AS.030.456 Chemical Applications of Group Theory

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Last Updated: May 11, 2021



This class will introduce group theory in the chemical/physical context. In addition to the fundamentals of (practical/applied) group theory, this course will explore how the tools of group theory enable powerful, general statements to be made about the behavior of chemical systems from the atomics scale to the macroscale, often without requiring detailed calculations or knowledge of most microscopic details. It is particularly targeted at upper level chemistry and physics undergraduates who have a basic knowledge of quantum mechanics and a brief familiarity with linear algebra.

Note: In Spring 2021, it will be possible for students not physically present on the JHU campus, to take this course with online synchronous lectures.

Class Times: MW 12-1:15 PM Eastern Time
Classroom: Bloomberg 478 (on the campus map) and Online. Login to view details.

Prof. Tyrel M. McQueen
Zoom Office: Login to view details.
Office Hours: Login to view details.

Grading: 60% Homework, 5% Class Participation, 10% Each of Two Hour Exams, 15% Final Exam Presentation

Lowest homework score will be dropped.

Required Texts:
  1. Group Theory and Quantum Mechanics (M. Tinkham)

Supplementary Resources:
  1. Group Theory and Its Application to Physical Problems (M. Hamermesh)
  2. Chemical Applications of Group Theory (F.A. Cotton)

Tentative Schedule (can and will change!)
Week 1: The Big Picture: Why Group Theory? [TMMHO, GTQM Ch.1] (this week is ONLINE ONLY)
Week 2: Symmetry and Symmetry Operations [TMMHO, GTQM Ch.1&2]
Week 3: Introduction to Group Theory [GTQM Ch.2]
Week 4: Group Theory to Representation Theory [GTQM Ch.3]
Week 5: Applications 1: Crystallographic Point Groups and Crystal Fields [GTQM Ch.4]
Week 6: Introduction to Double Groups, Hour Exam 1 (Wednesday) [GTQM Ch.4]
Week 7: Applications 2: Rotation and Molecular Groups [GTQM Ch.5]
Week 8: Quantum Mechanics of Atoms [GTQM Ch.6]
Week 9: Applications 3: Electrons in The Hydrogen Molecule to Complex Molecules (NO class Monday) [GTQM Ch.7]
Week 10: Applications 3: Electrons in The Hydrogen Molecule to Complex Molecules [GTQM Ch.7]
Week 11: Applications 4: Complex Molecular Vibrational States, Hour Exam 2 (Wednesday) [GTQM Ch.7]
Week 12: Applications 5: Solid State Theory (NO class Wednesday) [GTQM Ch.8]
Week 13: Applications 6: Solid State Theory [GTQM Ch.8]
Week 14: Further Applications of Group Theory to The World [TMMHO]
Tuesday, May 11 Final Exam Presentations 9AM-Noon

  1. Introductions (Lecture1.pdf)
  2. Quanutm Mechanics and Linear Algebra Refresher (Lecture2.pdf)
  3. Abstract Group Theory Fundamentals (Lecture3.pdf)
  4. Group Representations (Lecture4.pdf)
  5. Grand Orthogonality Theorem and Characters (Lecture5.pdf)
  6. The Schrodinger Group to Blochs Theorem (Lecture6.pdf)
  7. Basis Functions, Generators, To Crystal Fields (Lecture7.pdf)
  8. The Cubic Crystal Field (Lecture8.pdf)
  9. Double Groups (Lecture9.pdf)
  10. From One to Two Electrons, Selection Rules (Lecture10.pdf)
  11. More Multielectrons, Towards The Full Rotational Group (Lecture11.pdf)
  12. Representations of the Full Rotational Group (Lecture12.pdf)
  13. Vector Momentum Addition and Time Reversal (Lecture13.pdf)
  14. Atomic Energy Levels I (Lecture14.pdf)
  15. Atomic Energy Levels II (Lecture15.pdf)
  16. From Atoms to Molecules (Lecture16.pdf)
  17. From Atoms to Molecules II (Lecture17.pdf)
  18. From Molecular Electronic to Vibrational Structure (Lecture18.pdf)
  19. Molecular Vibrations and Rotations (Lecture19.pdf)
  20. Introduction to Solid State Groups (Lecture20.pdf)
  21. Loose and Tight Binding (Lecture21.pdf)
  22. Spaghetti Diagrams and Compatibility Relations (Lecture22.pdf)
  23. Vibrational Band Structures (Lecture23.pdf)
  24. Other Applications of Group Theory (Lecture24.pdf)

Homework Assigments

These will be posted weekly.

Exam Information
  1. Hour Exam #1 (Sample Correct Answers). Hour Exam 1 is a take home exam. Wednesday, March 3rd will have no class so you can use that time for the exam if desired.
  2. Hour Exam #2 (Sample Correct Answers). Hour Exam 2 is a take home exam. Wednesday, April 7th will have no class so you can use that time for the exam if desired.
  3. Final Exam Rubric


These will be posted as mentioned in the class.

Lecture Notes

As a matter of course policy, lecture notes are not available online. You are welcome to stop by TMM's office to view them anytime.

Audit Policy

Graduate students are allowed to audit the course. It is required that you attend most of the lectures, and strongly recommended that you look at and complete the homework assignments.