Molecular Orbitals Of Transition Metal

This book starts with the most elementary ideas of molecular orbital theory and leads the reader progressively to an understanding of the electronic structure, geometry and, in some cases, reactivity of transition metal complexes. The qualitative orbital approach, based on simple notions such as symmetry, overlap and electronegativity, is the focus of the presentation and a substantial part of the book is associated with the mechanics of the assembly of molecular orbital diagrams. The first chapter recalls the basis for electron counting in transition metal complexes. The main ligand fields (octahedral, square planar, tetrahedral, etc.) are studied in the second chapter (sigma interactions) and the structure of the "d block" is used to trace the relationships between the electronic structure and the geometry of the complexes. The third chapter studies the change in analysis when the ligands have pi-type interactions with the metal. All these ideas are then used in the fourth chapter to study a series of selected applications of varying complexity (structure, reactivity). The fifth chapter deals with the "isolobal analogy" which points out the resemblance between the molecular orbitals of inorganic and organic species and provides a bridge between these two subfields of chemistry. The last chapter is devoted to a presentation of basic Group Theory with applications to some of the complexes studied in the earlier chapters.

Yves Jean is Professor at University Paris-Sud (Orsay, France) and Researcher at Ecole Polytechnique (Palaiseau, France).

Introduction

1

(2)

Chapter 1 Setting the scene

3

(34)

1.1. Electron count in a complex: the covalent model

4

(8)

1.1.1. Ligand classification (L or X)

4

(4)

1.1.2. Electron count and the 18-electron rule

8

(4)

1.2. An alternative model: the ionic model

12

(4)

1.2.1. Lewis bases as ligands

12

(2)

1.2.2. Equivalence of the covalent and ionic models: examples

14

(2)

1.3. Principles of orbital interactions

16

(3)

1.3.1. Interaction between two orbitals with the same energy

16

(1)

1.3.2. Interaction between two orbitals with different energies

17

(1)

1.3.3. The role of symmetry

18

(1)

1.3.4. σ and π interactions

19

(1)

1.4. Metal orbitals

19

(5)

1.4.1. Description of the valence orbitals

20

(3)

1.4.2. Orbital energies

23

(1)

1.5. Ligand orbitals

24

(6)

1.5.1. A single ligand orbital: σ interactions

24

(2)

1.5.2. Several orbitals: σ and π interactions

26

(4)

1.6. Initial orbital approach to MLe complexes

30

(3)

1.6.1. Simplified interaction diagram

30

(1)

1.6.2. Strong-field and weak-field complexes

31

(1)

1.6.3. Electronic configuration and the 18-electron rule

31

(1)

1.6.4. Analogy with the octet rule

32

(1)

Exercises

33

(4)

Chapter 2 Principal ligand fields: σ interactions

37

(60)

2.1. Octahedral ML6 complexes

38

(13)

2.1.1. Initial analysis of the metal-ligand orbital interactions

38

(3)

2.1.2. Complete interaction diagram

41

(7)

2.1.3. Electronic structure

48

(3)

2.2. Square-planar ML4 complexes

51

(2)

2.2.1. Characterization of the d block

51

(2)

2.2.2. Electronic structure for 16-electron d8 complexes

53

(1)

2.3. Square-based pyramidal ML5 complexes

53

(9)

2.3.1. Characterization of the d block (metal in the basal plane)

54

(2)

2.3.2. Characterization of the d block (metal out of the basal plane)

56

(4)

2.3.3. Electronic structure and geometry

60

(2)

2.4. Tetrahedral ML4 complexes

62

(7)

2.4.1. Characterization of the d block

63

(3)

2.4.2. Electronic structure

66

(1)

2.4.3. ML4 complexes: square-planar or tetrahedral?

66

(3)

2.5. Trigonal-bipyramidal ML5 complexes

69

(4)

2.5.1. Characterization of the d block

69

(3)

2.5.2. Electronic structure

72

(1)

2.6. Trigonal-planar ML3 complexes

73

(1)

2.6.1. Characterization of the d block

73

(1)

2.6.2. 16-electron d10 complexes

74

(1)

2.7. Linear ML2 complexes

74

(2)

2.7.1. Characterization of the d block

75

(1)

2.7.2. Electronic structure

76

(1)

2.8. Other complexes or MLn fragments

76

(9)

2.8.1. Pyramidal ML3 complexes

77

(2)

2.8.2. 'T-shaped' ML3 complexes

79

(2)

2.8.3. 'Butterfly' ML4 complexes

81

(2)

2.8.4. Bent ML2 complexes

83

(1)

2.8.5. ML complexes

84

(1)

Exercises

85

(4)

Appendix A: polarization of the d orbitals

89

(5)

Appendix B: Orbital energies

94

(3)

Chapter 3 π-type interactions

97

(44)

3.1. π-donor ligands: general properties

98

(6)

3.1.1. The nature of the π orbital on the ligand

98

(1)

3.1.2. 'Single-face' and 'double-face' π-donors

99

(1)

3.1.3. Perturbation of the d orbitals: the general interaction diagram

100

(1)

3.1.4. A first example: the octahedral complex [ML5Cl]

101

(3)

3.2. π-acceptor ligands: general properties

104

(7)

3.2.1. The nature of the π orbital on the ligand

104

(1)

3.2.2. 'Single-face' and 'double-face' π-acceptors

105

(2)

