Theoretical / proof-based
Statistical mechanics (chemistry) · Graduate · Chemistry
Topics
Ensembles and partition functions
- Microcanonical ensemble and Boltzmann entropy
- Canonical ensemble: partition function and Helmholtz free energy
- Grand canonical ensemble and chemical potential
- Isothermal–isobaric ensemble and Gibbs free energy
- Classical partition functions: translational, rotational, vibrational
- Quantum partition functions and low-temperature limits
- Equipartition theorem and its failures
- Ideal gas equation of state from statistical mechanics
- Chemical equilibrium from partition functions
- Standard thermodynamic quantities from molecular data
Interacting systems
- Virial expansion and equations of state
- Radial distribution function g(r) and structure factor
- Monte Carlo simulation: Metropolis algorithm and detailed balance
- Molecular dynamics: Verlet integrators and thermostats
- Ewald summation for electrostatic interactions
- Force fields for molecular simulation: AMBER, CHARMM, OPLS
- Free energy perturbation and thermodynamic integration
- Umbrella sampling and WHAM analysis
- Replica exchange molecular dynamics
- Phase transitions and critical exponents (introduction)
Non-equilibrium and transport
- Boltzmann transport equation
- Chapman–Enskog theory for transport coefficients
- Diffusion, viscosity, and thermal conductivity
- Fokker–Planck and Langevin equations
- Linear response theory and Onsager reciprocal relations
- Chemical reaction rates from transition state theory
- Master equation and stochastic chemical kinetics
- Fluctuation theorems and Jarzynski equality (intro)
- Non-equilibrium steady states
- Brownian motion and Einstein relation
Advanced chemical applications
- Ising model for adsorption and phase transitions
- Lattice models for polymer conformations
- Configurational integral for flexible molecules
- Electrolyte solutions: Debye–Hückel and Poisson–Boltzmann
- Semiclassical methods for molecular collisions
- Path integral molecular dynamics (overview)
- Coarse-grained models and multiscale simulation
- Statistical mechanics of surfaces and interfaces
- Reaction–diffusion systems and pattern formation
- Connecting simulation to experimental observables
Pricing
Graduate-level rates are set on consultation. See the pricing page for K–12 and undergraduate rates.