Elsevier S & T

Relativistic Electronic Structure Theory - Fundamentals

Schwerdtfeger, Peter

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Table of contents
  • Cover
  • Table of Contentsix
  • Prefacev
  • Chapter 1. Tour Historique1
  • 1. Introduction1
  • 2. Dirac Equation2
  • 3. Many Electron Systems7
  • 4. Relativity and Atomic Structure10
  • 5. Going to Molecules14
  • 6. Conclusions20
  • Chapter 2. The Dirac Operator23
  • 1. Introduction23
  • 2. Introducing the Dirac Equation26
  • 3. State Space and Interpretation31
  • 4. Solving the Dirac Equation34
  • 5. Useful Subspaces44
  • 6. Relativistic Observables46
  • 7. Electron-Positron Interpretation49
  • 8. Relativistic Invariance54
  • 9. Classification of External Fields61
  • 10. Properties of Dirac Operators65
  • 11. Short Description of the Nonrelativistic Limit69
  • 12. Spherical Symmetry77
  • 13. The Hydrogen Atom88
  • 14. Summary104
  • Chapter 3. Relativistic Self-consistent Fields107
  • 1. Introduction107
  • 2. Foundations112
  • 3. Finite Matrix Methods for Dirac Hamiltonians137
  • 4. DHFB Theory for Atoms157
  • 5. DHFB Theory for Molecules168
  • 6. Implementation: the Bertha Code178
  • 7. Open Shells: MCDF Theory186
  • 8. Survey of Relativistic Mean Field Calculations191
  • 9. Conclusions194
  • Chapter 4. Nuclear Charge Density Distributions in Quantum Chemistry203
  • 1. Introduction203
  • 2. Nuclear Structure205
  • 3. Nuclear Charge Density Distributions: Their Potential and Other Properties211
  • 4. Nuclear Charge Density Distribution Models221
  • 5. Nuclear Models in Quantum Chemistry234
  • 6. Other Properties Depending on the Nuclear Charge Distribution246
  • 7. Summary250
  • Chapter 5. Basis Sets for Relativistic Calculations259
  • 1. Introduction259
  • 2. The Dirac Equation for the Hydrogen Atom261
  • 3. Types of Basis Functions263
  • 4. The Kinetic Balance Requirement266
  • 5. The Optimization of Basis Sets270
  • 6. Describing the Small R Region273
  • 7. Basis Set Shell Structure275
  • 8. Family Basis Set277
  • 9. Basis Set Beyond the DHF279
  • 10. Large-Small Component Balance281
  • 11. Examples of 4-Component Basis Sets in Applications282
  • 12. Concluding Remarks288
  • Chapter 6. Post Dirac-Fock-Methods „ Electron Correlation291
  • 1. Introduction291
  • 2. The Dirac-Coulomb-Breit Hamiltonian293
  • 3. Approximate Hamiltonians303
  • 4. Many-Body Perturbation Theory307
  • 5. Configuration Interaction309
  • 6. Coupled Cluster Theory321
  • 7. Concluding Remarks329
  • Chapter 7. Post Dirac-Fock-Methods „ Properties332
  • 1. Introduction332
  • 2. Theory of Molecular Properties333
  • 3. Electromagnetic Interactions348
  • 4. Hamiltonians369
  • 5. Molecular Properties at the Closed-Shell 4-Component Relativistic Hartree-Fock Level379
  • 6. Closing Remarks394
  • Chapter 8. QED Theory of Atoms401
  • 1. The Principles of QED403
  • 2. QED Theory of the Interelectron Interaction in Atoms433
  • 3. QED Corrections for Light Atoms445
  • 4. QED Corrections in Heavy Atoms453
  • Chapter 9. Parity Violation468
  • 1. Introduction468
  • 2. The Weak Interactions and Atomic Physics471
  • 3. Heavy Ions as a Laboratory for Many-Body Theory475
  • 4. Parity Nonconservation in Cesium492
  • 5. Electron Dipole Moments517
  • Chapter 10. Relativistic Density Functional Theory: Foundations and Basic Formalism523
  • 1. Introduction524
  • 2. Field Theoretical Background536
  • 3. Foundations and Basic Formalism536
  • 4. Relativistic Exchange-Correlation Functional: Concepts and Illustrative Results559
  • 5. Concluding Remarks582
  • A. Appendix: Quantization of Noninteracting Fermions583
  • B. Appendix: Renormalization Scheme of Vacuum QED591
  • C. Appendix: Relativistic Homogeneous Electron Gas599
  • D. Appendix: Renormalization of Inhomogeneous Electron Gas610
  • E. Appendix: Gradient Corrections to the Relativistic LDA613
  • Chapter 11. Two-Component Methods and the Generalized Douglas-Kroll Transformation622
  • 1. Introduction622
  • 2. Methods to Decouple the Dirac Equation626
  • 3. The Douglas-Kroll Method641
  • 4. Numerical Results with DKH3 and DKH4652
  • 5. Transformation of the Wavefunction - Picture Change656
  • 6. Conclusions and Perspectives659
  • Chapter 12. Perturbation Theory of Relativistic Effects664
  • 1. Introduction. Why Perturbation Theory?665
  • 2. The Non-Relativistic Limit668
  • 3. Perturbation Theory Based on the Foldy-Wouthuysen Transformation692
  • 4. Direct Perturbation Theory700
  • 5. Stationary Direct Perturbation Theory715
  • 6. Quasidegenerate Direct Perturbation Theory721
  • 7. Many-Electron Systems728
  • 8. Direct Perturbation Theory Using Energy Gradients or the Finite Perturbations749
  • 9. Conclusions. Merits and Drawbacks of Direct Perturbation Theory751
  • 10. Appendix: The Concept of Effective Hamiltonians752
  • 11. Glossary754
  • Chapter 13. Perturbation Theory Based on Quasi-Relativistic Hamiltonians758
  • 1. Introduction758
  • 2. General Theory760
  • 3. Quasi-Relativistic Hamiltonians764
  • 4. Perturbation Energy Expansions767
  • 5. First-Order Properties771
  • 6. Computational Methods777
  • 7. Applications778
  • 8. Summary788
  • Chapter 14. Relativistic Effective Core Potentials793
  • 1. Introduction793
  • 2. Relativistic Effects795
  • 3. All-Electron Methods801
  • 4. Valence-Only Methods806
  • 5. Calibration Studies844
  • 6. Conclusions855
  • Chapter 15. Relativistic Solid State Theory863
  • 1. Introduction864
  • 2. Effects due to Relativistic Shifts in ε(k)865
  • 3. Electronic States: SO-Coupling and Crystal Symmetry869
  • 4. Electronic States: SO-Coupling and Spin Polarization886
  • 5. Magnetooptical and Magnetoelastic Effects900
  • 6. Conclusion909
  • Index919
Book details
  • Vendor Elsevier S & T
  • SKU 9780444512499
  • ISBN-13 9780080540467
  • Author Schwerdtfeger, Peter
  • Category Science
  • Subject Physical & Theoretical

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The first volume of this two part series is concerned with the fundamental aspects of relativistic quantum theory, outlining the enormous progress made in the last twenty years in this field. The aim was to create a book such that researchers who become interested in this exciting new field find it useful as a textbook, and do not have to rely on a rather large number of specialized papers published in this area.

· No title is currently available that deals with new developments in relativistic quantum electronic structure theory
· Interesting and relevant to graduate students in chemistry and physics as well as to all researchers in the field of quantum chemistry
· As treatment of heavy elements becomes more important, there will be a constant demand for this title