Physical Chemistry I Course Outline and Homework Problems

· Chapter 1. The Dawn of the Quantum Theory

MathChapter A / Complex Numbers

· Chapter 2. The Classical Wave Equation

MathChapter B / Probability and Statistics

· Chapter 3. The Schrodinger Equation and a Particle In a Box

3-1. The Schrodinger Equation Is the Equation for Finding the Wave Function of a Particle
3-2. Classical-Mechanical Quantities Are Represented by Linear Operators in Quantum Mechanics
3-3. The Schrodinger Equation Can be Formulated as an Eigenvalue Problem
3-4. Wave Functions Have a Probabilistic Interpretation
3-5. The Energy of a Particle in a Box Is Quantized
3-6. Wave Functions Must Be Normalized
3-7. The Average Momentum of a Particle in a Box is Zero
3-8. The Uncertainty Principle Says That sigmapsigmax>h/2
3-9. The Problem of a Particle in a Three-Dimensional Box is a Simple Extension of the One-Dimensional Case

Problems 1, 2, 3, 7, 10, 11, 17, 22, 27, 28, 29, 34

MathChapter C / Vectors

· Chapter 4. Some Postulates and General Principles of Quantum Mechanics

4-1. The State of a System Is Completely Specified by its Wave Function
4-2. Quantum-Mechanical Operators Represent Classical-Mechanical Variables
4-3. Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators
4-4. The Time Dependence of Wave Functions Is Governed by the Time-Dependent Schrodinger Equation
4-5. The Eigenfunctions of Quantum Mechanical Operators Are Orthogonal
4-6. The Physical Quantities Corresponding to Operators That Commute Can Be Measured Simultaneously to Any Precision

Problems 1, 3, 4, 5, 8, 10, 11, 16, 19, 33, 35, 38

MathChapter D / Spherical Coordinates

· Chapter 5. The Harmonic Oscillator and the Rigid Rotator : Two Spectroscopic Models

5-1. A Harmonic Oscillator Obeys Hooke's Law
5-2. The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the Reduced Mass of the Molecule
5-3. The Harmonic-Oscillator Approximation Results from the Expansion of an Internuclear Potential Around its Minimum
5-4. The Energy Levels of a Quantum-Mechanical Harmonic Oscillator Are Ev = hw(v + 1/2) with v= 0,1,2...
5-5. The Harmonic Oscillator Accounts for the Infrared Spectrum of a Diatomic Molecule
5-6. The Harmonic-Oscillator Wave Functions Involve Hermite Polynomials
5-7. Hermite Polynomials Are Either Even or Odd Functions
5-8. The Energy Levels of a Rigid Rotator Are E = h 2J(J+1)/2I
5-9. The Rigid Rotator Is a Model for a Rotating Diatomic Molecule

Problems 4, 5, 7, 13, 14, 18, 19, 21, 25, 37, 45, 47

· Chapter 6. The Hydrogen Atom

6-1. The Schrodinger Equation for the Hydrogen Atom Can Be Solved Exactly
6-2. The Wave Functions of a Rigid Rotator Are Called Spherical Harmonics
6-3. The Precise Values of the Three Components of Angular Momentum Cannot Be Measured Simultaneously
6-4. Hydrogen Atomic Orbitals Depend upon Three Quantum Numbers
6-5. s Orbitals Are Spherically Symmetric
6-6. There Are Three p Orbitals for Each Value of the Principle Quantum Number, n>= 2
6-7. The Schrodinger Equation for the Helium Atom Cannot Be Solved Exactly

Problems 1, 4, 10, 17, 18, 20, 22, 24, 26, 34, 46, 47

MathChapter E / Determinants

· Chapter 7. Approximation Methods

7-1. The Variational Method Provides an Upper Bound to the Ground-State Energy of a System
7-2. A Trial Function That Depends Linearly on the Variational Parameters Leads to a Secular Determinant
7-3. Trial Functions Can Be Linear Combinations of Functions That Also Contain Variational Parameters
7-4. Perturbation Theory Expresses the Solution to One Problem in Terms of Another Problem Solved Previously

Problems 2, 3, 7, 8, 11, 15, 18, 20, 21, 24, 28, 29

· Chapter 8. Multielectron Atoms

8-1. Atomic and Molecular Calculations Are Expressed in Atomic Units
8-2. Both Pertubation Theory and the Variational Method Can Yield Excellent Results for Helium
8-3. Hartree-Fock Equations Are Solved by the Self-Consistent Field Method
8-4. An Electron Has An Intrinsic Spin Angular Momentum
8-5. Wave Functions Must Be Antisymmetric in the Interchange of Any Two Electrons
8-6. Antisymmetric Wave Functions Can Be Represented by Slater Determinants
8-7. Hartree-Fock Calculations Give Good Agreement with Experimental Data
8-8. A Term Symbol Gives a Detailed Description of an Electron Configuration
8-9. The Allowed Values of J are L+S, L+S-1, .....,|L-S|
8-10. Hund's Rules Are Used to Determine the Term Symbol of the Ground Electronic State
8-11. Atomic Term Symbols Are Used to Describe Atomic Spectra

