Physical Chemistry

  1. Quantum Chemistry
    1. Historical Development and Experimental Foundations
      1. Black-Body Radiation
        1. Classical Predictions
          1. Planck's Quantum Hypothesis
            1. Planck's Constant
            2. The Photoelectric Effect
              1. Experimental Observations
                1. Einstein's Photon Theory
                  1. Work Function
                  2. Atomic Spectra
                    1. Line Spectra vs Continuous Spectra
                      1. Hydrogen Spectrum
                        1. Rydberg Formula
                          1. Bohr Model
                          2. Wave-Particle Duality
                            1. de Broglie Hypothesis
                              1. Matter Waves
                                1. Experimental Confirmation
                                2. The Heisenberg Uncertainty Principle
                                  1. Position-Momentum Uncertainty
                                    1. Energy-Time Uncertainty
                                      1. Physical Implications
                                    2. Postulates of Quantum Mechanics
                                      1. The Wavefunction
                                        1. Physical Interpretation
                                          1. Born Interpretation
                                            1. Normalization Condition
                                              1. Probability Density
                                              2. Operators in Quantum Mechanics
                                                1. Linear Operators
                                                  1. Hermitian Operators
                                                    1. Commutation Relations
                                                      1. Commutators and Observables
                                                      2. The Schrödinger Equation
                                                        1. Time-Dependent Schrödinger Equation
                                                          1. Time-Independent Schrödinger Equation
                                                            1. Hamiltonian Operator
                                                            2. Eigenvalue Equations
                                                              1. Eigenvalues and Eigenfunctions
                                                                1. Observable Quantities
                                                                  1. Measurement Postulate
                                                                  2. Expectation Values
                                                                    1. Definition and Calculation
                                                                      1. Physical Interpretation
                                                                        1. Variance and Standard Deviation
                                                                        2. Superposition Principle
                                                                          1. Linear Combinations of States
                                                                            1. Measurement and Wavefunction Collapse
                                                                          2. Exactly Solvable Model Systems
                                                                            1. The Free Particle
                                                                              1. Schrödinger Equation Solution
                                                                                1. Plane Wave Solutions
                                                                                  1. Normalization Issues
                                                                                  2. The Particle in a Box
                                                                                    1. One-Dimensional Box
                                                                                      1. Boundary Conditions
                                                                                        1. Energy Quantization
                                                                                          1. Wavefunctions
                                                                                          2. Two-Dimensional Box
                                                                                            1. Separable Solutions
                                                                                              1. Degeneracy
                                                                                              2. Three-Dimensional Box
                                                                                                1. Energy Levels
                                                                                                  1. Degeneracy Patterns
                                                                                                2. The Particle on a Ring
                                                                                                  1. Circular Boundary Conditions
                                                                                                    1. Angular Momentum Quantization
                                                                                                      1. Complex Wavefunctions
                                                                                                      2. Quantum Tunneling
                                                                                                        1. Barrier Penetration
                                                                                                          1. Transmission and Reflection Coefficients
                                                                                                          2. The Quantum Harmonic Oscillator
                                                                                                            1. Schrödinger Equation Solution
                                                                                                              1. Energy Quantization
                                                                                                                1. Zero-Point Energy
                                                                                                                  1. Wavefunctions and Probability Distributions
                                                                                                                    1. Classical vs Quantum Behavior
                                                                                                                    2. The Rigid Rotor
                                                                                                                      1. Spherical Coordinates
                                                                                                                        1. Angular Momentum
                                                                                                                          1. Rotational Energy Levels
                                                                                                                            1. Spherical Harmonics
                                                                                                                          2. The Hydrogen Atom
                                                                                                                            1. Schrödinger Equation in Spherical Coordinates
                                                                                                                              1. Separation of Variables
                                                                                                                                1. Radial and Angular Parts
                                                                                                                                2. Quantum Numbers
                                                                                                                                  1. Principal Quantum Number (n)
                                                                                                                                    1. Orbital Angular Momentum Quantum Number (l)
                                                                                                                                      1. Magnetic Quantum Number (ml)
                                                                                                                                        1. Physical Significance
                                                                                                                                        2. Atomic Orbitals
                                                                                                                                          1. Radial Wavefunctions
                                                                                                                                            1. Angular Wavefunctions (Spherical Harmonics)
                                                                                                                                              1. Orbital Shapes and Nodal Patterns
                                                                                                                                              2. Energy Levels
                                                                                                                                                1. Degeneracy
                                                                                                                                                  1. Comparison with Bohr Model
                                                                                                                                                  2. Electron Spin
                                                                                                                                                    1. Spin Quantum Number (ms)
                                                                                                                                                      1. Spin-Orbit Coupling
                                                                                                                                                        1. Total Angular Momentum
                                                                                                                                                      2. Approximation Methods
                                                                                                                                                        1. The Variational Principle
                                                                                                                                                          1. Variational Theorem
                                                                                                                                                            1. Trial Wavefunctions
                                                                                                                                                              1. Linear Variational Method
                                                                                                                                                                1. Applications to Simple Systems
                                                                                                                                                                2. Perturbation Theory
                                                                                                                                                                  1. Time-Independent Perturbation Theory
                                                                                                                                                                    1. First-Order Corrections
                                                                                                                                                                      1. Second-Order Corrections
                                                                                                                                                                        1. Degenerate Perturbation Theory
                                                                                                                                                                        2. Time-Dependent Perturbation Theory
                                                                                                                                                                          1. Transition Probabilities
                                                                                                                                                                            1. Fermi's Golden Rule
