CHEM 745/7450 - Statistical Mechanics

Semester: Winter 2024

Professor: P.N. Roy | Discipline: Theoretical | Campus: Waterloo


The course covers selected topics in the simulation of nanoscale systems. A review of essential concepts of statistical mechanics will first be covered. Simulation techniques such as Molecular Dynamics and Monte Carlo methods will be described. The Feynman path integral formulation of quantum statistical mechanics will be introduced. Simulations methods based on the Path Integral formalism will be described. Applications to quantum fluids and confined molecules will be presented.

Learning outcomes:

  • Understand the quantum dynamical nature of molecular motion.
  • Understand the theoretical foundations of classical and quantum molecular dynamics.
  • Become familiar with the formal tools and computational approaches used to describe and simulate the dynamics of atomic and molecular systems.
  • Proficiency in computer simulations and data analysis.
  • Develop critical thinking with regards to articles that appear in the literature.
  • Further develop Python coding skills.


Allen and Tildesley, Computer Simulation of Liquids, Oxford, 1987; McQuarrie, Statistical Mechanics, Harper and Row, 1976; Chandler, Introduction to Modern Statistical Mechanics, Oxford, 1987; Statistical Thermodynamics for Pure and Applied Sciences, 1st edition, Frederick Richard Wayne McCourt, 2021


Assignments (5) 30% In-class Test (3) 45% Term Project 25%


Proposed Course outline:

  1. Introduction: Phase Space, Hamiltonians, Classical and Quantum descriptions
  2. Review of statistical mechanics
  3. Classical molecular dynamics simulation of liquids
    • Integrators and thermostats
    • Interactions and forcefields
  4. Quantum effects: Feynman Path Integral formalism
    • Ring polymer isomorphism
    • Harmonic Oscillator, Translations
    • Rotors and tops
  5. Path Integral Molecular Dynamics simulations and applications
  6. Path Integral Monte Carlo simulations and applications
  7. Canonical correlation functions
    • Transport properties
    • Spectra
    • Quantum Dynamics


  • Fri: 9:00 am - 9:50 am in C2 278

Office Hours

No office hours provided.