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.

• Preface xiAbout the Author xivAbout the Companion Website xviMathematica 11 The Basic Math Assistant 12 Derivatives and Integrals 23 Differential Equations 44 Symbolic Mathematics 55 External Data 51 The Old Quantum Theory 81.1 Introduction 81.2 Blackbody Radiation 81.3 The Photoelectric Effect 121.4 Line Spectra 131.5 Bohr Theory of the Hydrogen Atom 151.6 Bohr-Sommerfeld Orbits 191.7 The Periodic Structure of the Elements 212 The Schrödinger Equation 242.1 TheWave-Particle Duality 242.2 De Broglie's Hypothesis 262.3 Heuristic Derivation of the Schrödinger Equation 292.4 Operators and Eigenvalues 312.5 TheWavefunction 323 Quantum Mechanics of Some Simple Systems 333.1 Particle in a Box 333.2 Free-Electron Model 373.3 Particle in a Ring 393.4 Free Electron Model for Aromatic Molecules 403.5 Particle in a Three-Dimensional Box 413.6 The Free Particle 433.7 Deltafunction Normalization 453.8 Particle in a Deltafunction PotentialWell 474 Principles of Quantum Mechanics 504.1 Hermitian Operators 504.2 Eigenvalues and Eigenfunctions 514.3 Expectation Values 524.4 Commutators and Uncertainties 534.5 Postulates of Quantum Mechanics 554.6 Dirac Bra-Ket Notation 574.7 The Variational Method 584.8 Perturbation Theory 605 The Harmonic Oscillator 645.1 Classical Oscillator 645.2 Harmonic Oscillator in Old Quantum Theory 665.3 Quantum Harmonic Oscillator 675.4 Harmonic-Oscillator Eigenfunctions 695.5 Operator Formulation of the Harmonic Oscillator 705.6 Quantum Theory of Radiation 725.7 The Anharmonic Oscillator 746 Quantum Theory of Angular Momentum 766.1 Rotation in Two Dimensions 766.2 Spherical Polar Coordinates 786.3 Rotation in Three Dimensions 796.4 Spherical Harmonics 816.5 Electron Spin 836.6 Pauli Spin Algebra 846.7 General Theory of Angular Momentum 856.8 Addition of Angular Momenta 867 Molecular Vibration and Rotation 887.1 Molecular Spectroscopy 887.2 Vibration of Diatomic Molecules 887.3 The Morse Potential 907.4 Vibration of Polyatomic Molecules 937.5 Normal Modes of a Triatomic Molecule 947.6 Rotation of Diatomic Molecules 968 The Hydrogen Atom 998.1 Schrödinger Equation for Hydrogenlike Atoms 998.2 Hydrogen Atom Ground State 1018.3 Hydrogenic 2s and 3s Orbitals 1058.4 Solving the Schrödinger Equation 1068.5 ;;- and ;;-Orbitals 1088.6 Radial Distribution Functions 1108.7 Summary on Atomic Orbitals 1118.8 Connection between Hydrogen Atom and Harmonic Oscillator 1119 The Helium Atom 1149.1 Experimental Energies 1149.2 Schrödinger Equation and Simple Variational Calculation 1149.3 Improved Computations on the Helium Ground State 1179.4 The Hydride Ion H− 1199.5 Spinorbitals and the Exclusion Principle 1199.6 Excited States of Helium 12010 Atomic Structure and the Periodic Law 12310.1 The Periodic Table 12310.2 Slater Determinants 12310.3 Self-Consistent Field Theory 12610.4 Lithium and Beryllium Atoms 12710.5 Aufbau Principles 13110.6 Atomic Configurations and Term Symbols 13210.7 Periodicity of Atomic Properties 13510.8 Relativistic Effects 13711 The Chemical Bond 14011.1 The Hydrogen Molecule 14011.2 Valence Bond Theory 14211.3 Hybrid Orbitals and Molecular Geometry 14311.4 Hypervalent Compounds 