12669 - Lab-based Course of Physical Chemistry of Materials

Learning outcomes

The course provides an introduction mainly based on practical computer exercises, with informal presentation of theoretical background, to (a) molecular mechanics modelling technique, and (b) Monte Carlo and (c) molecular dynamics computer simulation techniques. The course does not assume any previous knowledge of statistical physics and computer programming languages. The exercises rely on in-house and open source software. Familiarity with the Unix (Linux) operating system may be useful although not necessary (an introductory survey of the essential features and commands relevant to the course will be given).

Course contents

Introduction to UNIX (Linux): login and logout; basic utilisation the X11 environment; fundamental Unix commands; elementary management of files and directories; usage of Emacs and GNUplot. Introduction to Molecular Mechanics (MM) modelling techniques: force fields MM2, MM3 and their parameterisation; stretching, bending, torsion and non-bonding energies; building of a molecular structure by means of the Z matrix (molden), XYZ PDB and MOL formats; visualisation of a molecular structure (rasmol); determination of the minimal energy MM structure (tinker); non-derivative, simulated-annealing, and genetic minimisation algorithms; MM computation of ring energies for cicloalkanes; MM computation of energies for the chair, half-chair, twisted, planar and boat conformations of cyclohexane; effect of the minimisation algorithm on the successful identification of the minimum energy conformation; calculation of the conformational energy profile for n-butane. Introduction to Monte Carlo (MC) simulations: fundamentals of statistical physics; distribution functions; microscopic reversibility principle; sampling from a distribution and Von Neumann rejection method; concepts of pseudo random number generators; random MC particles moves and Metropolis algorithm; Lennard-Jones (LJ) potential; equilibration and production runs; MC simulation of a LJ fluid; effect of the acceptance ratio and sampling width for MC moves; analysis of simulations results and computation of average observables; effect of the potential cutoff and periodic boundary conditions; effect of sample size and analysis of fluctuations; structure of a liquid phase liquid and radial correlation function; virial theorem and computation of the pressure; MC simulations at constant pressure; MC simulation of the liquid-vapour transition along an isobar of the LJ fluid. Introduction molecular dynamics (MD) simulations: Hamilton equations of motion; finite differences approximations; symplectic integrators for the equations of motion; MD simulation of a LJ fluid; effect of the time step on the conservation of total energy; computation of static and dynamic observables; virial theorem and computation of the pressure; computation of temperature; MD simulations at constant temperature and pressure; correlation functions; velocity auto-correlation function; diffusion coefficient; MD simulation of the liquid-vapour transition along an isotherm of the LJ fluid; localisation of the transition with the Maxwell construction; construction of the coexistence and spinodal curves; metastability, comparison with the van der Waals fluid.

Readings/Bibliography

Michael P. Allen and Dominique J. Tildesley, "Computer Simulation of Liquids", (Clarendon Press, Oxford, 1987). Daan Frenkel and Berend Smit, "Understanding Molecular Simulation: from Algorithms to Applications", (Academic Press, San Diego, 1996). Andrew Leach, "Molecular Modelling: Principles and Applications", (2nd Edition), (Prentice Hall, Harlow, 2001). Frank Jensen, "Introduction to Computational Chemistry", (John Wiley & Sons, Chichester, 1999).

Teaching methods

The course allows the students to use and experiment with the most relevant computational techniques discussed within the "Chemical Physics of Materials" course. Lectures are held in the computer laboratory and are structured as a frequent alternation between concise presentations of theoretical background material with practical exercises with the computer. Students are encouraged to discuss the physical meaning of the numerical results obtained from the computer programs and devise algorithms for extracting useful information from the simulations raw data. Lectures are preferentially held in English. Students are encouraged to use the English language for posing questions and for discussing the outcomes of the computer experiments.

Assessment methods

Students are divided in small groups of two-three persons and write at the end of the term two short papers critically discussing the outcomes of the: (a) MC and MD simulations, and (b) MM computations. The papers must be delivered at least one week before the final examination. The evaluation of these papers contributes to the final mark of the "Chemical Physics of Materials" examination.

Teaching tools

Handouts and other didactic material (in English language) provided during lectures. Computer simulations and other calculations are run under the Unix (Linux - Debian http://www.debian.org) operating system. The computational softwares are either simple Fortran 77 and 90 codes specifically developed in-house for the purpose and compiled with g95 (http://www.g95.org), and other open source packages: tinker (http://dasher.wustl.edu/tinker), molden (http://www.cmbi.kun.nl/%7Eschaft/molden/molden.html), rasmol (http://www.openrasmol.org).

Office hours

See the website of Roberto Berardi