SubjectsSubjects(version: 955)
Course, academic year 2019/2020
Statistical Thermodynamics, Molecular Modeling and Simulation - M403002
Title: Statistická termodynamika, molekulové modelování a simulace
Guaranteed by: Department of Physical Chemistry (403)
Faculty: Faculty of Chemical Engineering
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, C+Ex [HT]
Capacity: unlimited / unlimited (unknown)
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Kolafa Jiří prof. RNDr. CSc.
Malijevský Alexandr prof. Mgr. Ph.D., DSc.
Interchangeability : N403023
Examination dates   Schedule   
Annotation -
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.
Last update: Pátková Vlasta (09.01.2018)
Aim of the course -

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

Last update: Pátková Vlasta (09.01.2018)
Literature -

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

Last update: Pátková Vlasta (09.01.2018)
Learning resources -

Last update: Pátková Vlasta (09.01.2018)
Syllabus -

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.

Last update: Kolafa Jiří (08.02.2018)
Registration requirements -

Physical chemistry I and II

Last update: Pátková Vlasta (09.01.2018)
Course completion requirements -

Elaboration of an individual project.

Comutational tests.

Oral exam.

Last update: Řehák Karel (02.03.2018)
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
6 / 6 168 / 168
Coursework assessment
Form Significance
Defense of an individual project 10
Report from individual projects 20
Continuous assessment of study performance and course -credit tests 50
Oral examination 20