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SSP Project Summary:
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Simulation of the crystal structure of ice
This project is to examine the stability of the various crystal
structures found in ice. Calculations will be based around the CETEP
parallel code which solves the Schroedinger Equation for many electrons
in the potential of the hydrogen and Oxygen ions. This density
functional theory approach is currently the most accurate method
available for such calculations. In addition to using the pre-existing
code, it is hoped that some way can be found to incorporate the effects
of zero-point motion of the hydrogen atoms in order to explain the
observed differences between normal and deuterated ice. Contact with
experimentalists working on neutron scattering from ice may be possible
during the project.
Tasks
- Learn the underlying principles of the density functional
theory. Learn to use CETEP as a black box code, and learn the
parallelisation strategy as applied to density functional
theory based on plane waves. No new coding is required at this
stage, but the form of data output, especially the form of the
wavefunction, should be appreciated for subsequent analysis
work. (1-2 weeks).
- Carry out some preliminary calculations of the energy of
various arrangements of the hydrogen atoms on a fixed oxygen
lattice. Write some code to automate the setting up of initial
configurations of the hydrogens. (2-6 weeks)
If time allows it may then be possible to do one or more of the
following:
- Evaluate the response to pressure of the diamond structure of
ice, in particular to follow the transitions from covalent and
hydrogen bonding to ionic bonding at high pressure. (2-4
weeks)
- Write a code to simulate the allowed long range order of the
hydrogen atoms relative to the oxygens. The form of this will
be similar to the Ising model on a diamond lattice and will
thus make contact with the work done on the preliminary
courses. (2-4 weeks)
- Evaluate the vibrational frequencies associated with the
lowest energy arrangements, with a view to understanding the
zero-point energy differences between water and heavy
(deuterated) water. This will involve either writing a lattice
dynamics code (basically, a big symmertic matrix
diagonalisation problem) or modifying a pre-existing code.
(2-4 weeks)
Expertise
Knowledge of Fortran is essential for the coding parts of the project.
An elementary understanding of quantum mechanics and crystallography
would be very useful. In fact a background in physics or quantum
chemistry would be a distinct advantage.
Resources
Cray T3D. We already have time allocated under Edinburgh ACIDs which
could be used for this project. Of course, we would not turn down the
offer of more.
We can supply existing parallelised code for the fixed ions, the
project would require some coding to incorporate the motion of the
hydrogen ions.
References
M.C.Payne, M.P.Teter, D.C.Allan, T.A.Arias and J.D.Joannopolous,
Rev.Mod.Phys. 64, 1045 (1992).
Cezary Czaplewski worked on this project.
Compressed PostScript of the project's final report will be
available here
(515 kbytes) .
Webpage maintained by
mario@epcc.ed.ac.uk