Wilson Methods in Computational Chemistry

Volume 2 Relativistic Effects in Atoms and Molecules
1988
ISBN: 978-1-4613-0711-2
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 306 Seiten, eBook

Zielgruppe

Research

Autoren/Hrsg.

Wilson, Stephen

Inhaltsverzeichnis

1. Relativistic Atomic Structure Calculations.- 1. Methods of Relativistic Atomic Structure Calculation.- 1.1. Introduction.- 1.2. Methods Based on HDC.- 1.2.1. The Central Field Approximation.- 1.2.2. Method of Superposition of Configurations.- 1.2.3. Model Potential Methods.- 1.2.4. The Dirac-Fock (DF) Model for Closed Shells.- 1.2.5. Average of Configuration DF Models.- 1.2.6. Multiconfiguration Dirac-Fock Models.- 1.3. Corrections to HDC.- 1.3.1. The Covariant Coulomb Interaction.- 1.3.2. Effect of Nuclear Charge and Mass.- 1.3.3. Radiative Corrections.- 1.3.4. Relativistic Many-Body Theory.- 2. Basic Formulas of Relativistic Atomic Structure Theory.- 2.1. Techniques of Angular Momentum Theory.- 2.2. Matrix Elements of Operators for Dirac Central Field Orbitals.- 2.2.1. One-Body Even Operators.- 2.2.2. One-Body Odd Operators.- 2.2.3. Examples of One-Body Operators: Kinetic Energy and Radiation Multipole Operators.- 2.2.4. Two-Body Operators.- 2.3. Classification of Many-Electron States in jj Coupling.- 2.4. Angular Momentum Diagrams and Many-Electron States.- 2.5. Matrix Elements for General Many-Electron States.- 2.6. The Calculation of Radiative Transition Probabilities.- 3. Implementation of the Theory.- 3.1. Angular Coefficients.- 3.2. Radial Integrals.- 3.3. Construction of Radial Functions.- 3.4. Data Organization and Handling.- 3.5. Methods That Do Not Involve Finite Difference Techniques.- 4. Outlook.- References.- 2. Relativistic Molecular Structure Calculations.- 1. Introduction.- 2. Relativistic Molecular Quantum Mechanics.- 2.1. The Dirac Equation.- 2.2. The Dirac-Coulomb Hamiltonian.- 2.3 The Breit Interaction.- 3. Relativistic Independent Electron Models.- 3.1. The Bare-Nucleus Model.- 3.2. The Dirac-Hartree-Fock Model.- 3.3. Other Independent Electron Models.- 4. Electron Correlation.- 4.1. The Nonrelativistic Limit.- 4.2. Relativistic Correlation Effects.- 4.3. Relativistic Many-Body Perturbation Theory.- 5. The Algebraic Approximation.- 5.1. Basis Sets for Nonrelativistic Calculations.- 5.2. The Dirac Equation in the Algebraic Approximation.- 5.3. The Matrix Bare-Nucleus Method.- 5.4. The Matrix Dirac-Hartree-Fock Method.- 5.5. Electron Correlation Calculations.- 6. Conclusions and Future Prospects.- References.- 3. The Relativistic Effective Core Potential Method.- 1. Introduction.- 2. The Effective Core Potential Method.- 2.1. General Theory.- 2.2. The Projection Operator Method.- 2.3. The Pseudo-Orbital Method.- 3. Relativistic Quantum Mechanics.- 3.1. General Remarks.- 3.2. The Cowan-Griffin Method.- 3.3. The Sucher Projection Method.- 4. The Relativistic Effective Core Potential.- 4.1. The Two-Component Approach.- 4.2. The Four-Component Approach.- 5. Applications.- 5.1. The AuH and AgH Molecules.- 5.2. The Pb2 and PbS Molecules.- 5.3. The PtH Molecule.- 6. Conclusions.- References.- 4. Semiempirical Relativistic Molecular Structure Calculations.- 1. Introduction.- 1.1. Relativistic Effects: What Do We Want to Describe?.- 1.2. The Landscape: Relationship to Other Methods.- 1.3. The Nonrelativistic Predecessors.- 2. Methods.- 2.1. Spin-Orbit Effects in Semiempirical Treatments.- 2.2. “Quasirelativistic” Extended Hiickel Calculations.- 2.3. Relativistic Extended Hiickel Methods.- 2.4. Relativistic CNDO-like Methods.- 2.5. Technical Details: Quaternions.- 3. Applications.- 3.1. Total Energies and Bonding.- 3.2. One-Electron Energies.- 3.3. Magnetic-Resonance Parameters and Related Properties.- Appendix A: Where to Find REX Parameters.- Appendix B: The ITEREX 87 Program.- References.- 5. Relativistic Many-Body Perturbation Theory.- 1. Introduction.- 2. Fundamental Problems.- 2.1. Lorentz In variance.- 2.2. Continuum Dissolution.- 3. Electron Correlation Methods.- 3.1. Configuration Interaction.- 3.2. Coupled-Cluster Methods.- 3.3. Many-Body Perturbation Theory.- 4. Diagrammatic Many-Body Perturbation Theory.- 4.1. Brillouin—Wigner Perturbation Theory.- 4.2. Rayleigh—Schrödinger Perturbation Theory.- 4.3. Second-Quantized Methods and the Particle—Hole Formalism.- 4.4. Diagrammatic Methods and the Linked Diagram Theorem.- 4.5. Excitations Involving Virtual Pair Production.- 5. Relativistic Basis Sets.- 5.1. The Problem of Variational Collapse.- 5.2. The Kinetic Balance Approximation.- 5.3. Spinor Basis Sets.- 5.4. Nonlinear Basis Set Parameters.- 5.5. Finite Nuclear Approximations.- 5.6. Four-Index Transformation Techniques.- 6. A Comparison of Methods.- 6.1. The Relativistic Pair Equation.- 6.2. B-Spline Basis Sets.- 6.3. Spinor-Type Basis Sets.- 6.4. The Variational-Perturbation Method.- 7. Basis-Set Studies of Relativistic Many-Body Perturbation Theory.- 7.1. Relativistic Sum Rules.- 7.2. One-Body Perturbations.- 7.3. Many-Body Corrections to Mean-Field Reference Functions.- 8. Summary and Conclusions.- References.- of Previous Volume.- Author Index.