| Intitulé de l’enseignement | Code UE | Crédits |
| Advanced Statistical Mechanics for Chemists | CHIM-M1-C | 4 ECTS |
Level: M1
Coordinator: Damien Laage
Total teaching hours: 32h
Lectures: 32 h
Course description and content
This course provides chemists with a thorough introduction to the fundamental concepts of statistical mechanics and to the numerical methods used to simulate the dynamics of complex molecular systems. Designed for both theorists and experimentalists, it connects theoretical foundations with practical applications relevant to chemistry, biochemistry, soft matter, environmental chemistry and material science.
The course first introduces the transition from classical to statistical mechanics and develops the time-dependent formalisms required to describe molecular motions. It then introduces key stochastic and deterministic approaches used to model dynamic processes in chemical and biochemical environments. Emphasis is placed on connecting theory with molecular simulation techniques, and on illustrating how these tools can elucidate a variety of processes including chemical kinetics, transport properties, spectroscopy, and conformational dynamics.
Syllabus
1. Brief introduction to Lagrangian and Hamiltonian formalisms, Liouville equation and phase-space evolution
2. Time-dependent statistical mechanics
- Time-correlation functions and Green–Kubo relations
- Transport properties and diffusion
- Chemical kinetics from microscopic dynamics
3. Stochastic processes in chemical systems
- Langevin equation and Brownian motion
- Friction and memory effects
- Fokker–Planck equation
- Mean first-passage times and reaction-rate theories
4. Numerical simulation methods
- Molecular dynamics and Monte Carlo simulations
- Enhanced sampling techniques and Free-energy calculations
Learning goals
By the end of this course, students will be able to:
- Select and justify the most appropriate simulation or theoretical approach to address a given chemical or biochemical problem.
- Apply time-dependent statistical mechanics to model dynamical processes at the molecular scale.
- Interpret molecular simulation results in terms of underlying statistical-mechanical principles.
- Compute or analyze basic observables (e.g., correlation functions, diffusion coefficients, free energies) derived from molecular simulations.
- Understand the strengths and limitations of major simulation techniques and stochastic models.
Prerequisites
Students are expected to have solid foundations in general physical-chemistry (L3), statistical thermodynamics (L3), chemical kinetics (L3) and basic calculus (L3).
Grading
Written exams: 100 %