A complete, up-to-date treatment of ligand field theory and its applications Ligand Field Theory and Its Applications presents an up-to-date account of ligand field theory, the model currently used to describe the metal-ligand interactions in transition metal compounds, and the way it is used to interpret the physical properties of the complexes. It examines the traditional electrostatic crystal field model, still widely used by physicists, as well as covalent approaches such as the angular overlap model, which interprets the metal ligand interactions using parameters relating directly to chemical behavior. Written by internationally recognized experts in the field, this book provides a comparison between ligand field theory and more sophisticated treatments as well as an account of the methods used to calculate the energy levels in compounds of the transition metals. It also covers physical properties such as stereochemistry, light absorption, and magnetic behavior. An emphasis on the interpretation of experimental results broadens the book's field of interest beyond transition metal chemistry into the many other areas where these metal ions play an important role. As clear and accessible as Brian Figgis's 1966 classic Introduction to Ligand Fields, this new book provides inorganic and bioinorganic chemists as well as physical chemists, chemical physicists, and spectroscopists with a much-needed overview of the many significant changes that have taken place in ligand field theory over the past 30 years.

BRIAN N. FIGGIS, DSc, is Professor of Inorganic Chemistry at the University of Western Australia. <p> L A. HITCHMAN, DSc, is Reader in Chemistry at the University of Tasmania.

Preface

xv

Introduction

1

(26)

The Concept of a Ligand Field

1

(3)

The Scope of Ligand Field Theory

4

(1)

The d and Other Orbitals

5

(9)

The Symmetry Properties of Molecules and Wavefunctions

14

(3)

The Molecular Point Groups

14

(1)

The Representations of Wavefunctions

15

(1)

Typical Applications in Ligand Field Theory

16

(1)

Qualitative Demonstration of the Ligand Field Effect

17

(4)

The Physical Properties Affected by Ligand Field Theory

21

(3)

Thermochemical Properties and Geometric Distortions

21

(1)

Spectral Properties

22

(1)

Magnetic Properties

23

(1)

Crystal Fields and Ligand Fields

24

(3)

Quantitative Basis Of Crystal Fields

27

(26)

Crystal Field Theory

27

(3)

The Octahedral Crystal Field Potential

30

(3)

The Effect of Voct on the d Wavefunctions

33

(5)

The Evaluation of δ

38

(2)

The Tetrahedral and Cubic Potentials

40

(1)

Naming the Real d Orbitals

41

(1)

Potentials for Lower Symmetries

41

(4)

Tetragonally Distorted Octahedron

41

(3)

Trigonally Distorted Octahedron

44

(1)

Other Parameterization Schemes

45

(3)

The A and B Coefficients

46

(1)

The Parameters Ds and Dt

47

(1)

Limitations of Crystal Field Theory: Ligand Field Theory

48

(2)

f Orbitals and the Crystal Field Potential

50

(3)

The Angular Overlap Model

53

(30)

Basis of the Angular Overlap Model (AOM)

53

(8)

Simple MO Picture of the Bonding in Transition-Metal Complexes

54

(4)

Derivation of AOM Parameters Using the Wolfsberg--Helmholtz Approximation

58

(2)

Derivation of the d Orbital Energies and Wavefunctions in a Complex Using the AOM

60

(1)

AOM Expressions for Complexes of Various Symmetries

61

(12)

Octahedral Complexes

61

(3)

Tetragonally Distorted Octahedral, Planar, and Linear Complexes: The Importance of d-s Mixing

64

(3)

Tetrahedral, Distorted Tetrahedral, and Square-Based Pyramidal Complexes

67

(1)

Trigonal Bipyramidal Complexes

68

(1)

Variation of AOM Parameters with Bond Distance

69

(1)

Typical AOM Parameters

70

(3)

Extensions of the AOM for Some Polyatomic Ligands

73

(3)

Phase-Coupled Ligators

73

(1)

Off-Axis Bonds and Interactions with Nonbonding Electron Pairs

74

(2)

Approximations in the Derivation of Bonding Parameters

76

(2)

Advantages of the AOM Compared to the Electrostatic Crystal Field Theory

78

(2)

Calculations of Electronic Spectra and Magnetic Properties Using Computer Programs Based on the AOM

80

(3)

The Origin And Calculation of δ

83

(9)

Calculations Based on Electrostatic Interactions

83

(1)

One-Electron Molecular Orbital Calculations

84

(3)

All-Electron Molecular Orbital Calculations

87

(2)

Symmetries Lower Than Cubic

89

(1)

f Electron Systems

89

(1)

Real Electron Density Distribution

90

(2)

Energy Levels Of Transition Metalions

92

(20)

Introduction

92

(1)

Free Transition Ions

93

(2)

Free Ion Terms

95

(8)

Term Wavefunctions

103

(4)

Spin-Orbit Coupling

107

(5)

Effect Of Ligand Fields On The Energy Levels Of Transition Ions

112

(33)

The Effect of a Cubic Ligand Field on S and P Terms

112

(3)

S Terms

113

(1)

P Terms

113

(2)

The Effect of a Cubic Ligand Field on D Terms

115

(2)

The Effect of a Cubic Ligand Field on F Terms

117

(4)

The Effect of a Cubic Ligand Field on G, H, and I Terms

121

(1)

