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Physical Chemistry IV (Statistical Thermodynamics and Molecular Simulation) - MC260P129
Title: Fyzikální chemie IV (Statistická termodynamika a molekulové simulace)
Czech title: Fyzikální chemie IV (Statistická termodynamika a molekulové simulace)
Guaranteed by: Department of Physical and Macromolecular Chemistry (31-260)
Faculty: Faculty of Science
Actual: from 2022
Semester: winter
E-Credits: 4
Examination process: winter s.:
Hours per week, examination: winter s.:2/1, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Note: enabled for web enrollment
Guarantor: doc. RNDr. Peter Košovan, Ph.D.
Teacher(s): doc. RNDr. Peter Košovan, Ph.D.
Incompatibility : MC260P105
Annotation -
Last update: doc. RNDr. Peter Košovan, Ph.D. (13.10.2020)
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.
Literature -
Last update: doc. RNDr. Peter Košovan, Ph.D. (08.03.2019)
  1. T.J.H. Vlugt, J.P.J.M. van der Eerden, M. Dijkstra, B. Smit, D. Frenkel: Introduction to Molecular Simulation and Statistical Thermodynamics, TU Delft online textbook http://homepage.tudelft.nl/v9k6y/imsst/index.html
  2. D. Frenkel and B. Smit: Understanding Molecular Simulation, https://www.sciencedirect.com/book/9780122673511/understanding-molecular-simulation
  3. L. Reichl: Moder course in statistical physics, https://onlinelibrary.wiley.com/doi/book/10.1002/9783527690497
  4. D. Mc.Quarrie: Statistical Thermodynamics
  5. D. Chandler: INtroduction to modern Statistical Mechanics
  6. J. Kolafa: Molekulové modelování a simulace VŠCHT (2015) pdf online: https://ufch.vscht.cz/files/uzel/0014046/y83PKc7MBQA.pdf
  7. T. Boublík: Statistická tedmodanamika, Academia, Praha, (2000)
  8. I. Nezbeda, J. Kolafa, I. Kotrla: Úvod do počítačových simulací: medoty molekulové dynamiky a Monte Carlo, Karolinum, Praha, (2002)
Requirements to the exam -
Last update: doc. RNDr. Peter Košovan, Ph.D. (13.10.2020)

Oral exam within the scope of the sylabus. In the time of covid-19 restrictions it is possible to the the oral exam by a videoconference.

Individual project selected from the topics proposed by the lecturer. The lecturer may approve also a different topic, proposed by the student.
Syllabus -
Last update: doc. RNDr. Peter Košovan, Ph.D. (08.03.2019)
  1. Statistical thermodynamics in isolated systems - overview of statistics, probability of states, microstates vs. macrostates, entropy, most probable distribution
  2. Systems at constant temperature - the Boltzmann distribution, partition function, thermodynamic variables from the partition function, fluctuations, thermodynamic ensembles - concepts, definitions, concepts and examples
  3. 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
  4. Interacting systems - quantum-mechanical and classical statistical thermodynamics, configuration integral, configuration space and phase space, virial expansion in real gases
  5. The Monte Carlo simulation method - sampling the configuration space, Metropolis algorithm, detailed balance, ergodicity, simple sampling and importance sampling, initialization, equilibration, sampling
  6. 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
  7. 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,
  8. Statistical thermodynamics of the liquid state - pair correlation function, statistical theories of the liquid state - integral equations and perturbation theories
  9. 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
  10. Solutions of electrolytes and polyelectrolytes, Debye length and Bjerrum length, long-range interactions in simulations - Ewald summation and related techniques,
  11. Biased sampling in Monte Carlo, simulations in the grandcanonical ensemble, isothermal-isobaric ensemble, reaction ensemble and constant pH ensemble
  12. Thermodynamic integration for calculating free energies in simulations, Gibbs ensemble for simulating phase equilibria
  13. (optional) Non-equilibrium statistical thermodynamics, and non-equilibrium simulations
 
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