Class at Faculty of Science |

MC260P129

Statistical thermodynamics in isolated systems - overview of statistics, probability of states, microstates vs. macrostates, entropy, most probable distribution

Systems at constant temperature - the Boltzmann distribution, partition function, thermodynamic variables from the partition function, fluctuations, thermodynamic ensembles - concepts, definitions, concepts and examples

Systems of non-interacting particles - single-particle partition function, monoatomic, diatomic and polyatomic ideal gas, Fermi-Dirac and Bose-Einstein statistics, ideal gas mixtures and chemical equilibria

Interacting systems - quantum-mechanical and classical statistical thermodynamics, configuration integral, configuration space and phase space, virial expansion in real gases

The Monte Carlo simulation method - sampling the configuration space, Metropolis algorithm, detailed balance, ergodicity, simple sampling and importance sampling, initialization, equilibration, sampling

Simulations of interacting particles - interaction potentials, computer model, periodic boundary conditions, examples of interaction potentials, theorem of corresponding states and reduced units, short-range vs. long-range interactions, computing ensemble averages and thermodynamic properties from the simulation, statistical analysis of correlated time series

The Ising model in 1D, 2D and 3D - phase transitions, coexistence, spontaneous symmetry breaking, ergodicity, the mean-field approach, MC simulation of the Ising model, single-particle trial moves and collective trial moves,

Statistical thermodynamics of the liquid state - pair correlation function, statistical theories of the liquid state - integral equations and perturbation theories

Molecular dynamics - sampling the phase space vs. sampling the configuration space, numerical integration of equations of motion, MD at constant temperature, computing thermodynamic variables and transport coefficients, Green-Kubo relations

Solutions of electrolytes and polyelectrolytes, Debye length and Bjerrum length, long-range interactions in simulations - Ewald summation and related techniques,

Biased sampling in Monte Carlo, simulations in the grandcanonical ensemble, isothermal-isobaric ensemble, reaction ensemble and constant pH ensemble

Thermodynamic integration for calculating free energies in simulations, Gibbs ensemble for simulating phase equilibria

(optional) Non-equilibrium statistical thermodynamics, and non-equilibrium simulations

The course of Statistical Thermodynamics and Molecular Simulation is primarily intended for students of the master programme of Physical Chemistry, and for PhD students of related programmes (Physical Chemistry, Macromolecular Chemistry, Biophysical Chemistry, and Molecular Modeling). First part of the course introduces the basic principles of Statistical Thermodynamics, which are then applied to ideal, non-interacting systems. In the sequel, it introduces the Monte Carlo and molecular dynamics simulation methods, which are then used for statistico-mechanical description of more complicated interacting systems in the condensed phase.

In the time of covid-19 restrictions, the lectures will be held online by means of a videoconference. Recording of the lectures will be made available to students via google drive.