Advances in Quantum Chemistry (eBook)

Theory of Confined Quantum Systems - Part One

eBook Download: EPUB

2009 | 1. Auflage
690 Seiten
Elsevier Science (Verlag)
978-0-08-091202-8 (ISBN)

Infos

Advances in Quantum Chemistry presents surveys of current developments in this rapidly developing field. With invited reviews written by leading international researchers, each presenting new results, it provides a single vehicle for following progress in this interdisciplinary area.
* Publishes articles, invited reviews and proceedings of major international conferences and workshops
* Written by leading international researchers in quantum and theoretical chemistry
* Highlights important interdisciplinary developments

Inhalt

Front cover 1
Half title page 2
Editorial board 3
Title page 4
Copyright page 5
Contents 6
Preface 10
Contributors 12
Chapter 1. Properties of Confined Hydrogen and Helium Atoms 14
1. Introduction 14
2. Some General Properties 15
3. H in a Spherical Box 18
4. H in Confining Oscillator Potential 32
5. Off-centre Confinement 34
6. Summary 36
References 37
Chapter 2. Exact Relations for Confined One-Electron Systems 38
1. Introduction: Some Notes on History 39
2. Some General Constructions and Notations 41
3. Commutation Relations and Hypervirial Theorems 46
4. Energy and Region Modifications 53
5. The System in an External Potential 64
6. On Mean Values and Other Properties of Confined Systems 71
7. Spherically Confined Isotropic Harmonic Oscillator 81
8. Information Theoretical Uncertainty-like Relationships 82
9. Afterword 84
Acknowledgments 85
References 85
Chapter 3. The Hydrogen Atom Confined in Semi-infinite Spaces Limited by Conoidal Boundaries 92
1. Introduction 93
2. Sample of Comments on Articles About Confined Atoms and Molecules 95
3. Review of The Superintegrability of The Schrödinger Equation for The Free Hydrogen Atom and its Ionization Limit 103
4. Overview of the Confinement of the Hydrogen Atom by a Conoidal Boundary as a Symmetry-Breaking Effect 116
5. Preview of Problems on Confined Atoms and Molecules of Current and Future Investigations 126
6. Discussion 132
Acknowledgements 133
References 134
Chapter 4. The Hydrogen and Helium Atoms Confined in Spherical Boxes 136
1. Introduction 136
2. Methods used in Various Studies of the Confined Hydrogen Atom 138
3. Soft Spherical Confinement for Hydrogen Atom Revisited 161
4. Treatment of the Confined Hydrogen Atom Under Neumann Boundary Conditions 164
5. The Helium Atom Confined in Spherical Boxes 165
6. Other Approaches 177
7. Conclusions 179
Acknowledgments 180
References 180
Chapter 5. Exact Solutions for Confined Model Systems Using Kummer Functions 186
1. Introduction 186
2. Solutions of Kummer's Equation 189
3. K -dimensional Systems 197
4. Confined Hydrogen Atom in 3-d and 2-d 203
5. Two-dimensional Harmonic Oscillator 209
6. The Constant Potential 209
7. Summary 211
Acknowledgements 212
Appendix 212
References 214
Chapter 6. Perturbation Theory for a Hydrogen-like Atom Confined Within an Impenetrable Spherical Cavity 216
1. Introduction 216
2. Asymptotic Expansions for Large Box Radii 218
3. Expansions for Small Box Radii 227
4. Variational and Numerical Solutions 233
5. Perturbation Theory Results for Small Box Radii 235
6. Intermediate Box Sizes 245
7. Concluding Remarks 249
References 251
Chapter 7. Comparative Study Between the Hartree-Fock and Kohn-Sham Models for the Lowest Singlet and Triplet States of the Confined Helium Atom 254
1. Introduction 254
2. Hartree-Fock and Kohn-Sham Models for Two-electron Systems 255
3. Methodology 259
4. Results and Discussion 259
5. Conclusions 266
Acknowledgments 267
References 267
Chapter 8. Thomas--Fermi--Dirac--Weizsäcker Density Functional Formalism Applied to the Study of Many-electron Atom Confinement by Open and Closed Boundaries 268
1. Introduction 268
2. Many-electron Atom Confinement by Closed Boundaries 270
3. Many-electron Atom Confinement by Open Boundaries 288
4. Conclusions 294
References 295
Chapter 9. Confined Atoms Treated as Open Quantum Systems 298
1. Physically Confined Systems are Open Systems 298
2. Mechanics of an Open System 299
3. Virial Theorem and the Definition of Pressure 302
4. Calculation of Pressure in Terms of the Surface Virial 306
5. Discussion and Conclusions 329
Acknowledgements 330
References 330
Subject Index 332

Produkt-Details

• Erscheint lt. Verlag: 20.6.2009
• Mitarbeit: Herausgeber (Serie): Erkki J. Brandas, John R. Sabin
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Naturwissenschaften ► Biologie
• Themenwelt: Naturwissenschaften ► Chemie ► Physikalische Chemie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
• Themenwelt: Technik
• ISBN-10: 0-08-091202-8 / 0080912028
• ISBN-13: 978-0-08-091202-8 / 9780080912028