Methods in Computational Chemistry: Volume 2

Thisvolume isdevotedtomethodsfor thestudyoftheeffectsofrelativity on theelectronicstructure ofatomsand molecules. The accurate descrip- tionofrelativisticeffectsinheavyatomshaslongbeenrecognizedasoneof the central problems ofatomic physics. Contemporary relativistic atomic structure calculations can be performed almost routinely. Recent years have seen agrowinginterestin thestudyoftheeffects ofrelativityon the structureofmolecules. Even for molecularsystemscontainingatoms from thesecondrowoftheperiodictable theenergyassociatedwith relativistic effects is often larger than that arising from electron correlation. For moleculescontainingheavieratoms relativistic effects become increasingly important,andforsystemscontainingveryheavyatomsrelativityisknown todominatemanychemicalproperties. In this volum~, one of the pioneers of relativistic atomic structure calculations,Ian P. Grant,providesadetailedsurveyofthecomputational techniquesemployedincontemporarystudiesoftheeffectsofrelativityon atomicstructure. Thisisanareaofresearchinwhichcalculationscanoften lead to a particularly impressive degreeofagreement between theoryand experiment. Furthermore, theseatomicstudies haveprovided manyofthe foundations of a fully relativistic quantum chemistry. However, the spherical symmetry ofatoms allows significantsimplificationsto bemade in their quantum mechanical treatment, simplifications which are not possibleinstudiesofmolecules. Inparticular, as is wellknown from non- relativistictheoriesofmolecularelectronicstructure,itisalmostobligatory to invoke the algebraic approximation in molecular work and use finite basis set expansions. The problem of describing relativistic effects in molecules is addressed in Chapter2 by Stephen Wilson. This chapter is devotedtoab initiorelativisticmolecularstructurecalculationsinwhichall electrons are explicitly considered. The problem of induding relativistic effects in molecular studies is also addressed in Chapters3 and 4. In Chapter 3, Odd Gropen describes the use of relativistic effective core ix x Preface potentials in calculations on molecular systems involving heavy atoms. This approach can lead to more tractable algorithms than the methods described in Chapter2 and thus significantly extends the range of applications. The use of semiempirical methods has yielded a wealth of informationabouttheinfluenceofrelativityonthechemistryoftheheavier elements. Thisimportantarea is reviewed inChapter4 by Pekka Pyykk6. Finally, inChapter5, Harry M.

Table of Contents:
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-Schrodinger 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.