Chapter 1 Quantum Theory 1
1.1 Classical Description of Particles and Waves 2
1.1.1 Newtonian mechanics 2
1.1.2 Waves 3
1.2 Particle Behaviors of Waves 6
1.2.1 Black-body radiation 6
1.2.2 Photoelectric effect 7
1.3 The Wave Behaviors of Particles 9
1.3.1 The de Broglie hypothesis 9
1.3.2 Electron diffraction 9
1.3.3 The uncertainty principle 11
1.4.1 Wave functions 13
1.4 The Schr?dinger Equation 13
1.4.2 The Schr?dinger equation 15
1.4.3 Dynamical variables and expectation values 17
1.4.4 The stationary state 18
1.5 Simple Systems 19
1.5.1 One-dimensional free particles 19
1.5.2 Particles in one-dimensional potential box 20
1.5.3 Particles in three-dimensional potential box 25
Appendix 1.1 Operators and Hermitian Operators 27
Appendix 1.2 Physical Constants and Conversion Factors of Energy Units 30
Exercises 31
Chapter 2 Atoms 35
2.1 The Hydrogen Atom 36
2.1.1 The Schrodinger equation 36
2.1.2 Angular wave functions 38
2.1.3 Angular momentum 43
2.1.4 Radial wave functions 45
2.1.5 Energy levels and wave functions 47
2.2 Helium Atom 50
2.2.1 Atomic units 50
2.2.2 The orbital approximation 50
2.2.3 Electron shielding effect 52
2.2.4 The repulsive potential 53
2.3 Pauli Exclusion Principle 54
2.3.1 The spin of electrons 54
2.3.2 Pauli exclusion principle 55
2.3.3 Hund rule 57
2.4.1 Configuration 58
2.4 Many-Electron Atoms 58
2.4.2 Slater orbitals 59
2.4.3 Terms 60
2.4.4 The term energy 61
2.4.5 Terms of(np)2 62
Appendix 2.1 Operators in Spherical Polar Coordinates 65
Exercises 68
Chapter 3 Diatomic Molecules 71
3.1 The Interactions between Atoms 72
3.2 Hydrogen Molecular Ion and Hydrogen Molecule 76
3.2.1 Symmetry of homonuclear diatomics 76
3.2.2 The LCAO scheme 79
3.2.3 The hydrogen molecule 83
3.3.1 The variation method 85
3.3 Molecular Orbital(MO)Method 85
3.3.2 The simple molecular orbital method 87
3.3.3 The principles of bonding 88
3.4 Homonuclear Diatomic Molecules 90
3.4.1 Construction and classification of molecular orbitals 90
3.4.2 Energy level sequences 93
3.4.3 The orbital symmetry correlation 94
3.4.4 The ground state 96
3.5 Heteronuclear Diatomic Molecules 98
3.5.1 The comparison with homonuclear diatomics 98
3.5.2 A review on the correlation diagram 101
3.6 The Valence Bond(VB)Method 102
3.6.1 The wave function of H2 102
3.6.2 The valence bond method 104
3.6.3 The diatomic molecules 107
3.6.4 The relationship between the molecular orbital approximation and the valence bond approximation 108
Appendix 3.1 The Evaluation of Integrals in the Treatment of H2+ 110
Exercises 111
Chapter 4 Symmetry and Group Theory 115
4.1 Symmetry Operations and Symmetry Elements 116
4.1.1 Geometrical significance 116
4.1.2 Multiplication of symmetry operations 117
4.2 Matrix Representation and Properties of Symmetry Operations 118
4.2.1 Matrix representation 118
4.2.2 Properties of symmetry operations 123
4.3 The Group 125
4.3.1 Definition 125
4.3.2 Conjugate classes 126
4.4 Classification of Point Groups 127
4.4.1 The cyclic group 127
4.4.2 Acyclic groups involving a rotational symmetry axis 128
4.4.3 Point groups with several rotational symmetry axes 129
4.4.4 Point groups of linear molecules 130
4.4.5 Symmetries of molecules 131
4.5 Group Representations 131
4.5.1 Reducible and irreducible representations 131
4.5.2 Properties of irreducible representations 133
4.6 Group Theory and Wave Functions 136
4.6.1 Symmetry of wave functions 136
4.6.2 Symmetry and molecular orbitals 137
4.6.3 Direct product 141
Appendix 4.1 Character Tables of Some Typical Point Groups 143
Exercises 148
Chapter 5 Polyatomic Molecules 152
5.1 Molecular Orbitals and Energy Levels 153
5.1.1 Introduction 153
5.1.2 H2O 154
5.1.3 BH3 158
5.1.4 CH4 159
5.1.5 C2H4 161
