Understanding Physical Chemistry
May 2013, ©2014
Understanding Physical Chemistry takes an innovative approach to teaching this fundamentally important subject, by stressing core ideas such as the entropic forces that drive all chemical processes and the quantum states that dictate the structures and colors of atoms and molecules. This elegant and streamlined textbook (of under 400 pages) aims to instill a deep understanding of physical chemistry by focusing exclusively on those ideas that are deemed to be either too important or too interesting to exclude. These core ideas are demystified by explaining where they come from, why they make sense, and how they may be applied to understanding topics ranging from molecular spectroscopy and chemical reactivity to biological self-assembly and liquid computer simulation strategies. Another unique feature of this groundbreaking textbook is the insight it provides into the scientific discovery process by highlighting the personal perspectives and conceptual struggles of people such as Gibbs, Einstein, and Schrödinger, who pioneered this interesting and practically important field.
1 The Basic Ideas 1
1.1 Things to Keep in Mind 1
1.2 Why Is Energy So Important? 5
1.3 Quantization Is Everywhere 12
1.4 Thermal Energies and Populations 22
1.5 Classical Energy Hyperspheres 35
Homework Problems 43
2 Introduction to Chemical Thermodynamics 49
2.1 What Is Thermodynamics Good For? 49
2.2 The Laws of Thermodynamics 53
2.3 Important Ideal Gas Examples 60
Homework Problems 76
3 Axiomatic Foundations of Thermodynamics 81
3.1 Fundamental Equation and Postulates 81
3.2 Temperature and Thermal Equilibrium 92
3.3 Chemical and Phase Equilibria 94
3.4 Euler and Gibbs-Duhem Relations 103
3.5 Transformed Potential Functions 106
3.6 Other Sorts of Thermodynamic Work 112
Homework Problems 114
4 Thermodynamic Calculation Strategies and Applications 119
4.1 Reduction of Thermodynamic Derivatives 119
4.2 Chemical Reaction Thermodynamics 128
4.3 Self-Assembly Thermodynamics 132
4.4 Spontaneous Consequences 137
Homework Problems 147
5 Nonideal Systems and Computer Simulations 151
5.1 Quantifying Nonidealities 151
5.2 Simple Models of Molecular Fluids 154
5.3 Supermolecule Statistical Mechanics 168
5.4 Mixed Points of View on Entropy 173
5.5 Kirkwood, Widom, and Jarzynski 179
Homework Problems 190
6 Introduction to Quantum Mechanics 195
6.1 The Dawn of Quantum Phenomena 195
6.2 The Rise of Wave Mechanics 196
6.3 Wave Equations and Eigenfunctions 198
6.4 Quantum Operators and Observables 203
6.5 Formal Postulates of Quantum Mechanics 221
Homework Problems 224
7 Simple Systems and Chemical Applications 227
7.1 Free, Confined, and Obstructed Particles 227
7.2 Quantum Harmonic Oscillators 240
7.3 Raising and Lowering Operators 246
7.4 Eigenvectors, Brackets, and Matrices 248
7.5 Three-Dimensional Systems 251
Homework Problems 260
8 Atoms and Spinning Particle-Waves 265
8.1 The Hydrogen Atom 265
8.2 Spin Angular Momentum 272
8.3 Fermi, Bose, and Pauli Exclusion 278
8.4 Multielectron Atoms and the Periodic Table 282
Homework Problems 289
9 Covalent Bonding and Optical Spectroscopy 293
9.1 Covalent Bond Formation 293
9.2 Molecular Bonding Made Easy 304
9.3 Time-Dependent Processes 311
9.4 Optical Spectroscopy 315
9.5 Introduction to Ab Initio Methods 328
Homework Problems 335
10 Chemical and Photon-Molecule Reactions 341
10.1 Gas Phase Reaction Equilibria 341
10.2 Principles of Reaction Dynamics 352
10.3 Prediction of Reaction Rate Constants 355
10.4 Photon-Molecule Reactions 364
Homework Problems 372
A: Answers to Problems That Test Your Understanding 379
B: Fundamental Constants and Mathematical Identities 385
C: Periodic Table 389
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