Physical Chemistry II
Purpose of Course showclose
Physical Chemistry II is quite different from Physical Chemistry I. In this second semester of the Physical Chemistry course, you will study the principles and laws of quantum mechanics as well as the interaction between matter and electromagnetic waves. During the late 19th century and early 20th century, scientists opened new frontiers in the understanding of matter at the molecular, atomic, and subatomic scale. These studies resulted in the development of quantum physics, which nowadays is still considered one of the greatest achievements of human mind. While present day quantum physics “zooms in” to look at subatomic particles, quantum chemistry “zooms out” to look at large molecular systems in order to theoretically understand their physical and chemical properties. Quantum chemistry has created certain “tools” (or computational methods) based on the laws of quantum mechanics that make it theoretically possible to understand how electrons and atomic nuclei interact with each other to form any kind of matter, ranging from diamond crystals to DNA strands to proteins to plastic polymers. Using these tools, quantum chemists can simulate complex biological systems, such as nucleic acids, proteins, and even cells, in order to understand their functions and behavior. These tools are increasingly used by researchers at pharmaceutical companies as they need to simulate the interaction of a potential drug molecule with the target receptor, such as a protein binding pocket on the surface of a cell. Scientists use computational tools of quantum chemistry to predict the optical and electronic properties of novel materials to be used in advanced technologies, such as organic photovoltaics (OPVs) for solar energy harvesting and organic light emitting diodes (OLEDs) for electronic displays. In these applications, scientists can “calculate” the range of sunlight frequencies a certain material can absorb or the color of the emitted light in a pixel fabricated using certain molecules. Quantum chemistry treats light as both a wave and a particle and uses wavefunctions to describe systems composed by “tangible” matter, such as electrons and nuclei. A substantial portion of the course is dedicated to the theoretical understanding of the interactions between light (electromagnetic radiations) and matter (molecules, electrons, nuclei, etc.). These interactions are at the base of modern image techniques used in the medical field, such as magnetic resonance imaging (MRI).
This senior course in quantum chemistry usually serves as an introduction to more advanced graduate courses in theoretical chemistry, rather than concluding your degree in chemistry. With the knowledge gained in this course, you will be able to calculate the energies of simple systems, such as small molecules. Keep in mind that these calculations of quantum chemistry are fairly complicated, thus you will learn several approximation techniques to aid your calculations of more advanced molecular systems. You will also be able to correlate the outcome of your calculation to certain physical properties of the molecule. In particular, you will learn how the spectroscopy properties are strictly interconnected with the electronic structure of molecules.
Course Information showclose
Primary Resources: This course is comprised of a range of different free, online materials. However, the course makes primary use of the following materials:
 Everyscience.com
 Macquarie University: Professor James Cresser’s “Lecture Notes”
 Boston University: Professor Dan Dill’s “Lecture Notes”
 Southern Methodist University: Professor Werner Horsthemke’s “Physical Chemistry II Lecture Notes”
 Concordia College: Professor Darin J. Ulness’s “Old Course Notes”
 The Final Exam
In order to “pass” this course, you will need to earn a 70% or higher on the Final Exam. Your score on the exam will be tabulated as soon as you complete it. If you do not pass the exam, you may take it again.
Time Commitment: This course should take you a total of 124.5 hours to complete. Each unit includes a “time advisory” that lists the amount of time you are expected to spend on each subunit. These should help you plan your time accordingly. It may be useful to take a look at these time advisories and determine how much time you have over the next few weeks to complete each unit and then set goals for yourself. For example, Unit 1 should take you 18 hours. Perhaps you can sit down with your calendar and decide to complete subunit 1.1 (a total of 4 hours) on Monday night, subunit 1.2 (a total of 4 hours) on Tuesday night, and so forth.
Tips/Suggestions: As noted in the “Course Requirements,” multivariable calculus (MA103) is a prerequisite for this course. If you are struggling with the mathematics as you progress through this course, consider taking a break to revisit MA103.
As you work through the resources in this course, take careful notes and mark down any important equations, formulas, and definitions that stand out to you. These notes will serve as a useful review as you prepare for your Final Exam.
Learning Outcomes showclose
 Describe the difference between classical and quantum mechanics.
 Explain the failure of classical mechanics in elucidating the black body radiation, the photoelectric effect, and atomic emission spectra.
 Define the waveparticle duality.
 Define the uncertainty principle.
 Solve the Hamiltonian for a particle in box, on a ring, and on a sphere.
 Solve the Schrodinger equation for hydrogenlike systems.
 Use technique of approximation to compute the Schrodinger equation for polyatomic systems.
 Describe the difference between the Valence Bond and the Molecular Orbital Theories.
 Identify the symmetry elements in a molecule.
 Predict and explain the outcome of electromagnetic radiations interacting with matter.
 Define Raman spectroscopy.
 Predict the vibrational spectra of molecules based on their electronic structure.
 Explain the selection rules for a molecule to be Raman or IR active.
 Explain the difference between fluorescence and phosphorescence.
 Describe the principle of operation of LASERs.
 Explain the effect of magnetic fields on electrons and nuclei.
Course Requirements showclose
√ Have access to a computer.
√ Have continuous broadband Internet access.
√ Have the ability/permission to install plugins (e.g., Adobe Reader or Flash) and software.
√ Have the ability to download and save files and documents to a computer.
√ Have the ability to open Microsoft Office files and documents (.doc, .ppt, .xls, etc.).
√ Have competency in the English language.
√ Have read the Saylor Student Handbook.
√ Have strong skills in mathematics. Knowledge of using computational software, such as MatLab or Mathematica, will greatly facilitate your work and learning.
√ Have completed the following mathematics courses: multivariable calculus (MA103), linear algebra (MA211), and differential equations (MA221). Physical Chemistry I (CHEM105) is conceptually very different from Physical Chemistry II (this course), and the scientific concepts learned in Physical Chemistry I are not necessary to understand Physical Chemistry II. However, it is highly recommended that you take CHEM105 first, so you can master the use of multivariable calculus (partial derivatives) to solve chemistry problems. Another important prerequisite that some students in college take is calculusbased PhysicsClassical Mechanics; the Saylor Foundation offers the algebrabased equivalent of such a course: PHYS101. Engineering courses such as ME102/ME202 could complement PHYS101.
Unit Outline show close
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Unit 1: Origins of Quantum Theory
Quantum mechanics originated in the late nineteenth century, when classical physics dramatically failed to explain certain experimental results. The three main experimental observations that could not be explained by classical physics include phenomena related to the blackbody radiation, the photoelectric effect, and the emission of atomic spectra. Although physicists initially tried to patch up classical theory, it gradually became clear that new ideas were necessary. In this unit, you will learn in details about the origins of quantum mechanics.
Unit 1 Time Advisory show close
Unit 1 Learning Outcomes show close

1.1 Mathematical Review for Physical Chemistry
 Reading: Washington State University: Professor Kirk Peterson’s “Chem 332: Physical Chemistry II”
Link: Washington State University: Professor Kirk Peterson’s “Chem 332: Physical Chemistry II” (PDF)
Instructions: Please click on the link above, and scroll down to the bottom of the webpage to the “Class Resources” heading. Select the “mini PChem math review” link to download the PDF file, and read the entire document (8 pages). Review these mathematical methods useful to solve problems in Physical Chemistry. Reading and taking notes on this text should take approximately 4 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Washington State University: Professor Kirk Peterson’s “Chem 332: Physical Chemistry II”

1.2 Mathematical Concepts in Quantum Mechanics
 Reading: Everyscience.com’s “Principles of Quantum Mechanics”
Link: Everyscience.com’s “Principles of Quantum Mechanics” (HTML)
Instructions: Please click on the link above, and read this entire webpage, which provides mathematical tool useful to solve quantum mechanical problems. Studying this resource should take approximately 2 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Assessment 1”
Link: The Saylor Foundation’s “Assessment 1” (DOC)
Instructions: Complete the attached assessment questions to check your understanding of the material covered thus far. Once you have completed the assessment, you may check your answers against the “Answer Key” (DOC).
Completing this assessment should take approximately 1 hour.
 Reading: Everyscience.com’s “Principles of Quantum Mechanics”

1.3 Review of Classical Mechanics
 Web Media: YouTube: Stanford University: Leonard Susskind’s “Lecture 1  Modern Physics: Classical Mechanics”
Link: YouTube: Stanford University: Leonard Susskind’s “Lecture 1  Modern Physics: Classical Mechanics” (YouTube)
Instructions: Please click on the link above, and watch the entire video. This lecture provides a good review of classical mechanics. Studying this resource should take approximately 1 hour to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Rochester Institute of Technology: Professor Michael Richmond’s “Review of Classical Mechanics”
Link: Rochester Institute of Technology: Professor Michael Richmond’s “Review of Classical Mechanics” (HTML)
Instructions: Please click on the link above, and read the entire webpage. This subunit is meant to be a quick review of classical mechanics concepts. These concepts have been explained in detail in PHYS101 (algebrabased). Studying this resource should take approximately 1 hour to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Web Media: YouTube: Stanford University: Leonard Susskind’s “Lecture 1  Modern Physics: Classical Mechanics”

