A Primer on Quantum Chemistry 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…mehr
A Primer on Quantum Chemistry 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 moreSupplemental online material including problems, solutions, and details of Mathematica computationsA 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.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
S. M. Blinder, PhD, is Professor Emeritus of Chemistry and Physics at the University of Michigan, Ann Arbor, USA, and a senior scientist with Wolfram Research in Champaign, Illinois. He has published extensively on quantum chemistry and related fields.
Inhaltsangabe
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
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
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