Subject: An Introduction to Relativistic Electronic Structure Theory in Quantum Chemistry
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An Introduction to Relativistic Electronic Structure Theory in Quantum
Chemistry

C.
Brian Kellogg
Center for Computational Quantum Chemistry
University
of Georgia
Athens, GA

Relativistic effects have been found to play a crucial role in the
description of the electronic structure of heavy elements. Ab initio
quantum mechanical methods which are based upon many-electron extensions of
Dirac's relativistic single-particle wave equation have proven to be extremely
effective in properly describing the electronic structure of molecules which
contain heavy atoms, though these methods are prohibitively expensive for most
systems of chemical interest. These notes begin with a review of Dirac's
equation for a single particle, and some many-electron extensions of this
equation. Next, many of the most widely used relativistic quantum chemical
techniques are discussed. Finally, the major effects of special relativity on
atomic electronic structure are explored and quantified, and the consequences of
these effects on molecular structure and chemical behavior are discussed.

These notes are currently also available in POSTSCRIPT
format.

Table of Contents

Contents

1 The Dirac Equation

1.1 Klein-Gordon Equation

1.2 Dirac's Free Particle Equation

1.3 Hydrogenic Solutions of Dirac's Equation

1.4 Electron Spin Angular Momentum and Magnetic Moment

2 Dirac-Hartree-Fock Method

2.1 A Many Electron Hamiltonian

2.2 Atomic Solutions

2.3 Molecular Solutions: Finite Basis set expansion

2.4 Selection of the Basis

3 DHF-Based Correlated Methods

3.1 Configuration Interaction

3.2 Multi-configuration Self Consistent Field Method

3.3 Second-Order Perturbation Theory

3.4 Coupled-Cluster

4 Two-Component Methods

The Foldy-Wouthoysen Transformation

4.2 Perturbative Relativistic Treatments

4.3 The Douglas-Kroll Transformation

5 Relativistic Effective Core Potentials

5.1 Effective Core Potentials

5.2 Relativistic Effective Core Potentials

5.3 Ab Initio Model Potentials

5.4 Defining the Core

6 Relativistic Effects in Atoms

6.1 Direct, Indirect, and Spin-Orbit Effects

6.2 Periodic Trends in the Main Group

6.3 Chemical Consequences

References

This document is copyright 1996,
Thu May 29 08:12:02 EDT
1997