Orbital Interactions in Chemistry

THOMAS A. ALBRIGHT, PhD, is Professor Emeritus in theDepartment of Chemistry at the University of Houston. He was aCamille and Henry Dreyfus Teacher-Scholar and an Alfred P. SloanResearch Fellow. He has been interested in exploring reactiondynamics in organometallic chemistry. The late JEREMY K. BURDETT, PhD, was Professor and Chairof the Chemistry Department at the University of Chicago. Dr.Burdett was awarded the Tilden Prize and Meldola Medal by the RoyalSociety of Chemistry. He was also a Camille and Henry DreyfusTeacher-Scholar and a Fellow of the John Guggenheim MemorialFoundation and Alfred P. Sloan Foundation. MYUNG-HWAN WHANGBO, PhD, is Distinguished Professor inthe Chemistry Department of North Carolina State University. He hasbeen awarded the Camille and Henry Dreyfus Fellowship, theAlexander von Humboldt Research Award to Senior Scientists, theHo-Am Prize in Science, and Docteur Honoris Causa from Universit deNantes.

Preface xi

About the Authors xiii

Chapter 1 Atomic and Molecular Orbitals 1

1.1 Introduction 1

1.2 Atomic Orbitals 1

1.3 Molecular Orbitals 7

Problems 13

References 14

Chapter 2 Concepts of Bonding and Orbital Interaction 15

2.1 Orbital Interaction Energy 15

2.1.1 Degenerate Interaction 16

2.1.2 Nondegenerate Interaction 18

2.2 Molecular Orbital Coefficients 20

2.2.1 Degenerate Interaction 21

2.2.2 Nondegenerate Interaction 22

2.3 The Two-Orbital Problem—Summary 24

2.4 Electron Density Distribution 26

Problems 31

References 31

Chapter 3 Perturbational Molecular Orbital Theory 32

3.1 Introduction 32

3.2 Intermolecular Perturbation 35

3.3 Linear H3, HF, and the Three-Orbital Problem 38

3.4 Degenerate Perturbation 43

Problems 45

References 46

Chapter 4 Symmetry 47

4.1 Introduction 47

4.2 Symmetry of Molecules 47

4.3 Representations of Groups 53

4.4 Symmetry Properties of Orbitals 59

4.5 Symmetry-Adapted Wavefunctions 62

4.6 Direct Products 65

4.7 Symmetry Properties, Integrals, and the Noncrossing Rule 67

4.8 Principles of Orbital Construction Using Symmetry Principles 69

4.9 Symmetry Properties of Molecular Vibrations 73

Problems 75

References 77

Chapter 5 Molecular Orbital Construction from Fragment Orbitals 78

5.1 Introduction 78

5.2 Triangular H3 78

5.3 Rectangular and Square Planar H4 82

5.4 Tetrahedral H4 84

5.5 Linear H4 86

5.6 Pentagonal H5 and Hexagonal H6 88

5.7 Orbitals of Cyclic Systems 91

Problems 94

References 96

Chapter 6 Molecular Orbitals of Diatomic Molecules and Electronegativity Perturbation 97