1.4 The Failure of Classical Physics and the Origins of Quantum Mechanics
 Reading: Macquarie University: Professor James Cresser’s “The Early History of Quantum Mechanics” Lecture Notes
Link: Macquarie University: Professor James Cresser’s “The Early History of Quantum Mechanics” Lecture Notes (PDF)
Instructions: Please click on the link and select “Ch2: The Early History of Quantum Mechanics” to access the PDF file of the lecture notes. While reading the material, take notes repeating the mathematical derivation of the Plank’s constant. Professor Cresser’s notes provide an historical background on the origins of quantum mechanics. Studying this resource should take approximately 0.75 hours to complete. Note that this reading covers the material you need to know for subunit 1.4.4.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Weber State University: Professor Bradley W. Carroll’s “Three Failures of Classical Physics”
Link: Weber State University: Professor Bradley W. Carroll’s “Three Failures of Classical Physics” (HTML)
Instructions: Please click on the link and read the entire webpage. Make sure you understand why classical mechanics was inadequate at explaining certain experimental observations, that is, why electrons do not fall into the nucleus of an atom, and so forth. Studying this resource should take approximately 1.25 hours to complete. Note that this reading covers the material you need to know for subunits 1.4.1–1.4.4.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Macquarie University: Professor James Cresser’s “The Early History of Quantum Mechanics” Lecture Notes

1.4.1 Blackbody Radiation and the Ultraviolet Catastrophe
Note: This subunit is covered by the readings assigned beneath subunit 1.4. In particular, please focus on Section 1 of Professor Carroll’s “Three Failures of Classical Physics” to learn about blackbody radiation.

1.4.2 The Photoelectric Effect
Note: This topic is covered by the reading assigned beneath subunit 1.4. Please review Section 2 of Professor Carroll’s “Three Failures of Classical Physics” to learn about the photoelectric effect.

1.4.3 Atomic Spectra
Note: This topic is covered by the reading assigned beneath subunit 1.4. Please review Section 3 of Professor Carroll’s “Three Failures of Classical Physics” to learn about the inability of classical physics to explain the emission spectra of the hydrogen atom.

1.4.4 Historical Background of Quantum Mechanics
Note: This topic is covered by the reading assigned beneath subunit 1.4. Please review Professor James Cresser’s “The Early History of Quantum Mechanics” Lecture Notes for a narrative of the experimental work that led to quantum theory.

1.5 The WaveParticle Duality
 Reading: Morningside College: Dave Slaven’s “WaveParticle Duality: Light,” “WaveParticle Duality: Electrons,” “The Meaning of the Wave,” and “From Many Waves, One”
Link: Morningside College: Dave Slaven’s “WaveParticle Duality: Light”, “WaveParticle Duality: Electrons”, “The Meaning of the Wave”, and “From Many Waves, One” (HTML)
Instructions: Please click on the links above, and read these four webpages. While studying this resource, pay close attention to the mathematical model of a single wave and a wave packet, and understand the relationship among momentum, energy, and frequency in waves. These resources provide a full overview of the waveparticle duality: how electrons behave like waves and how waves have “matter” properties. Studying these resources should take approximately 2.5 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Web Media: YouTube: Adam Beatty’s “Wave Particle Duality”
Link: YouTube: Adam Beatty's “Wave Particle Duality” (YouTube)
Instructions: Please click on the link above, and watch the entire video. This resource provides a recorded explanation of the waveparticle duality: how electrons behave like waves and how waves have “matter” properties. Studying this resource should take approximately 0.5 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Morningside College: Dave Slaven’s “WaveParticle Duality: Light,” “WaveParticle Duality: Electrons,” “The Meaning of the Wave,” and “From Many Waves, One”

1.6 The de Broglie Wavelength
 Reading: University of California, Davis: UC Davis ChemWiki’s “De Broglie Wavelength”
Link: University of California, Davis: UC Davis Chemwiki’s “De Broglie Wavelength” (HTML)
Instructions: Clicking on the above link opens the resource webpage. While reading this resource, repeat the mathematical derivation of the De Broglie equation. This resource shows you the derivation of the De Broglie equation from Einstein’s equation and Plank’s equation. Studying this resource should take approximately 0.50 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Web Media: YouTube: Physics Academy’s “Quantum Mechanics 006: The de Broglie Wavelength”
Link: YouTube: Physics Academy’s “Quantum Mechanics 006: The de Broglie Wavelength” (YouTube)
Instructions: By clicking on the above link to access a video showing the derivation of the De Broglie equation. While watching the video, repeat the derivation on your own. Studying this resource should take approximately 0.5 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Assessment 2”
Link: The Saylor Foundation’s “Assessment 2” (DOC)
Instructions: Complete the attached assessment questions to check your understanding of the material covered thus far. Once you have completed the assessment, you may check your answers against the “Answer Key” (DOC).
Completing this assessment should take approximately 1 hour.
 Reading: University of California, Davis: UC Davis ChemWiki’s “De Broglie Wavelength”

Unit 2: Principles of Quantum Theory
In the classical world, Newton’s laws and laws of conservation of energy are used daily to predict the outcome of certain events. For instance, the trajectory of a cannonball can be predicted with good accuracy, given certain parameters such as the shooting angle, mass of the cannonball, air resistance, and so forth. In the world of quantum mechanics, where objects possess very small masses and move at high speeds, the Schrodinger equation is used to predict the behavior of a system comprised of quantum mechanical particles (electrons, nuclei, etc.). Unlikely in classical mechanics, where the outcomes of the calculations are undoubtedly clear (for instance, the cannon ball will hit the ground at a precise coordinate point), the results of the Schrodinger equation gives the probability of an event to occur. In the quantum world, for a given set of parameters, a large number of events can occur, and the Schrodinger equation will predict the probability that such events will happen, given a distribution of results rather than a single answer. In this unit, you will encounter the Schrodinger equation for the first time.
Unit 2 Time Advisory show close
Unit 2 Learning Outcomes show close

2.1 Fundamental Postulates of Quantum Mechanics
 Reading: Washington State University: Professor Kirk Peterson’s “Chem 332: Physical Chemistry II”
Link: Washington State University: Professor Kirk Peterson’s “Chem 332: Physical Chemistry II” (PDF)
Instructions: To access Professor Peterson’s resources, click on the link and scroll down to the bottom of the webpage to the “Class Recourses” heading. Select the “Postulates of Quantum Mechanics” link to open the PDF file, and read and learn about these postulates. Make sure you understand the “practical” meaning of these equations, that is, why the wavefunction of a quantum mechanical system is normalized, and so forth. These postulates constitute the base of quantum mechanical problems and calculations. Studying this resource should take approximately 1 hour to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Georgia Institute of Technology: Professor David Sherrill’s “Postulates of Quantum Mechanics”
Link: Georgia Institute of Technology: Professor David Sherrill’s “Postulates of Quantum Mechanics” (HTML)
Instructions: Please click on the link to access Professor Sherrill’s resource, and read the entire webpage. Make sure you understand the “practical” meaning of these equations, that is, which physical observables (momentum, kinetic energy, etc.) are associated with Hermitian operators, and so forth. These postulates constitute the base of quantum mechanical problems and calculations. Studying this resource should take approximately 1 hour to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: YouTube: Dony Lee’s “QM0.1: Postulates of Quantum Mechanics”
Link: YouTube: Dony Lee’s “QM0.1: Postulates of Quantum Mechanics” (YouTube)
Instructions: Please click on the link above, and watch the brief video lecture. This video covers the fundamental postulates of quantum mechanics; as for the above readings, make sure you understand the “practical” meaning of these equations and how they are used in quantum mechanical calculations. Studying this resource should take approximately 0.5 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Washington State University: Professor Kirk Peterson’s “Chem 332: Physical Chemistry II”