                                                                                                                                                                        3. Multi-Electron Atoms
                                                                                                                                                                          1. The Many-Electron Problem
                                                                                                                                                                            1. Electron-Electron Repulsion
                                                                                                                                                                              1. Inability to Solve Exactly
                                                                                                                                                                              2. The Orbital Approximation
                                                                                                                                                                                1. Independent Particle Model
                                                                                                                                                                                  1. Effective Nuclear Charge
                                                                                                                                                                                  2. Electron Spin and the Pauli Exclusion Principle
                                                                                                                                                                                    1. Antisymmetry Requirement
                                                                                                                                                                                      1. Slater Determinants
                                                                                                                                                                                      2. Electron Configuration
                                                                                                                                                                                        1. Aufbau Principle
                                                                                                                                                                                          1. Hund's Rules
                                                                                                                                                                                          2. Electron Shielding and Penetration
                                                                                                                                                                                            1. Screening Effects
                                                                                                                                                                                              1. Orbital Energies in Multi-Electron Atoms
                                                                                                                                                                                              2. Self-Consistent Field Methods
                                                                                                                                                                                                1. Hartree-Fock Method
                                                                                                                                                                                                  1. Iterative Solution Process
                                                                                                                                                                                                    1. Basis Sets
                                                                                                                                                                                                    2. Atomic Term Symbols
                                                                                                                                                                                                      1. Russell-Saunders Coupling
                                                                                                                                                                                                        1. Ground State Terms
                                                                                                                                                                                                          1. Hund's Rules for Terms
                                                                                                                                                                                                        2. Chemical Bonding and Molecular Structure
                                                                                                                                                                                                          1. The Born-Oppenheimer Approximation
                                                                                                                                                                                                            1. Separation of Nuclear and Electronic Motion
                                                                                                                                                                                                              1. Potential Energy Surfaces
                                                                                                                                                                                                              2. Valence Bond Theory
                                                                                                                                                                                                                1. Electron Pairing
                                                                                                                                                                                                                  1. Hybridization
                                                                                                                                                                                                                    1. sp3 Hybridization
                                                                                                                                                                                                                      1. sp2 Hybridization
                                                                                                                                                                                                                        1. sp Hybridization
                                                                                                                                                                                                                        2. Resonance Theory
                                                                                                                                                                                                                          1. Limitations of VB Theory
                                                                                                                                                                                                                          2. Molecular Orbital Theory
                                                                                                                                                                                                                            1. Linear Combination of Atomic Orbitals (LCAO)
                                                                                                                                                                                                                              1. Bonding and Antibonding Orbitals
                                                                                                                                                                                                                                1. Molecular Orbital Diagrams
                                                                                                                                                                                                                                  1. Homonuclear Diatomic Molecules
                                                                                                                                                                                                                                    1. H2+ Ion
                                                                                                                                                                                                                                      1. H2 Molecule
                                                                                                                                                                                                                                        1. First and Second Period Diatomics
                                                                                                                                                                                                                                        2. Heteronuclear Diatomic Molecules
                                                                                                                                                                                                                                          1. Electronegativity Effects
                                                                                                                                                                                                                                            1. Polar Bonds
                                                                                                                                                                                                                                          2. Extended Systems
                                                                                                                                                                                                                                            1. Hückel Molecular Orbital Theory
                                                                                                                                                                                                                                              1. π-Electron Systems
                                                                                                                                                                                                                                                1. Conjugated Molecules
                                                                                                                                                                                                                                                  1. Aromaticity
                                                                                                                                                                                                                                                  2. Computational Methods
                                                                                                                                                                                                                                                    1. Density Functional Theory (DFT)
                                                                                                                                                                                                                                                      1. Exchange-Correlation Functionals
                                                                                                                                                                                                                                                        1. Basis Set Considerations

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                                                                                                                                                                                                                                                    4. Molecular Spectroscopy