6.1 Introduction 97

6.2 Orbital Hybridization 98

6.3 Molecular Orbitals of Diatomic Molecules 99

6.4 Electronegativity Perturbation 105

6.5 Photoelectron Spectroscopy and Through-Bond Conjugation 112

Problems 118

References 122

Chapter 7 Molecular Orbitals and Geometrical Perturbation 123

7.1 Molecular Orbitals of AH2 123

7.2 Geometrical Perturbation 128

7.3 Walsh Diagrams 131

7.4 Jahn–Teller Distortions 134

7.4.1 First-Order Jahn–Teller Distortion 135

7.4.2 Second-Order Jahn–Teller Distortion 136

7.4.3 Three-Center Bonding 139

7.5 Bond Orbitals and Photoelectron Spectra Of AH2 Molecules 141

Problems 147

References 150

Chapter 8 State Wavefunctions and State Energies 151

8.1 Introduction 151

8.2 The Molecular Hamiltonian and State Wavefunctions 152

8.3 Fock Operator 154

8.4 State Energy 156

8.5 Excitation Energy 157

8.6 Ionization Potential and Electron Affinity 160

8.7 Electron Density Distribution and Magnitudes of Coulomb and Exchange Repulsions 160

8.8 Low versus High Spin States 162

8.9 Electron–Electron Repulsion and Charged Species 164

8.10 Configuration Interaction 165

8.11 Toward More Quantitative Treatments 170

8.12 The Density Functional Method 174

Problems 176

References 177

Chapter 9 Molecular Orbitals of Small Building Blocks 179

9.1 Introduction 179

9.2 The AH System 179

9.3 Shapes of AH3 Systems 182

9.4 π-Bonding Effects of Ligands 190

9.5 The AH4 System 193

9.6 The AHn Series—Some Generalizations 198

Problems 201

References 202

Chapter 10 Molecules with Two Heavy Atoms 204

10.1 Introduction 204

10.2 A2 H6 Systems 204

10.3 12-Electron A2 H4 Systems 208

10.3.1 Sudden Polarization 211

10.3.2 Substituent Effects 214

10.3.3 Dimerization and Pyramidalization of AH 2 218

10.4 14-Electron AH2 BH2 Systems 220

10.5 AH3 BH2 Systems 223

10.6 AH3 BH Systems 232

Problems 234

References 238

Chapter 11 Orbital Interactions through Space and through Bonds 241

11.1 Introduction 241

11.2 In-Plane σ orbitals of Small Rings 241

11.2.1 Cyclopropane 241

11.2.2 Cyclobutane 246

11.3 Through-Bond Interaction 253

11.3.1 The Nature of Through-Bond Coupling 253

11.3.2 Other Through-Bond Coupling Units 256

11.4 Breaking a C–C Bond 258

Problems 265

References 269

Chapter 12 Polyenes and Conjugated Systems 272

12.1 Acyclic Polyenes 272

12.2 Hückel Theory 274

12.3 Cyclic Systems 277

12.4 Spin Polarization 285

12.5 Low- versus High-Spin States in Polyenes 289

12.6 Cross-Conjugated Polyenes 291

12.7 Perturbations of Cyclic Systems 294

12.8 Conjugation in Three Dimensions 303

Problems 306

References 310

Chapter 13 Solids 313

13.1 Energy Bands 313

13.2 Distortions in One-Dimensional Systems 328

13.3 Other One-Dimensional Systems 334

13.4 Two- and Three-Dimensional Systems 339

13.5 Electron Counting and Structure 350

13.6 High-Spin and Low-Spin Considerations 353

Problems 353

References 357

Chapter 14 Hypervalent Molecules 359

14.1 Orbitals of Octahedrally Based Molecules 359

14.2 Solid-State Hypervalent Compounds 373

14.3 Geometries of Hypervalent Molecules 383

Problems 392

References 399

Chapter 15 Transition Metal Complexes: A Starting Point at the Octahedron 401

15.1 Introduction 401

15.2 Octahedral ML6 402

15.3 π-Effects in an Octahedron 406

15.4 Distortions from an Octahedral Geometry 416

15.5 The Octahedron in the Solid State 423

Problems 431

References 434

Chapter 16 Square Planar, Tetrahedral ML 4 Complexes, and Electron Counting 436

16.1 Introduction 436

16.2 The Square Planar ML4 Molecule 436

16.3 Electron Counting 438

16.4 The Square Planar-Tetrahedral ML4 Interconversion 448

16.5 The Solid State 453

Problems 460

