Electrons Atoms and Molecules in Inorganic Chemistry. A worked Examples Approach

Contents......Page 3
Preface......Page 8
1.1 Cathode and Anode Rays......Page 11
1.2 Charge of the Electron......Page 14
1.3 Mass of Electron and Proton......Page 16
1.4 Rutherford's Atomic Model......Page 19
1.5 Quantum of Energy......Page 20
1.6 Hydrogen Atom Line-Emission Spectra; Electrons in Atoms Exist Only in Very Specific Energy States......Page 23
1.7 Bohr's Quantum Theory of the Hydrogen Atom......Page 25
1.9 The Corpuscular Nature of Electrons, Photons, and Particles of Very Small Mass......Page 28
1.11 The Corpuscular Nature of Electromagnetic Waves......Page 31
The Photoelectric Effect......Page 32
The Compton Effect......Page 35
1.12 de Broglie's Considerations......Page 36
1.13 Werner Heisenberg's Uncertainty Principle, or the Principle of Indeterminacy......Page 37
1.14 The Probability of Finding an Electron and the Wave Function......Page 38
Elementary Particles......Page 39
Suggestions for Further Reading......Page 42
2 Electrons in Atoms......Page 44
2.1 The Wave Function (the Schrödinger Equation)......Page 46
2.2 Properties of the wave function......Page 48
2.3 Schrödinger Equation of the Hydrogen Atom......Page 49
2.4 Transformation of the Schrödinger Equation From Cartesians to Spherical Polar Coordinates......Page 50
2.5 The Angular Equation......Page 56
2.6 The Φ-Equation......Page 57
2.7 The Θ-Equation......Page 60
2.8 The Radial Equation......Page 66
2.9 The Final Solution for the Full Wave Function, ψnlm(r,θ,ϕ)......Page 75
2.10 The Orthonormal Properties of the Real Wave Functions......Page 80
The Quantum Numbers l and Angular Momentum......Page 85
Picture and Represent Precisely ml Vectors of p- and d-Orbitals......Page 87
2.12 The Spin Quantum Number, s......Page 93
2.13 The Boundary Surface of s-Orbital......Page 94
2.14 The Boundary Surface of p-Orbitals......Page 96
2.15 The Boundary Surface of d-Orbitals......Page 100
2.16 Calculating the Most Probable Radius......Page 108
2.17 Calculating the Mean Radius of an Orbital......Page 109
2.18 The Structure of Many-Electron Atoms......Page 117
2.19 The Pauli Exclusion Principle......Page 118
2.20 Slater Determinant......Page 120
2.21 Penetration and Shielding......Page 122
2.22 The Building-Up Principle......Page 126
2.23 Term Structure for Polyelectron Atoms......Page 130
2.24 Term Wave Functions and Single Electron Wave Functions......Page 138
2.25 Spin-Orbital Coupling......Page 140
2.26 Spin-Orbital Coupling in External Magnetic Field......Page 142
Suggestions for Further Reading......Page 153
3 Chemical Bonding......Page 155
3.1 Electronegativity and Electropositivity......Page 157
3.2 Electronegativity and Electropositivity Trends......Page 158
3.3 Molecular and Nonmolecular Compounds......Page 159
3.5 Metallic Bonding and General Properties of Metals......Page 160
Conductivity and Mobility of Electrons......Page 161
Malleability, Cohesive Force, Number of Valence Electrons......Page 162
Free Electron Theory......Page 163
Crystal Structures of Metals (Metallic Structures)......Page 164
Alloy and Metallic Compounds......Page 166
Lattice Energy and Cohesion of Atomic Lattice......Page 167
Born-Haber Cycle and Heat of Formation......Page 171
Ionic Crystal Structures and the Radius Ratio......Page 172
Stoichiometric and Nonstoichiometric Defects......Page 177
Ionic Character and Covalency Interference......Page 178
Solubility of the Ionic Salts......Page 179
Exceptions to the Octet Rule......Page 181
Bonding and Polarity......Page 182
3.8 Coordinate Covalent Bond (Dative Bonding)......Page 183
Nomenclature of Complexes......Page 184
Complex Formation......Page 186
Coordinative Comproportionation Reaction......Page 189
