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| Time-dependent electron localization function Burnus, Tobias |
| Haupttitel | Time-dependent electron localization function |
| Autor | Burnus, Tobias |
| Seitenzahl | 90 S. |
| Auch erschienen in | Deposit-Server der Deutschen Nationalbibliothek, http://d-nb.info/98587676X |
| Fachbereich/Einrichtung | FB Physik |
| Arbeitsbereich/Institut | Institut für Theoretische Physik |
| Erscheinungsjahr | 2004 |
| Dokumente | Dataobject from FUDOCS_document_000000000598
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| Freie Schlagwörter | Time-dependent density-functional theory, zeitabhängige Dichtefunktionaltheorie, Elektronen-Lokalisierungsfunktion |
| DDC | 530 Physik |
| Dokumententyp/-Sammlungen | Examensarbeit |
| Medientyp/Format | Text |
| Abstract | The electron localization function ELF, which is crafted to reveal chemical bonds and their properties, has been generalized to the time-dependent regime. This allows the time-resolved visualization of the formation, modulation and breaking of bonds and gives thus insight into the dynamics of excited electrons. This has been illustrated by the pi–pi* transition of ethyne induced by a laser field, and by the destruction of bonds and the formation of lone-pairs in a scattering process of a proton with ethene. In the second part, an optimal control algorithm is used to determine an optimized laser pulse of a HOMO–LUMO transition of the diatomic molecule lithium fluoride. |
| Inhalt | Preface iii Acknowledgement iv Contents vii 1 Density functional theory 1 1.1 The Hohenberg--Kohn theorem 1 1.2 The Kohn--Sham formalism 4 1.3 Time-dependent DFT – the Runge--Groß theorem 7 1.4 Pseudo potentials 8 2 The time-dependent electron localization function 11 2.1 Introduction 11 2.2 The static electron localization function 13 2.3 Derivation of the time-dependent ELF 14 2.3.1 Spherical average and Taylor expansion of P(sigma)(r, r + s, t) 15 2.3.2 Derivation of D(sigma) in the single-particle picture 17 2.3.3 Calculation of C_(sigma) 19 2.3.4 Comparison with the static ELF 20 2.4 Application of the TDELF 21 2.4.1 Excitation of molecules 21 2.4.2 Proton scattering 23 2.5 Conclusions 26 3 Optimal control 29 3.1 Introduction 29 3.2 Algorithm 29 3.2.1 Iteration algorithm 32 3.3 Optimizing the HOMO–LUMO transition of LiF 33 3.3.1 Calculation of H |psi> = E_i |psi_i> 33 3.3.2 Discretization 36 3.3.3 The five-point discretization 39 3.3.4 Solving the eigenvalue problem 41 3.3.5 Time propagation 41 3.3.6 Absorbing boundaries 43 3.4 Application of the optimal control algorithm 43 3.5 Conclusions 51 4 Conclusion 53 A TDELF auxiliary calculations 55 A.1 Simplification of C_(sigma) 55 A.2 Deriving the time-dependent ELF for a simplified, two-particle case 57 B Optimal control for many-particle systems 59 B.1 Calculation of the overlap B.2 Calculation of the dipole moment C Proof for the overlap of two Slater wave functions 65 D Atomic, "convenient" and SI Units 67 D.1 Atomic Units 67 D.2 "Convenient units" 68 D.3 Comparison and conversion 68 D.4 Constants 68 Abbreviations and Acronyms 71 Used symbols 73 References 75 |
| Sprache | Englisch |
| Rechte | Everyone may use this work according to the terms and conditions of the Lizenz für die freie Nutzung unveränderter Inhalte (Licence for Free Usage of Invariable Content). The licence text can be obtained at http://www.ifross.de/Lizenzen/LizenzFuerUnveraenderteInhalte.html. |
| Anmerkungen des Autors | Adviser of the Diplomarbeit: Prof. Dr. Eberhard K. U. Groß |
| Zugriffstatistik | |
| Statische URL | http://edocs.fu-berlin.de/docs/receive/FUDOCS_document_000000000598 |
| Erstellt am | 17.12.2008 - 10:28:37 |
| Letzte Änderung | 07.04.2009 - 13:55:28 |
