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 sub-atomic 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

Welcome to CHEM106: Physical Chemistry II.  Below, please find some general information about the course and its requirements.
 
Primary Resources: This course is comprised of a range of different free, online materials.  However, the course makes primary use of the following materials:
Requirements for Completion: In order to complete this course, you will need to work through each unit and all of its assigned materials.  Pay special attention to Units 1 and 2, as these lay the groundwork for understanding the more advanced, exploratory material presented in the latter units.  You will also need to complete:
  • The Final Exam
Note that you will only receive an official grade on your Final Exam.  However, in order to adequately prepare for this exam, you will need to work through all of the resources in this course.
 
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

Upon successful completion of this course, the student will be able to:
  • 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 wave-particle 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 hydrogen-like 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

In order to take this course, you must:

√    Have access to a computer.

√    Have continuous broadband Internet access.

√    Have the ability/permission to install plug-ins (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 calculus-based Physics-Classical Mechanics; the Saylor Foundation offers the algebra-based equivalent of such a course: PHYS101.  Engineering courses such as ME102/ME202 could complement PHYS101.

Unit Outline show close


Expand All Resources Collapse All Resources
  • 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.

  • 1.2 Mathematical Concepts in Quantum Mechanics  
  • 1.3 Review of 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.

  • 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 Wave-Particle Duality  
  • 1.6 The 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.

  • 2.2 The Schrodinger Equation  
  • 2.3 Wavefunctions and the Born Interpretation  
  • 2.4 Wave Functions and the Heisenberg’s Uncertainty Principles  
  • 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)  
  • 3.1.1 Particle in a One-Dimensional 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 one-dimensional quantum mechanical systems.

  • 3.1.2 Example of One-Dimensional 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 One-Dimensional 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 One-Dimensional 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 Two-Dimensional 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  
  • 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  
  • 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 Two-Components 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 hydrogen-like 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 well-defined 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 Single-electron Systems (Hydrogen-like Systems)  
    • Reading: Boston University: Professor Dan Dill’s “One-Electron Atom” and “One-Electron Atom Radial Functions”

      Link: Boston University: Professor Dan Dill’s “One-Electron Atom” and “One-Electron Atom Radial Functions” (PDF)
       
      Instructions: For Professor Dill’s notes, click on the links above, scroll down the webpage to the italic headings: “One-Electron Atom” and “One-Electron 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 one-electron 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.

  • 4.1.1 One-Electron Atoms/Ions (Hydrogen-Like 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 “One-Electron 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 “One-Electron 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 “One-Electron 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 “One-Electron Atom Radial Functions” to learn about shell amplitudes and their energies.

  • 4.2 The Structure of Multiple-Electron Atoms  
    • Reading: Boston University: Professor Dan Dill’s “Many-Electron Atoms: Fermi Holes and Fermi Heaps”

      Link: Boston University: Professor Dan Dill’s “Many-Electron Atoms: Fermi Holes and Fermi Heaps” (PDF)
       
      Instructions: Please click on the link and scroll down the webpage to the italic heading, “Many-Electron 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.

  • 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 “Many-Electron 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 “Many-Electron 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 “Many-Electron 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 Spin-Orbit 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 Spin-Orbit 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 two-electron 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 BY-NC-SA 3.0. The original version can be found here.

  • 4.2.8 Term Symbols  
  • 4.3 Introduction to Techniques of Approximation  
    • Reading: University of Southampton: Professor Chris-Kriton Skylaris’s “Perturbation Theory”

      Link: University of Southampton: Professor Chris-Kriton 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.

  • 4.3.1 Time-Independent 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 time-independent perturbation theory.

  • 4.3.2 Time-Dependent 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 time-dependent 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 H2+ molecule-ion and the H2 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  
  • 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 Born-Oppenheimer 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 Born-Oppenheimer approximation.

  • 5.2 Molecular Orbitals Theory  
  • 5.3 Molecular Orbitals Description of Diatomic Molecules  
  • 5.3.1 The Hydrogen Molecule  
  • 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.

  • 5.3.3 Bonding in Heteronuclear Diatomic Molecules  
  • 5.4 Molecular Orbitals Description of Polyatomic Molecules  
  • 5.4.1 The Huckel Theory and Applications  
  • 5.4.2 Self-Consistent Field (Hartree-Fock Method) Calculations and Density Functional 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 California-Davis: UC Davis ChemWiki’s “Group Theory”

      Link: University of California-Davis: 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.

  • 6.2 Symmetry in Molecular Structures  
  • 6.3 Character Tables and Symmetry Labels  
  • 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  
  • 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.

  • 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.

  • 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 vibrational-rotation 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  
  • 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 (UV-Vis) light interact with molecules.  UV-Vis light possesses sufficient energy to cause electronic transition.  During an electronic transition, electrons jump from their (low-energy) ground state configuration into a high-energy 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  
  • 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 Franck-Condon 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 Franck-Condon 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.

  • 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.

  • 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 re-emitted 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  
  • 9.2 Nuclear Magnetic Resonance  
  • 9.3 Electron Spin Resonance  
  • Final Exam