2.2 The Schrodinger Equation
 Reading: Everyscience.com’s “The One Dimensional Schrodinger Equation”
Links: Everyscience.com’s “The One Dimensional Schrodinger Equation” (HTML)
Instructions: Please click on the link and read the entire webpage. While reading, solve the Hamiltonian following the steps indicated in the reading. This provides a glance of the Schrodinger equation. Studying this resource should take approximately 1 hour to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Macquarie University: Professor James Cresser’s “Interference and Diffraction & Wave Mechanics” Lecture Notes
Link: Macquarie University: Professor James Cresser’s “Interference and Diffraction & Wave Mechanics” Lecture Notes (PDF)
Instructions: Please click on the link and select “Ch6: The Schrodinger Wave Equation” to download the PDF file, and read the entire text (18 pages). While reading, following the math steps indicated in the reading to find the wavefunction of the system by solving the Hamiltonian. Also make sure you understand important concepts such as boundary and continuity conditions. Professor Cresser’s notes provide a deeper explanation of the Schrodinger equation. Studying this resource should take approximately 3 hours to compete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: YouTube: Praba Siva’s “Schrodinger Equation – Step Wise Derivation Part 1/3,” “Part 2/3,” and “Part 3/3”
Links: YouTube: Praba Siva’s “Schrodinger Equation – Step Wise Derivation Part 1/3”, “Part 2/3”, and “Part 3/3” (YouTube)
Instructions: Watch these three videos. While watching the videos, follow the instructor by doing the same math on a sheet of paper until you are comfortable deriving the Schrodinger equation on your own. This video tutorial shows a stepbystep derivation of the Schrodinger equation. Studying these resources should take approximately 1 hour to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Assessment 3”
Link: The Saylor Foundation’s “Assessment 3” (DOC)
Instructions: Complete the attached assessment questions to check your understanding of the material covered thus far. Once you have completed the assessment, you may check your answers against the “Answer Key” (DOC).
Completing this assessment should take approximately 1 hour.
 Reading: Everyscience.com’s “The One Dimensional Schrodinger Equation”

2.3 Wavefunctions and the Born Interpretation
 Reading: Everyscience.com’s “Wavefunctions and the Born Interpretation”
Link: Everyscience.com’s “Wavefunctions and the Born Interpretation” (HTML)
Instructions: Clink on the above link to access the webpage. Please read the entire webpage and note the role of the wavefunction as the “source of all measurable information of a quantum mechanical system.” Studying this resource should take approximately 0.5 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Everyscience.com’s “Wavefunctions and the Born Interpretation”

2.4 Wave Functions and the Heisenberg’s Uncertainty Principles
 Reading: Robert B. Griffiths’s “Consistent Quantum Theory”
Link: Robert B. Griffiths’s “Consistent Quantum Theory” (PDF)
Instructions: Please click on the link, find “Chapter 2: Wave Functions,” select the PDF link for the text, and read sections 2.1–2.4. This resource explains the physical interpretation of the wavefunction. Studying this resource should take approximately 2.0 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Macquarie University: Professor James Cresser’s “The Wave Function” Lecture Notes
Links: Macquarie University: Professor James Cresser’s “The Wave Function” Lecture Notes (PDF)
Instructions: Please click on the link, select the link to “Ch3: The Wave Function” to access the PDF file, and read the entire chapter (8 pages). Make sure you understand the concept of “probability waves” and the derivation of the Heisenberg uncertainty principle. Studying this resource should take approximately 1.5 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Everyscience.com’s “Heisenberg’s Uncertainty Principle”
Link: Everyscience.com’s “Heisenberg’s Uncertainty Principle” (HTML)
Instructions: Please click on the link and read the entire webpage for a quick explanation and useful review of “Heisenberg’s Uncertainty Principle.” This resource is useful to quickly review the mathematical proof of the Uncertainly Principle. Make sure you know how to derive the uncertainty in momentum and position. Studying this resource should take approximately 0.5 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Web Media: YouTube: Physics Academy’s “Quantum Mechanics 008: Measurement and Heisenberg’s Uncertainty Principle”
Link: YouTube: Physics Academy’s “Quantum Mechanics 008: Measurement and Heisenberg’s Uncertainty Principle” (YouTube)
Instructions: Please click on the link above, and watch the video. This short video tutorial covers the concept of measurement via entanglement, the double slit experiment, and Heisenberg’s uncertainty principle. Studying this resource should take approximately 0.5 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Assessment 4”
Link: The Saylor Foundation’s “Assessment 4” (DOC)
Instructions: Complete the attached assessment questions to check your understanding of the material covered thus far. Once you have completed the assessment, you may check your answers against the “Answer Key” (DOC).
Completing this assessment should take approximately 1 hour.
 Reading: Robert B. Griffiths’s “Consistent Quantum Theory”

Unit 3: Practical Problems in Quantum Mechanics
In this unit, you will begin to use the equations and principles of quantum mechanics to solve some simple problems, involving relatively simple mathematics. Although the examples presented here involve mostly “imaginary” particles in ideal quantum systems, these examples will serve as an introduction to quantum mechanical calculations. The principles learned using these ideal systems (e.g., particle in a box) can be used later in “real” systems (molecules). As the system under study becomes more and more complex, you will learn how to adopt certain techniques of approximation to simplify your calculation and still obtain fairly accurate results.
Unit 3 Time Advisory show close
Unit 3 Learning Outcomes show close

3.1 Particle in a Box (Translational Motion)
 Reading: Boston University: Professor Dan Dill’s “Analytic Solution of the Schrödinger Equation: Particle in a Box” and “Example of OneDimensional Quantum System”
Link: Boston University: Professor Dan Dill’s “Analytic Solution of the Schrödinger Equation: Particle in a Box” and “Example of OneDimensional Quantum System” (PDF)
Instructions: Please click on the first and second links above and scroll down the webpage to the italic headings, “Particle in a Box” and “Example of OneDimensional Quantum System.” To open each set of notes, click on the hyperlink next to these italicized headings. A PDF file of each section will open up. Read each PDF file in its entirety (7 pages and 6 pages, respectively). While reading the material, repeat each mathematical derivation on scratch paper. Studying this resource should take approximately 2 hours to complete. Note that this reading also covers the material you need to know for subunits 3.1.1–3.1.4.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: The Chemistry Hypermedia Project’s “Particle in a Box”
Link: The Chemistry Hypermedia Project’s “Particle in a Box” (HTML)
Instructions: Please click on the link and read the Chemistry Hypermedia Project webpage, which provides a glance of the particle in a box problem. While reading the material, repeat each mathematical derivation on scratch paper. Studying this resource should take approximately 1.5 hours to complete. Note that this reading also covers the material you need to know for subunits 3.1.1–3.1.4.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Everyscience.com’s “Particle in a TwoDimensional Box”
Link: Everyscience.com’s “Particle in a TwoDimensional Box” (HTML)
Instructions: Please click on the link and read the entire webpage, which presents the problem in 2D. While reading the material, repeat each mathematical derivation on scratch paper. Studying this resource should take approximately 1 hour to complete. Note that this reading also covers the material you need to know for subunits 3.1.1–3.1.4.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Web Media: Kansas State University: Physics Education Research Group’s “Visual Quantum Mechanics – Quantum Tunneling”
Link: Kansas State University: Physics Education Research Group’s “Visual Quantum Mechanics – Quantum Tunneling” (Adobe Shockwave)
Instructions: Please click on the link above and follow the steps on the webpage to simulate tunneling. Studying this resource should take approximately 1 hour to complete. Please note that this program requires Adobe Shockwave. If you do not already have Shockwave, you can download a free version here. Note that this reading also covers the material you need to know for subunits 3.1.1–3.1.4.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Web Media: YouTube: Praba Siva’s “Schrodinger Equation – For Particle in a 1 D, 2D, 3D Box” and David Colarusso’s “What Is Quantum Tunneling?”
Links: YouTube: Praba Siva’s “Schrodinger Equation – For Particle in a 1 D, 2D, 3D Box” and David Colarusso’s “What Is Quantum Tunneling?” (YouTube)
Instructions: Please click on the links above, and watch these videos. These are short videos that explain how to solve the Schrodinger equation for one, two, and threedimensional systems (Praba Siva’s video) and explain the phenomenon of quantum tunneling (David Colarusso’s video). Note that these videos also cover the material you need to know for subunits 3.1.1–3.1.4. Studying these resources should take approximately 0.5 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Assessment 5”
Link: The Saylor Foundation’s “Assessment 5” (DOC)
Instructions: Complete the attached assessment questions to check your understanding of the material covered thus far. Once you have completed the assessment, you may check your answers against the “Answer Key” (DOC).
Completing this assessment should take approximately 1 hour.
 Reading: Boston University: Professor Dan Dill’s “Analytic Solution of the Schrödinger Equation: Particle in a Box” and “Example of OneDimensional Quantum System”

3.1.1 Particle in a OneDimensional Box
Note: This topic is covered by the readings assigned beneath subunit 3.1. In particular, please focus on Chemistry Hypermedia Project’s “Particle in a Box” and Professor Dan Dill’s “Analytic Solution of the Schrödinger Equation: Particle in a Box” to learn about onedimensional quantum mechanical systems.

3.1.2 Example of OneDimensional Quantum Systems
Note: This topic is covered by the readings assigned beneath subunit 3.1. In particular, please focus on Professor Dan Dill’s “Example of OneDimensional Quantum System” to learn about the behavior of quantum particles “confined” into quantum wells with different energy barriers.

