SubjectsSubjects(version: 902)
Course, academic year 2022/2023
Statistical Thermodynamics, Molecular Modeling and Simulation - M403002
Title: Statistická termodynamika, molekulové modelování a simulace
Guaranteed by: Department of Physical Chemistry (403)
Actual: from 2019
Semester: summer
Points: summer s.:6
E-Credits: summer s.:6
Examination process: summer s.:
Hours per week, examination: summer s.:3/1 [hours/week]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
For type: Master's (post-Bachelor)
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Kolafa Jiří prof. RNDr. CSc.
Malijevský Alexandr doc. Mgr. Ph.D., DSc.
Interchangeability : N403023
Annotation -
Last update: Pátková Vlasta (09.01.2018)
The course covers the fundamentals of statistical thermodynamics of classical molecular systems and its applications in molecular modelling. The lecture includes general methods of mathematical statistics, which can be used in many other fields.
Aim of the course -
Last update: Pátková Vlasta (09.01.2018)

The students will be able to:

Understand fundamentals of (classical) molecular systems

Apply statistical and simulation methods for stochastic processes

Determine measurable (macroscopic) quantities from the molecular characteristics of matter

Literature -
Last update: Pátková Vlasta (09.01.2018)

R:Malijevský A, Lekce ze statistické termodynamiky, VŠCHT, Praha, 2009, 978-80-7080-710-1

R:Nezbeda I.,Kolafa J.,Kotrla M., Úvod do počítačových simulací. Metody Monte Carlo a molekulární dynamiky, Karolinum, Praha, 2003, 80-246-0649-6

A: Atkins P.W., de Paula J., Physical Chemistry, Oxford University Press, 2010, 978-0-19-954337-3

A: Frenkel D.,Smit B, Understanding Molecular Simulation � From Algorithms to Applications, New York, 2002, Academic Press, 0-12-267351-4

A: Allen M. P.,Tildesley D. J., Computer Simulation of Liquids, Oxford, Clarendon Press, 2002, 0-19-855375-7

Learning resources -
Last update: Pátková Vlasta (09.01.2018)

Syllabus -
Last update: Kolafa Jiří prof. RNDr. CSc. (08.02.2018)

1. Classical thermodynamics - a brief overview. Basic principles of statistical mechanics, ergodic hypothesis. Phase space.

2. Mathematical statistics - main distributions: binomial, Poisson, Gaussian. Mean and fluctuation. Stirling's formula (derivation).

3. Microcanonical ensemble. Entropy as a measure of chaos. A link between statistical mechanics and thermodynamics.

4. Virial and equipartition theorem. Calculation of energy and specific heats - examples.

5. Canonical and grand-canonical ensembles. Thermodynamic functions and their fluctuations. Partition function.

6. Ideal gas: from the partition function towards the equation of state.

7. Non-ideal systems. Molecular models. Correlation functions and structure factor. Virial expansion.

8. Application I: Calculation of equilibrium constant for the chemical reactions in the gas phase.

9. Application II: harmonic ideal crystal and black-body radiation.

10. Modeling in chemistry: forces between molecules, force field. Molecular mechanics. Boundary conditions, calculation of long-range forces.

11. Molecular dynamics: integrators, integrals of motion. Thermostat and barostat.

12. Monte Carlo: Markov Chain, Metropolis Algorithm. Random numbers. MC in different ensembles. Optimization.

13. Computer Experiment: design, measurement of quantities, analysis of uncertainties.

14. Kinetic quantities in equilibrium and non-equilibrium MD. Brownian dynamics and dissipative particle dynamics.

Registration requirements -
Last update: Pátková Vlasta (09.01.2018)

Physical chemistry I and II

Course completion requirements -
Last update: Řehák Karel doc. Ing. CSc. (02.03.2018)

Elaboration of an individual project.

Comutational tests.

Oral exam.

Teaching methods
Activity Credits Hours
Obhajoba individuálního projektu 0,5 14
Účast na přednáškách 1,5 42
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi 1,5 42
Práce na individuálním projektu 1 28
Příprava na zkoušku a její absolvování 1 28
Účast na seminářích 0,5 14
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