Complexation Equilibrium......Page 190
Multiligand Complexation......Page 191
Stepwise Formation Constants and the Sequential Analysis......Page 192
Hard and Soft Interactions, HSAB......Page 194
Chemical Features of Hard and Soft Ions, and Classification......Page 197
Hard-Soft Interaction and Anion Polarizability......Page 198
Chelate Effect......Page 199
Entropy and Chelate Formation......Page 200
Macrocyclic Effect......Page 201
Donor Atom Basicity......Page 204
Solvent Competition......Page 205
Stability and Metal Oxidation State......Page 206
Stability and Metal Ionization Potential......Page 209
van der Waals Forces......Page 212
Ion-Induced Dipole Forces, Ion-Dipole Forces, and Hydrogen Bonding......Page 214
3.10 Covalent Networks and Giant Molecules......Page 220
Graphite, Fullerenes, Graphene, Carbon Nanotubes, and Asbestos......Page 222
Suggestions for Further Reading......Page 233
4 Molecular Symmetry......Page 235
4.1 Molecular Symmetry......Page 236
Proper Rotation Axis, Cn......Page 238
Plane of Symmetry, σ......Page 241
Center of Symmetry, i......Page 243
Sn: Improper Rotation Axis......Page 244
4.3 The Symmetry and Point Group......Page 246
Dipole Moments and Polarity......Page 247
Equivalent Atoms: (Or Group of Atoms)......Page 252
Crystal Symmetry......Page 253
4.5 Group Theory: Properties of the Groups and Their Elements......Page 258
4.6 Similarity Transforms, Conjugation, and Classes......Page 260
Matrices and Vectors......Page 262
Matrix Representation of Symmetry Operation......Page 263
Matrix Representation of Point Group......Page 266
Irreducible Representations......Page 268
Irreducible and Degenerate Representations......Page 269
Translation Motion......Page 270
Rotational Motion......Page 272
Mullikan Notation......Page 274
Atomic orbital Representation......Page 275
4.10 Character Tables......Page 277
Properties of the Characters of Representations......Page 278
4.11 Relation Between any Reducible and Irreducible Representations......Page 280
The Direct Product......Page 282
4.12 Group Theory and Quantum Mechanics: Irreducible Representations and Wave Function......Page 283
Suggestions for Further Reading......Page 288
5 Valence Bond Theory & Orbital Hybridization......Page 289
5.1 Valence Bond Theory......Page 290
5.2 VSEPR Theory and Molecular Geometry......Page 291
5.4 Procedures to Diagram Molecular Structure......Page 292
5.5 Valence Bond Theory and Metallic Bonds......Page 296
5.6 Orbital Hybridization......Page 298
5.7 Rehybridization and Complex Formation......Page 299
5.8 Hybridization and σ-/π-Bonding......Page 302
Trigonal Planar Hybridization......Page 304
Trigonal Bipyramidal Hybridization......Page 309
Tetragonal Pyramidal Hybridization......Page 311
Square Planar Hybridization......Page 312
Tetrahedral Hybridization......Page 314
Octahedral Hybridization......Page 316
5.10 Hybrid Orbitals as Symmetry Adapted Linear Combination of Atomic Orbitals (SALC)......Page 319
5.11 Molecular Wave Function as Symmetry Adapted Linear Combination of Atomic Orbitals (SALC)......Page 330
Suggestions for Further Reading......Page 338
6 Molecular Orbital Theory......Page 339
6.1 Molecular Orbital Theory Versus Valence Bond Theory......Page 340
6.3 The Linear Combination of Atomic Orbitals-Molecular Orbital (LCAO-MO) and Hückel Approximations......Page 341
6.4 Atomic Orbitals Combinations for the Second Row Diatomic Molecules......Page 346
6.5 Heterodiatomic Molecules......Page 355
6.6 Polyatomic Molecules......Page 357
6.7 Molecular Orbitals for a Centric Molecule......Page 359
6.8 Properties Derived From Molecular Wave Function......Page 374
6.9 Band Theory: Molecule Orbital Theory and Metallic Bonding Orbit......Page 402