3.2.3. Perturbation of the d orbitals: the general interaction diagram

107

(1)

3.2.4. A first example: the octahedral complex [ML5CO]

108

(3)

3.3. Complexes with several π-donor or π-acceptor ligands

111

(14)

3.3.1. The trans-[ML4Cl2] octahedral complex

111

(5)

3.3.2. The trans-[ML4(CO)2] octahedral complex

116

(1)

3.3.3. Construction of the d-block orbitals 'by hand'

117

(6)

3.3.4. [MCl6] and [M(CO)6] octahedral complexes

123

(2)

3.4. π complexes: the example of ethylene

125

(8)

3.4.1. Orbital interactions: the Dewar-Chatt-Duncanson model

125

(1)

3.4.2. Electronic structure of a d6 complex [ML5(η²-C2H4)]

126

(3)

3.4.3. Metallocenes Cp2M

129

(1)

3.4.4. Cp2MLn complexes

130

(3)

3.5. πinteractions and electron counting

133

(2)

Exercises

135

(3)

Appendix C: The carbonyl ligand, a double-face π-acceptor

138

(3)

Chapter 4 Applications

141

(44)

4.1. Conformational problems

141

(15)

4.1.1. d8-[ML(η²-C2H4)] complexes

141

(3)

4.1.2. d6-[ML5(η²-C2H4)] complexes: staggered or eclipsed conformation?

144

(3)

4.1.3. d6-[ML4(η²-C2H4)2] complexes: coupling of two π-acceptor ligands

147

(5)

4.1.4. Orientation of H2 in the 'Kubas complex' [W(CO)3(PR3)2(η²-H2)]

152

(4)

4.2. 'Abnormal' bond angles

156

(9)

4.2.1. Agostic interactions

156

(4)

4.2.2. d6 ML5 complexes: a 'T-shaped' or 'Y-shaped' geometry?

160

(5)

4.3. Carbene complexes

165

(5)

4.3.1. Ambiguity in the electron count for carbene complexes

165

(1)

4.3.2. Two limiting cases: Fischer carbenes and Schrock carbenes

166

(4)

4.4. Bimetallic complexes: from a single to a quadruple bond

170

(6)

4.4.1. σ,π and δ interactions

171

(1)

4.4.2. M2L10 complexes

172

(2)

4.4.3. The [Re2(Cl)8]²- complex: a staggered or an eclipsed conformation?

174

(2)

4.5. The reductive elimination reaction

176

(5)

4.5.1. Definition

176

(1)

4.5.2. Simplified model for the reaction [LnMR2] -> [Ln,M] + R-R

176

(2)

4.5.3. An example: d8-[L2MR2] -> d10-[L2M] + R-R.

178

(3)

4.6. Principal references used

181

(1)

Exercises

181

(4)

Chapter 5 The isolobal analogy

185

(20)

5.1. The analogy between fragments of octahedral ML6 and of tetrahedral CH4

185

(9)

5.1.1. Fragment orbitals by the valence-bond method

187

(3)

5.1.2. Fragment molecular orbitals

190

(4)

5.2. Other analogous fragments

194

(1)

5.3. Applications

195

(5)

5.3.1. Metal-metal bonds

195

(4)

5.3.2. Conformational problems

199

(1)

5.4. Limitations

200

(2)

Exercises

202

(3)

Chapter 6 Elements of group theory and applications

205

(48)

6.1. Symmetry elements and symmetry operations

205

(5)

6.1.1. Reflection planes

205

(1)

6.1.2. Inversion centre

206

(1)

6.1.3. Rotation axes

207

(2)

6.1.4. Improper rotation axes

209

(1)

6.2. Symmetry groups

210

(10)

6.2.1. Definitions

210

(1)

6.2.2. Determination of the symmetry point group

211

(1)

6.2.3. Basis of an irreducible representation

212

(3)

6.2.4. Characters

215

(2)

6.2.5. Character tables

217

(3)

6.3. The reduction formula

220

(5)

6.3.1. The reduction formula

220

(1)

6.3.2. Characters of a reducible representation

221

(1)

6.3.3. Applications

222

(2)

6.3.4. Direct products

224

(1)

6.4. Symmetry-adapted orbitals

225

(4)

6.4.1. Projection operator

225

(1)

6.4.2. Application

225

(4)

6.5. Construction of MO: H2O as an example

229

(2)

6.5.1. Symmetry and overlap

229

(1)

6.5.2. Molecular orbitals for H2O

230

(1)

6.6. Symmetry-adapted orbitals in several MLn complexes

231

(16)

6.6.1. Square-planar ML4 complexes

231

(3)

6.6.2. Tetrahedral ML4 complexes

234

(2)

6.6.3. Trigonal-planar ML3 complexes

236

(2)

6.6.4. Trigonal-bipyramidal ML5 complexes

238

(2)

6.6.5. Octahedral ML6 complexes

240

(2)

6.6.6. Trigonal-planar ML3 complexes with a 'π system' on the ligands

242

(5)

Exercises

247

(6)

Answers to exercises

253

(18)

Bibliography

271

(2)

Index

273

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Molecular Orbitals Of Transition Metal Complexes

Summary

Author Biography

Table of Contents

Supplemental Materials

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Molecular Orbitals Of Transition Metal Complexes

Summary

Author Biography

Table of Contents

Supplemental Materials

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