3.1.3 Barrier Penetration and Tunneling
Note: This topic is covered by the readings assigned beneath subunit 3.1. In particular, please focus on David Colarusso’s “What Is Quantum Tunneling?” and Professor Dan Dill’s “Example of OneDimensional Quantum System” to learn about the unique phenomenon of quantum tunneling.

3.1.4 Particle in a 2D or 3D Box
Note: This topic is covered by the readings assigned beneath subunit 3.1. In particular, please focus on Everyscience.com’s “Particle in a TwoDimensional Box” and Praba Siva’s web media, “Schrodinger Equation – For Particle in a 1 D, 2D, 3D Box,” to learn about the behavior of quantum particles in more than one dimension.

3.2 Vibrational Motion
 Reading: Everyscience.com’s “Molecular Vibrations” and “Anharmonic Oscillator”
Links: Everyscience.com’s “Molecular Vibrations” and “Anharmonic Oscillator” (HTML)
Instructions: Please click on the “Molecular Vibrations” and “Anharmonic Oscillator” links and read these webpages in their entirety. While reading the material, repeat the mathematical derivation of the vibrational terms. Studying this resource should take approximately 1.5 hours to complete. Note that these readings also cover the materials you need to know for subunits 3.2.1–3.2.3.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Boston University: Professor Dan Dill’s “Harmonic Oscillator”
Link: Boston University: Professor Dan Dill’s “Harmonic Oscillator” (PDF)
Instructions: For Professor Dill’s notes, please click on the link above, scroll down the webpage to the italic heading, “Harmonic Oscillator,” and click on the hyperlink to the PDF next to the heading. Read the entire PDF (18 pages). While reading the material, repeat the mathematical derivation of the harmonic potential and understand the difference between harmonic and anharmonic vibrational terms. Studying this resource should take approximately 3 hours to complete. Note that this reading also covers the materials you need to know for subunits 3.2.1–3.2.3.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Web Media: YouTube: Indian Institute of Technology, Madras: Professor K. Mangala Sunder’s “Lecture 4 Harmonic Oscillator and Molecular Vibration”
Link: YouTube: Indian Institute of Technology, Madras: Professor K. Mangala Sunder’s “Lecture 4 Harmonic Oscillator and Molecular Vibration” (YouTube)
Instructions: Please click on the link above, and watch the entire video. While watching the video, repeat the mathematical derivation following the professor’s notes on the board. Studying this resource should take approximately 1.5 hours to complete. Note that this video lecture also covers the material you need to know for subunits 3.2.1–3.2.3.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Assessment 6”
Link: The Saylor Foundation’s “Assessment 6” (DOC)
Instructions: Complete the attached assessment questions to check your understanding of the material covered thus far. Once you have completed the assessment, you may check your answers against the “Answer Key” (DOC).
Completing this assessment should take approximately 1 hour.
 Reading: Everyscience.com’s “Molecular Vibrations” and “Anharmonic Oscillator”

3.2.1 Overview of Molecular Vibrations
Note: This subunit is covered by the readings assigned beneath subunit 3.2. In particular, please focus on Everyscience.com’s “Molecular Vibrations” to have an overview of molecular vibrations.

3.2.2 Harmonic Oscillator
Note: This subunit is covered by the readings assigned beneath subunit 3.2. In particular, please focus on Professor Dan Dill’s “Harmonic Oscillator” and Professor K. Mangala Sunder’s “Lecture 4 Harmonic Oscillator and Molecular Vibration” to learn how harmonic oscillators can be used to model molecular vibrations.

3.2.3 The Anharmonic Oscillator
Note: This subunit is covered by the readings assigned beneath subunit 3.2. In particular, please focus on Everyscience.com’s “Anharmonic Oscillator” to learn how the anharmonic oscillator is a better representation of molecular vibration as it allows bond dissociation at high vibrational excitations.

3.3 Angular Momentum and Rotational Motion
 Web Media: bpReidSoftware for Science and Mathematics’ “Particle on a Sphere – Spherical Harmonics”
Link: bpReidSoftware for Science and Mathematics’ “Particle on a Sphere – Spherical Harmonics” (HTML)
Instructions: Please click on the link above, and complete the exercises on the webpage to simulate the spherical harmonics. Please note that this program requires Oracle’s Java Runtime. If you do not already have it, you can download a free version here. Studying this resource should take approximately 0.5 hours to complete. Note that this resource also covers the material you need to know for subunits 3.3.1–3.3.5.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Everyscience’s “Polar Coordinates”
Link: Everyscience’s “Polar Coordinates” (HTML)
Instructions: Please click on link to learn about polar coordinates. In this resource, it is important that you learn how to transform Cartesian coordinates into polar coordinates. Studying this resource should take approximately 0.5 hours to complete. Note that this reading also covers the material you need to know for subunits 3.3.1–3.3.5.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Boston University: Professor Dan Dill’s “A Little Bit of Angular Momentum,” “Angular Motion in TwoComponents Systems,” and “Particle Moving on a Ring”
Link: Boston University: Professor Dan Dill’s “A Little Bit of Angular Momentum”, “Angular Motion in TwoComponents Systems”, and “Motion of a Particle on a Ring” (PDF)
Instructions: For Professor Dill’s notes, please click on the first and second link above and scroll down to the italic headings, “A little Bit of Angular Momentum” and “Angular Motion in TwoComponents Systems.” To download the PDF file, click on the hyperlinks next to the heading. Read the entire PDF files (4 pages and 18 pages, respectively). In this resource, you will use polar coordinates to solve the Schrodinger equation and derive parameters related to angular motion. Next, click on the “Motion of a Particle on a Ring” link and read the entire webpage, which offers an animated representation of the probability density of a particle moving on a ring. Studying these resources should take approximately 2 hours to complete. Note that these readings also cover the material you need to know for subunits 3.3.1–3.3.5.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: University of California Davis: UC Davis ChemWiki’s “Particle on a Ring” and “Particle on a Sphere”
Links: University of California Davis: UC Davis ChemWiki’s “Particle in a Ring” and “Particle in a Sphere” (HTML)
Instructions: Please click on the UC Davis ChemWiki links for a quick overview of a particle moving in a ring and in a sphere. Studying these resources should take approximately 0.5 hours to complete. Note that these readings also cover the material you need to know for subunits 3.3.1–3.3.5.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Web Media: YouTube: Yale Courses: “Quantum Mechanics III”
Link: YouTube: Yale Courses: “Quantum Mechanics III” (YouTube)
Also Available in:
HTML transcript, Mp3 audio, Mp4 video, Adobe Flash video from Open Yale Courses
Instructions: Please click on the link above, and watch the video. You can focus on the lecture portion starting from approximately minute 12:40 to learn about the quantum motion of a particle on a ring. Studying this resource should take approximately 1 hour to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Assessment 7”
Link: The Saylor Foundation’s “Assessment 7” (DOC)
Instructions: Complete the attached assessment questions to check your understanding of the material covered thus far. Once you have completed the assessment, you may check your answers against the “Answer Key” (DOC).
Completing this assessment should take approximately 1 hour.
 Web Media: bpReidSoftware for Science and Mathematics’ “Particle on a Sphere – Spherical Harmonics”

3.3.1 Angular Momentum
Note: This subunit is covered by the readings assigned beneath subunit 3.3. In particular, please focus on Professor Dan Dill’s “Angular Motion in TwoComponents Systems” to learn about angular momentum.

3.3.2 Polar and Spherical Coordinates
Note: This subunit is covered by the readings assigned beneath subunit 3.3. In particular, please focus on and Everyscience’s “Polar Coordinates” to learn how to transform Cartesian coordinates into polar and spherical coordinates.

3.3.3 Particle on a Ring
Note: This subunit is covered by the readings assigned beneath subunit 3.3. In particular, please focus on Professor Dan Dill’s “Particle Moving on a Ring,” ChemWiki’s “Particle on a Ring,” and the web media Yale courses, “Quantum Mechanics III,” from approximately minute 12:40, to learn about the quantum motion of a particle on a ring.

3.3.4 Particle on a Sphere
Note: This subunit is covered by the readings assigned beneath subunit 3.3. In particular, please focus on UC Davis ChemWiki’s “Particle on a Ring and Particle on a Sphere” and on the Web Media: “Particle on a Sphere – Spherical Harmonics.”

3.3.5 Spin
Note: This subunit is covered by the readings assigned beneath subunit 3.3. In particular, please focus on Professor Dan Dill’s “A Little Bit of Angular Momentum” to learn about spin angular momentum.

