A practical and accessible guide to the applications of quantum chemistry
Quantum chemistry, the branch of physical chemistry which applies quantum mechanical principles to the study of chemical systems, has become an integral part of the study of matter. Concerned with understanding quantum effects at the atomic and molecular level, quantum chemistry underlies an immense range of modern technologies.
A Primer on Quantum Chemistry provides a lucid introduction to the difficult mathematical and conceptual foundations of this essential field. It incorporates Mathematica for operations in algebra and calculus, enabling readers to focus on the physical and chemical principles. It thereby equips students with the tools used by professional scientists in applications of quantum chemistry.
A Primer on Quantum Chemistry readers will also find: - Detailed treatment of subjects including the Schrödinger equation and many more - Supplemental online material including problems, solutions, and details of Mathematica computations - A carefully developed pedagogical approach that streamlines student progress through the subject
A Primer on Quantum Chemistry is a must-own for graduate and advanced undergraduate students in chemistry, physics, and related subjects.
Table of Contents
Preface xi
About the Author xiv
About the Companion Website xvi
Mathematica 1
1 The Basic Math Assistant 1
2 Derivatives and Integrals 2
3 Differential Equations 4
4 Symbolic Mathematics 5
5 External Data 5
1 The Old Quantum Theory 8
1.1 Introduction 8
1.2 Blackbody Radiation 8
1.3 The Photoelectric Effect 12
1.4 Line Spectra 13
1.5 Bohr Theory of the Hydrogen Atom 15
1.6 Bohr-Sommerfeld Orbits 19
1.7 The Periodic Structure of the Elements 21
2 The Schrödinger Equation 24
2.1 TheWave-Particle Duality 24
2.2 De Broglie's Hypothesis 26
2.3 Heuristic Derivation of the Schrödinger Equation 29
2.4 Operators and Eigenvalues 31
2.5 TheWavefunction 32
3 Quantum Mechanics of Some Simple Systems 33
3.1 Particle in a Box 33
3.2 Free-Electron Model 37
3.3 Particle in a Ring 39
3.4 Free Electron Model for Aromatic Molecules 40
3.5 Particle in a Three-Dimensional Box 41
3.6 The Free Particle 43
3.7 Deltafunction Normalization 45
3.8 Particle in a Deltafunction PotentialWell 47
4 Principles of Quantum Mechanics 50
4.1 Hermitian Operators 50
4.2 Eigenvalues and Eigenfunctions 51
4.3 Expectation Values 52
4.4 Commutators and Uncertainties 53
4.5 Postulates of Quantum Mechanics 55
4.6 Dirac Bra-Ket Notation 57
4.7 The Variational Method 58
4.8 Perturbation Theory 60
5 The Harmonic Oscillator 64
5.1 Classical Oscillator 64
5.2 Harmonic Oscillator in Old Quantum Theory 66
5.3 Quantum Harmonic Oscillator 67
5.4 Harmonic-Oscillator Eigenfunctions 69
5.5 Operator Formulation of the Harmonic Oscillator 70
5.6 Quantum Theory of Radiation 72
5.7 The Anharmonic Oscillator 74
6 Quantum Theory of Angular Momentum 76
6.1 Rotation in Two Dimensions 76
6.2 Spherical Polar Coordinates 78
6.3 Rotation in Three Dimensions 79
6.4 Spherical Harmonics 81
6.5 Electron Spin 83
6.6 Pauli Spin Algebra 84
6.7 General Theory of Angular Momentum 85
6.8 Addition of Angular Momenta 86
7 Molecular Vibration and Rotation 88
7.1 Molecular Spectroscopy 88
7.2 Vibration of Diatomic Molecules 88
7.3 The Morse Potential 90
7.4 Vibration of Polyatomic Molecules 93
7.5 Normal Modes of a Triatomic Molecule 94