14611.5 Boron Hydrides 14812 Diatomic Molecules 15012.1 The Hydrogen Molecule-Ion 15012.2 The LCAO Approximation 15312.3 MO Theory of Homonuclear Diatomic Molecules 15412.4 Variational Computation of Molecular Orbitals 15612.5 Heteronuclear Molecules 15813 Polyatomic Molecules and Solids 16013.1 Hückel Molecular Orbital Theory 16013.2 Conservation of Orbital Symmetry;Woodward-Hoffmann Rules 16313.3 Valence-Shell Model 16613.4 Transition Metal Complexes 16813.5 The Hydrogen Bond 17113.6 Proteins and Nucleic Acids 17213.7 Band Theory of Metals and Semiconductors 17514 Molecular Symmetry and Group Theory 17814.1 The Ammonia Molecule 17814.2 Mathematical Theory of Groups 18014.3 Group Theory in Quantum Mechanics 18114.4 Molecular Orbitals for Ammonia 18214.5 Selection Rules 18414.6 TheWater Molecule 18514.7 Walsh Diagrams 18614.8 Molecular Symmetry Groups 18714.9 Dipole Moments and Optical Activity 19215 The Hartree-Fock Method 19415.1 Hartree Self-Consistent Field Theory 19415.2 DeterminantalWavefunctions 19715.3 Hartree-Fock Equations 19915.4 Hartree-Fock Equations using Second Quantization 20315.5 Roothaan Equations 20615.6 Atomic Hartree-Fock Results 21015.7 Electron Correlation 21315.8 Post Hartree-Fock Methods 21416 Density Functional Theory 21716.1 Thomas-Fermi Model 21716.2 The Hohenberg-Kohn Theorems 22116.3 Density Functionals 22216.4 Slater's X-Alpha Method 22316.5 The Kohn-Sham Equations 22416.6 Chemical Potential 22517 Metaphysical Aspects of the Quantum Theory 22717.1 Introduction 22717.2 The Copenhagen Interpretation 22817.3 Superposition 22917.4 Schrödinger's Cat 23017.5 The Einstein-Podolsky-Rosen Experiment 23117.6 Bell's Theorem 23417.7 Conclusion 23618 Quantum Computers 23818.1 Prospects of Quantum Computation 23818.2 Qubits 23918.3 Quantum Gates and Circuits 24018.4 Simulation of a Stern-Gerlach Experiment 24618.5 Quantum Fourier Transform 24718.6 Phase Estimation Algorithm 25018.7 Many-Electron Systems 25218.8 Atomic and Molecular Hamiltonians 25318.9 Time-Evolution of a Quantum System 25618.10 Trotter Expansions 25718.11 Simulations of Molecular Structure 258Bibliography 260Index 261

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.

• Preface xiAbout the Author xivAbout the Companion Website xviMathematica 11 The Basic Math Assistant 12 Derivatives and Integrals 23 Differential Equations 44 Symbolic Mathematics 55 External Data 51 The Old Quantum Theory 81.1 Introduction 81.2 Blackbody Radiation 81.3 The Photoelectric Effect 121.4 Line Spectra 131.5 Bohr Theory of the Hydrogen Atom 151.6 Bohr-Sommerfeld Orbits 191.7 The Periodic Structure of the Elements 212 The Schrödinger Equation 242.1 TheWave-Particle Duality 242.2 De Broglie's Hypothesis 262.3 Heuristic Derivation of the Schrödinger Equation 292.4 Operators and Eigenvalues 312.5 TheWavefunction 323 Quantum Mechanics of Some Simple Systems 333.1 Particle in a Box 333.2 Free-Electron Model 373.3 Particle in a Ring 393.4 Free Electron Model for Aromatic Molecules 403.5 Particle in a Three-Dimensional Box 413.6 The Free Particle 433.7 Deltafunction Normalization 453.8 Particle in a Deltafunction PotentialWell 474 Principles of Quantum Mechanics 504.1 Hermitian Operators 504.2 