Unit 4: Quantum Chemistry: Atomic Structure and Spectra
In this unit, you will start to apply quantum mechanics to solve real chemistry problems, thus finally approaching quantum chemistry. Your studies will begin with the simplest system, the hydrogenlike atoms (or ions), which is comprised by a nuclei and a single electron orbiting around it. As additional electrons enter the system under study, the wavefunction describing the system will become more complex, and you will use approximation techniques to simplify your calculations. You will discover how a particular atomic structure results in a welldefined ground state electronic configuration. This electronic configuration is responsible for the atom photon absorption and emission spectra, as well as its ionization energy, electron affinity, and degenerate energy levels.
Unit 4 Time Advisory show close
Unit 4 Learning Outcomes show close

4.1 The Structure of Singleelectron Systems (Hydrogenlike Systems)
 Reading: Boston University: Professor Dan Dill’s “OneElectron Atom” and “OneElectron Atom Radial Functions”
Link: Boston University: Professor Dan Dill’s “OneElectron Atom” and “OneElectron Atom Radial Functions” (PDF)
Instructions: For Professor Dill’s notes, click on the links above, scroll down the webpage to the italic headings: “OneElectron Atom” and “OneElectron Atom Radial Functions.” To open these PDF files, click on the hyperlink next to these headings. Read the entire documents (10 pages and 8 pages, respectively). While reading the material, please follow the mathematical derivation of the eigenvalues for a oneelectron system, shell amplitudes, and radial functions. Studying this resource should take approximately 5 hours to complete. Note that these resources also cover the material you need to know for subunits 4.1.1–4.1.4.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Boston University: Professor Dan Dill’s “OneElectron Atom” and “OneElectron Atom Radial Functions”

4.1.1 OneElectron Atoms/Ions (HydrogenLike Atoms/Ions)
Note: This subunit is covered by the readings assigned beneath subunit 4.1. In particular, please focus on pages 1–5 of Professor Dan Dill’s “OneElectron Atom” to learn about the quantum mechanics of systems consisting of a single electron and an atomic nucleus.

4.1.2 Effective Potential Energy
Note: This subunit is covered by the readings assigned beneath subunit 4.1. In particular, please focus on pages 5–6 of Professor Dan Dill’s “OneElectron Atom” to learn about the effective potential energy in atomic systems.

4.1.3 Atomic Orbitals and Their Energies
Note: This subunit is covered by the readings assigned beneath subunit 4.1. In particular, please focus on pages 7–10 of Professor Dan Dill’s “OneElectron Atom” to learn about the energy of atomic orbitals.

4.1.4 Shell Amplitudes and Shell Energies
Note: This subunit is covered by the readings assigned beneath subunit 4.1. In particular, please focus on Professor Dan Dill’s “OneElectron Atom Radial Functions” to learn about shell amplitudes and their energies.

4.2 The Structure of MultipleElectron Atoms
 Reading: Boston University: Professor Dan Dill’s “ManyElectron Atoms: Fermi Holes and Fermi Heaps”
Link: Boston University: Professor Dan Dill’s “ManyElectron Atoms: Fermi Holes and Fermi Heaps” (PDF)
Instructions: Please click on the link and scroll down the webpage to the italic heading, “ManyElectron Atoms: Fermi Holes and Fermi Heaps.” To open the PDF file, click on the link next to the heading. Read the entire PDF (17 pages). While reading the material, pay close attention on how the introduction of extra electrons changes the terms of the Schrodinger equation. Studying this resource should take approximately 2 hours to complete. Note that this reading also covers the material you need to know for subunits 4.2.1–4.2.6.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Southern Methodist University: Professor Werner Horsthemke’s “Physical Chemistry II Lecture Notes”
Link: Southern Methodist University: Professor Werner Horsthemke’s “Physical Chemistry II Lecture Notes” (PDF)
Instructions: Please click on the “Physical Chemistry II Lecture Notes” link, scroll down the webpage to the section, “Lecture Notes,” and click on the “PC2Set5.pdf” link. This set of notes will open as a PDF file, and you can read the entire document (29 pages). Make sure you understand how the Pauli Principle, the Aufbau Principle, and Hund’s Rule and their application derive the electronic configuration of atoms. Studying this resource should take approximately 2 hours to complete. Note that this reading also covers the material you need to know for subunits 4.2.1–4.2.6.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Boston University: Professor Dan Dill’s “ManyElectron Atoms: Fermi Holes and Fermi Heaps”

4.2.1 The Orbital Approximation
Note: This subunit is covered by the readings assigned beneath subunit 4.2. In particular, please focus on pages 1–6 of Professor Dan Dill’s “ManyElectron Atoms: Fermi Holes and Fermi Heaps.”

4.2.2 Pauli Principle
Note: This subunit is covered by the readings assigned beneath subunit 4.2. In particular, please focus on pages 7–10 of Professor Dan Dill’s “ManyElectron Atoms: Fermi Holes and Fermi Heaps.”

4.2.3 The Pauli Exclusion Principle
Note: This subunit is covered by the readings assigned beneath subunit 4.2. In particular, please focus on pages 11–17 of Professor Dan Dill’s “ManyElectron Atoms: Fermi Holes and Fermi Heaps.”

4.2.4 Aufbau Principle
Note: This subunit is covered by the readings assigned beneath subunit 4.2. In particular, please focus on page 5.17 of Professor Werner Horsthemke’s “Physical Chemistry II Lecture Notes” to learn about the Aufbau Principle.

4.2.5 Hund’s Rule
Note: This subunit is covered by the readings assigned beneath subunit 4.2. In particular, please focus on pages 5.13, 5.18, and 5.23 of Professor Werner Horsthemke’s “Physical Chemistry II Lecture Notes” to learn about Hund’s Rule.

4.2.6 SpinOrbit Coupling
Note: This subunit is covered by the readings assigned beneath subunit 4.2. In particular, please focus on pages 5.24–5.29 of Professor Werner Horsthemke’s “Physical Chemistry II Lecture Notes” to learn about SpinOrbit Coupling.

4.2.7 The Helium Atom
 Reading: MIT’s OpenCourseWare: Professor Griffin and Professor Voorhis’s “Helium Atom”
Links: MIT’s OpenCourseWare: Professor Griffin and Professor Voorhis’s “Helium Atom” (PDF)
Instructions: Please click on the MIT link above, scroll down the webpage to “Lecture 25” (note: the title of this lecture is different, but the Helium Atom file will open up), and click on the PDF link to download the lecture. Read the entire document (8 pages). As you read through this resource, repeat the approximation technique used to solve this twoelectron system. Studying this resource should take approximately 1 hour to complete.
Terms of Use: Robert Guy Griffin and Troy Van Voorhis, Physical Chemistry 5.61, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed August 16, 2012). License: Creative Commons BYNCSA 3.0. The original version can be found here.
 Reading: MIT’s OpenCourseWare: Professor Griffin and Professor Voorhis’s “Helium Atom”

4.2.8 Term Symbols
 Reading: University of California Davis: UC Davis ChemWiki’s “Atomic Term Symbols”
Link: University of California Davis: UC Davis ChemWiki’s “Atomic Term Symbols” (HTML)
Instructions: Please click on the link to and read “Atomic Term Symbols.” This resource will teach you how to derive the term symbols. Studying this resource should take approximately 1 hour to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: University of California Davis: UC Davis ChemWiki’s “Atomic Term Symbols”

4.3 Introduction to Techniques of Approximation
 Reading: University of Southampton: Professor ChrisKriton Skylaris’s “Perturbation Theory”
Link: University of Southampton: Professor ChrisKriton Skylaris’s “Perturbation Theory” (PDF)
Instructions: Please click on the link above, and under the heading “Perturbation Theory,” select the “Lecture notes” link to access the PDF file. Please read this entire chapter of lecture notes (42 pages). Studying this resource should take approximately 4 hours to complete. Note that this resource also covers the material you need to know for subunits 4.3.1–4.3.3.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Assessment 8”
Link: The Saylor Foundation’s “Assessment 8” (DOC)
Instructions: Complete the attached assessment questions to check your understanding of the material covered thus far. Once you have completed the assessment, you may check your answers against the “Answer Key” (DOC).
Completing this assessment should take approximately 1 hour.
 Reading: University of Southampton: Professor ChrisKriton Skylaris’s “Perturbation Theory”

4.3.1 TimeIndependent Perturbation Theory
Note: This subunit is covered by the readings assigned beneath subunit 4.3. In particular, please focus on pages 2–12 to learn about timeindependent perturbation theory.

4.3.2 TimeDependent Perturbation Theory
Note: This subunit is covered by the readings assigned beneath subunit 4.3. In particular, please focus on pages 12–27 to learn about timedependent perturbation theory.

4.3.3 Applications of Perturbation Theory
Note: This subunit is covered by the readings assigned beneath subunit 4.3. In particular, please focus on pages 28–41 to learn about applications of perturbation theory.

