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Inhaltsverzeichnis

Frontmatter

1. Introduction

Abstract
The area of the relativistic theory of atoms and molecules, with its contacts “upstream” to relativistic quantum mechanics and QED, and “downstream” to atomic and molecular physics and all branches of heavy-element chemistry, has now become so vast that a detailed exposition of the entire domain by the same author is hardly thinkable. The purpose of the present compilation is to make available the comprehensive bibliography, assembled by the author over the years, on the art of solving the Dirac equation, or approximations thereof, for atoms and molecules.
P. Pyykkö

2. One-Particle Problems

Abstract
The special theory of relativity of Einstein (1905) was incorporated into the old quantum theory of Bohr by Sommerfeld (1916) and collaborators (Green 1923, Sommerfeld and Heisenberg 1922). (See also Foersterling (1920), Landé (1924).
P. Pyykkö

3. Quantum Electrodynamical Effects

Without Abstract
P. Pyykkö

4. Multielectron Atoms: Methods

Abstract
The general reviews, including ones on atoms, were already given in Table 1.1. The Table 4.1. below summarizes articles on general methods, especially angular-momentum coupling. Table 4.2. lists the published programs. The various numerical, four-component, all-electron SCF methods are included in Table 4.3., including the Dirac-Hartree ones without exchange and the Dirac-Fock (DF) and multiconfiguration, MCDF ones with full, non-local exchange as well as the random phase approximation (RPA) and other treatments of correlation. The corresponding LCAO approaches are discussed separately in Table 4.4. The various LDF (Local Density Functional) ones, including the Dirac-Slater (DS) model and the “mean-field theory” are summarized in Table 4.5. The simplest, Thomas-Fermi model is discussed separately in Table 4. 6. The independent-particle models, approximating the atomic mean field by a local one, are listed in Table 4.7.
P. Pyykkö

5. Multielectron Atoms: Results

Abstract
In this chapter we summarize the available relativistic results for various properties of atoms with more than one electron. All relevant references in the Bibliography should appear in at least one table, and may be included in several ones.
P. Pyykkö

6. Symmetry

Abstract
The molecular orbitals, spanned by jj-coupled basis functions, are classified using double-group theory. The general theory is summarized in Table 6.1. and the available tabulations are listed in Table 6.2. Time-reversal symmetry aspects are discussed separately in Table 6.3.
P. Pyykkö

7. Molecular Calculations

Abstract
In this chapter we review the relativistic calculations on molecules. One-electron molecules form a rather special case, discussed in Table 7.1. The other tables are classified by the method of calculation. The LCAO — DF calculations on molecules are listed in Table 7.2. and the one-centre expansions (OCE) (mostly DF, with one DS calculation) in Table 7.3. The four-component DS “Discrete Variational Method” (DVM) calculations are given in Table 7.4. and the DS “Multiple Scattering” (MS) Xα ones in Table 7.5. The “quasirelativistic” or one-component approximation to the DS MS Xα method is discussed separately in Table 7.6. Molecular pseudopotential calculations are summarized in Table 7.7. (for the available pseudopotentials, see the Tables 4.8.–4.10). The perturbative Hartree-Fock-Slater (P-HFS) method, including both 1st- and 2nd-order contributions, is covered by Table 7.8.
P. Pyykkö

8. Solid-State Theory

Abstract
Solid-state calculations fall, strictly speaking, outside the present review. Because of some methodological points of contact, and because of the interest in chemical properties in Ch. 9, a small sample of the available literature is included in Table 8.1. For the particular case of the Kronig-Penney model (a chain of delta-functions), see Table 2.4.
P. Pyykkö

9. Relativistic Effects and Heavy-Element Chemistry

Abstract
Perhaps the most dramatic impact of relativity on chemical thought is the insight that the chemical differences between row 5 (Z=41–54) and row 6 (Z=73–86) contain large, if not dominant, relativistic contributions. The development of this story is outlined in Table 9.1.
P. Pyykkö

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