Please use this identifier to cite or link to this item:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/92974Full metadata record
| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 蔡政達 | zh_TW |
| dc.contributor.advisor | Jeng-Da Chai | en |
| dc.contributor.author | 王昱揚 | zh_TW |
| dc.contributor.author | Yu-Yang Wang | en |
| dc.date.accessioned | 2024-07-10T16:07:26Z | - |
| dc.date.available | 2024-07-11 | - |
| dc.date.copyright | 2024-07-10 | - |
| dc.date.issued | 2024 | - |
| dc.date.submitted | 2024-07-08 | - |
| dc.identifier.citation | F. Jensen, Introduction to Computational Chemistry (Wiley, New York, 2007).
T. Helgaker, P. Jørgensen, and J. Olsen, Molecular Electronic-Structure Theory (Wiley, New York, 2000). R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules (Oxford University, New York, 1989). P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964). W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). S. Kümmel and L. Kronik, Rev. Mod. Phys. 80, 3 (2008). A. J. Cohen, P. Mori-Sánchez, and W. Yang, Science 321, 792 (2008). J.-D. Chai, J. Chem. Phys. 136, 154104 (2012). J.-D. Chai, J. Chem. Phys. 140, 18A521 (2014). J.-D. Chai, J. Chem. Phys. 146, 044102 (2017). D. Zhang and D. G. Truhlar, J. Chem. Theory Comput. 16, 5432 (2020). R. Bauernschmitt and R. Ahlrichs, J. Chem. Phys. 104, 9047 (1996). E. K. Gross, L. N. Oliveira, and W. Kohn, Phys. Rev. A 37, 2809 (1988). L. N. Oliveira, E. K. Gross, and W. Kohn, Phys. Rev. A 37, 2821 (1988). Á. Nagy, Phys. Rev. A 57, 1672 (1998). E. Schrödinger, Phys. Rev. 28, 1049 (1926). L. Marchildon, Quantum Mechanics: From Basic Principles to Numerical Methods and Applications (Springer-Verlag, Berlin, 2002). E. Merzbacher, Quantum Mechanics (Wiley, New York, 1998). M. Born and R. Oppenheimer, Ann. Phys. 389, 457 (1927). M. Levy, Proc. Natl. Acad. Sci. USA 76, 6062 (1979). M. Levy, Phys. Rev. A 26, 1200 (1982). M. Levy and J. P. Perdew, in Density Functional Methods in Physics, edited by R. M. Dreizler and J. da Providência (Plenum, New York, 1985). N. H. March, Adv. Phys. 6, 1 (1957). E. H. Lieb, Rev. Mod. Phys. 53, 603 (1981). E. Fermi, Rend. Accad. Naz. Lincei 6, 32 (1927). L. H. Thomas, Math. Proc. Camb. Philos. Soc. 23, 542 (1927). E. Teller, Rev. Mod. Phys. 34, 627 (1962). N. L. Balàzs, Phys. Rev. 156, 42 (1967). N. D. Mermin, Phys. Rev. 137, A1441 (1965). U. Von Barth and L. Hedin, J. Phys. C 5, 1629 (1972). M. M. Pant and A. K. Rajagopal, Solid State Commun. 10, 1157 (1972). P. W. Ayers and W. Yang, J. Chem. Phys. 124, 224108 (2006). F. Schwabl, Statistical Mechanics, (Springer-Verlag, Berlin, 2002). P. Coleman, Introduction to Many-Body Physics, (Cambridge University Press, Cambridge UK, 2015). L. O. Wagner, E. M. Stoudenmire, K. Burke, and S. R. White, Phys. Rev. Lett. 111, 093003 (2013). M. Penz, A. Laestadius, E. I. Tellgren, and M. Ruggenthaler, Phys. Rev. Lett. 123, 037401 (2019). M. Penz, A. Laestadius, E. I. Tellgren, M. Ruggenthaler, and P. E. Lammert, Phys. Rev. Lett. 125, 249902 (2020). S. Lang, Linear Algebra, (Springer-Verlag, New York, 1987). P. K. Suetin, A. I. Kostrikin, and Y. I. Manin, Linear Algebra and Geometry (OPA, Amsterdam, 1997). J. B. Conway, A Course in Functional Analysis (Springer, New York, 1990). J. Harris and R. Jones, J. Phys. F 4, 1170 (1974). G. L. Oliver and J. P. Perdew, Phys. Rev. A 20, 397 (1979). S. Obara and A. Saika, J. Chem. Phys. 84, 3963 (1986). S. Obara and A. Saika, J. Chem. Phys. 89, 1540 (1988). M. Head-Gordon and J. A. Pople, J. Chem. Phys. 89, 5777 (1988). T. P. Hamilton and H. F. Schaefer III, Chem. Phys. 150, 163 (1991). R. Lindh, U. Ryu, and B. Liu, J. Chem. Phys. 95, 5889 (1991). P. A. Dirac, Math. Proc. Camb. Philos. Soc. 26, 376 (1930). J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992). R. Binning and L. Curtiss, J. Comput. Chem. 11, 1206 (1990). V. A. Rassolov, J. A. Pople, M. A. Ratner, and T. L. Windus, J. Chem. Phys. 109, 1223 (1998). V. A. Rassolov, M. A. Ratner, J. A. Pople, P. C. Redfern, and L. A. Curtiss, J. Comput. Chem. 22, 976 (2001). D. A. Gilbert et al., Q-Chem User’s Guide (Q-Chem, Pittsburgh, 2012). E. Berquist et al., Q-Chem 6.0 User’s Manual (Q-Chem, Pleasanton, 2022). A. D. Becke, J. Chem. Phys. 88, 2547 (1988). C. F. Bunge, J. A. Barrientos, and A. V. Bunge, At. Data and Nucl. Data Tables 53, 113 (1993). M. Mitani and