Multiplets of Transition-Metal Ions in Crystals

Multiplets of Transition-Metal Ions in Crystals provides information pertinent to ligand field theory. This book discusses the fundamentals of quantum mechanics and the theory of atomic spectra. Comprised of 10 chapters, this book starts with an overview of the qualitative nature of the splitting of the energy level as well as the angular behavior of the wavefunctions. This text then examines the problem of obtaining the energy eigenvalues and eigenstates of the two-electron systems, in which two electrons are accommodated in the t2g and eg shells in a variety of ways. Other chapters discuss the ligand-field potential, which is invariant to any symmetry operation in the group to which symmetry of the system belongs. This book discusses as well the approximate method of expressing molecular orbitals (MO) by a suitable linear combination of atomic orbitals (AO). The final chapter discusses the MO in molecules and the self-consistent field theory of Hartree–Fock. This book is a valuable resource for research physicists, chemists, electronic engineers, and graduate students.

Preface

Acknowledgments

Introduction 1

I. Single d-Electron in a Ligand Field

1.1 Single d-Electron in a Cubic Field

1.2 Group Theoretical Preliminaries

II. Two Electrons in a Cubic Field

2.1 Formulation of the Two-Electron Problem

2.2 Two-Electron Wavefunctions

2.3 Term Energies

III. Many Electrons in a Cubic Field

3.1 Many-Electron Wavefunctions

3.2 Formulas for Calculating Matrix Elements

3.3 Energy Matrices in the Three-Electron System

IV. Electrons and Holes

4.1 Complementary States

4.2 Matrix Elements in Complementary States

4.3 Energy Matrices

V. Multiplets in Optical Spectra

5.1 Energy Level Diagrams

5.2 Optical Transitions

5.3 Comparison between Theory and Experiments

VI. Low-Symmetry Fields

6.1 Single Electron in Fields of Low Symmetry

6.2 Wigner-Eckart Theorem

6.3 Many Electrons in Fields of Low Symmetry

VII. Spin-Orbit Interaction

7.1 The Problem of a Single d-Electron

7.2 Double-Group

7.3 The Method of Operator Equivalent

7.4 Spin-Orbit Interaction in Many-Electron Systems

VIII. Fine Structure of Multiplets

8.1 Kramers Degneracy

8.2 Higher-Order Splittings of Cubic Terms

8.3 Effective Hamiltonian

8.4 Zeeman Effects

8.5 Linear Stark Effects

IX. Interaction between Electron and Nuclear Vibration

9.1 Nuclear Vibrations

9.2 Linear Interaction in Nondegenerate Electronic States

9.3 Static Jahn-Teller Effect

9.4 Dynamical Jahn-Teller Effect

X. Molecular Orbital and Heitler-London Theories

10.1 Strong- and Weak-Field Schemes

10.2 Simple Description of MO Theory

10.3 MO Theory for Open-Shells

10.4 Covalency in Ligand-Field Theory

10.5 Calculation of Covalency

Appendix I. Character Tables for the Thirty-Two Double Point Groups, G

Appendix II. Tables of Clebsch-Gordan Coefficients, <Γ1Υ1Γ2Υ2|ΓΥ>, with Cubic Bases

Appendix III. Wigner Coefficients <j1m1j2m2|jm>

Appendix IV. Matrix Elements of Coulomb Interaction

Appendix V. Complementary States in the (t2,e) Shell

Appendix VI. Tables of Clebsch-Gordan Coefficients with Trigonal Bases, <Γ1M1Γ2M2|ΓM> = <ΓM|Γ1M1Γ2M2>*

Appendix VII. Tables of Reduced Matrices of Spin-Orbit Interaction

Appendix VIII. Calculation of <aSΓ||L||a’SΓ’>

Appendix IX. Symmetric and Antisymmetric Product Representations

Subject Index