Unit 5: Quantum Chemistry: Molecular Structure
In our daily life, only certain rare gasses exist as single atoms (e.g., helium, etc). The matter and materials we deal with everyday are mainly in their molecular (e.g., plastics or gasoline), crystalline (salt), or metallic (aluminum cans) state. In these states, atoms of one or more elements combine to form larger molecules, crystals, and so forth. In this unit, you will start to go over techniques of quantum chemistry designed to study large molecular systems. Of course, you will start from simple models, such as the H_{2}^{+} moleculeion and the H_{2} molecule. Bonds will initially be described in terms of Valence Bond Theory before approaching the Molecular Orbital Model.
Unit 5 Time Advisory show close
Unit 5 Learning Outcomes show close

5.1 Separating Electronic and Nuclear Motion
 Reading: Boston University: Professor Dan Dill’s “Molecular Structure: Separating Electronic and Nuclear Motion”
Link: Boston University: Professor Dan Dill’s “Molecular Structure: Separating Electronic and Nuclear Motion” (PDF)
Instructions: For Professor Dill’s notes, please click on the link above, scroll down to the italic heading “Molecular Structure: Separating Electronic and Nuclear Motion,” and select the hyperlink next to this heading to download the PDF file. Please read the entire text (4 pages). Pay attention to how and why the motion of nuclei in a molecule can be separated from the motion of electrons. Studying this resource should take approximately 2 hours to complete. Note that this resource also covers the material you need to know for subunits 5.1.1–5.1.2.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Boston University: Professor Dan Dill’s “Molecular Structure: Separating Electronic and Nuclear Motion”

5.1.1 Adiabatic Approximation
Note: This subunit is covered by the readings assigned beneath subunit 5.1. In particular, please focus on pages 1–2 to learn about the adiabatic approximation.

5.1.2 The BornOppenheimer Approximation
Note: This subunit is covered by the readings assigned beneath subunit 5.1. In particular, please focus on pages 3–4 to learn about the BornOppenheimer approximation.

5.2 Molecular Orbitals Theory
 Reading: MIT’s OpenCourseWare Professor Griffin and Professor Voorhis’s Physical Chemistry: “Molecular Orbital Theory – Part I” and “Part II” and “Modern Electronic Structure Theory”
Links: MIT’s OpenCourseWare: Professor Griffin and Professor Voorhis’s “Molecular Orbital Theory – Part I” and “Part II” and “Modern Electronic Structure Theory” (PDF)
Instructions: Please click on the links to download the PDFs. In these resources, you will learn how to carry out a linear combination of atomic orbitals to form molecular orbitals and how to compute the energies of these molecular orbitals. Please read these three PDFs in their entirety (11 pages, 14 pages, and 8 pages, respectively). Studying these resources should take approximately 4.0 hours to complete.
Terms of Use: Terms of Use: Robert Guy Griffin and Troy Van Voorhis, Physical Chemistry 5.61, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed August 16, 2012). License: Creative Commons BYNCSA 3.0. The original version can be found here.  Reading: Everyscience.com’s “Molecular Orbital Theory”
Link: Everyscience.com’s “Molecular Orbital Theory” (HTML)
Instructions: Please click on the “Molecular Orbital Theory” link and read this webpage for a glance at MO Theory. Pay attention to the difference between a bonding and an antibonding molecular orbital. Studying this resource should take approximately 0.5 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: MIT’s OpenCourseWare Professor Griffin and Professor Voorhis’s Physical Chemistry: “Molecular Orbital Theory – Part I” and “Part II” and “Modern Electronic Structure Theory”
 5.3 Molecular Orbitals Description of Diatomic Molecules

5.3.1 The Hydrogen Molecule
 Reading: University of Waterloo: Professor Chung (Peter) Chieh’s “Molecular Orbitals of H2”
Link: University of Waterloo: Professor Chung (Peter) Chieh’s “Molecular Orbitals of H2” (HTML)
Instructions: Please read the webpage. While studying this resource, reproduce the LCAO and build your own MO energy diagram. Studying this resource should take approximately 1 hour to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: University of Waterloo: Professor Chung (Peter) Chieh’s “Molecular Orbitals of H2”

5.3.2 Bonding in Homonuclear of Diatomic Molecules
 Reading: Cartage.org’s “Molecular Orbitals of Homonuclear Diatomics”
Link: Cartage.org’s “Molecular Orbitals of Homonuclear Diatomics” (HTML)
Instructions: Please read the webpage. While studying this resource, reproduce the LCAO and build your own MO energy diagram. In contrast to the hydrogen molecule MO (subunit 5.3.1) that was built just using the H 1s atomic orbitals, these MOs are constructed using a larger set of atomic orbitals, resulting in a more complex MO diagram. Studying this resource should take approximately 1 hour to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Cartage.org’s “Molecular Orbitals of Homonuclear Diatomics”

5.3.3 Bonding in Heteronuclear Diatomic Molecules
 Reading: Institut für Physikalische und Theoretische Chemie der Technischen Universität Carolo – Wilhelmina zu Braunschweig’s “Heteronuclear Molecules AB”
Link: Institut für Physikalische und Theoretische Chemie der Technischen Universität Carolo – Wilhelmina zu Braunschweig’s “Heteronuclear Molecules AB” (HTML)
Instructions: Please read the webpage. While studying this resource, reproduce the LCAO and build your own MO energy diagram. In contrast to subunit 5.3.2, these MOs have an “unsymmetrical” look, as they have been built using atomic orbitals from different atoms, thus with different energies. Studying this resource should take approximately 1 hour to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Institut für Physikalische und Theoretische Chemie der Technischen Universität Carolo – Wilhelmina zu Braunschweig’s “Heteronuclear Molecules AB”
 5.4 Molecular Orbitals Description of Polyatomic Molecules

5.4.1 The Huckel Theory and Applications
 Reading: Oxford University: Professor Mark Brouard’s “Huckel Theory for Polyatomic Molecules”
Link: Oxford University: Professor Mark Brouard’s “Huckel Theory for Polyatomic Molecules” (PDF)
Instructions: Please click on the link and select the “Notes for lectures 7 and 8” link under the “Valence” section to access the PDF file and visualize some practical applications of the Huckel Theory to molecules with conjugated bonds. Please read this entire lecture (11 pages). Studying this resource should take approximately 1 hour to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Tennessee Tech University: Professor Northrup’s “Huckel Molecular Orbital Theory (HMO Theory)”
Link: Tennessee Tech University: Professor Northrup’s “Huckel Molecular Orbital Theory (HMO Theory)” (PDF)
Instructions: Read these lecture notes to learn about Huckel Theory.
Studying this resource should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Oxford University: Professor Mark Brouard’s “Huckel Theory for Polyatomic Molecules”

5.4.2 SelfConsistent Field (HartreeFock Method) Calculations and Density Functional Theory
 Reading: Cambridge University: Professor Nicholas Handy’s “Self Consistent Field Theory”
Link: Cambridge University: Professor Nicholas Handy’s “Self Consistent Field Theory” (HTML)
Instructions: Please click on the “Self Consistent Field Theory” link above, and read Professor Handy’s webpage to learn about selfconsistent field theory. Studying this resource should take approximately 3 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Assessment 9”
Link: The Saylor Foundation’s “Assessment 9” (DOC)
Instructions: Complete the attached assessment questions to check your understanding of the material covered thus far. Once you have completed the assessment, you may check your answers against the “Answer Key” (DOC).
Completing this assessment should take approximately 1 hour.
 Reading: Cambridge University: Professor Nicholas Handy’s “Self Consistent Field Theory”

Unit 6: Symmetry in Molecular Structures
In order to better understand the spectroscopy portion of this course (Units 7–9), you need to learn about molecular symmetry and some point group theory. Symmetrical molecules behave very differently with respect to unsymmetrical ones when it comes to interaction with light.
Unit 6 Time Advisory show close
Unit 6 Learning Outcomes show close

6.1 Symmetry and Group Theory
 Reading: University of CaliforniaDavis: UC Davis ChemWiki’s “Group Theory”
Link: University of CaliforniaDavis: UC Davis ChemWiki’s “Group Theory” (HTML)
Instructions: Click on the link above to the UC Davis ChemWiki, and read the entire webpage to learn about group theory. Pay close attention to the symmetry elements of each molecule and how they are used to derive the point group. Studying this resource should take approximately 4 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: University of CaliforniaDavis: UC Davis ChemWiki’s “Group Theory”

6.2 Symmetry in Molecular Structures
 Reading: Reading: University of CaliforniaDavis: UC Davis ChemWiki’s “Group Theory and its Application to Chemistry”
Link: University of CaliforniaDavis: UC Davis ChemWiki’s “Group Theory and its Application to Chemistry” (HTML)
Instructions: Click on the link above to the UC Davis ChemWiki, and read the entire webpage to learn about the chemical applications of group theory. Studying this resource should take approximately 3 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Reading: University of CaliforniaDavis: UC Davis ChemWiki’s “Group Theory and its Application to Chemistry”

