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

  • This topic

    Kinetic propertic

    1. Diffusion
    2. Equilibrium and non-equilibrium molecular dynamics
    3. Brownian dynamics and Dissipative particle dynamics
  • SIMOLANT - Computer simulations of phase transitions