Quantum Chemistry

Introduction to Quantum Chemistry


The notebooks in ipynb directory can be run via by clicking on the badge above.

CHEM 3PA3 Quantum Mechanics and Spectroscopy. An introduction to quantum chemistry and its applications in spectroscopy and structure and unusual phenomena at the nanoscale. Web Site


  1. Basics of Jupyter, Python, and Programming
  2. From Newton to Schrödinger
  3. The Schrödinger Equation
  4. The Particle in a Box
  5. Particles confined in two and three dimensions.
  6. The Postulates of Quantum Mechanics
  7. 1-electron atoms
  8. Approximate Methods
  9. Many-electron systems: Structure and Spectroscopy
  10. 2-electron atoms
  11. Many-electron atoms
  12. The Born-Oppenheimer Approximation
  13. Molecules
  14. Simple Approaches for Many-Electron Systems
  15. Hartree-Fock Theory and Ab Initio Methods
  16. The Harmonic Oscillator
  17. Elementary Spectroscopy
  18. Vibrational Spectroscopy
  19. The Rigid Rotor and Rotational Spectroscopy


Your assignments will be turned in using Microsoft Teams. For instructions on how to turn in an assignment with Microsoft Teams, see the webpage.

  1. Introduction to Jupyter.
  2. Basic Python.
  3. Introduction to Numpy.
  4. Computing Course Marks with Jupyter, Python, Numpy, and syzygy.
  5. Introduction to QM and the Schrödinger equation


Your exam has 3 parts. The first two parts are worth 40%. The last part is worth 20%. An overview and simple download links are below. Here are more detailed instructions.

  1. Part 1 (20 questions worth 2 points each; 2 bonus questions worth 2 points each)
  2. Part 2 (5 Long-form problems)
  3. Part 3 (Oral exam. +/- 10 points for your defense of your answers in parts 1 and 2; up to 20 points for your responses to questions randomly selected from those listed here.) html version

You can find the exam on binder, under ipynb/Final Exam Part #.ipynb, where # is the part of the exam you are interested in.

Extra Credit

Extra credit problems should be sent to the instructor in a private chat message via Microsoft Teams.

  1. Basics of Jupyter, Python, and Programming.
  2. Problems from Randy Dumont’s book and his course.
  3. Problem Sets from Jack Simons’ and Jeff Nichols’ Quantum Mechanics in Chemistry
  4. Problems from Jack Simons’ An Introduction to Theoretical Chemistry, 2nd edition.
  5. Problems from many other quantum chemistry textbooks are also acceptable. These are not (to my knowledge) legally available free online, though you can try Sci-Hub, and there are occasionally other links (of likewise questionable legality and permanence). Good examples are:
  6. Relevant assignments and exams from MIT, especially the courses on quantum chemistry from 2005, 2007, 2013, 2017, and 2018. Answer keys are sometimes, but not always, provided.
  7. Old assignments, quizzes, exams, and problems from previous iterations of this course and related courses at McMaster. Answer keys are often, but not always, provided (often after a blank version of the assignment/assessment that you can use to practice).
  8. You can turn in answers to the various questions that appear in the course notes, or in other materials I post online.

Administrative Documents

Learning Objectives

Know, understand, and be able to use key equations:

  1. Time-dependent Schrödinger equation.
  2. Time-independent Schrödinger equation
  3. Fermi’s golden rule
  4. Time-correlation formulation for spectral broadening

Understand key concepts/notation:

  1. Bra-ket notation.
  2. Hermitian operators
  3. Eigenfunctions/eigenvalues
  4. Expansion in a complete orthonormal set
  5. Dirac delta function
  6. Commutators/Simulataneously observable operators
  7. Heisenberg Uncertainty Principle
  8. De Broglie wavelength
  9. Planck’s law
  10. Expectation values
  11. Probabilistic interpretation of the wavefunction
  12. Slater determinants
  13. Allowable and non-allowable wavefunctions.
  14. Allowable and non-allowable operators.

Ground-state wavefunctions, eigenenergies, quantum numbers, and selection rules for:

  1. Particle-in-a-box.
  2. Harmonic Oscillator
  3. Rigid Rotor
  4. One-electron atom
  5. Angular momentum (L, S, J, etc.)

Atoms & Molecules:

  1. Concept of effective nuclear charge.
  2. Hartree-Fock
  3. Molecular orbital theory; linear combination of atomic orbitals
  4. Valence bond theory.
  5. Term Symbols
  6. Hund’s Rules
  7. Born-Oppenheimer Approximation

Computational methods/approaches.

  1. Perturbation Theory
  2. Variational Principle
  3. Evaluating expectation values
  4. “Fundamental experiments” of quantum mechanics like blackbody radiation and the photoelectric effect.
  5. Hartree-Fock

Reference Materials

Materials from McMaster (my notes and Randy Dumont’s book) are likely to be especially helpful. The introductory and more advanced textbooks from Jack Simons are likewise excellent. The (free) Coursera course from John Daily mirrors the content of this course, albeit with less depth.

  1. Randy Dumont’s book, An Emergent Reality Part 2. Quantum Mechanics (courtesy of Randy Dumont)
  2. From Newton to Schrödinger (Paul’s notes)
  3. The Particle in a Box (Paul’s notes)
  4. Notes on the Analogy between Quantum Mechanics’ Math and Linear Algebra
  5. The Harmonic Oscillator (courtesy of Rogelio Cuevas-Saavedra)
  6. Rogelio’s Slides from Brock University (courtesy of Rogelio Cuevas-Saavedra)
  7. The (Heisenberg) Uncertainty Principle(Paul’s notes)
  8. Jack Simon’s video on the Born-Oppenheimer Approximation and Electronic Wavefunctions
  9. The Born-Oppenheimer Approximation and the Molecular Potential Energy Surface (Paul’s notes)
  10. The (Hydrogenic) 1-electron atom (Paul’s notes)
  11. The (Helium-like) 2-electron atom (Paul’s notes)
  12. The many-electron atom (Paul’s notes)
  13. Molecular wavefunctions (Paul’s notes)
  14. Spectroscopy (Paul’s notes)
  15. Notes on time-dependent perturbation and spectroscopy from MIT
  16. Quantum Mechanics in Chemistry by Jack Simons and Jeff Nichols (free online textbook)
  17. An Introduction to Theoretical Chemistry, 2nd edition by Jack Simons. (free online textbook)
  18. Seymour Blinder’s online Quantum Chemistry Notes These are really excellent.
  19. David Sherrill’s introductory to quantum chemistry notes Anything by David Sherrill is well worth reading. He writes beautifully!
  20. A similar GitHub-based course from Iowa State University
  21. Chemistry Libre Texts, including MacQuarrie and Simon, Chapters 1-15, Chang’s Biophysical Chemistry, and the notes
  22. Online materials from MIT’s Quantum Chemistry courses in 2005, 2007, 2013, 2017, and 2018.
  23. Online courses from EdX and Coursera.

Other resources

Keys to assignments are not always available. But where available, instructors can join the (private) GitHub with the answer keys by e-mailing Paul Ayers,, from your official e-mail account. Where possible, nbgrader can be used to mark assignments. New contributions to the problem bank are most welcome too!


This public repository contains course materials for CHEM 3PA3, an introduction to quantum chemistry. The main course content is conveyed through, and assessed by, Jupyter notebooks and is made available via the Creative Commons Zero CC0 version 1.0 license. However, where I have reposted/adapted content from other sources, those sources retain their copyright/license.