6.10 Conductors, Insulators, and Semiconductors......Page 405
Suggestions for Further Reading......Page 409
7 Crystal Field Theory......Page 410
d-Orbitals in Cubic Crystal Field......Page 412
f-Orbitals in Cubic Crystal Field......Page 413
Octahedral Crystal field Potential, VOct.......Page 414
Square Planar Crystal Field Potential, VSq.Pl.......Page 419
Tetragonal Crystal Field Potential, VTetrag.......Page 422
Tetrahedral Crystal Field Potential, VTd......Page 424
The Linear Combination of Atomic Orbitals, LCAO-MO, and Energy Calculation......Page 426
The Perturbation Theory for Degenerate Systems......Page 428
The Splitting of d-Orbitals in Octahedral Crystal Field, Voct.......Page 430
The Splitting of d-Orbitals in Tetrahedral Crystal Field, VTd......Page 437
The Splitting of d-Orbitals in Tetragonal Crystal Field, VD4h......Page 442
The Effect of the Cubic Crystal Field on P Term......Page 449
The Effect of a Cubic Crystal Field on D Term......Page 453
The Effect of a Cubic Crystal Field on F Term......Page 454
The Effect of a Cubic Crystal Field on G, H, and I......Page 462
The Determinantal Wave Functions of d2 in Strong Field of Tetragonal Structure, Trans-ML4Z2......Page 464
The Symmetry and the Energy of Determinant Wave Functions of D2 in a Strong Field of Trans-ML4Z2......Page 465
The Appropriate Hamiltonian in Strong Field......Page 466
The Diagonal Interelectronic Repulsion......Page 467
The Nondiagonal Interelectronic Repulsion and the Energy of Each Level of the d2 Configuration in Strong Field of Trans-ML4Z2......Page 470
Suggestions for Further Reading......Page 477
8 Ligand Field Theory......Page 478
8.1 The Advantages and Disadvantages of Crystal Field Theory......Page 479
8.2 Symmetry and Orbital Splitting by Ligand Field......Page 480
Orbital Correlation Table......Page 485
Term Correlation Tables......Page 487
Correlation Diagram of Strong and Weak Field States of Oh......Page 488
Method of Descending Symmetry (Descending Multiplicities of the Orbital States)......Page 492
Correlation Diagram of Weak and Strong Field States of Td......Page 493
Orgel Diagram of D Term Configuration......Page 495
Orgel Diagram of F Term......Page 496
Configuration and Term Interactions......Page 500
The Advantages......Page 505
dn and d10-n Diagrams......Page 506
d5 Diagram......Page 509
Suggestions for Further Reading......Page 510
9 Vibrational Rotational Spectroscopy......Page 511
9.1 Infrared and Raman Spectroscopy......Page 513
9.3 The Classical Explanation of Infrared and RAMAN Spectroscopy......Page 515
9.4 Rotation of Diatomic Molecules......Page 517
Rigid and Nonrigid Models......Page 520
9.5 Vibration of Diatomic Molecules......Page 521
Vibrational Energy Levels......Page 522
Anharmonic Oscillation......Page 527
9.6 The Quantum Mechanics of the Translation, Vibration, and Rotation Motions......Page 529
9.7 Vibration-Rotation Energies of Diatomic Molecules (Vibrational-Rotational State)......Page 535
9.9 Polyatomic Molecular Motions and Degrees of Freedom......Page 538
9.10 Normal Modes of Vibration, Normal Coordinates, and Polyatomic Molecules......Page 539
9.12 Vibrational Displacements......Page 542
9.13 Vibrational Energy and Normal Coordinates......Page 543
9.14 Stretching Vibrations of Linear Molecules......Page 549
9.15 Symmetry and Normal Modes of Vibration......Page 551
9.16 Assigning the Normal Modes of Vibration......Page 555
Normal Modes of Vibration for Linear Triatomic Molecule......Page 558
9.17 Force Constants and the GF-Matrix Method......Page 561
Some of the G Matrix Elements Have the Following General Formulas:......Page 571
IR-Selection Rules......Page 574
Raman Selection Rules......Page 577