6.3 Character Tables and Symmetry Labels
 Reading: University of CaliforniaDavis: UC Davis ChemWiki’s “Character Table” and “Understanding Character Tables of Symmetry Groups”
Links: University of CaliforniaDavis: UC Davis ChemWiki’s “Character Table” and “Understanding Character Tables of Symmetry Groups” (HTML)
Instructions: Click on the links above and read through the entire webpages to learn about character tables and their applications to spectroscopy. Studying these resources should take approximately 2 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Assessment 10”
Link: The Saylor Foundation’s “Assessment 10” (DOC)
Instructions: Complete the attached assessment questions to check your understanding of the material covered thus far. Once you have completed the assessment, you may check your answers against the “Answer Key” (DOC).
Completing this assessment should take approximately 1 hour.
 Reading: University of CaliforniaDavis: UC Davis ChemWiki’s “Character Table” and “Understanding Character Tables of Symmetry Groups”

Unit 7: Spectroscopy I: Rotational and Vibrational Spectra
This is the first unit of the spectroscopy portion of the course. When electromagnetic waves interact with matter, the outcome of the interaction depends on both the nature of the molecule and the frequency of the interacting light. Infrared (IR) light usually causes atoms within a molecule to vibrate and/or rotate. In this unit, you will learn how to correlate the electronic structure of molecules and their symmetry to vibrational and rotational phenomena.
Unit 7 Time Advisory show close
Unit 7 Learning Outcomes show close

7.1 Molecular Spectroscopy and Symmetry
 Reading: Southern Methodist University: Professor Werner Horsthemke’s “Physical Chemistry II Lecture Notes”
Link: Southern Methodist University: Professor Werner Horsthemke’s “Physical Chemistry II Lecture Notes” (PDF)
Instructions: For Professor Horsthemke’s notes, click on the link above, scroll down the webpage to the “Lecture Notes” section, and click of the “PC2Set7.pdf” link. This set of notes will open as a PDF file, and you can read the entire set. Pay close attention on how the shape of the molecule results in different types of vibration. Studying this resource should take approximately 6 hours to complete.
Terms of Use: Please respect the copyright and terms of use on the webpage displayed above.
 Reading: Southern Methodist University: Professor Werner Horsthemke’s “Physical Chemistry II Lecture Notes”

7.2 Pure Rotational Spectroscopy
 Reading: Everyscience.com’s “Molecular Rotation”
Link: Everyscience.com’s “Molecular Rotation” (HTML)
Instructions: Please click on the link above to access the Everyscience.com website. Then, select the links to and read the webpages for “An Introduction to Spectroscopy” through “Rotational Raman Spectra.” Studying this resource should take approximately 6 hours to complete. Note that this resource also covers the material you need to know for subunits 7.2.1–7.2.9.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Everyscience.com’s “Molecular Rotation”

7.2.1 An Introduction to Spectroscopy
Note: This subunit is covered by the readings assigned beneath subunit 7.2. In particular, please focus on topic 1 to receive an introduction to spectroscopy.

7.2.2 Intensities of Spectral Lines
Note: This subunit is covered by the readings assigned beneath subunit 7.2. In particular, please focus on topic 2 to learn about the intensity of spectral lines.

7.2.3 Introduction to Rigid Rotors
Note: This subunit is covered by the readings assigned beneath subunit 7.2. In particular, please focus on topic 3 to receive an introduction to rigid rotors.

7.2.4 Spherical Rotors
Note: This subunit is covered by the readings assigned beneath subunit 7.2. In particular, please focus on topic 4 to learn about spherical rotors.

7.2.5 Symmetric Rotors
Note: This subunit is covered by the readings assigned beneath subunit 7.2. In particular, please focus on topic 5 to learn about symmetric rotors.

7.2.6 Linear and Asymmetric Rotors
Note: This subunit is covered by the readings assigned beneath subunit 7.2. In particular, please focus on topic 6 to learn about linear and asymmetric rotors.

7.2.7 Centrifugal Distortion
Note: This subunit is covered by the readings assigned beneath subunit 7.2. In particular, please focus on topic 7 to learn about centrifugal distortions.

7.2.8 Rotational Selection Rules
Note: This subunit is covered by the readings assigned beneath subunit 7.2. In particular, please focus on topic 8 to learn about rotational selection rules.

7.2.9 Rotational Raman Spectra
Note: This subunit is covered by the readings assigned beneath subunit 7.2. In particular, please focus on topic 9 to learn about rotational Raman spectra.

7.3 Vibrational Spectroscopy
 Reading: Everyscience.com’s “Vibrational Spectroscopy”
Link: Everyscience.com’s “Vibrational Spectroscopy” (HTML)
Instructions: Please click on the link above and then select the links from “Molecular Vibrations” through “Vibrational Raman Spectra of Diatomic Molecules.” Read all six web pages. Studying this resource should take approximately 2 hours to complete. Note that this reading also covers the material you need to know for subunits 7.3.1–7.3.5.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Concordia College: Professor Darin J. Ulness’s “Molecules and Molecular Spectroscopy”
Link: Concordia College: Professor Darin J. Ulness’s “Molecules and Molecular Spectroscopy” (PDF)
Instructions: Please click on the link and select the “Old Course Notes” hyperlink to open the PDF file. Read pages 243–248. Studying this resource should take approximately 2 hours to complete. Note that this reading also covers the material you need to know for subunits 7.3.1–7.3.5.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Everyscience.com’s “Vibrational Spectroscopy”

7.3.1 Molecular Vibrations and Spectroscopy
Note: This subunit is covered by the readings assigned beneath subunit 7.3. In particular, please focus on Professor Darin J. Ulness’s “Molecules and Molecular Spectroscopy,” sections 17.1 and 17.2, to learn about molecular vibrations and their application to spectroscopy.

7.3.2 Vibrational Selection Rules
Note: This subunit is covered by the readings assigned beneath subunit 7.3. In particular, please focus on topic 2 in Everyscience.com’s “Vibrational Spectroscopy” to learn about vibrational selection rules.

7.3.3 Anharmonic Oscillation
Note: This subunit is covered by the readings assigned beneath subunit 7.3. In particular, please focus on topic 3 in Everyscience.com’s “Vibrational Spectroscopy” to learn about anharmonic oscillations.

7.3.4 Vibration – Rotation Spectra
Note: This subunit is covered by the readings assigned beneath subunit 7.3. In particular, please focus on topic 4 in Everyscience.com’s “Vibrational Spectroscopy” to learn about vibrationalrotation spectra.

7.3.5 Combination Differences
Note: This subunit is covered by the readings assigned beneath subunit 7.3. In particular, please focus on topic 5 in Everyscience.com’s “Vibrational Spectroscopy” to learn how you can use the method of combination differences to determine the rotational constant of a vibrationally excited state.

7.3.6 Raman Spectroscopy
 Reading: Connexions: Courtney Payne and Andrew R. Barron’s “Raman and SurfaceEnhanced Raman Spectroscopy”
Link: Connexions: Courtney Payne and Andrew R. Barron’s “Raman and SurfaceEnhanced Raman Spectroscopy” (HTML)
Instructions: Please read the entire webpage to learn how particular types of light scattering (Stoke and Antistoke) can be used to determine the structure of certain molecules. Studying this resource should take approximately 0.25 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Assessment 11”
Link: The Saylor Foundation’s “Assessment 11” (DOC)
Instructions: Complete the attached assessment questions to check your understanding of the material covered thus far. Once you have completed the assessment, you may check your answers against the “Answer Key” (DOC).
Completing this assessment should take approximately 1 hour.
 Reading: Connexions: Courtney Payne and Andrew R. Barron’s “Raman and SurfaceEnhanced Raman Spectroscopy”

Unit 8: Spectroscopy II: Electronic Transitions
The previous unit dealt with IR causing rotational and vibrational phenomena within a molecule. In this unit, you will learn what happens when a more energetic radiation, such as ultraviolet or visible (UVVis) light interact with molecules. UVVis light possesses sufficient energy to cause electronic transition. During an electronic transition, electrons jump from their (lowenergy) ground state configuration into a highenergy excited state. The excited electrons then find their way back to the ground state, and here some interesting phenomena might occur, such as fluorescence and phosphorescence. Some direct applications of electronic transitions include LASERs.
Unit 8 Time Advisory show close
Unit 8 Learning Outcomes show close

