Topic outline

  • General

    The presentations are in English. Optional (not compulsory) parts are marked orange and/or + sign.

    Skripta a  vzorový zkouškový test vč. řešení v češtině viz níže.

  • Introduction

    Popular introduction to modeling in chemistry and simulation with examples.

  • Statistical thermodynamics

    1. Microcanonical ensemble and the ergodic hypothesis
    2. Canonical ensemble and Boltzmann probability
    3. Thermodynamics and the Boltzmann equation for entropy
    4. Optional: isobaric and grand-canonical ensembles

  • Models + exercises

       1. Model hierarchy
       2. Atom-atom interactions
       3. Force field in molecular modeling
       4. Construction of force fields
       5. External forces
       6. Lattice models

  • Molecular dynamics – the Verlet method

    1. Newton equations of motion
    2. Verlet method
    3. Leap-frog method and its equivalence to the Verlet method
    4. Show: planet revolution
    5. Velocity Verlet

  • Other methods, temperature in MD

    1.    Optional: Gear methods
    2.    Temperature in MD
    3.    Thermostats:
          • based on the Maxwell-Boltzmann distribution
          • based on velocity rescaling (Berendsen method)
          • Nosé-Hoover method (qualitatively)
          • workout: thermostats in SIMOLANT (see below for the installation of SIMOLANT)

  • Monte Carlo methods

    Monte Carlo methods

    1. Naïve Monte Carlo
    2. Metropolis method
    3. Markov chains
    4. Acceptance ratio

    Workout: comparison of MC and MD using SIMOLANT

  • Simulation methodology and workout 1

    Lecture:

    1. Pseudoexperiment – start, equilibration, measurement
    2. Boundary conditions
    3. Errors of correlated time series
    4. Mechanical quantities: temperature, internal energy, pressure
    5. Entropic quantities (thermodynamic integration, Widom, integrating reversible work, local density method)

    Workout:

    • Verify the Clausius–Clapeyron equation by simulations of a 2D model of matter

  • Structural quantities and workout 2

    1. Radial distribution function
    2. Experiment: structure factor and RDF
    3. RDF from simulations
    4. Examples

  • Short and long range forces

    1. Short-range forces: cutoff, correction
    2. Electrostatic forces: smooth cutoff; Ewald summation; reaction field (qualitatively)

  • Molecular systems

    1. Polymers and Rosenbluth sampling
    2. Reptation
    3. MC of rigid models
    4. SHAKE
    5. Optional: Optimization

  • Kinetic properties

    1. Diffusion
    2. Equilibrium and non-equilibrium molecular dynamics
    3. Brownian dynamics and Dissipative particle dynamics

  • SIMOLANT - Computer simulations of phase transitions

    screenshot of SIMOLANT

    A number of phenomena are shown using a two-dimensional molecular model of matter: condensation of gas and crystallization of liquid on cooling, melting and evaporation on heating up, crystal defects, capillary action, atmosphere in a gravitational field, nucleation, diffusion ... and more. 

    We can simulate using Monte Carlo and molecular dynamics methods at constant energy and temperature, with different thermostats, at different boundary conditions, change the step length,  show the radial distribution function, and visualize the number of neighbors.

    The program is written in C and C++ using the FLTK toolkit. Executables are available both for Windows (MinGW) and Linux. After downloading the respective zip-file, unpack it to a suitable folder and run simolant.

    SIMOLANT is a free software (GPL3). For the latest version, linux executables, and sources, see http://www.vscht.cz/fch/software/simolant/

    Installing SIMOLANT for Windows (32 bit):

    • create a folder (e.g., Desktop\SIMOLANT)
    • unzip the installation file simolant-win32.zip there
    • run simolant.exe