Relativistic Electronic Structure Theory - Fundamentals (eBook)

Front Cover 1
Relativistic Electronic Structure Theory: Part 1. Fundamentals 4
Copyright Page 5
Table of Contents 10
Preface 6
Chapter 1. Tour Historique 22
1. Introduction 22
2. Dirac Equation 23
3. Many Electron Systems 28
4. Relativity and Atomic Structure 31
5. Going to Molecules 35
6. Conclusions 41
Chapter 2. The Dirac Operator 44
1. Introduction 44
2. Introducing the Dirac Equation 47
3. State Space and Interpretation 52
4. Solving the Dirac Equation 55
5. Useful Subspaces 65
6. Relativistic Observables 67
7. Electron-Positron Interpretation 70
8. Relativistic Invariance 75
9. Classification of External Fields 82
10. Properties of Dirac Operators 86
11. Short Description of the Nonrelativistic Limit 90
12. Spherical Symmetry 98
13. The Hydrogen Atom 109
14. Summary 125
Chapter 3. Relativistic Self-consistent Fields 128
1. Introduction 128
2. Foundations 133
3. Finite Matrix Methods for Dirac Hamiltonians 158
4. DHFB Theory for Atoms 178
5. DHFB Theory for Molecules 189
6. Implementation: the Bertha Code 199
7. Open Shells: MCDF Theory 207
8. Survey of Relativistic Mean Field Calculations 212
9. Conclusions 215
Chapter 4. Nuclear Charge Density Distributions in Quantum Chemistry 224
1. Introduction 224
2. Nuclear Structure 226
3. Nuclear Charge Density Distributions: Their Potential and Other Properties 232
4. Nuclear Charge Density Distribution Models 242
5. Nuclear Models in Quantum Chemistry 255
6. Other Properties Depending on the Nuclear Charge Distribution 267
7. Summary 271
Chapter 5. Basis Sets for Relativistic Calculations 280
1. Introduction 280
2. The Dirac Equation for the Hydrogen Atom 282
3. Types of Basis Functions 284
4. The Kinetic Balance Requirement 287
5. The Optimization of Basis Sets 291
6. Describing the Small R Region 294
7. Basis Set Shell Structure 296
8. Family Basis Set 298
9. Basis Set Beyond the DHF 300
10. Large-Small Component Balance 302
11. Examples of 4-Component Basis Sets in Applications 303
12. Concluding Remarks 309
Chapter 6. Post Dirac-Fock-Methods — Electron Correlation 312
1. Introduction 312
2. The Dirac-Coulomb-Breit Hamiltonian 314
3. Approximate Hamiltonians 324
4. Many-Body Perturbation Theory 328
5. Configuration Interaction 330
6. Coupled Cluster Theory 342
7. Concluding Remarks 350
Chapter 7. Post Dirac-Fock-Methods — Properties 353
1. Introduction 353
2. Theory of Molecular Properties 354
3. Electromagnetic Interactions 369
4. Hamiltonians 390
5. Molecular Properties at the Closed-Shell 4-Component Relativistic Hartree-Fock Level 400
6. Closing Remarks 415
Chapter 8. QED Theory of Atoms 422
1. The Principles of QED 424
2. QED Theory of the Interelectron Interaction in Atoms 454
3. QED Corrections for Light Atoms 466
4. QED Corrections in Heavy Atoms 474
Chapter 9. Parity Violation 489
1. Introduction 489
2. The Weak Interactions and Atomic Physics 492
3. Heavy Ions as a Laboratory for Many-Body Theory 496
4. Parity Nonconservation in Cesium 513
5. Electron Dipole Moments 538
Chapter 10. Relativistic Density Functional Theory: Foundations and Basic Formalism 544
1. Introduction 545
2. Field Theoretical Background 557
3. Foundations and Basic Formalism 557
4. Relativistic Exchange-Correlation Functional: Concepts and Illustrative Results 580
5. Concluding Remarks 603
A. Appendix: Quantization of Noninteracting Fermions 604
B. Appendix: Renormalization Scheme of Vacuum QED 612
C. Appendix: Relativistic Homogeneous Electron Gas 620
D. Appendix: Renormalization of Inhomogeneous Electron Gas 631
E. Appendix: Gradient Corrections to the Relativistic LDA 634
Chapter 11. Two-Component Methods and the Generalized Douglas-Kroll Transformation 643
1. Introduction 643
2. Methods to Decouple the Dirac Equation 647
3. The Douglas-Kroll Method 662
4. Numerical Results with DKH3 and DKH4 673
5. Transformation of the Wavefunction - Picture Change 677
6. Conclusions and Perspectives 680
Chapter 12. Perturbation Theory of Relativistic Effects 685
1. Introduction. Why Perturbation Theory? 686
2. The Non-Relativistic Limit 689
3. Perturbation Theory Based on the Foldy-Wouthuysen Transformation 713
4. Direct Perturbation Theory 721
5. Stationary Direct Perturbation Theory 736
6. Quasidegenerate Direct Perturbation Theory 742
7. Many-Electron Systems 749
8. Direct Perturbation Theory Using Energy Gradients or the Finite Perturbations 770
9. Conclusions. Merits and Drawbacks of Direct Perturbation Theory 772
10. Appendix: The Concept of Effective Hamiltonians 773
11. Glossary 775
Chapter 13. Perturbation Theory Based on Quasi-Relativistic Hamiltonians 779
1. Introduction 779
2. General Theory 781
3. Quasi-Relativistic Hamiltonians 785
4. Perturbation Energy Expansions 788
5. First-Order Properties 792
6. Computational Methods 798
7. Applications 799
8. Summary 809
Chapter 14. Relativistic Effective Core Potentials 814
1. Introduction 814
2. Relativistic Effects 816
3. All-Electron Methods 822
4. Valence-Only Methods 827
5. Calibration Studies 865
6. Conclusions 876
Chapter 15. Relativistic Solid State Theory 884
1. Introduction 885
2. Effects due to Relativistic Shifts in e(k) 886
3. Electronic States: SO-Coupling and Crystal Symmetry 890
4. Electronic States: SO-Coupling and Spin Polarization 907
5. Magnetooptical and Magnetoelastic Effects 921
6. Conclusion 930
Index 940