9.19 Center of Symmetry and the Mutual Exclusion Rule......Page 581
9.20 Isolation of a Particular Type of Motion......Page 582
9.21 Detecting the Changes of Symmetry Through Reaction......Page 587
Suggestions for Further Reading......Page 588
10 Electronic Spectroscopy......Page 591
Molar Extinction Coefficient, Oscillator Strength, and Dipole Strength......Page 593
The Transition Moment and Electronic Transitions......Page 595
Even and Odd Functions and the Symmetry Considerations......Page 596
Symmetry Representations and the Allowed Transitions......Page 597
10.3 Basis of the Selection Rules......Page 598
Orbital Selection Rules......Page 599
Vibrational Selection Rules......Page 600
10.5 Unexpected Weak Absorbance......Page 601
10.6 Spectroscopy of Electronic Excitations......Page 603
Jahn-Teller Theorem and Vibronic Coupling: d1 Configuration......Page 607
The Expected Position of Absorption Peaks: d2 Configuration......Page 609
Configuration Interaction: d3 Configuration......Page 611
Spectrochemical Series......Page 613
Octahedral Versus Tetrahedral: d5 Configuration......Page 615
Simultaneous Pair Excitations: Bridged Dinuclear Metal Centers......Page 618
Bandwidth in the Electronic Spectra......Page 620
The Low-Spin Versus High-Spin: d6 Configuration......Page 621
The Effect of Low Symmetry......Page 624
Band Intensity and Ligand-Field: d7 Configuration......Page 627
d8 Configuration: d 2 Versus d8 Complexes......Page 629
Calculation of Dq and β for Octahedral Ni(II) Complexes......Page 630
d9 Configuration: π-Binding......Page 632
Intensely Colored Metal Complexes......Page 636
Donor-Acceptor Complexes......Page 637
Configuration Interaction, Absorption of the Unpolarized Light......Page 638
10.9 The Magnetic Dipole Moment and the Absorbance Intensity......Page 641
Circular Dichroism Spectroscopy......Page 642
The Effects of Lower Symmetry......Page 645
Absolute Configuration......Page 646
Kuhn anisotropy Factor and Deducing the Energy Levels Within the Molecule......Page 647
Suggestions for Further Reading......Page 650
11 Magnetism......Page 652
11.1 Magnetic Susceptibility......Page 653
11.2 Types of Magnetic Behaviors......Page 654
11.3 Diamagnetic Behavior......Page 657
11.4 Spin-Only Magnetic Susceptibility, Magnetic Moment, and Thermal Spreading......Page 659
11.5 Orbital Magnetic Moment......Page 664
11.6 Second-Order Zeeman Effect and Van Vleck Equation......Page 667
11.7 Spin-Orbital Coupling and Magnetic Susceptibility......Page 669
11.8 Spin-Orbital Coupling: In A and E Ground Terms......Page 676
11.9 Spin-Orbital Coupling: In T Ground Terms......Page 677
11.10 Curie Law, Deviation, and Data Representations......Page 683
Spin Crossover Compounds......Page 686
11.12 Structure-Linked Crossover, Thermal Isomerization......Page 693
Homobinuclear Interaction......Page 696
Coupling Mechanisms in Binuclear Compounds......Page 705
11.14 Measurement of the Magnetic Susceptibility......Page 706
Gouy's Method......Page 707
Faraday's Method......Page 710
Quincke's Method......Page 711
NMR Method......Page 713
Suggestions for Further Reading......Page 714
Summation Formulas......Page 716
Binomial Expansion......Page 717
Logarithms......Page 718
Derivative of a Function......Page 719
Antiderivatives or Indefinite Integrals......Page 722
Important Mathematical Functions......Page 724
Hermite Polynomials......Page 725
Associated Legendre Functions......Page 726
Taylor Series......Page 727
Matrices......Page 728
Determinants......Page 732
Cn Groups......Page 733
Cnv Groups......Page 734
Cnh Groups......Page 735
Dn Groups......Page 736
Dnd Groups......Page 737
Dnh Groups......Page 738
S2n Groups......Page 739
Cubic Groups......Page 740
Linear Groups......Page 741
Index......Page 742