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CHE 372 |
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I: MATHEMATICAL PRELIMINARIES |
| Operators |
| Operator Algebra |
| Addition and Subtraction of Operators |
| Commutators |
| Linear Operators |
| Eigenfunctions and Eigenvalues |
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II: EARLY QUANTUM THEORY |
| Black-body Radiator |
| The Photoelectric Effect |
| Hydrogen Line Spectra |
| Einstein Explains the Photoelectric Effect |
| The Bohr Model |
| Sommerfeld's Corrections |
| Wave-Particle Duality |
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III. POSTULATES OF QUANTUM MECHANICS |
| The Postulates |
| The Correspondence Principle |
| Normalization |
| The Kinetic Energy Operator |
| Hermitian Operators |
| Principle of Complementarity |
| Uncertainty Relations |
| Orthogonality |
| The Variational Principle |
| The Dirac Delta Function |
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IV. SOLUTIONS TO MODEL PROBLEMS |
| Particle-in-a-1D Box |
| Particle-in-a-3D Box |
| Degeneracy |
| The Rigid Rotor |
| The One-Dimensional Harmonic Oscillator |
| A Variational Calculation for the Particle-in-a-1D Box |
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V. ATOMIC STRUCTURE |
| Solving the Hydrogen Atom Schrodinger Equation |
| Allowed Quantum Numbers |
| Angular Momentum |
| The Hydrogen Atom Wave Functions: Pictures and Equations |
| Orbital Angular Momentum of Hydrogenic Atoms |
| Working with Hydrogen Atom Wave Functions |
| Electron Spin |
| Stern-Gerlach Experiment |
| The Helium Atom |
| Pauli Exclusion Principle |
| Excited States of Helium |
| The Variation Method |
| Hartree-Fock Wave Functions |
| Periodicity and the Aufbau Principle |
| Atomic Term Symbols: The Vector Model of the Atom |
| Hund's Rules |
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VI. CHEMICAL BONDING |
| The Born-Oppenheimer Approximation |
The Hydrogen Molecule Ion ( ) |
| LCAO-MO Variational Approach to
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| LCAO-MO Approach for Homonuclear Diatomics |
| An Aside on Notation |
| MO Energy Diagrams |
| Molecular Electron Configurations |
| Bond Order |
| MO Theory Applied to Heteronuclear Diatomics |
| MO Treatment of Polyatomic Molecules |
| Valence Bond Theory |
| Hybridization |
| Huckel Molecular Orbital Theory |
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VII. MOLECULAR SPECTROSCOPY |
| Electromagnetic Radiation |
| Dipole Moments |
| Selection Rules |
| The Boltzmann Distribution Law |
| The Schrodinger Equation for Nuclear Motion |
| Rotational Spectroscopy of Diatomic Molecules |
| Using the Harmonic Oscillator as a Model |
| Vibrational Spectroscopy of Diatomic Molecules |
| Ro-vibrational Spectroscopy of Diatomic Molecules |
| Rotational Spectroscopy of Nonlinear Molecules |
| What are Normal Coordinates? |
| Normal Modes of Vibration |
| Vibrational Spectroscopy of Polyatomic Molecules |
| Raman Scattering |
| An Overview of Electronic Spectroscopy |
| The Franck-Condon Principle |
| Franck-Condon Factors |
| Oscillator Strength |
| Fluorescence |
| Phosphorescence |
| Jablonski Diagrams |
| Dissociation and the Continuum |
| Predissociation |
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transitions |
| d - d transitions |
| Free Electron Molecular Orbital Theory |
| Determining Dissociation Energies |
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VIII. THE KINETIC THEORY OF GASES |
| Equipartition of Energy |
| Total Energy and Ideal Heat Capacity |
| The Binomial Distribution |
| The Gaussian Distribution |
| The Maxwell-Boltzmann Distribution |
| 1D M-B Velocity Distribution |
| Maxwell-Boltzmann Distribution of Speeds |
| Multidimensional Maxwell-Boltzmann Distributions |
| Types of Average Speeds |
| Specific Fractions of Molecules |
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IX. STATISTICAL MECHANICS |
| The Microscopic State of a System: Small Systems |
| The Microscopic State of a System: Moderate to Large Systems |
| Stirling's Approximation |
| Lagrange's Method of Undetermined Multipliers |
| The Maxwell-Boltzmann Distribution |
| Evaluation of Beta |
| The Molecular Partition Function |
| What is the Partition Function? |
| The Boltzmann Entropy Equation |
| Evaluating the constant beta |
| Connections to Thermodynamics |
| The Canonical Partition Function |
| Distinguishability/Indistinguishability |
| The Third Law of Thermodynamics |
| Residual Entropy |
| Internal Contributions to the Molecular Partition Function |
| The Translational Partition Function |
| The Vibrational Partition Function for Diatomic Molecules |
| The Rotational Partition Function for Diatomic Molecules |
| The Electronic Partition Function |
| Partition Functions for Polyatomic Molecules |
| The Equilibrium Constant |
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X. CHEMICAL KINETICS |
| Empirical Rate Laws |
| Integrated Rate Laws |
| Zeroth Order |
| First Order |
| Second Order |
| Half-Life Relations |
| Temperature Dependence of Reaction Rates |
| Reaction Mechanisms |
| Reversible First-Order Reactions |
| Consecutive First-Order Reactions |
| Collision Theory |
| Potential Energy Surfaces |
| Trajectories on a Potential Energy Surface |
| Activated Complex or Transition State Theory |
| Chain Reactions |
| A Mechanism for Enzyme-Catalyzed Reactions |
| Explosions |
| XI. OTHER STUFF |
| State Vectors |
| Dirac Notation |
| An Introduction to Matrix Mechanics |
| The Operator Approach to the One-Dimensional Harmonic Oscillator |