Quantum chemistry and spectroscopy

Cover
Title Page
Copyright Page
About the Author
Acknowledgments
CONTENTS
PREFACE
1 From Classical to Quantum Mechanics
	1.1 Why Study Quantum Mechanics?
	1.2 Quantum Mechanics Arose out of the Interplay of Experiments and Theory
	1.3 Blackbody Radiation
	1.4 The Photoelectric Effect
	1.5 Particles Exhibit Wave-Like Behavior
	1.6 Diffraction by a Double Slit
	1.7 Atomic Spectra and the Bohr Model of the Hydrogen Atom
2 The Schrödinger Equation
	2.1 What Determines If a System Needs to Be Described Using Quantum Mechanics?
	2.2 Classical Waves and the Nondispersive Wave Equation
	2.3 Waves Are Conveniently Represented as Complex Functions
	2.4 Quantum Mechanical Waves and the Schrödinger Equation
	2.5 Solving the Schrödinger Equation: Operators, Observables, Eigenfunctions, and Eigenvalues
	2.6 The Eigenfunctions of a Quantum Mechanical Operator Are Orthogonal
	2.7 The Eigenfunctions of a Quantum Mechanical Operator Form a Complete Set
	2.8 Summing Up the New Concepts
3 The Quantum Mechanical Postulates
	3.1 The Physical Meaning Associated with the Wave Function Is Probability
	3.2 Every Observable Has a Corresponding Operator
	3.3 The Result of an Individual Measurement
	3.4 The Expectation Value
	3.5 The Evolution in Time of a Quantum Mechanical System
	3.6 Do Superposition Wave Functions Really Exist?
4 Using Quantum Mechanics on Simple Systems
	4.1 The Free Particle
	4.2 The Particle in a One-Dimensional Box
	4.3 Two- and Three-Dimensional Boxes
	4.4 Using the Postulates to Understand the Particle in the Box and Vice Versa
5 The Particle in the Box and the Real World
	5.1 The Particle in the Finite Depth Box
	5.2 Differences in Overlap between Core and Valence Electrons
	5.3 Pi Electrons in Conjugated Molecules Can Be Treated as Moving Freely in a Box
	5.4 Why Does Sodium Conduct Electricity and Why Is Diamond an Insulator?
	5.5 Traveling Waves and Potential Energy Barriers
	5.6 Tunneling through a Barrier
	5.7 The Scanning Tunneling Microscope and the Atomic Force Microscope
	5.8 Tunneling in Chemical Reactions
	5.9 (Supplemental) Quantum Wells and Quantum Dots
6 Commuting and Noncommuting Operators and the Surprising Consequences of Entanglement
	6.1 Commutation Relations
	6.2 The Stern–Gerlach Experiment
	6.3 The Heisenberg Uncertainty Principle
	6.4 (Supplemental) The Heisenberg Uncertainty Principle Expressed in Terms of Standard Deviations
	6.5 (Supplemental) A Thought Experiment Using a Particle in a Three-Dimensional Box
	6.6 (Supplemental) Entangled States, Teleportation, and Quantum Computers
7 A Quantum Mechanical Model for the Vibration and Rotation of Molecules
	7.1 The Classical Harmonic Oscillator
	7.2 Angular Motion and the Classical Rigid Rotor
	7.3 The Quantum Mechanical Harmonic Oscillator
	7.4 Quantum Mechanical Rotation in Two Dimensions
	7.5 Quantum Mechanical Rotation in Three Dimensions
	7.6 The Quantization of Angular Momentum
	7.7 The Spherical Harmonic Functions
	7.8 Spatial Quantization
8 The Vibrational and Rotational Spectroscopy of Diatomic Molecules
	8.1 An Introduction to Spectroscopy
	8.2 Absorption, Spontaneous Emission, and Stimulated Emission
	8.3 An Introduction to Vibrational Spectroscopy
	8.4 The Origin of Selection Rules
	8.5 Infrared Absorption Spectroscopy
	8.6 Rotational Spectroscopy
	8.7 (Supplemental) Fourier Transform Infrared Spectroscopy
	8.8 (Supplemental) Raman Spectroscopy
	8.9 (Supplemental) How Does the Transition Rate between States Depend on Frequency?
