems, while outperforming KS-DFT for multi-reference systems. In particular, TAO-DFT is shown to describe static correlation through fractional orbital occupations.
Similar to linear-response time-dependent DFT (LR-TD-DFT) and real-time time-dependent DFT (RT-TD-DFT), LR-TD-TAO-DFT has been proposed and utilized to extract excitation energies. In this thesis, we aim to extend TAO-DFT to real-time TAO-DFT. The often made small perturbation aprroximation in LR theory is dropped for universality. The ill-defined Hartree--exchange--correlation-theta (HXCθ) action functional in the previous work is also revised. Specifically, we apply RT-TAO-DFT to hydrogen molecules. The phenomenon of high harmonic generation (HHG), which falls outside the scope of LR theory, is simulated and discussed. Simulation results suggest that RT-TAO-DFT with suitable θ performs similar to RT-TD-DFT for single-reference systems. While for multi-reference systems, RT-TAO-DFT with sufficiently large θ fixes the symmetry-breaking issue between spin-restricted and spin-unrestricted formulations. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-10-24T16:37:12Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-10-24T16:37:12Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 摘要 i
Abstract iii Contents v List of Figures vii Chapter 1 Introduction 1 Chapter 2 Theory 11 2.1 Ground-State TAO-DFT . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 LR-TD-TAO-DFT . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 From Generalizations of Theorems to RT-TAO . . . . . . . . . . . . 16 2.4 Expression of the TAO Ensemble . . . . . . . . . . . . . . . . . . . 19 2.5 From One-Electron States to a Basis of Fock Space . . . . . . . . . . 21 2.6 Ensemble Average Evaluated by One-Electron States . . . . . . . . . 26 2.7 Expression of the RT-TAO Potential . . . . . . . . . . . . . . . . . . 31 2.8 Some Details of Derivations . . . . . . . . . . . . . . . . . . . . . . 35 2.9 Approximations for the HXCθ Potential . . . . . . . . . . . . . . . . 37 2.10 Practical Scheme of RT-TAO . . . . . . . . . . . . . . . . . . . . . . 38 Chapter 3 Results 43 3.1 High Harmonic Generation . . . . . . . . . . . . . . . . . . . . . . . 43 3.2 Time-Dependent Observables . . . . . . . . . . . . . . . . . . . . . 45 3.3 Computational Details . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.4 H 2 at the Equilibrium Geometry . . . . . . . . . . . . . . . . . . . . 48 3.5 H 2 at the Stretched Geometry . . . . . . . . . . . . . . . . . . . . . 52 3.6 Discussions of Symmetry-Breaking Effects . . . . . . . . . . . . . . 53 Chapter 4 Conclusions 57 References 61 Appendix A — Systems Perpendicular to the Laser Polarization 67 Appendix B — HHG Spectra without Window Functions 75 | - |
| dc.language.iso | en | - |
| dc.subject | 即時含時密度泛函理論 | zh_TW |
| dc.subject | 即時熱輔助佔據密度泛函理論 | zh_TW |
| dc.subject | 含時熱輔助佔據密度泛函理論 | zh_TW |
| dc.subject | real-time time-dependent density functional theory | en |
| dc.subject | real-time thermally assisted-occupation density functional theory | en |
| dc.subject | time-dependent thermally assisted-occupation density functional theory | en |
| dc.title | 即時熱輔助佔據密度泛函理論 | zh_TW |
| dc.title | Real-Time Thermally Assisted-Occupation Density Functional Theory | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 111-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 趙聖德;薛宏中 | zh_TW |
| dc.contributor.oralexamcommittee | Sheng-Der Chao;Hung-Chung Hsueh | en |
| dc.subject.keyword | 即時熱輔助佔據密度泛函理論,即時含時密度泛函理論,含時熱輔助佔據密度泛函理論, | zh_TW |
| dc.subject.keyword | real-time thermally assisted-occupation density functional theory,real-time time-dependent density functional theory,time-dependent thermally assisted-occupation density functional theory, | en |
| dc.relation.page | 79 | - |
| dc.identifier.doi | 10.6342/NTU202303862 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2023-08-13 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 物理學系 | - |
| dc.date.embargo-lift | 2023-12-01 | - |
| 顯示於系所單位： | 物理學系 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-111-2.pdf | 36.4 MB | Adobe PDF | 檢視/開啟 |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。