Multiplets of Transition-Metal Ions in Crystals

Multiplets of Transition-Metal Ions in Crystals

1st Edition - January 28, 1970

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  • Author: Satoru Sugano
  • eBook ISBN: 9780323154796

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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.

Table of Contents

  • Preface


    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

    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

    Appendix IX. Symmetric and Antisymmetric Product Representations

    Subject Index

Product details

  • No. of pages: 348
  • Language: English
  • Copyright: © Academic Press 1970
  • Published: January 28, 1970
  • Imprint: Academic Press
  • eBook ISBN: 9780323154796

About the Author

Satoru Sugano

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