Eigenvalues and Eigenfunctions 514.3 Expectation Values 524.4 Commutators and Uncertainties 534.5 Postulates of Quantum Mechanics 554.6 Dirac Bra-Ket Notation 574.7 The Variational Method 584.8 Perturbation Theory 605 The Harmonic Oscillator 645.1 Classical Oscillator 645.2 Harmonic Oscillator in Old Quantum Theory 665.3 Quantum Harmonic Oscillator 675.4 Harmonic-Oscillator Eigenfunctions 695.5 Operator Formulation of the Harmonic Oscillator 705.6 Quantum Theory of Radiation 725.7 The Anharmonic Oscillator 746 Quantum Theory of Angular Momentum 766.1 Rotation in Two Dimensions 766.2 Spherical Polar Coordinates 786.3 Rotation in Three Dimensions 796.4 Spherical Harmonics 816.5 Electron Spin 836.6 Pauli Spin Algebra 846.7 General Theory of Angular Momentum 856.8 Addition of Angular Momenta 867 Molecular Vibration and Rotation 887.1 Molecular Spectroscopy 887.2 Vibration of Diatomic Molecules 887.3 The Morse Potential 907.4 Vibration of Polyatomic Molecules 937.5 Normal Modes of a Triatomic Molecule 947.6 Rotation of Diatomic Molecules 968 The Hydrogen Atom 998.1 Schrödinger Equation for Hydrogenlike Atoms 998.2 Hydrogen Atom Ground State 1018.3 Hydrogenic 2s and 3s Orbitals 1058.4 Solving the Schrödinger Equation 1068.5 ;;- and ;;-Orbitals 1088.6 Radial Distribution Functions 1108.7 Summary on Atomic Orbitals 1118.8 Connection between Hydrogen Atom and Harmonic Oscillator 1119 The Helium Atom 1149.1 Experimental Energies 1149.2 Schrödinger Equation and Simple Variational Calculation 1149.3 Improved Computations on the Helium Ground State 1179.4 The Hydride Ion H− 1199.5 Spinorbitals and the Exclusion Principle 1199.6 Excited States of Helium 12010 Atomic Structure and the Periodic Law 12310.1 The Periodic Table 12310.2 Slater Determinants 12310.3 Self-Consistent Field Theory 12610.4 Lithium and Beryllium Atoms 12710.5 Aufbau Principles 13110.6 Atomic Configurations and Term Symbols 13210.7 Periodicity of Atomic Properties 13510.8 Relativistic Effects 13711 The Chemical Bond 14011.1 The Hydrogen Molecule 14011.2 Valence Bond Theory 14211.3 Hybrid Orbitals and Molecular Geometry 14311.4 Hypervalent Compounds 14611.5 Boron Hydrides 14812 Diatomic Molecules 15012.1 The Hydrogen Molecule-Ion 15012.2 The LCAO Approximation 15312.3 MO Theory of Homonuclear Diatomic Molecules 15412.4 Variational Computation of Molecular Orbitals 15612.5 Heteronuclear Molecules 15813 Polyatomic Molecules and Solids 16013.1 Hückel Molecular Orbital Theory 16013.2 Conservation of Orbital Symmetry;Woodward-Hoffmann Rules 16313.3 Valence-Shell Model 16613.4 Transition Metal Complexes 16813.5 The Hydrogen Bond 17113.6 Proteins and Nucleic Acids 17213.7 Band Theory of Metals and Semiconductors 17514 Molecular Symmetry and Group Theory 17814.1 The Ammonia Molecule 17814.2 Mathematical Theory of Groups 18014.3 Group Theory in Quantum Mechanics 18114.4 Molecular Orbitals for Ammonia 18214.5 Selection Rules 18414.6 TheWater Molecule 18514.7 Walsh Diagrams 18614.8 Molecular Symmetry Groups 18714.9 Dipole Moments and Optical Activity 19215 The Hartree-Fock Method 19415.1 Hartree Self-Consistent Field Theory 19415.2 DeterminantalWavefunctions 19715.3 Hartree-Fock Equations 19915.4 Hartree-Fock