References 463

Chapter 17 Five Coordination 465

17.1 Introduction 465

17.2 The C4v M5 Fragment 466

17.3 Five Coordination 468

17.4 Molecules Built Up from ML5 Fragments 480

17.5 Pentacoordinate Nitrosyls 489

17.6 Square Pyramids in The Solid State 492

Problems 498

References 500

Chapter 18 The C2v ML3 Fragment 503

18.1 Introduction 503

18.2 The Orbitals of A C2v ML3 Fragment 503

18.3 ML3-Containing Metallacycles 511

18.4 Comparison of C2v ML3 and C4v ML5 Fragments 518

Problems 523

References 525

Chapter 19 The ML2 and ML4 Fragments 527

19.1 Development of the C2v ML4 Fragment Orbitals 527

19.2 The Fe(CO)4 Story 529

19.3 Olefin–ML 4 Complexes and M2 L8 Dimers 533

19.4 The C2v ML2 Fragment 537

19.5 Polyene–ML2 Complexes 539

19.6 Reductive Elimination and Oxidative Addition 552

Problems 561

References 566

Chapter 20 Complexes of ML3 , MCp and Cp2 M570

20.1 Derivation of Orbitals for a C3v ML3 Fragment 570

20.2 The CpM Fragment Orbitals 582

20.3 Cp2 M and Metallocenes 592

20.4 Cp2 MLn Complexes 595

Problems 607

References 613

Chapter 21 The Isolobal Analogy 616

21.1 Introduction 616

21.2 Generation of Isolobal Fragments 617

21.3 Caveats 621

21.4 Illustrations of the Isolobal Analogy 623

21.5 Reactions 634

21.6 Extensions 639

Problems 646

References 649

Chapter 22 Cluster Compounds 653

22.1 Types of Cluster Compounds 653

22.2 Cluster Orbitals 657

22.3 Wade’s Rules 660

22.4 Violations 671

22.5 Extensions 677

Problems 681

References 687

Chapter 23 Chemistry on the Surface 691

23.1 Introduction 691

23.2 General Structural Considerations 693

23.3 General Considerations of Adsorption on Surfaces 696

23.4 Diatomics on a Surface 699

23.5 The Surface of Semiconductors 721

Problems 728

References 731

Chapter 24 Magnetic Properties 735

24.1 Introduction 735

24.2 The Magnetic Insulating State 736

24.2.1 Electronic Structures 736

24.2.2 Factors Affecting the Effective On-Site Repulsion 738

24.2.3 Effect of Spin Arrangement on the Band Gap 740

24.3 Properties Associated with the Magnetic Moment 741

24.3.1 The Magnetic Moment 741

24.3.2 Magnetization 743

24.3.3 Magnetic Susceptibility 743

24.3.4 Experimental Investigation of Magnetic Energy Levels 745

24.4 Symmetric Spin Exchange 745

24.4.1 Mapping Analysis for a Spin Dimer 745

24.4.2 Through-Space and Through-Bond Orbital Interactions Leading to Spin Exchange 748

24.4.3 Mapping Analysis Based on Broken-Symmetry States 751

24.5 Magnetic Structure 754

24.5.1 Spin Frustration and Noncollinear Spin Arrangement 754

24.5.2 Long-Range Antiferromagnetic Order 755

24.5.3 Ferromagnetic and Ferromagnetic-Like Transitions 759

24.5.4 Typical Cases Leading to Ferromagnetic Interaction 760

24.5.5 Short-Range Order 763

24.6 The Energy Gap in the Magnetic Energy Spectrum 763

24.6.1 Spin Gap and Field-Induced Magnetic Order 763

24.6.2 Magnetization Plateaus 765

24.7 Spin–Orbit Coupling 766

24.7.1 Spin Orientation 766

24.7.2 Single-Ion Anisotropy 770

24.7.3 Uniaxial Magnetism versus Jahn–Teller Instability 771

24.7.4 The Dzyaloshinskii–Moriya Interaction 774

24.7.5 Singlet–Triplet Mixing Under Spin–Orbit Coupling 777

24.8 What Appears versus What Is 778

24.8.1 Idle Spin in Cu3(OH)4SO4 778

24.8.2 The FM–AFM versus AFM–AFM Chain 779

24.8.3 Diamond Chains 780

24.8.4 Spin Gap Behavior of a Two-Dimensional Square Net 782

24.9 Model Hamiltonians Beyond the Level of Spin Exchange 785

24.10 Summary Remarks 785

Problems 786

References 789

Appendix I Perturbational Molecular Orbital Theory 793

Appendix II Some Common Group Tables 803

Appendix III Normal Modes for Some Common Structural Types 808

Index 813