Problems 1, 3, 5, 10, 19, 22, 26, 28, 30, 31, 39, 47

9-1. The Born-Oppenheimer Approximation Simplifies the Schrodinger Equation for Molecules
9-2. H2+ Is the Prototypical Species of Molecular-Orbital Theory
9-3. The Overlap Integral Is a Quantitative Measure of the Overlap of Atomic Orbitals Situated on Different Atoms
9-4. The Stability of a Chemical Bond Is a Quantum-Mechanical Effect
9-5. The Simplest Molecular Orbital Treatment of H2+ Yields a Bonding Orbital and an Antibonding Orbital
9-6. A Simple Molecular-Orbital Treatment of H2 Places Both Electrons in a Bonding Orbital
9-7. Molecular Orbitals Can Be Ordered According to Their Energies
9-8. Molecular-Orbital Theory Predicts that a Stable Diatomic Helium Molecule Does Not Exist
9-9. Electrons Are Placed into Moleular Orbitals in Accord with the Pauli Exclusion Principle
9-10. Molecular-Orbital Theory Correctly Predicts that Oxygen Molecules Are Paramagnetic
9-11. Photoelectron Spectra Support the Existence of Molecular Orbitals
9-12. Molecular-Orbital Theory Also Applies to Heteronuclear Diatomic Molecules
9-13. An SCF-LCAO-MO Wave Function Is a Molecular Orbital Formed from a Linear Combination of Atomic Orbitals and Whose Coefficients Are Determined Self-Consistently
9-14. Electronic States of Molecules Are Designated by Molecular Term Symbols
9-15. Molecular Term Symbols Designate the Symmetry Properties of Molecular Wave Functions
9-16. Most Molecules Have Excited Electronic States

Problems 1, 2, 8, 9, 12, 13, 14, 19, 25, 26, 32, 40

10-1. Hybrid Orbitals Account for Molecular Shape
10-2. Different Hybrid Orbitals Are Used for the Bonding Electrons and the Lone Pair Electrons in Water
10-3. Why is BeH2 Linear and H2O Bent?
10-4. Photoelectron Spectroscopy Can Be Used to Study Molecular Orbitals
10-5. Conjugated Hydrocarbons and Aromatic Hydrocarbons Can Be Treated by a Pi-Electron Approximation
10-6. Butadiene is Stabilized by a Delocalization Energy

Problems 1, 2, 5, 7, 8, 10, 19, 21, 31, 32, 37, 47

· Chapter 12. Group Theory : The Exploitation of Symmetry

12-1. The Exploitation of the Symmetry of a Molecule Can Be Used to Significantly Simplify Numerical Calculations
12-2. The Symmetry of Molecules Can Be Described by a Set of Symmetry Elements
12-3. The Symmetry Operations of a Molecule Form a Group
12-4. Symmetry Operations Can Be Represented by Matrices
12-5. The C3V Point Group Has a Two-Dimenstional Irreducible Representation
12-6. The Most Important Summary of the Properties of a Point Group Is Its Character Table
12-7. Several Mathematical Relations Involve the Characters of Irreducible Representations
12-8. We Use Symmetry Arguments to Prediect Which Elements in a Secular Determinant Equal Zero
12-9. Generating Operators Are Used to Find Linear Combinations of Atomic Orbitals That Are Bases for Irreducible Representations

Problems 1, 2, 3, 4, 9, 11, 14, 18, 24, 27, 31, 36

· Chapter 13. Molecular Spectroscopy

13-1. Different Regions of the Electromagnetic Spectrum Are Used to Investigate Different Molecular Processes
13-2. Rotational Transitions Accompany Vibrational Transitions
13-3. Vibration-Rotation Interaction Accounts for the Unequal Spacing of the Lines in the P and R Branches of a Vibration-Rotation Spectrum
13-4. The Lines in a Pure Rotational Spectrum Are Not Equally Spaced
13-5. Overtones Are Observed in Vibrational Spectra
13-6. Electronic Spectra Contain Electronic, Vibrational, and Rotational Information
13-7. The Franck-Condon Principle Predicts the Relative Intensities of Vibronic Transitions
13-8. The Rotational Spectrum of a Polyatomic Molecule Depends Upon the Principal Moments of Inertia of the Molecule
13-9. The Vibrations of Polyatomic Molecules Are Represented by Normal Coordinates
13-10. Normal Coordinates Belong to Irreducible Representation of Molecular Point Groups
13-11. Selection Rules Are Derived from Time-Dependent Perturbation Theory
13-12. The Selection Rule in the Rigid Rotator Approximation Is Delta J = (plus or minus) 1
13-13. The Harmonic-Oscillator Selection Rule Is Delta v = (plus or minus) 1
13-14. Group Theory Is Used to Determine the Infrared Activity of Normal Coordinate Vibrations

Problems 1, 2, 3, 7, 11, 12, 14, 16, 20, 27, 38, 49