7.6 Rotation of Diatomic Molecules 96
8 The Hydrogen Atom 99
8.1 Schrödinger Equation for Hydrogenlike Atoms 99
8.2 Hydrogen Atom Ground State 101
8.3 Hydrogenic 2s and 3s Orbitals 105
8.4 Solving the Schrödinger Equation 106
8.5 ;;- and ;;-Orbitals 108
8.6 Radial Distribution Functions 110
8.7 Summary on Atomic Orbitals 111
8.8 Connection between Hydrogen Atom and Harmonic Oscillator 111
9 The Helium Atom 114
9.1 Experimental Energies 114
9.2 Schrödinger Equation and Simple Variational Calculation 114
9.3 Improved Computations on the Helium Ground State 117
9.4 The Hydride Ion H- 119
9.5 Spinorbitals and the Exclusion Principle 119
9.6 Excited States of Helium 120
10 Atomic Structure and the Periodic Law 123
10.1 The Periodic Table 123
10.2 Slater Determinants 123
10.3 Self-Consistent Field Theory 126
10.4 Lithium and Beryllium Atoms 127
10.5 Aufbau Principles 131
10.6 Atomic Configurations and Term Symbols 132
10.7 Periodicity of Atomic Properties 135
10.8 Relativistic Effects 137
11 The Chemical Bond 140
11.1 The Hydrogen Molecule 140
11.2 Valence Bond Theory 142
11.3 Hybrid Orbitals and Molecular Geometry 143
11.4 Hypervalent Compounds 146
11.5 Boron Hydrides 148
12 Diatomic Molecules 150
12.1 The Hydrogen Molecule-Ion 150
12.2 The LCAO Approximation 153
12.3 MO Theory of Homonuclear Diatomic Molecules 154
12.4 Variational Computation of Molecular Orbitals 156
12.5 Heteronuclear Molecules 158
13 Polyatomic Molecules and Solids 160
13.1 Hückel Molecular Orbital Theory 160
13.2 Conservation of Orbital Symmetry;Woodward-Hoffmann Rules 163
13.3 Valence-Shell Model 166
13.4 Transition Metal Complexes 168
13.5 The Hydrogen Bond 171
13.6 Proteins and Nucleic Acids 172
13.7 Band Theory of Metals and Semiconductors 175
14 Molecular Symmetry and Group Theory 178
14.1 The Ammonia Molecule 178
14.2 Mathematical Theory of Groups 180
14.3 Group Theory in Quantum Mechanics 181
14.4 Molecular Orbitals for Ammonia 182
14.5 Selection Rules 184
14.6 TheWater Molecule 185
14.7 Walsh Diagrams 186
14.8 Molecular Symmetry Groups 187
14.9 Dipole Moments and Optical Activity 192
15 The Hartree-Fock Method 194
15.1 Hartree Self-Consistent Field Theory 194
15.2 DeterminantalWavefunctions 197
15.3 Hartree-Fock Equations 199
15.4 Hartree-Fock Equations using Second Quantization 203
15.5 Roothaan Equations 206
15.6 Atomic Hartree-Fock Results 210
15.7 Electron Correlation 213
15.8 Post Hartree-Fock Methods 214
16 Density Functional Theory 217
16.1 Thomas-Fermi Model 217
16.2 The Hohenberg-Kohn Theorems 221
16.3 Density Functionals 222
16.4 Slater's X-Alpha Method 223
16.5 The Kohn-Sham Equations 224
16.6 Chemical Potential 225
17 Metaphysical Aspects of the Quantum Theory 227
17.1 Introduction 227
17.2 The Copenhagen Interpretation 228
17.3 Superposition 229
17.4 Schrödinger's Cat 230
17.5 The Einstein-Podolsky-Rosen Experiment 231
17.6 Bell's Theorem 234
17.7 Conclusion 236
18 Quantum Computers 238
18.1 Prospects of Quantum Computation 238
18.2 Qubits 239
18.3 Quantum Gates and Circuits 240
18.4 Simulation of a Stern-Gerlach Experiment 246
18.5 Quantum Fourier Transform 247
18.6 Phase Estimation Algorithm 250
18.7 Many-Electron Systems 252
18.8 Atomic and Molecular Hamiltonians 253
18.9 Time-Evolution of a Quantum System 256
18.10 Trotter Expansions 257
18.11 Simulations of Molecular Structure 258
Bibliography 260
Index 261