8.1 Electronic Spectroscopy of Molecules
 Reading: The Chemical Educator, Vol. 12, No. 4: David P. Richardson and Raymond Chang’s “Lecture Demonstrations of Fluorescence and Phosphorescence”
Link: The Chemical Educator, Vol. 12, No. 4: David P. Richardson and Raymond Chang’s “Lecture Demonstrations of Fluorescence and Phosphorescence” (HTML)
Instructions: Read this article in The Chemical Educator for an interesting explanation of the difference between fluorescence and phosphorescence. From the link above, click on the image of the PDF version under "Full Text" on the right side of the page. Note that this reading also covers the material you need to know for subunits 8.1.1–8.1.6.
Studying this resource should take approximately 1.5 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Concordia College: Professor Darin J. Ulness’s “Molecules and Molecular Spectroscopy”
Link: Concordia College: Professor Darin J. Ulness’s “Molecules and Molecular Spectroscopy” (PDF)
Instructions: Please click on the link and select the “Old Course Notes” hyperlink to download the PDF file. Read pages 253–259. Studying this resource should take approximately 4.5 hours to complete. Note that this reading also covers the material you need to know for subunits 8.1.1–8.1.6.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: The Chemical Educator, Vol. 12, No. 4: David P. Richardson and Raymond Chang’s “Lecture Demonstrations of Fluorescence and Phosphorescence”

8.1.1 The Structure of the Electronic State
Note: Subunits 8.1.1–8.1.6 are covered by the readings assigned beneath subunit 8.1., which is mainly based on the readings from Professor Darin J. Ulness’s “Molecules and Molecular Spectroscopy,” section 17.4. In particular, please focus on David P. Richardson and Raymond Chang’s “Lecture Demonstrations of Fluorescence and Phosphorescence” to learn about the difference between fluorescence and phosphorescence.

8.1.2 Absorption Spectra
Note: Subunits 8.1.1–8.1.6 are covered by the readings assigned beneath subunit 8.1., which is mainly based on the readings from Professor Darin J. Ulness’s “Molecules and Molecular Spectroscopy,” section 17.4. In particular, please focus on David P. Richardson and Raymond Chang’s “Lecture Demonstrations of Fluorescence and Phosphorescence” to learn about the difference between fluorescence and phosphorescence.

8.1.3 Emission Spectra
Note: Subunits 8.1.1–8.1.6 are covered by the readings assigned beneath subunit 8.1., which is mainly based on the readings from Professor Darin J. Ulness’s “Molecules and Molecular Spectroscopy,” section 17.4. In particular, please focus on David P. Richardson and Raymond Chang’s “Lecture Demonstrations of Fluorescence and Phosphorescence” to learn about the difference between fluorescence and phosphorescence.

8.1.4 Fluorescence and Phosphorescence Spectra
Note: Subunits 8.1.1–8.1.6 are covered by the readings assigned beneath subunit 8.1., which is mainly based on the readings from Professor Darin J. Ulness’s “Molecules and Molecular Spectroscopy,” section 17.4. In particular, please focus on David P. Richardson and Raymond Chang’s “Lecture Demonstrations of Fluorescence and Phosphorescence” to learn about the difference between fluorescence and phosphorescence.

8.1.5 FranckCondon Activity
Note: Subunits 8.1.1–8.1.6 are covered by the readings assigned beneath subunit 8.1., which is mainly based on the readings from Professor Darin J. Ulness’s “Molecules and Molecular Spectroscopy,” section 17.4. In particular, please focus on David P. Richardson and Raymond Chang’s “Lecture Demonstrations of Fluorescence and Phosphorescence” to learn about the difference between fluorescence and phosphorescence.

8.1.6 The FranckCondon Principle
Note: Subunits 8.1.1–8.1.6 are covered by the readings assigned beneath subunit 8.1., which is mainly based on the readings from Professor Darin J. Ulness’s “Molecules and Molecular Spectroscopy,” section 17.4. In particular, please focus on David P. Richardson and Raymond Chang’s “Lecture Demonstrations of Fluorescence and Phosphorescence” to learn about the difference between fluorescence and phosphorescence.

8.2 Lasers and Applications
 Reading: Concordia College: Professor Darin J. Ulness’s “Lasers”
Link: Concordia College: Professor Darin J. Ulness’s “Lasers” (PDF)
Instructions: For Professor Ulness’s notes, please click on the link above, and select the “Old Course Notes” hyperlink to download the PDF file. Read pages 260–266. Studying this resource should take approximately 3 hours to complete. Note that this resource also covers the material you need to know for subunits 8.2.1–8.2.5.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Concordia College: Professor Darin J. Ulness’s “Lasers”

8.2.1 Anatomy of the Laser
Note: Subunits 8.2.1–8.2.5 are covered by the readings assigned beneath subunit 8.2., which is mainly based on the readings from Professor Darin J. Ulness’s “Molecules and Molecular Spectroscopy,” Chapter 18.

8.2.2 Physics of Laser Operation
Note: Subunits 8.2.1–8.2.5 are covered by the readings assigned beneath subunit 8.2., which is mainly based on the readings from Professor Darin J. Ulness’s “Molecules and Molecular Spectroscopy,” Chapter 18.

8.2.3 Population Inversion
Note: Subunits 8.2.1–8.2.5 are covered by the readings assigned beneath subunit 8.2., which is mainly based on the readings from Professor Darin J. Ulness’s “Molecules and Molecular Spectroscopy,” Chapter 18.

8.2.4 Stimulated Emission
Note: Subunits 8.2.1–8.2.5 are covered by the readings assigned beneath subunit 8.2., which is mainly based on the readings from Professor Darin J. Ulness’s “Molecules and Molecular Spectroscopy,” Chapter 18.

8.2.5 Applications of Lasers
Note: Subunits 8.2.1–8.2.5 are covered by the readings assigned beneath subunit 8.2., which is mainly based on the readings from Professor Darin J. Ulness’s “Molecules and Molecular Spectroscopy,” Chapter 18.
 Assessment: The Saylor Foundation’s “Assessment 12”
Link: The Saylor Foundation’s “Assessment 12” (DOC)
Instructions: Complete the attached assessment questions to check your understanding of the material covered thus far. Once you have completed the assessment, you may check your answers against the “Answer Key” (DOC).
Completing this assessment should take approximately 1 hour.
 Assessment: The Saylor Foundation’s “Assessment 12”

Unit 9: Spectroscopy III: Magnetic Resonance
In this unit, you will learn about the interaction of matter with certain radio frequencies in the presence of a magnetic field. These frequencies can be absorbed and reemitted by the nuclei or electrons, resulting in unique spectra that correlate with the structure of interacting molecules.
Unit 9 Time Advisory show close
Unit 9 Learning Outcomes show close

9.1 Magnetic Resonance Spectroscopy
 Reading: MIT – Advanced Chemical Experimentation and Instrumentation Laboratory: “Magnetic Resonance Spectroscopy”
Link: MIT – Advanced Chemical Experimentation and Instrumentation Laboratory: “Magnetic Resonance Spectroscopy” (HTML)
Instructions: On the left vertical menu, please select “Lecture Handouts.” Open the “Magnetic Resonance Spectroscopy” link and read the document. Studying this resource should take approximately 6 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: MIT – Advanced Chemical Experimentation and Instrumentation Laboratory: “Magnetic Resonance Spectroscopy”

9.2 Nuclear Magnetic Resonance
 Reading: Sheffield Hallam University: OnLine Learning: “Nuclear Magnetic Resonance Spectroscopy”
Link: Sheffield Hallam University: OnLine Learning: “Nuclear Magnetic Resonance Spectroscopy” (HTML)
Instructions: The webpage from Sheffield Hallam University gives you a glance at the theoretical principles of NMR. Studying this resource should take approximately 5 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Sheffield Hallam University: OnLine Learning: “Nuclear Magnetic Resonance Spectroscopy”

9.3 Electron Spin Resonance
 Reading: University of South Carolina: H. A. Farach and C. P. Poole’s “Overview of Electron Spin Resonance and Its Applications”
Link: University of South Carolina: H. A. Farach and C. P. Poole’s “Overview of Electron Spin Resonance and Its Applications” (HTML)
Instructions: Read this webpage from the University of South Carolina for a detailed overview of ESR and its applications. Studying this resource should take approximately 5 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Assessment 13”
Link: The Saylor Foundation’s “Assessment 13” (DOC)
Instructions: Complete the attached assessment questions to check your understanding of the material covered thus far. Once you have completed the assessment, you may check your answers against the “Answer Key” (DOC).
Completing this assessment should take approximately 1 hour.
 Reading: University of South Carolina: H. A. Farach and C. P. Poole’s “Overview of Electron Spin Resonance and Its Applications”

Final Exam
 Final Exam: The Saylor Foundation’s “CHEM106 Final Exam”
Link: The Saylor Foundation’s “CHEM106 Final Exam”
Instructions: You must be logged into your Saylor Foundation School account in order to access this exam. If you do not yet have an account, you will be able to create one, free of charge, after clicking the link.
 Final Exam: The Saylor Foundation’s “CHEM106 Final Exam”