Equations using Second Quantization 20315.5 Roothaan Equations 20615.6 Atomic Hartree-Fock Results 21015.7 Electron Correlation 21315.8 Post Hartree-Fock Methods 21416 Density Functional Theory 21716.1 Thomas-Fermi Model 21716.2 The Hohenberg-Kohn Theorems 22116.3 Density Functionals 22216.4 Slater's X-Alpha Method 22316.5 The Kohn-Sham Equations 22416.6 Chemical Potential 22517 Metaphysical Aspects of the Quantum Theory 22717.1 Introduction 22717.2 The Copenhagen Interpretation 22817.3 Superposition 22917.4 Schrödinger's Cat 23017.5 The Einstein-Podolsky-Rosen Experiment 23117.6 Bell's Theorem 23417.7 Conclusion 23618 Quantum Computers 23818.1 Prospects of Quantum Computation 23818.2 Qubits 23918.3 Quantum Gates and Circuits 24018.4 Simulation of a Stern-Gerlach Experiment 24618.5 Quantum Fourier Transform 24718.6 Phase Estimation Algorithm 25018.7 Many-Electron Systems 25218.8 Atomic and Molecular Hamiltonians 25318.9 Time-Evolution of a Quantum System 25618.10 Trotter Expansions 25718.11 Simulations of Molecular Structure 258Bibliography 260Index 261

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.

• Preface xiAbout the Author xivAbout the Companion Website xviMathematica 11 The Basic Math Assistant 12 Derivatives and Integrals 23 Differential Equations 44 Symbolic Mathematics 55 External Data 51 The Old Quantum Theory 81.1 Introduction 81.2 Blackbody Radiation 81.3 The Photoelectric Effect 121.4 Line Spectra 131.5 Bohr Theory of the Hydrogen Atom 151.6 Bohr-Sommerfeld Orbits 191.7 The Periodic Structure of the Elements 212 The Schrödinger Equation 242.1 TheWave-Particle Duality 242.2 De Broglie's Hypothesis 262.3 Heuristic Derivation of the Schrödinger Equation 292.4 Operators and Eigenvalues 312.5 TheWavefunction 323 Quantum Mechanics of Some Simple Systems 333.1 Particle in a Box 333.2 Free-Electron Model 373.3 Particle in a Ring 393.4 Free Electron Model for Aromatic Molecules 403.5 Particle in a Three-Dimensional Box 413.6 The Free Particle 433.7 Deltafunction Normalization 453.8 Particle in a Deltafunction PotentialWell 474 Principles of Quantum Mechanics 504.1 Hermitian Operators 504.2 Eigenvalues and Eigenfunctions 514.3 Expectation Values 524.4 Commutators and Uncertainties 534.5 Postulates of Quantum Mechanics 554.6 Dirac Bra-Ket Notation 574.7 The Variational Method 584.8 Perturbation Theory 605 The Harmonic Oscillator 645.1 Classical Oscillator 645.2 Harmonic Oscillator in Old Quantum Theory 665.3 Quantum Harmonic Oscillator 675.4 Harmonic-Oscillator Eigenfunctions 695.5 Operator Formulation of the Harmonic Oscillator 705.6 Quantum Theory of Radiation 725.7 The Anharmonic Oscillator 746 Quantum Theory of Angular Momentum 766.1 Rotation in Two Dimensions 766.2 Spherical Polar Coordinates 786.3 Rotation in Three Dimensions 796.4 Spherical Harmonics 816.5 Electron Spin 836.6 Pauli Spin Algebra 846.7 General Theory of Angular Momentum 856.8 Addition of Angular Momenta 867 Molecular Vibration and Rotation 887.1 Molecular Spectroscopy 887.2 Vibration of Diatomic Molecules 887.3 The Morse Potential 907.4 Vibration of Polyatomic Molecules 937.5 Normal Modes of a Triatomic Molecule 947.6 Rotation of Diatomic Molecules 968 The Hydrogen Atom 