Quantum Chemistry & 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
A
B
C
D
E
F
G
H
I
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Z