9 The Hydrogen Atom
	9.1 Formulating the Schrödinger Equation
	9.2 Solving the Schrödinger Equation for the Hydrogen Atom
	9.3 Eigenvalues and Eigenfunctions for the Total Energy
	9.4 The Hydrogen Atom Orbitals
	9.5 The Radial Probability Distribution Function
	9.6 The Validity of the Shell Model of an Atom
10 Many-Electron Atoms
	10.1 Helium: The Smallest Many-Electron Atom
	10.2 Introducing Electron Spin
	10.3 Wave Functions Must Reflect the Indistinguishability of Electrons
	10.4 Using the Variational Method to Solve the Schrödinger Equation
	10.5 The Hartree–Fock Self-Consistent Field Method
	10.6 Understanding Trends in the Periodic Table from Hartree–Fock Calculations
11 Quantum States for Many-Electron Atoms and Atomic Spectroscopy
	11.1 Good Quantum Numbers, Terms, Levels, and States
	11.2 The Energy of a Configuration Depends on Both Orbital and Spin Angular Momentum
	11.3 Spin-Orbit Coupling Breaks Up a Term into Levels
	11.4 The Essentials of Atomic Spectroscopy
	11.5 Analytical Techniques Based on Atomic Spectroscopy
	11.6 The Doppler Effect
	11.7 The Helium-Neon Laser
	11.8 Laser Isotope Separation
	11.9 Auger Electron and X-Ray Photoelectron Spectroscopies
	11.10 Selective Chemistry of Excited States: O([sup(3)]P) and O([sup(1)]D)
	11.11 (Supplemental) Configurations with Paired and Unpaired Electron Spins Differ in Energy
12 The Chemical Bond in Diatomic Molecules
	12.1 Generating Molecular Orbitals from Atomic Orbitals
	12.2 The Simplest One-Electron Molecule: H[sub(2)][sup(+)]
	12.3 The Energy Corresponding to the H[sub(2)][sup(+)] Molecular Wave Functions ψ[sub(g)] and ψ[sub(u)]
	12.4 A Closer Look at the H[sub(2)][sup(+)] Molecular Wave Functions ψ[sub(g)] and ψ[sub(u)]
	12.5 Homonuclear Diatomic Molecules
	12.6 The Electronic Structure of Many-Electron Molecules
	12.7 Bond Order, Bond Energy, and Bond Length
	12.8 Heteronuclear Diatomic Molecules
	12.9 The Molecular Electrostatic Potential
13 Molecular Structure and Energy Levels for Polyatomic Molecules
	13.1 Lewis Structures and the VSEPR Model
	13.2 Describing Localized Bonds Using Hybridization for Methane, Ethene, and Ethyne
	13.3 Constructing Hybrid Orbitals for Nonequivalent Ligands
	13.4 Using Hybridization to Describe Chemical Bonding
	13.5 Predicting Molecular Structure Using Qualitative Molecular Orbital Theory
	13.6 How Different Are Localized and Delocalized Bonding Models?
	13.7 Molecular Structure and Energy Levels from Computational Chemistry
	13.8 Qualitative Molecular Orbital Theory for Conjugated and Aromatic Molecules: The Hückel Mode
	13.9 From Molecules to Solids
	13.10 Making Semiconductors Conductive at Room Temperature
14 Electronic Spectroscopy
	14.1 The Energy of Electronic Transitions
	14.2 Molecular Term Symbols
	14.3 Transitions between Electronic States of Diatomic Molecules
	14.4 The Vibrational Fine Structure of Electronic Transitions in Diatomic Molecules
	14.5 UV-Visible Light Absorption in Polyatomic Molecules
	14.6 Transitions among the Ground and Excited States
	14.7 Singlet–Singlet Transitions: Absorption and Fluorescence
	14.8 Intersystem Crossing and Phosphorescence
	14.9 Fluorescence Spectroscopy and Analytical Chemistry
	14.10 Ultraviolet Photoelectron Spectroscopy
	14.11 Single Molecule Spectroscopy
	14.12 Fluorescent Resonance Energy Transfer (FRET)
	14.13 Linear and Circular Dichroism
	14.14 Assigning + and – to Σ Terms of Diatomic Molecules
15 Computational Chemistry
	15.1 The Promise of Computational Chemistry
	15.2 Potential Energy Surfaces
	15.3 Hartree–Fock Molecular Orbital Theory: A Direct Descendant of the Schrödinger Equation
	15.4 Properties of Limiting Hartree–Fock Models
	15.5 Theoretical Models and Theoretical Model Chemistry
	15.6 Moving Beyond Hartree–Fock Theory
	15.7 Gaussian Basis Sets
	15.8 Selection of a Theoretical Model
	15.9 Graphical Models
	15.10 Conclusion
16 Molecular Symmetry
	16.1 Symmetry Elements, Symmetry Operations, and Point Groups
	16.2 Assigning Molecules to Point Groups
	16.3 The H[sub(2)]O Molecule and the C[sub(2v)] Point Group
	16.4 Representations of Symmetry Operators, Bases for Representations, and the Character Table
	16.5 The Dimension of a Representation
	16.6 Using the C[sub(2v)] Representations to Construct Molecular Orbitals for H[sub(2)]O
	16.7 The Symmetries of the Normal Modes of Vibration of Molecules
	16.8 Selection Rules and Infrared versus Raman Activity
	16.9 (Supplemental) Using the Projection Operator Method to Generate MOs That Are Bases for Irreducible Representations
17 Nuclear Magnetic Resonance Spectroscopy
	17.1 Intrinsic Nuclear Angular Momentum and Magnetic Moment
	17.2 The Energy of Nuclei of Nonzero Nuclear Spin in a Magnetic Field
	17.3 The Chemical Shift for an Isolated Atom
	17.4 The Chemical Shift for an Atom Embedded in a Molecule
	17.5 Electronegativity of Neighboring Groups and Chemical Shifts
	17.6 Magnetic Fields of Neighboring Groups and Chemical Shifts
	17.7 Multiplet Splitting of NMR Peaks Arises through Spin–Spin Coupling
	17.8 Multiplet Splitting When More Than Two Spins Interact
	17.9 Peak Widths in NMR Spectroscopy
	17.10 Solid-State NMR
	17.11 NMR Imaging
	17.12 (Supplemental)The NMR Experiment in the Laboratory and Rotating Frames
	17.13 (Supplemental) Fourier Transform NMR Spectroscopy
	17.14 (Supplemental) Two-Dimensional NMR
APPENDIX A: Math Supplement
APPENDIX B: Point Group Character Tables
APPENDIX C: Answers to Selected End-of-Chapter Problems
CREDITS
INDEX
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