Strong-Field Configurations

121

(1)

Transition from Weak to Strong Ligand Fields

122

(4)

Correlation Diagrams

126

(5)

Tanabe-Sugano Diagrams

131

(10)

Spin-Pairing Energies

141

(4)

Influence Of the d Configuration On The Geometry And Stability Of Complexes

145

(34)

Dependence of the Geometry of a Complex on Its d Configuration

146

(20)

Nondegenerate Electronic States

146

(2)

Degenerate States: The Jahn-Teller Effect

148

(12)

Bond Length Differences Between High-and Low-spin Complexes

160

(3)

Variation of Bond Lengths on Crossing the Transition Series

163

(3)

Dependence of the Stability of a Complex on Its d Configuration

166

(13)

Thermodynamic Effects

167

(9)

Kinetic Effects

176

(3)

The Electronic Spectra Of Complexes

179

(49)

Important Features of Electronic Spectra

179

(25)

Band Intensities

179

(10)

Band Energies

189

(6)

Band Widths and Shapes

195

(6)

Effect of Temperature on Electronic Bands

201

(3)

Characteristic Spectra of Complexes of First-Row Transition Ions

204

(10)

Hexaaqua Complexes of First-Row Ions

204

(7)

Tetrahedral and Planar Complexes of First-Row Transition Ions

211

(3)

Typical Spectra of Second-and Third-Row Transition Ions

214

(1)

The Spectrochemical and Nephelauxetic Series

215

(6)

The Spectrochemical Series

215

(3)

The Nephelauxetic Series

218

(3)

Charge Transfer Spectra

221

(3)

Luminescence Spectra

224

(4)

Magnetic Properties Of Complex Ions

228

(54)

The Theory of Magnetic Susceptibility

228

(9)

General

228

(4)

Paramagnetism

232

(1)

Quantum Mechanical Treatment of Paramagnetic Susceptibilities

233

(4)

The Magnetic Properties of Free Ions

237

(4)

The First-Order Zeeman Effect

237

(1)

The Second-Order Zeeman Effect

238

(1)

States kT

239

(2)

States kT

241

(1)

Quenching of Orbital Angular Momentum by Ligand Fields

241

(3)

The Magnetic Properties of A and E Terms

244

(4)

The Magnetic Properties of T Terms

248

(8)

Splitting by Spin-Orbit Coupling

248

(3)

The Calculation of µeff

251

(3)

Departure from Cubic Symmetry

254

(2)

t2(g) Electron Delocalization

256

(3)

General

256

(1)

A and E Terms

257

(2)

T Terms

259

(1)

The Magnetic Properties of Complexes with A and E Ground Terms

259

(5)

Octahedral Complexes

259

(2)

Tetrahedral Complexes

261

(3)

The Magnetic Properties of Complexes with T Ground Terms

264

(4)

Summary

268

(1)

Spin-Free-Spin-Paired Equilibria

269

(3)

Magnetic Exchange

272

(10)

The Heisenberg Hamiltonian

272

(1)

Mechanism of Magnetic Exchange: Superexchange

273

(4)

Some Examples of Superexchange in Clusters

277

(5)

Electron Paramagnetic Resonance Spectra Of Complexes

282

(29)

Nature of the EPR Experiment

282

(12)

Introduction

282

(2)

Features of EPR Spectra

284

(10)

The Spin Hamiltonian

294

(2)

Interpretation of the Spin Hamiltonian Parameters

296

(12)

The g Tensor

296

(5)

The Hyperfine Tensor

301

(7)

The Zero-Field Splitting Tensor

308

(1)

Electron Nuclear Double Resonance

308

(3)

Actinide Element Compounds

311

(14)

Ligand Fields and f Electron Systems

311

(3)

Actinide Element Compounds

314

(1)

f Electrons and Voct

315

(2)

Uv/vis Spectra of Actinide Complexes

317

(2)

Magnetic Properties of Actinide Complexes

319

(6)

Appendix A1

325

(3)

A1.1 The Spherical Harmonics

325

(1)

A1.2 Integration of Products of Spherical Harmonics

325

(3)

Appendix A2

328

(2)

A2.1 The Associated Legendre Polynomials to Order 6

328

(2)

Appendix A3

330

(1)

A3.1 The Energies Resulting from the Application of Vtrig

330

(1)

Appendix A4

331

(1)

A4.1 Relationships Between Some of the Coefficients in the Operators Defined in Section 2.8.1

331

(1)

Appendix A5

332

(2)

A5.1 Matrix Elements of the Crystal Field Potential Vcf from a General Distribution of Effective Point Charges

332

(2)

Appendix A6

334

(2)

A6.1 Energies of the Terms of dn using Condon-Shortley Parameters

334

(2)

Appendix A7

336

(1)

A7.1 The Curie Law for Magnetic Behavior

336

(1)

Appendix A8

337

(2)

A8.1 The Operators Lx, Ly, Sx, and Sy

337

(2)

Appendix A9

339

(1)

A9.1 Expressions for the Magnetic Moments of Terms in Cubic Symmetry

339

(1)

List Of Commonly Used Symbols

340

(2)

Fundamental Constants

342

(3)

Index

345

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Ligand Field Theory and Its Applications

9780471317760

0471317764

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