998.1 Schrödinger Equation for Hydrogenlike Atoms 998.2 Hydrogen Atom Ground State 1018.3 Hydrogenic 2s and 3s Orbitals 1058.4 Solving the Schrödinger Equation 1068.5 ;;- and ;;-Orbitals 1088.6 Radial Distribution Functions 1108.7 Summary on Atomic Orbitals 1118.8 Connection between Hydrogen Atom and Harmonic Oscillator 1119 The Helium Atom 1149.1 Experimental Energies 1149.2 Schrödinger Equation and Simple Variational Calculation 1149.3 Improved Computations on the Helium Ground State 1179.4 The Hydride Ion H− 1199.5 Spinorbitals and the Exclusion Principle 1199.6 Excited States of Helium 12010 Atomic Structure and the Periodic Law 12310.1 The Periodic Table 12310.2 Slater Determinants 12310.3 Self-Consistent Field Theory 12610.4 Lithium and Beryllium Atoms 12710.5 Aufbau Principles 13110.6 Atomic Configurations and Term Symbols 13210.7 Periodicity of Atomic Properties 13510.8 Relativistic Effects 13711 The Chemical Bond 14011.1 The Hydrogen Molecule 14011.2 Valence Bond Theory 14211.3 Hybrid Orbitals and Molecular Geometry 14311.4 Hypervalent Compounds 14611.5 Boron Hydrides 14812 Diatomic Molecules 15012.1 The Hydrogen Molecule-Ion 15012.2 The LCAO Approximation 15312.3 MO Theory of Homonuclear Diatomic Molecules 15412.4 Variational Computation of Molecular Orbitals 15612.5 Heteronuclear Molecules 15813 Polyatomic Molecules and Solids 16013.1 Hückel Molecular Orbital Theory 16013.2 Conservation of Orbital Symmetry;Woodward-Hoffmann Rules 16313.3 Valence-Shell Model 16613.4 Transition Metal Complexes 16813.5 The Hydrogen Bond 17113.6 Proteins and Nucleic Acids 17213.7 Band Theory of Metals and Semiconductors 17514 Molecular Symmetry and Group Theory 17814.1 The Ammonia Molecule 17814.2 Mathematical Theory of Groups 18014.3 Group Theory in Quantum Mechanics 18114.4 Molecular Orbitals for Ammonia 18214.5 Selection Rules 18414.6 TheWater Molecule 18514.7 Walsh Diagrams 18614.8 Molecular Symmetry Groups 18714.9 Dipole Moments and Optical Activity 19215 The Hartree-Fock Method 19415.1 Hartree Self-Consistent Field Theory 19415.2 DeterminantalWavefunctions 19715.3 Hartree-Fock Equations 19915.4 Hartree-Fock Equations using Second Quantization 20315.5 Roothaan Equations 20615.6 Atomic Hartree-Fock Results 21015.7 Electron Correlation 21315.8 Post Hartree-Fock Methods 21416 Density Functional Theory 21716.1 Thomas-Fermi Model 21716.2 The Hohenberg-Kohn Theorems 22116.3 Density Functionals 22216.4 Slater's X-Alpha Method 22316.5 The Kohn-Sham Equations 22416.6 Chemical Potential 22517 Metaphysical Aspects of the Quantum Theory 22717.1 Introduction 22717.2 The Copenhagen Interpretation 22817.3 Superposition 22917.4 Schrödinger's Cat 23017.5 The Einstein-Podolsky-Rosen Experiment 23117.6 Bell's Theorem 23417.7 Conclusion 23618 Quantum Computers 23818.1 Prospects of Quantum Computation 23818.2 Qubits 23918.3 Quantum Gates and Circuits 24018.4 Simulation of a Stern-Gerlach Experiment 24618.5 Quantum Fourier Transform 24718.6 Phase Estimation Algorithm 25018.7 Many-Electron Systems 25218.8 Atomic and Molecular Hamiltonians 25318.9 Time-Evolution of a Quantum System 25618.10 Trotter Expansions 25718.11 Simulations of Molecular Structure 258Bibliography 260Index 261