5.2 Molecular Geometry 163
5.2.1 Walsh rule 163
5.2.2 AH2 164
5.2.3 AH3 165
5.2.4 Other types of molecules 166
5.3.1 Localization of chemical bond 167
5.3 Valence Bond Orbitals 167
5.3.2 The influence of hybridization on bond angles 168
5.3.3 sp-hybridization 170
5.3.4 sp2-hybridization 171
5.3.5 sp3-hybridization 173
5.3.6 Hydrocarbons 175
5.3.7 Non-equivalent hybridization 176
5.4 The Bond Lengths 177
5.4.1 Experimental data 177
5.4.2 Variation of C-H bond length 178
5.4.3 C-C bond lengths and hybridizations 179
5.5 Valence-Shell Electron Pair Repulsion(VSEPR)Theory 181
5.5.1 The VSEPR rule 181
5.5.2 The lone-pair orbitals and molecular geometry 183
Exercises 184
Chapter 6 Conjugated Molecules 187
6.1 The Hückel Molecular Orbital Method 189
6.1.1 The Hückel theory 189
6.1.2 Linear polyenes 191
6.1.3 The cyclic polyenes 195
6.2 More about Energy Levels and Molecular Orbitals 199
6.2.1 Bound and sum of energy levels 199
6.2.2 Alternant hydrocarbons 200
6.3 Electron Densities and Bond Orders 203
6.3.1 Atomic charges 203
6.3.2 Bond orders 204
6.3.3 Free valence 206
6.4.1 The resonance energy 207
6.4 Aromaticity 207
6.4.2 The eight-parameter scheme 209
6.4.3 The five-parameter scheme 210
6.5 Chemical Reactions 211
6.5.1 Frontier orbitals 211
6.5.2 Odd alternants 215
6.5.3 Orientation of electrophilic aromatic substitution 216
6.5.4 Pericyclic reactions 217
6.6 Conjugated Molecules Containing Hetero-atoms 221
Exercises 223
Chapter 7 Transition-Metal Complexes 227
7.1 Atoms and Orbitals in Electrostatic Field 229
7.1.1 Square ligand field 229
7.1.2 Octahedral field 230
7.2 Group Theoretical Analysis 233
7.2.1 Orbitals 233
7.2.2 Splitting of terms 236
7.2.3 The strong field scheme 238
7.2.4 The correlation diagram 241
7.3 Optical Spectra and Magnetic Properties 243
7.3.1 The absorption spectra 243
7.3.2 The spectrochemical sequence 245
7.3.3 High-spin and low-spin complexes 246
7.4 Stereochemistry 249
7.4.1 Lower coordinations 249
7.4.2 Jahn-Teller distortion 251
7.5.1 б-bonding 253
7.5 Molecular Orbital Treatment 253
7.5.2 d2sp3 hybridization 256
7.5.3 Eighteen-electron rule 257
7.6 π-Bonding and Covalent Complexes 259
7.6.1 Picture of π-bonding 259
7.6.2 π-ligands and related complexes 260
Exercises 264
Chapter 8 Cluster Compounds and Bare Clusters 267
8.1 Main Group Cluster Compounds 269
8.1.1 Polyhedral hydrocarbons CnHn 269
8.1.2 Boron hydrides 270
8.2 The Three-Center Bond 272
8.3.1 B6H? 277
8.3 Molecular Orbital Treatment 277
8.3.2 B5H9(B5H?) 280
8.3.3 Main group cluster compounds and clusters 282
8.4 Transition-Metal Cluster Compounds 283
8.4.1 Tri-degree cores 283
8.4.2 Isolobal similarity 285
8.4.3 Electron counting rules 286
8.4.4 Capped polyhedra 288
8.4.5 Conjunctive cluster molecules 289
8.5 Metalloboranes and Organometallic Cluster Molecules 291
8.5.1 Mixed-type cluster molecules 291
8.5.2 Conjunctive mixed-type cluster molecules 293
8.5.3 Inconformity to 18-electron rule 294
8.6.1 Introductory remarks 295
8.6 Bare Clusters 295
8.6.2 Alkali-metal clusters 296
8.6.3 Carbon clusters 299
Exercises 302
Chapter 9 The Solids 304
9.1 Electrons in Long-Chain Molecules 306
9.1.1 Model molecules 306
9.1.2 The group Cn 307
9.1.3 Energy levels and energy bands 309
9.2 Bands and Bloch Functions 311
9.2.1 The Bloch function 311
9.2.2 The meaning of k 312
9.2.3 Bands 314
9.3.1 Band structures 317
9.3 A Survey of Polymer Chains 317
9.3.2 K2Pt(CN)4 319
9.3.3 The Fermi energy 323
9.4 The Density of States 323
9.5 The Peierls Distortion 325
9.5.1 Dimeric unit 325
9.5.2 Peierls distortion 328
9.6 The Two-Dimensional Lattices 330
9.6.1 Bloch function 330
9.6.2 The Brillouin zone 332
9.6.3 The band structure 333
Exercises 337
References 339
Index 342