Introduction to statistical mechanics lab

Instructions

The following exercises are to be completed in the computational laboratory.
The computational lab will be from 13:00 to 16:00 on Monday, Tuesday, Thursday and Friday.
During these 4 days demonstrators will be available in the computer room to answer all your questions.
The start date is given in the table below according to the session.
There is an introductory lecture to the lab in Room 236 at 13:00 on the Start Date of your session.

The deadline is at 12:00 of the day indicated in the table below ("Report Deadline").
Work submitted late will be penalised.
There's a link set up on Blackboard for submitting a wiki the report for this experiment.
Blackboard is bb.imperial.ac.uk, and the link is in folder
3rd Year Chemistry Laboratories (2015 - 2016) / Y3C Third Year Computational Laboratory / Wiki submission.

Session Start Date End Date Report Deadline
1 12 / 10 / 2015 16 / 10 / 2015 23 / 10 / 2015
2 26 / 10 / 2015 30 / 10 / 2015 06 / 11 / 2015
3 09 / 11 / 2015 13 / 11 / 2015 20 / 11 / 2015
4 23 / 11 / 2015 27 / 11 / 2015 04 / 12 / 2015
5 07 / 12 / 2015 11 / 12 / 2015 18 / 12 / 2015

In each exercise there are a number of explicit Questions and often also an opportunity to Speculate on the results obtained. The final report will be expected to contain answers to these questions and, where you feel able, further speculation.

Questions related to this computational experiment can be directed to Prof. Nicholas Harrison and Dr Giuseppe Mallia.

Introduction & Background Material

The properties of materials (solids, liquids, gases) are a statistical average over the many different energy states of the molecules making up the material. The vibrational free energy of H2 can be computed analytically by summing over the harmonic vibrations of the molecule. This cannot be done by hand for a real material containing many atoms.

In this laboratory you will use a simple model of atomic interactions to calculate the energy and vibrations of a crystal of MgO. These vibrational energy levels will then be used to compute the free energy of the crystal and to predict how the material expands when heated. In the last final stage you will go beyond the harmonic (and quasi-harmonic) approximation and expand the crystal using a technique called molecular dynamics - essentially reproducing the actual vibration motions of the atoms. Fortunately the computer will do most of the work !

The Software: RedHat Linux, DLVisualize and GULP

DLVisualize is a general purpose graphical user interface for modelling. It will give you relatively easy access to a number of quantum mechanical and empirical simulation codes. In this case the interface to the molecular modelling code GULP (General Utility Lattice Program) will be used.

Linux provides an excellent environment for numerical simulations so the first step is to reboot your computer into RedHat Linux.

The environment is not hugely dissimilar to that provided by Microsoft Windows. You will find a web browser (Mozilla) on the tool bar and under the Start Menu you will find some office tools (Writer, Math etc.) which are similar to those in Microsoft Office (Word, Excel etc.) and you may find them useful in plotting your data and writing your report.

Starting DLVisualize

  • Open a terminal - right mouse click on the background, select Open Terminal
  • In the terminal type the command source /usr/local/chemistry/progs/thermlab_setup 
    Press enter.
    This sets up the environment you need to use DLViz
  • type dlv to start DLViz

There are websites devoted to both DLV and GULP where you can find some additional information.

Further information about DLV

Further information about GULP

Exercises

The exercises below should be completed in sequence. Although there will be supervisors present during the laboratory the exercises are designed to facilitate self study - there are many extensions of the exercises that might occur to you !

  1. Calculating the internal energy of an MgO crystal
  2. Lattice Vibrations - Computing the Phonons
  3. Calculating the Free Energy in the Harmonic Approximation
  4. The Thermal Expansion of MgO
  5. Molecular Dynamics

How to start DLVisualize

  • Open a terminal - right mouse click on the background, select Open Terminal
  • In the terminal type the command source /usr/local/chemistry/progs/thermlab_setup 
    Press Enter
    This sets up the environment you need to use DLViz
  • type dlv to start DLViz

How to save a picture for your report

The best way to output plots for printing/publication is to use postscript output via

Select File -> Print

which allows you to choose a white background even when the on-screen background is black.

Additional material

  1. Vibrations in crystals by Prof. Nicholas Harrison
  2. Introduction

Exercises