Y. Yoshioka, Theor. Chem. Acc. 131, 1169 (2012). S. Dasgupta and J. M. Herbert, J. Comput. Chem. 38, 869 (2017). V. I. Lebedev, USSR Comp. Math. Math. Phys. 16, 10 (1976). V. I. Lebedev, Zh. Vychisl. Mat. Mat. Fiz. 15, 48 (1975). Y. Shao et al., Mol. Phys. 113, 184 (2015). K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure (Van Nostrand Reinhold, New York, 1979). M. Klein and R. Aziz, Inert Gases: Potentials, Dynamics, and Energy Transfer in Doped Crystals (Springer-Verlag, Berlin, 1984). K. T. Tang and J. P. Toennies, Z. Phys. D 1, 91 (1986). R. A. Aziz and M. J. Slaman, Chem. Phys. 130, 187 (1989). R. J. Gdanitz, Chem. Phys. Lett. 348, 67 (2001). J. L. Duncan, Mol. Phys. 28, 1177 (1974). | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/92974 | - |
| dc.description.abstract | 科恩—沈呂九密度泛函理論（KS-DFT）在常見的交換關聯泛函下，對多參考系統可能算得錯誤的自旋密度及其相關性質。氫分子的解離是典型的例子；在其自旋極化解中，可違背現實，出現自旋對稱性破缺，導致 KS-DFT 在同一交換關聯泛函下的自旋極化解與自旋非極化解不一致。近期數值結果表明，藉適當的虛擬溫度，熱輔助佔據密度泛函理論（TAO-DFT）能解決這個問題。本文基於 TAO-DFT 構建了一套線性響應理論，證明在足夠的虛擬溫度下，TAO-DFT 必能消除多參考系統中的自旋對稱性破缺；並以 TAO-DFT 計算不同虛擬溫度下 H2、N2、He2 及 Ne2 的解離及扭曲的乙烯分子，作為例證。 | zh_TW |
| dc.description.abstract | For multireference systems, Kohn-Sham density functional theory (KS-DFT) with conventional exchange-correlation (xc) functionals can yield erroneous spin densities and related properties. A typical example is the dissociation of H2, where unphysical spin-symmetry breaking can arise in the spin-polarized solutions, resulting in distinct spin-polarized and spin-unpolarized solutions derived from the same xc functional in KS-DFT. Recently, thermally-assisted-occupation density functional theory (TAO-DFT) has been shown numerically to resolve this problem when an appropriate fictitious temperature is chosen. In this thesis, a linear response theory based on TAO-DFT is constructed to prove that TAO-DFT with a sufficiently high fictitious temperature can always eliminate the spin-symmetry breaking in multireference systems. As an illustration, TAO-DFT calculations with various fictitious temperatures are performed for the dissociation of H2, N2, He2, and Ne2, along with twisted ethylene. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-07-10T16:07:26Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2024-07-10T16:07:26Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Master’s Thesis Acceptance Certificate i
Acknowledgements ii Abstract (Chinese) iii Abstract iv 1 Introduction 1 1.1 Overview 1 1.2 DFT and TAO-DFT 2 1.3 Spin-Symmetry Breaking in DFT 7 1.4 Outline of the Thesis 9 2 Theory 10 2.1 Iteration of Self-Consistent Equations 10 2.2 Criterion of Spin Symmetry 12 2.3 Undamped-Iteration Kernel 16 2.4 Linear Response Theory with a Basis Set 21 2.5 High-Fictitious-Temperature Limit 23 3 Numerical Investigations 28 3.1 H2 Dissociation 29 3.2 N2 Dissociation 31 3.3 He2 Dissociation 33 3.4 Ne2 Dissociation 35 3.5 Twisted Ethylene 37 4 Conclusions 39 References 40 | - |
| dc.language.iso | en | - |
| dc.subject | 密度泛函理論 | zh_TW |
| dc.subject | 強關聯系統 | zh_TW |
| dc.subject | 自旋 | zh_TW |
| dc.subject | 線性響應理論 | zh_TW |
| dc.subject | 對稱性破缺 | zh_TW |
| dc.subject | 三重態不穩定性 | zh_TW |
| dc.subject | Spin | en |
| dc.subject | Density functional theory | en |
| dc.subject | Triplet instability | en |
| dc.subject | Symmetry breaking | en |
| dc.subject | Linear response theory | en |
| dc.subject | Strongly correlated systems | en |
| dc.title | 熱輔助佔據密度泛函理論中自旋對稱性之恢復 | zh_TW |
| dc.title | Restoration of Spin Symmetry in Thermally-Assisted-Occupation Density Functional Theory | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 112-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 薛宏中;關肇正 | zh_TW |
| dc.contributor.oralexamcommittee | Hung-Chung Hsueh;Chao-Cheng Kaun | en |
| dc.subject.keyword | 密度泛函理論,強關聯系統,自旋,線性響應理論,對稱性破缺,三重態不穩定性, | zh_TW |
| dc.subject.keyword | Density functional theory,Strongly correlated systems,Spin,Linear response theory,Symmetry breaking,Triplet instability, | en |
| dc.relation.page | 42 | - |
| dc.identifier.doi | 10.6342/NTU202401560 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2024-07-08 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 物理學系 | - |
| Appears in Collections: | 物理學系 | |
Files in This Item:
| File | Size | Format | |
|---|---|---|---|
| ntu-112-2.pdf | 3.53 MB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.